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An introspective essay by: Khadija Charles > that weird girl that people really like but tend to forget about.
With all of the innovation that is going on in social media it's hard to admit that I am friendless. How so, you ask. Well, yeah, I've got tons of friends on Facebook, and have been working a little wingspan on Twitter and I've also even started dabbling into things like Tumblr and I've got an undercover blog on Blogspot that's got like 2 fans, and I've got a work-in-progress blog on WordPress, but I don't have friends.
What I do have is a best friend that lives all the way in Seattle and a "friend-of-emotional-convenience" that I'm having a hard time navigating my friendship with. However, that's not to say that I don't have people I know and like and actually consider my friends in my lonely, fiendish mind but don't actually feel like they are when you realize you barely speak to each other. I'm closer to my estranged father than I am some of these "friends". I've realized, over time, that I'm very friendly and people like me. People think I'm cool, interesting, and from time to time oxymoronic by being mysterious and open all at the same time; this leaves me being quite memorable. However, I'm also (very oxymoronically) forgettable. For a while I couldn't figure out why and then an experience with getting employment made it all very clear.
In the state of New York, in order to work with children you have to complete a special type of background check. This one specifically checks your background for any instances of child abuse or maltreatment in your home as well as ANY home you've lived in for the past 28 years. Now, I never had any problem with this clearance because I don't have any child abuse in my background, as well I've always only went back 10 years because everything after that gets fuzzy. However, this time, this company was requiring my entire 22 years of life in addresses. For most people this wouldn't be an issue, but for me there were two things wrong with completing this form. One: I've lived in over 40 different places (5 different states 20 different cities) and Two: close to half of those places were domestic violence shelters (where the addresses have to stay confidential for the security of the women). I struggled, but eventually I got the information. It took a lot of sleuthing into my childhood emails and Google Maps, but I did it. Nevertheless, I digress; this is just a part of the problem. The problem that I realized I had was that with all the moving around I've done, I've conditioned myself to be the way that I am now. I've conditioned myself to be an oxymoron.
Wait? What? How? I know that's the first three words that pop up in your mind, unless you're a psychiatrist then you're like, "I knew it!" Nevertheless, I've literally became what I despise most about my life right now and why I feel like I no friends. I've come to find that in my childhood, because I got used to the pattern of moving around a lot, it became easier for me to adjust to making (and losing) friends that way. I could make friends easily because they felt comfortable with me and it was easy for them to move on (making it easier for me to) if they could forget me just as easily. I might have left an impression, or a moment that they might call upon when they think of their childhood with a nostalgic smile and a soft chuckle, but at the end of the day, there's no hard feelings. This worked a lot in my younger years, and got more complicated to achieve as I got older and as technology came into play because now these friends wanted to "keep in touch". However, I was just left to bear witness to their lives and how they've moved on. I ended up feeling resentful and jealous realizing that nothing can replace a friendship that is solidified by proximity and time. Therefore, no matter how cool, sweet, or funny I was people just wouldn't go the extra mile to keep up an active friendship with me.
Moreover, as time went on, I became harder to want to be friends with. My life was just too complicated and too depressing. Then I discovered a few other issues that played a major factor into my lack of friends. I was suffering from Bipolar Disorder. So in a nutshell I was essentially a nut case. I can't handle my emotions effectively and end up pulling into myself and pushing others away. In an effort to not burden people with my illness or my problems I saved them the text message breakup and just faded away. In doing that I missed out on a LOT of things, a LOT of opportunities, and a LOT of friendships. Another issue that I noted was that I'm just an oddball. I look very young, and most of the time I act very young, but I'm stepping into that weird ADULT threshold where I can act older than I actually am. I can engage in older activities, but at this point don't have anyone to engage with. I wrote a poem called "Weird" that was about this predicament (kind of) *warning there are expletives*:
People are weird.No let me rephrase that.I'm weird. I'm not like other people.
I don't have friends. I don't go out. I don't retell stories that start with, "I remember that time when I...when we...when this..."I don't hang out or chill or "Hey, let's do (insert awesome activity) at/on/this (insert time/day of week/month/year/season).I don't have raging Facebook posts/pics of all the places I've gone/things I've done.
Don't have rings/necklaces/bracelets or tattoos/piercings from when I went (insert awesome place).I'm fucking boring.
I don't have a black book, notches in my belt, or reasons to get dirty looks.
I don't live on the edge or between the lines.
I don't have a tag that says, "I'm cool because I've been/done/had/went/saw/was a part of... etc."I don't have a tag that says, "I'm uncool because...." you get the point.
I'm just here.Not really doing one thing or another. Not really being one thing or another. Not really fitting in, but not really sticking out. Like shit. What am I really? I guess, I'm just weird. Because I'm not weird, and I'm normal, I'm like oatmeal. Kind of bland, but I've got a dash of cinnamon and sugar so I'm not all that bad, but still there's no bang...This needs to change.
I ponder a lot on this, well mostly on that last part. How can I change this? How can I over turn years of habituation? And yet, before I even delve into that I have to ask myself, why is this an issue? What's wrong with being a loner and having no friends? What's wrong with just staying home and playing Lego's with my 1 year old or gorging myself with all my favorite shows on Netflix? Well, because that's just no way to live, especially not for a 22 year old. I was always one to preach on the soapbox that my life wasn't over just because I had a child. And it's not, especially when you have people waiting in the wings to babysit. If the opportunity arises I should be able to jump on it like a San Fran streetcar! But here's the kicker, it has, and I just let that streetcar pass me by. I live in New York City! There's no way that I shouldn't be able to get myself out there and MAKE friends and ENGAGE in cool activities, but I can't. Why, you ask? Well to be frank, I'm scared. And I don't know how. These past few years have brought on a lot of changes, especially emotional ones. These changes that have turned me into a shadow of the person that I used to be, and I can't get past that. This talent that I've cultivated over the years has left me hollow and shy, really shy. To top it off the problems just keep piling up and the stress just keeps pushing me down. Every once in a while I raise my hand up to ask for help and it just dangles there in the breeze, waiting. No response. This in turn pushes me farther down than I was before. And as easily as I found it to train others to forget me, I have started to forget myself. This need to change.
If you can identify with some of the things I have talked about and are looking to come out of your shell you can find me at:
You can also contact me if you are interested in being a part of a documentary I am going to be working on about slipping through the cracks.


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Pueblo de Oro conducted a tree planting activity at The Enclave at Pueblo Golf last November 19, 2016. Pueblo de Oro employees and sellers, led by Vice President and General Manager forMindanao, Chrysler Acebu, kicked off the early-morning event with a stimulating Zumba session before planting some 60 African talisay and palm trees along the main road leading to the subdivision.
The Enclave at Pueblo Golf is an exclusive community comprised of 40 townhouse units and nine ridge lots. Because it is surrounded by greens, homeowners could live amid natural and tranquil surroundings, enjoy the lush view of the fairways and greens, savor the refreshing breeze and be taken with the awe-inspiring sunrises and captivating sunsets. To date, approximately 30% of the available units have been sold.

subset: commoncrawl


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D7000 + 35mm f1.8 - Early shots of Lucky
Started Mar 26, 2014 | Discussions thread
iAnoop • Regular Member • Posts: 121
D7000 + 35mm f1.8 - Early shots of Lucky
Mar 26, 2014
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<< Back to AJC.org
National Immigration Policy & Advocacy
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Our badly broken immigration system must be fixed through federal legislation.
From its founding in 1906, AJC has been a strong voice in support of fair and generous treatment of immigrants, participating actively in many of the major immigration debates of our time. AJC continues to reaffirm its commitment to fair and generous immigration policies, as fundamentally good for the United States and consistent with Jewish values.
Our commitment to appropriate immigration policies is not only about the Jewish community, which today constitutes only a small portion of the immigration flow. It is fundamentally about what we see as in the best interests of our country overall, as well as assuring that our nation acts in accord with its highest values. American immigration policies must be consistent with safeguarding our national security through maintaining control over our nation's borders and enforcing the nation's immigration laws in a fashion consistent with due process and humane treatment. We are also committed to measures that better incorporate newcomers into American society and culture.
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UUSU is a democratic student led organistion which provides a range of services for the 26,000 University of Ulster students based on its Jordanstown , Coleraine, Belfast and Magee campuses.As well as offering services such as academic representation,advice, welfare , volunteering and sports, UUSU also operates a number of commercial operations such as shops, bars and catering facilities. Seven student officers elected by the student membership serve for a 12 month period and are supported by 60 permanent staff across the four campuses.
Ulster University Students' Union
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Last updated -2 years 5 weeks ago
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TDF Stage 20 - The Final Test For Contador, Schleck, Armstrong, Wiggins, Kloden, and Schleck
At 20km to the final summit in the final climb and the teams of the lead riders are at the front of the peloton, ripping it away from the rest of the field. We pick up the final mountain stage in the penultimate stage of the Tour de France at the bottom of Mont Ventoux with the Teams of Team Garmin-Slipstream for Bradley Wiggins (4), Team Astana for Alberto Contador (1), Lance Armstrong (3), and Andreas Kloden (5) and Team Saxo Bank for Andy Schleck (2), and Frank Schleck (6).
They are flying up Mont Ventoux with the jersey's unzipped and flapping in the wind. Pumping peddles and challenges from the Schleck brothers are taking it to Contador and Armstrong and both riders are covering every move!
The unrelenting gradient, the length, and the exposed terrain make Mont Ventoux one of the more difficult climbs in cycling. From Bédoin, the Mont Ventoux gains 1622 meters and requires 22.7 kilometers of uninterrupted climbing. The average gradient is 7.6%, but nearly half the climb ascends at gradients between 9% and 10%. Though lower slopes ascend under a pine forest canopy, the majority of the climb passes through exposed open terrain as the road snakes through white limestone scree to the summit. Wind is a frequent visitor to Mont Ventoux. The Mistral winds, a dry wind out of the north, blow through the Provence region and can hit speeds exceeding 100 km/hr. When they occur, the high winds exponentially increase the difficulty of this climb. Image and Caption Credit: steephill.tv
This excerpted and edited from steephill.tv-
Profile Details - Montélimar → Mont-Ventoux
This year's edition of the Ventoux stage takes a hilly route to the Géant. It sets out from Montélimar and begins a gradual ascent to the first climb of the day, the category 3 Côte de Citelle. The Côte climbs 5.2 kilometers at a relatively easy gradient and summits at kilometer 14. It offers a nice warm-up and may send the early breakaway on its merry way.
A brief descent follows this early climb and the stage crosses bumpy terrain as it passes through Salles-sous-Bois, Montbrison-sur-Lez, and Rousset-les-Vignes. The first intermediate sprint takes place in Les Pilles at kilometer 48. From Les Pilles, the course climbs gradually to the second categorized climb of the day. A picturesque climb on narrow roads, the Col d'Ey carries at category 3 rating. It lasts 6.7 kilometers and climbs at a steady gradient of 4.8%. The narrow road wraps around the hill and offers a panoramic view of the surrounding countryside cultivated with Lavender and vineyards.
After descending the Col d'Ey, the stage climbs again almost immediately. After passing through Eygarliers, the riders will climb the Col de Fontaube, a category 4 col. The Col de Fontaube climbs 4.7 kilometers at an average gradient of 4.2%. This is not an especially difficult ascent and none of the favorites will have any difficulty here. The Col de Fontaube summits at kilometer 87.
The next 30 kilometers cover rolling terrain. The stage passes through Aurel at kilometer 105 before climbing the fourth climb of the day. The Col des Abeilles lasts 7.7 kilometers and has an average gradient of 4%. Though some riders may be feeling the effects of the repeated climbing, the Col des Abeilles is nothing to fear. The organizers have given the climb a category 3 rating as a consequence of its length more than its pitch, which is not especially difficult. From the summit of the Col des Abeilles, there remains 45.5 kilometers to race, including 21.1 kilometers of hors catégorie goodness.
The road descends for the next 17 kilometers to the second intermediate sprint at Mormoiron at kilometer 138.5. The road begins to climb just after the sprint, and 5.5 kilometers later, the riders will reach Bédoin. This town signals the start of the final climb of the day, Mont Ventoux.
Reference Here>>
This from VeloNews(VN), CyclingNews(CN), Versus(VS), and various resources -
13:32 GMT - 20km to go for the breakaway. Garmin are also riding hard behind, showing that they too can put the pressure on.
13:34 GMT - The Roche group is now 1'05" back...that's a pity, he had a chance of getting into the top 20 in his first Tour.
Cancellara has blown now. Cavendish sits up from a group...probably the second group on the road, not certain. He smiles at the camera - no worries.
13:35 GMT - Posthuma leads the break, 18.6km from the top of the climb. They have just 3'57" now, so it's very unlikely any of those will win today.
David Millar now hits the front of the Contador group, driving the speed up again. Wiggins sits on his wheel.
Up front, Arrieta jumps...Martin goes after him.
13:37 GMT - Garate, Riblon and Martin are together now. They have a sidewind but it's just 14km/h at this point.
Will be interesting to see if this acceleration in pace behind will affect Contador. He's lighter than most of the other riders and might be more affected by the wind.
13:38 GMT - Garate goes again....he gets a gap on Martin and Arrieta. They get him back.
Millar still leads behind, Wiggins and VDV on his wheel. They have to give their all on this climb - Wiggins has a chance to be the best-ever British finisher in the Tour if he can finish higher than fourth. Robert Millar has that distinction until now.
13:40 GMT (15.9km remaining from 167km) - Millar is getting every last bit of energy out.
The leading riders have 15.9km to go...3'24 is the gap. That's not enough.
13:44 GMT (14km remaining from 167km) - The crowds are really big here....huge.. Hincapie has been dropped from the Contador group. Saxo Bank are driving it now...
13:45 GMT - Vande Velde, Karpets, Astarloza (Euskaltel), Jurgen Van Den Broucke (Silence Lotto) are with the Contador group...so too the Schlecks, Wiggins, and about 20 others..
13:46 GMT - This is going to be absolute mayhem...the group will explode on the climb.
13:49 GMT - Chris Anker Sorensen is dropped, so too Cyril Lemoine (Skil Shimano). Karpets is also gone now...
13:50 GMT (12km remaining from 167km) - Martin and Garate have slightly distanced Riblon.
13:50 GMT - Frank Schleck attacks! He's jumped...Armstrong goes with him...
Frank Schleck is still taking digs... Contador is staying with him, too.
One Garmin got popped, looks like Vande Velde
EuroHoody: Wiggins still there
CPelkey: Andy goes!
EuroHoody: Vandenbroucke is there for Silence
EuroHoody: Andy Schleck takes over!
Andy Schleck is at the front, setting tempo. He has Contador, Armstrong, Frank ....
EuroHoody: Astaloza, VdV off back
CPelkey: Wiggo is there, too.
EuroHoody: Andy Schleck ramps it up again, AC marks the move
EuroHoody: Danglers are 2:37 off the front with 12km to go
CPelkey: And again... Andy Schleck goes again. Contador is with him.
Armstrong fighting back
EuroHoody: ASchleck ramps it up again!
CPelkey: Armstrong chases... almost joins and Andy hits the gas again.
EuroHoody: Contador glued to his wheel
CPelkey: Frank Schleck is back with Armstrong who is losing seconds...
EuroHoody: Kloden OFF the back
CPelkey: Armstrong has regained contact. Frank Schleck and Wiggins are there, too.
EuroHoody: Andy S, Contador, Nibali, LA, Kreuziger, FSchleck and Wiggins
EuroHoody: ASchleck ramps again!
EuroHoody: Contador follows
CPelkey: Andy Schleck has only Contador with him.
EuroHoody: Watch for Frank Schleck to bridge up - if he can
CPelkey: Frank Schleck has Armstrong glomped on to his wheel.
EuroHoody: 5 at front: LA, AC, the two Schlecks and Wiggins
EuroHoody: Nibali is there, too
EuroHoody: 6 at front for GC group
CPelkey: Frank Schleck takes a dig... Armstrong goes with him, though, as does the rest of the group.
EuroHoody: Looks like orders are for Contador to mark ASchleck, and LA to mark FSchleck
EuroHoody: Garate and Martin are still dangling at 2:15
EuroHoody: Kloden 45sec off the AC-LA group
CPelkey: The two leaders are 10km from the finish.
EuroHoody: Contador group is picking up some leftovers from the breakaway
13:57 GMT - Frank Schleck goes, Armstrong marks him... Contador, Wiggins and Nibali are there....and Andy Schleck, of course...
13:59 GMT (10km remaining from 167km) - The leaders are just 2'15 ahead.. Kloden is coming back, so too Van den Broeck..
10 km for the leaders...
14:00 GMT - Wiggins looks good...he's just followed so far, saving his energy....
14:03 GMT (8.8km remaining from 167km) - Andy Schleck and Alberto Contador, first and second overall, are clear and leaving the others behind... Van den Broeck attacks...
The Armstrong/Wiggins group are going quite slow now....they have been cracked by Schleck's acceleration.. But those fighting for third overall are all together.
Juan Manuel Garate (Rabobank) and Tony Martin (Columbia HTC)
Joost Postuma (Rabobank), Aleksandr Kuschynski (Liquigas), Anthony Geslin (Française des Jeux), Samuel Dumoulin (Cofidis), Daniele Righi (Lampre), Maxime Bouet (Agritubel), Cyril Lemoine (Skil Shimano), Mickael Delage (Silence Lotto) and Jose Ivan Gutierrez (Caisse d'Epargne) at 0.32
Alberto Contador (Astana), Andy Schleck (Saxo Bank), Vincenzo Nibali (Liquigas), Bradley Wiggins (Garmin), Lance Armstrong (Astana), Frank Schleck (Saxo Bank) at 2.00
Bradley Wiggins and Frank Schleck only need to gain from 16 to 18 seconds respectively in order to take a podium position from Lance Armstrong.
EuroHoody: LA is 20sec behind Contador, ASchleck, with Bouet hitching a wheel from the break
CPelkey: Man, Martin looks shelled up there. He is still hanging with Garate, but the boy looks tired.
EuroHoody: Nibali is reaching ASchleck and Contador, Bouet's "free ride" is over
CPelkey: Wiggins is stepping it up at the front of the Armstrong/FSchleck group
EuroHoody: Wiggo on the front, with FSchleck, LA, Kloden, Van Den Broeck, Kreuzisger about 20sec back
EuroHoody: Garate, Martin still dangling at 1:46
CPelkey: The wind is considerably lighter .... but it is a headwind.
EuroHoody: Pellizotti has trimmed leader's gap to 1:24
CPelkey: It's Kloden and Armstrong setting tempo at the front of the yellow jersey group.
EuroHoody: Andy Schleck attacks!
EuroHoody: Frank Schleck on his wheel!
CPelkey: Andy Schleck attacks!
Frank goes too!
EuroHoody: Kloden popped
EuroHoody: Wiggins pulls up, Contador and Armstrong
CPelkey: Contador and Armstrong fight back on.
EuroHoody: Nibali there, too
CPelkey: Nibali, too
EuroHoody: As many are commenting, those four seconds that Armstrong "won" yesterday could pay huge dividends
CPelkey: Garate and Martin are about 3.3km from the summit. They look like they are marching to an execution ... and here comes Pellizotti.
EuroHoody: The Schlecks cannot shake Armstrong ... not yet, at least
CPelkey: Wiggo pops
EuroHoody: Wiggins struggling!
EuroHoody: Nibali on Wiggins' wheel
EuroHoody: He has 45sec gap with 1km to go
EuroHoody: Schlecks have to drop Armstrong if they want to move FSchleck up on the podium
EuroHoody: Wiggins is clawwwwwwwwwwwwwing back
EuroHoody: Andy setting tempo, Contador grimacing
CPelkey: Oh man... the Schleck/Contador group is coming up on Pellizotti
EuroHoody: Now we have the two Schlecks, Armstrong and Contador
EuroHoody: Martin counters!
CPelkey: Wow...
EuroHoody: Catches Garate
EuroHoody: Of these two, my personal choice to win would be Martin
CPelkey: Martin at the front. A Strong cross wind.
Pellizotti about to be caught by chasing foursome
CPelkey: And they're not that far behind the two leaders, either.
EuroHoody: Martin and Garate have gap to win the stage
EuroHoody: Pellizotti caught by Schleck group
CPelkey: Pellizotti is in there.
EuroHoody: Garate attacks on last switchback
CPelkey: Garate goes again... He wins
EuroHoody: Wins!
EuroHoody: Looking good for Armstrong to conserve third!
EuroHoody: Andy Schleck sweeps into final switchback, sprinting for third
CPelkey: Andy Schleck comes across for third.
CPelkey: Contador, then Armstrong
EuroHoody: Contador fourth, Armstrong fifth, FSchleck 6th
CPelkey: Wiggo is fighting to hold his GC spot... good work
EuroHoody: Wiggins might have kept 5th
Pellizotti has been caught...Andy S. and Contador sige by side...
Garate goes for it! He gets the win...wow, that came up fast. Martin next.
Andy Schleck leads them around the last bend.....he's going for second....
He gets third, with Contador on his wheel...looking very comfortable. He waves at the crowd. Armstrong is gapped but is next across the line, securing third in Paris. Frank Schleck was also there, but Wiggins lost time... He was perhaps 30 second back...
Juan Manuel Garate (Rabobank) and Tony Martin (Columbia HTC)
Franco Pellizotti (Liquigas) at 1.42
Alberto Contador (Astana), Andy Schleck (Saxo Bank), Vincenzo Nibali (Liquigas) and Christophe Riblon (AG2R La Mondiale), Jurgen Van Den Broeck (Silence Lotto), Bradley Wiggins (Garmin), Lance Armstrong (Astana), Frank Schleck (Saxo Bank), Jose Ivan Gutierrez (Caisse d'Epargne) and Andreas Kloden (Astana) and Maxime Bouet (Agritubel) at 1.59
# 1. Manuel Garate Juan Rabobank, 167km in 4:39:21
# 2. Tony Martin Team Columbia - Htc, at 0:03
# 3. Andy Schleck Team Saxo Bank at 00:38
# 4. Alberto Contador Astana at 00:38
# 5. Lance Armstrong Astana at 00:41
# 6. Frank Schleck Team Saxo Bank at 00:43
# 7. Roman Kreuziger Liquigas at 00:46
EuroHoody: Great ride by Armstrong - keeps podium spot - not bad for a guy pushing 38!
# CPelkey: 1. Manuel Garate Juan Rabobank, 167km in 4:39:21
# 2. Tony Martin Team Columbia - Htc, at 0:03
# 3. Andy Schleck Team Saxo Bank at 00:38
# 4. Alberto Contador Astana at 00:38
# 5. Lance Armstrong Astana at 00:41
# 6. Frank Schleck Team Saxo Bank at 00:43
# 7. Roman Kreuziger Liquigas at 00:46
# 8. Franco Pellizotti Liquigas at 00:56
# 9. Vincenzo Nibali Liquigas at 00:58
# 10. Bradley Wiggins Garmin - Slipstream at 01:03
EuroHoody: Garate's win saves a disastrous Tour for Rabobank
EuroHoody: Wiggins keeps 4th by 3sec
# CPelkey: 1. Manuel Garate Juan Rabobank, 167km in 4:39:21
# 2. Tony Martin Team Columbia - Htc, at 0:03
# 3. Andy Schleck Team Saxo Bank at 00:38
# 4. Alberto Contador Astana at 00:38
# 5. Lance Armstrong Astana at 00:41
# 6. Frank Schleck Team Saxo Bank at 00:43
# 7. Roman Kreuziger Liquigas at 00:46
# 8. Franco Pellizotti Liquigas at 00:56
# 9. Vincenzo Nibali Liquigas at 00:58
# 10. Bradley Wiggins Garmin - Slipstream at 01:03
# 11. Broeck Jurgen Van Den Silence - Lotto at 01:39
# 12. Andréas KlÖden Astana at 01:42
# 13. Christophe Riblon Ag2r La Mondiale at 01:47
# 14. Joost Posthuma Rabobank at 01:56
# 15. Christophe Le Mevel Francaise Des Jeux at 02:26
# 16. Christian Vande Velde Garmin - Slipstream at 02:34
# 17. Maxime Bouet Agritubel at 02:42
# 18. Mikel Astarloza Euskaltel - Euskadi at 02:44
CPelkey: Well here's a look at the GC picture after this tough, tough stage:
# 1. Alberto Contador Astana, 3295.5km in 81:46:17
# 2. Andy Schleck Team Saxo Bank, at 4:11
# 3. Lance Armstrong Astana at 05:24
# 4. Bradley Wiggins Garmin - Slipstream at 06:01
# 5. Frank Schleck Team Saxo Bank at 06:04
# 6. Andréas Kloden Astana at 06:42
# 7. Vincenzo Nibali Liquigas at 07:35
# 8. Christian Vande Velde Garmin - Slipstream at 12:04
# 9. Roman Kreuziger Liquigas at 14:16
# 10. Christophe Le Mevel Francaise Des Jeux at 14:25
# 11. Mikel Astarloza Euskaltel - Euskadi at 14:44
CPelkey: Well, we usually reserve that one for the end of an escape attempt, but as far as the GC picture is concerned, this Tour is over. All that's left is the parade into Paris.


text:
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Writing Lesson 12
Middle schoolers write a composition about one person that they admire very much and explain why they admire him or her. They use a proofreading guide to check for correct spelling, punctuation, and grammar. Additionally, they write a minimum of four paragraphs in response to the prompt.
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I went to a Pizza place close to the Met a few years ago after I read a short review in the NY Times. I can't remember which street but it was close to Madison Ave - just west of it a few steps I think. It had very thin crust, maybe a couple of tables inside, maybe not - it was small. I think it must be close to a private school because there were a few students there too.
Anyone know which one I'm talking about? I could go up and down Madison and keep looking west but I might miss it by a street and I don't even know if it's still there. It was great to find a cheap place close to the museum.


text:
The vote by the British people to leave the European Union has been interpreted in some quarters as a vote for isolationism; for withdrawal from Europe and the world, where Britain could somehow 'go it…
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|Publication number
|Publication type
|Application number
|Publication date
|Nov 28, 1978
|Filing date
|Jun 29, 1977
|Priority date
|Jun 29, 1977
|Publication number
|Tingye Li
|Original Assignee
|Bell Telephone Laboratories, Incorporated
|Export Citation
|BiBTeX, EndNote, RefMan
|Patent Citations (4), Non-Patent Citations (8), Referenced by (35), Classifications (7)
|External Links: USPTO, USPTO Assignment, Espacenet
The present invention relates to the field of optical communications. In recent years, increasing interest and attention have been attracted to processing and transmitting large amounts of communications information from many sources to many destinations on tiny beams of light carried in optical waveguides. In order to route information from each source to each destination, it is necessary to provide modulating apparatus for first impressing the information upon light at its source. Then the light is switched appropriately along its way so that it follows a path to its intended destination at the same time as other sources of light are switched or coupled along correct paths to their correct destinations.
In the prior art a variety of modulator and switch devices have been proposed which use substrates of crystalline material such as gallium arsenide (GaAs), lithium niobate (LiNbO3), or lithium tantalate (LiTaO3), the optical properties of which are sensitive to electric fields produced by means of a voltage source connected to electrodes deposited thereon. The amount of light leaving such a device can be varied in its intensity or amplitude for modulation or can be turned on and off in intensity in a given direction when switching action is desired.
The suitability of a given modulator or switch device relates to practical considerations.
The device should require a minimum of parts or structures to accomplish its operation thereby to decrease the number of steps in its manufacture and to decrease the likelihood of device malfunction.
The device should require no critical sizes or shapes of parts or critical separations or gaps in its construction.
The device as a whole should be small enough to permit ready fabrication of hundreds or thousands of copies on a single substrate as in an integrated optics switching array.
The device should be able to modulate or switch energy from light sources such as lasers having considerable energy in higher order modes. Many prior art devices are mode-sensitive in that if energy other than that in a single mode is provided, then depth of modulation or extinction ratio and freedom from crosstalk are impaired.
The device should avoid sending unwanted light in uncontrolled directions since buildups of stray light can be highly disadvantageous in densely packed arrays of devices.
The device should feature low capacitance so that it can follow wide bandwidth modulating signals or fast-risetime switching pulses.
The device should require low energy (often measured in microwatts per megahertz) to perform its operation. Given a device capacitance, a lower operating voltage implies a lower energy requirement.
Where a critical condition must be satisfied in order to permit the most advantageous operation the device should be readily tunable, preferably electrically, so that the condition can be met.
The present invention has as an object to provide an optical modulator/switch of an alternative type to the optical modulators and switches of the prior art by providing a structure which is advantageous in each of the above-listed respects.
In the invention, a strip multimode waveguide is employed, meaning a waveguide having length, width and thickness surrounded by lower refractive index material or otherwise such as to confine light by the well-known phenomenon of total internal reflection. The waveguide is of multimode type, meaning that its dimensions are large enough compared to the wavelength of light to be modulated or switched so that more than one electromagnetic optical mode can propagate therein. Light for processing from a source to be modulated or switched is permitted to enter at only one side of an input end of the waveguide. Introduction of the light in such laterally offset manner is accomplished by an accurately positioned light source or from an input strip waveguide of smaller width. The smaller waveguide is suitably of either single mode or multimode type. If good coupling to a multimode optical source be desired, the invention readily permits the same when a multimode introducing waveguide is used. Because the light enters from only one side per source, the invention can even accommodate two sources at once by means of a branched introducing waveguide or other suitable light introduction means.
The light introduced into the multimode main waveguide travels in even and odd modes, which in general have different propagation velocities, to an output end of the waveguide. At certain critical lengths the original light entering the multimode waveguide is reconstructed or concentrated either in double on either side of the output end or reproduced essentially intact on one or the other side of the output end. By applying a physical influence such as an electric field with appropriately positioned electrodes so as to impress or induce a laterally nonuniform but transversely or bilaterally symmetric refractive index change in the waveguide, the speed or velocity of propagation of the even modes relative to the odd modes can be differentially affected so as to control the way that the light exits from the output end of the waveguide. Thus, modulation and switching functions are made possible.
In a number of the inventive embodiments one or more of the electrodes are symmetrically disposed on a face of the multimode waveguide, parallel to the waveguide length and have an electrode width of less than one-fourth of the waveguide width in order to produce the nonuniform fields required. The polarity and intensity of a voltage provided to the electrodes determine which side the light is switched or modulated into. Means of separating light exiting from one side of the output end from light exiting from the other output side can be readily provided, as in the form of a bilaterally symmetric branched output waveguide.
The multimode optical modulator/switch of the invention features simplicity in that its construction involves only a single undivided waveguide with branches at either end and electrodes deposited thereon. The waveguide width is not very critical because it is of multimode type, and there are no multiple waveguides of a directional coupler variety requiring a precise gap between them. The lengths of the inventive modulator/switch are on the order of 1 centimeter or less for a suitable waveguide width dimension when light of a given wavelength λ in the optical spectrum, including the visible, near-infrared, or ultraviolet range, is employed. There is low light loss because the light is guided all along its way, as by strip waveguides. Switching voltages and capacitance are low in view of the relatively miniature dimensions of the invention as demonstrated by calculations disclosed hereinbelow. The invention is readily tunable such as by adjusting the voltage providable to the electrodes.
The invention can find use as a single discrete modulator/switch component in optical fiber communication systems. It is readily adaptable to batch processing of large switching arrays in an integrated optics assembly for switching large number of communications sources to large numbers of destinations, and for providing digital logic devices and other apparatus utilizing the invention in various combinations.
FIG. 1 shows a greatly magnified plan view of an optical modulator/switch according to the present invention for use in an integrated optics circuit. The length L is considerably compressed in scale compared to width a for clarity.
FIG. 2 is a transverse cross-section of the inventive optical modulator/switch shown in FIG. 1, which operates by preponderately affecting the propagation of optical even modes.
FIGS. 3, 4 and 5 are graphs of electric field strength in modes of an optical electromagnetic wave which are drawn versus distance along the width of a multimode waveguide to show the even and odd modes as groups in a simplified manner facilitating a description of the operation of the present invention.
FIG. 6 is a cross-section of an embodiment of the invention for switching light by preponderately affecting the propagation of odd modes.
FIG. 7 is a cross-section of an embodiment of the invention for reduced voltage operation by affecting the propagation of both the even and the odd modes oppositely.
FIG. 8 shows a greatly magnified cutaway plan view of an optical modulator/switch according to the present invention for use as an encapsulated discrete component with optical fibers. As in FIG. 1 the length dimension is foreshortened.
FIG. 9 shows a cutaway profile view of the discrete component of FIG. 8.
FIG. 1 shows the inventive multimode optical modulator/switch as seen from above. The device includes a single multimode optical strip or channel waveguide 3 resembling a center strip having input double-waveguide branches 5 and 6 and output branches 7 and 8 at each end. The waveguide 3 and its input and output branches are located on or diffused, as by titanium indiffusion, into a substrate 4 of suitable material of a lower refractive index so that light of a wavelength λ in the near-infrared, visible optical, or ultraviolet regions of the spectrum propagates by total internal reflection therein. The lateral dimension or width of the waveguide 3 material is designated a, and the refractive index of the material is designated n. The waveguide 3 has a length L between an input end 14 joined with symmetric branches 5 and 6 for introduction of light energy and an output end 13 joining symmetric branches 7 and 8 for separation of light energy. Cuspate or prism-shaped low-index substrate portions 4A and 4B act as separation portions between braches 7 and 8 and 5 and 6. The branches respectively lead away from and lead toward output portion 13 and input portion 14. Branches 5, 6, 7 and 8 join in cross-section with waveguide 3 at left input side 3LSIN, right input side 3RSIN, left output side 3LSOUT, and right output side 3RSOUT respectively. The length L is dozens or hundreds of times the width a. The high-index waveguide 3 material has an undivided, unitary cross-section along all its length for propagation of optical modes. A slender electrode 9 at the center 15 of waveguide 3 and a wide electrode 10 are located on the top and bottom faces 16 and 17 (see FIG. 2) of the waveguide 3 and substrate 4. When a voltage V is applied to the electrodes a processing of optical energy 11 and 12 in a modulation or switching action is obtained. Electrodes 9 and 10 induce a refractive index change which may be either positive or negative but which is primarily centered in intensity beneath electrode 9 all along length L and is relatively small over other portions of the waveguide width.
For example, if light energy 11 having wavelength λ is introduced through branch 5 so as to be incident upon only the left side 3LSIN of the input end cross-section 14 of waveguide 3, the light propagates in many TE (transverse electric) and TM (transverse magnetic) modes. Each mode has a number, and the modes include odd modes (TE2, TM2, TE4, TM4, TE6, TM6, etc.) and even modes (TE1, TM1, TE3, TM3, TE5, TM5, etc.) propagating along the length of the waveguide 3 until the output end 13 is reached. For mode diagrams see "A Circular-Harmonic Computer Analysis of Rectangular Dielectric Waveguides" by J. E. Goell, The Bell System Technical Journal, Volume 48, No. 7, Sept. 1969, pp. 2133, 2140, 2147 and 2149. In the discussion of modes herein it is assumed for simplicity of description that all waveguides are single-moded in the thickness direction so that TEmn = TEml = TEm and similarly for TMm. However, this simplification is not believed to be necessary to the operation of the invention, many embodiments of which can be multimoded in the thickness direction.
Then the light energy 11 divides, or is separated, in a manner to be more fully described, along branches 7 and 8 propagating as light energy in the direction of the arrows drawn therein. Similarly, light energy 12 entering at branch 6 propagates in a symmetric fashion compared to light energy 11 and exits as part of the light energy in the direction of the arrows in guides 7 and 8.
It is found that depending on the light wavelength λ and the width a of waveguide 3 there are certain critical lengths in waveguides of the type having the same cross-sectional dimensions as waveguide 3. These critical lengths may be experimentally determined by microscopic observation, theoretical prediction, trial and error construction, or otherwise. If light energy 11 on left input side 3LSIN is the only entering light, then essentially all of the light will be concentrated at and exit along branch 8 on the side 3RSOUT at the output end 13 after propagation along the least critical length. At twice the least critical length all of the light is concentrated at left output side 3LSOUT and exits from branch 7. This latter action is to be expected, since the light energy is laterally shifted from side 3LSIN first to the right side of guide 3 midway along its length and then shifted back to the left side 3LSOUT due to travel along two least critical length portions.
In general, if light energy is incident on waveguide 3 through branch 5, then at odd integer multiples of the critical length, it will exit through branch 8. At even integer multiples of the critical length the energy will exit through branch 7. Correspondingly, light energy 12 incident through branch 6 will exit through branch 7 when L is an odd integer multiple of the least critical length and through branch 8 when L is an even integer multiple of the least critical length.
If light energy 11 is composed of not one but two or more quite distinct wavelengths, then waveguide 3 will present different effective lengths and may provide a form of filtering action in that the distinct wavelengths can be concentrated at opposite output sides of waveguide 3 and then be separated. Similarly, if light energy 11 and light energy 12 are each substantially monochromatic at different wavelengths, then a signal-combining or multiplexing function is permitted. It is further found that waveguide 3 at odd multiples of one-half the least critical length is such as to cause the entering energy 11 to be split approximately equally between branches 7 and 8. Thus, a light splitting or 3dB coupler effect can be obtained. The just-mentioned filtering, combining, and 3dB coupling properties of a passive multimode waveguide (without electrodes) have been recognized in the prior art and reference may be made to R. Ulrich et al. "Self-Imaging in Homogeneous Planar Waveguides", Applied Physics Letters, Vol. 27, No. 6, 1975, pp. 337-339.
In the present invention it is recognized that electrical control over the properties of the waveguide 3 may be advantageously exploited to produce a variety of useful modulator and switch embodiments. For instance as shown in FIG. 1, a waveguide 3 having a length L of an integer multiple most suitably between 1 and 4 inclusive of approximately one-half the least critical length is provided with a slender electrode 9. Electrode 9 can have an electrode width w of less than approximately one-quarter a and an electrode length approximately equal to that of waveguide 3. The waveguide length is selected so as to be less than about 1 centimeter so that the device will be suitably miniature in size. On a bottom side of the waveguide 3 opposite electrode 9 and extending all along the length of the waveguide material is an electrode 10 suitably equal to or greater in width than electrode 9 and having a length about equal to or greater than that of the waveguide 3. Electrodes 9 and 10 may be applied or constructed on or near the waveguide 3 in any suitable manner so as to accomplish their function. If an insulating layer or optical barrier layer is needed between each electrode and the waveguide, the same can be provided. As shown in FIG. 1, electrode 10 is of approximately the width of the waveguide 3 and both electrodes 9 and 10 are located or centered symmetrically with respect to a longitudinal center plane 15 of the waveguide width. A transverse conductor from a contact pad (not shown) may be used to provide voltage to electrode 9, although any such transverse conductor should be of relatively small area on waveguide 3 compared to electrode 9 so as not to disturb the electric fields of electrode 9.
FIG. 2 shows a cross-section through multimode switch 1 of FIG. 1. Again, electrodes 9 and 10 are shown located symmetrically with respect to center plane 15 with only slender electrode 9 having width w≦ a/4 touching a top surface, side, or face 16 of waveguide 3. Substrate 4 has a lower or bottom surface 17 upon which relatively wide electrode 10 has been deposited. Batteries B and adjustable potentiometer P as shown, or a waveform generator or other means for generating a tunable positive or negative voltage V, are connected via electrical switch S1, to electrode 9, and electrode 10 is suitably connected to ground or to any other appropriate point in the electrical circuit of which device 1 forms a part. The propagation of the even and odd waveguide modes is affected so that the optical energy as a whole essentially exits from a first side 3LSOUT of the output end 13 of the waveguide 3 when one value of the voltage V is provided and so that the optical energy exiting from the first side 3LSOUT is substantially changeable in intensity in response to a change in the voltage V so that the energy is processable with respect to the amount thereof leaving that side of the output end of the waveguide. Similar processing of the light exiting from side 3RSOUT can also be made to occur.
Some embodiments of the invention cause the electrodes and waveguide material to cooperate electrooptically by employing a substrate 4 composed of lithium niobate (LiNbO3) or lithium tantalate (LiTaO3) having a c-axis 18 perpendicular to the surface of the substrate 4. Multimode waveguide 3 is formed by deep titanium indiffusion in the electrooptic substrate so as to form the strip waveguide 3 with branches 5, 6, 7 and 8. The thickness of the waveguide 3 is on the order of the wavelength λ of the light energy or greater. The width a should be greater than or equal to twice the thickness of the waveguide 3. The indiffusion may not produce a precisely rectangular cross-section of the waveguide, in which case the effective width a of the multimode waveguide may be somewhat affected, but this can be taken into account in the design. When the voltage V is present, an electric field 19 substantially perpendicular to top surface 16 of waveguide 3 and substantially parallel to c-axis 18 is set up. The optical TM modes see a refractive index change via the r33 coefficient since their optical electric field is parallel to the c-axis. The optical TE modes see a refractive index change via the r13 coefficient since their optical electric field is normal to the c-axis. If desired, only TE modes or only TM modes may be used to the exclusion of the others, in which case only one of the coefficients enters the discussion.
The electric field set up when a voltage V is provided by suitable connections to the electrodes is such as to be transversely or bilaterally symmetric with respect to its component in the c-axis direction or other electrooptically most sensitive direction. The symmetry should be satisfied with respect to both field strength and field direction. A substantial lateral variation in field strength accompanies the symmetry. For example, the electric field 19 is substantially perpendicular to the substrate in FIG. 2 (neglecting fringing components perpendicular to the c-axis). The field 19 points "down" on either side of the center plane 15 parallel to the c-axis, so the field direction (downward) is bilaterally symmetric with respect to the center plane. Likewise, when the field vector magnitudes are equal at equal distances on either side of the center plane as they are in FIG. 2, the field strength is bilaterally symmetrical. However, a field having components which essentially point "up" on the left of center plane 15 and "down" on the right of center plane 15 is not bilaterally symmetric in field direction for the purposes of certain embodiments of the invention when the c-axis is parallel to center plane 15.
Likewise, a field having components which point to the left on the left side of center plane 15 and point to the right on the right side of center plane 15 (when the c-axis is perpendicular to center plane 15) is not bilaterally symmetric in field direction for the purposes of these embodiments of the present invention either, since a bilaterally symmetric field is intended to mean a field which points left on both sides of center plane 15 or right on both sides when the c-axis is parallel to the field and perpendicular to center plane 15.
The reason for the emphasis on symmetry of the components parallel to the most sensitive electrooptic direction is that these are the components which primarily are responsible for the refractive index changes utilized in the invention. Since the index changes must be bilaterally symmetric with respect to center plane 15 to accomplish the differential mode effects to be discussed more fully next, the field components which produce the index changes must be bilaterally symmetric in electrooptic crystals such as LiNbO3 and LiTaO3, too.
The differential mode effects of the invention will be clarified by a consideration of FIGS. 1 and 2 in light of FIGS. 3 and 4. If light energy of wavelength λ be incident through only branch 5 of device 1 of FIG. 1, the electric field diagram of input end 14 of waveguide 3 illustratively appears as shown in the right-hand portion of FIG. 3. A strong field portion 24 bearing substantial energy on the left side 3LSIN of center plane 15 and a field portion 25 of negligible strength on the right-hand side 3RSIN are incident at the input end 14 of waveguide 3. The corresponding energy distribution, not shown, is proportional to the square of the electric field of FIG. 3. The field as a whole may be mathematically described as the sum or composition of modes such that there are even modes 20 which are symmetric with respect to center plane 15 and odd modes which are antisymmetric (note opposite signs of fields 22 and 23) with respect to center plane 15. The odd modes and even modes add to yield field portion 24 bearing much energy on the left, but fields 20 and 23 of the odd and even modes respectively cancel to yield the negligible field portion 25 on the right.
It should be understood that the even modes shown as a group 20 are actually the sum, or composition, of many individual optical even modes which in general have different speeds of propagation through the waveguide 3 due to the mode-dependent wavenumber β of the waveguide. Likewise, the odd modes diagrammed as a group are actually many optical modes also having different individual speeds of propagation through the waveguide 3. It is because the even and odd modes as they propagate become cophased again at certain critical lengths along the waveguide 3 that simplified diagrams may be used and the subject of critical lengths enters the discussion. When the odd and even modes are reconstructed at the output end 13 of the waveguide in identical relative phase as at the input end 14, the energy exits from the output end as in FIG. 3 with the energy on the left, that is, through side 3LSOUT to branch 7. An important contribution of the present invention is that it teaches how to controllably reconstruct the modes so that the amount of exiting energy can be controlled and processed.
The present invention recognizes that it is possible by means of the electrical circuit shown to apply a voltage V to the electrodes 9 and 10 so as to affect the velocity of propagation of the optical modes which are even modes without by comparison affecting the propagation of the optical modes which are odd modes. In this way the even modes 20 are all made to suffer a 180� or π phase shift with respect to their unaffected phases at the output end 13 of the waveguide 3. With no phase shift the energy exits left as in FIG. 3. But when as shown in FIG. 4 a π phase shift occurs, the optical electric field 26 of the even modes is realtively inverted, while the odd modes are reconstructed as usual. The result is that the composition of the odd modes and the phase shifted even modes of FIG. 4 produces the resultant strong field portion 31 bearing most of the energy on the right-hand side of center plane 15 of waveguide 3 so that the light energy exits through branch 8. By contrast, a negligible electric field 30 and negligible energy are now found on the left-hand side exiting through branch 7.
The operation of the FIGS. 1 and 2 embodiment of the invention is such that at certain waveguide lengths it is possible to apply a changeable voltage to electrodes which will correspondingly change the phase of the even modes by π and thereby cause light to be shifted from the left-hand branch 7 to the right-hand branch 8 or vice versa. At one value of the electrical voltage the propagating optical energy becomes concentrated in multimode waveguide 3 at only a first output side of its cross-section and exits therefrom and at another value of the voltage the propagating optical energy becomes concentrated in waveguide 3 at only an opposite output side of its cross-section and exits therefrom. Thus, an important feature or function of the invention is that a change in voltage applied to the electrodes differentially affects the velocities and hence the phases of the even and odd modes relative to each other such that the spatial character of the light energy exiting in branches 7 and 8 may be substantially changed.
The invention is able to provide differential modal phase shifts because it is possible to induce laterally nonuniform refractive index changes in the waveguide 3. However, because all the modes are symmetrical in magnitude of field strength about center plane 15 it is important that the refractive index changes exhibit bilateral symmetry as hereinbefore mentioned so as to affect the velocities of the appropriate modes as much as possible. However, it is immaterial whether the phase shifts provided are positive 180� or negative 180� in view of the identity of trigonometric functions with respect to a π phase shift. This means that appropriate modes can be either speeded up or slowed down. Therefore, the refractive index changes can be either decreases or increases.
Next follows an explanation of how the electric field produced by the electrodes of FIGS. 1 and 2 can affect the even modes with little effect on the odd modes. When the length of waveguide 3 is such that light 11 in branch 5 would exit from branch 8 without any voltage applied between electrodes 9 and 10, the application of a voltage to the slender electrode 9 produces an electric field concentrated in the center of waveguide 3 around center plane 15. This is precisely where the energy in the even modes is the greatest and the energy in the odd modes is the least. Thus, the even modes can be readily phase shifted by a centrally located refractive index change without substantially affecting the odd modes. The phase shifting of the even modes under the influence of the voltage V shifts the light from branch 8 to branch 7, and the modulation/switching is accomplished.
It should be pointed out that the light once switched remains in the appropriate branch because branches 7 and 8 are suitably of symmetrical type separated by a cuspate or tapered portion 4A of substrate 4 so as to provide means of separating any of the optical energy exiting from the left output side from any of the optical energy exiting from the right output side of waveguide 3. Thus, optical energy exiting from the respective output sides passes into the respective branches and goes to distinct destinations without significant energy transfer or crosstalk between the branches.
Recognition of the fact that the even modes can be preferentially shifted in phase by locating an electrode such that the odd modes are substantially unchanged, naturally leads to consideration of electrodes which leave the even modes essentially unaffected but strongly shift the odd modes. In other words, the voltage applying means should affect the propagation of the optical modes which are odd modes without by comparison substantially affecting the propagation of the optical modes which are even modes. It is apparent from FIG. 5 that the odd modes have very little energy near center plane 15 and at point 34 but have concentrations of energy near the peaks of the antisymmetric fields where the even mode energy is less.
As shown in FIG. 5 phase shifting of the odd modes can suffice to switch light energy. Antisymmetric field portions 35 and 36 are respectively opposite in sign to field portions 22 and 23 of the odd modes of FIG. 3. The sum of the even mode field 33 and the odd modes of FIG. 5 yields a strong field portion 38 carrying most of the energy out the right side 3RSOUT of waveguide 3. Insignificant field portion 37 bearing negligible energy is all that remains on the left-hand side.
Accordingly, as shown in FIG. 6, an embodiment 40 of the invention for preponderately phase shifting the odd modes is shown. Multimode waveguide 3 with center plane 15, substrate 4 with c-axis and relatively wide grounded electrode 10 on the bottom side of waveguide 3 are the same as in FIG. 2. The difference is that the voltage source V is now connected to not one electrode but two and only two slender stripe electrodes 41 and 42. Electrodes 41 and 42 are of essentially the same shape and size located on and only on the top side or face 16 of waveguide 3. They are small in width, preferably less than one-fourth of width a of waveguide 3 and are bilaterally symmetrically displaced frofm the center plane 15. In this way two electric field portions 43 and 44 are impressed upon waveguide 3 between electrodes 41 and 10 and electrodes 42 and 10 respectively. The electrodes 41 and 42 are provided with means 45 for maintaining them at equal electrical potentials such as by means of a common connection together and to the voltage source or by a narrow connecting stripe, not shown, deposited on the top of waveguide 3 transverse to the electrodes 41 and 42. The field portions 43 and 44 electrooptically affect the propagation of the odd modes with less effect on the even modes in the even mode high energy portions near center plane 15. The electrodes produce two parallel zones of refractive index increase (or decrease) which are located symmetrically on either side of center plane 15 in transverse or bilateral symmetry.
FIG. 7 shows an additional advantageous embodiment 50 employing the principles of the present invention. A multimode waveguide 55 defined by shallow indiffused titanium of thickness b approximating λ and having center plane 15 is fashioned in LiNbO3 substrate 4 having thickness b'. Substrate 4 is cut so that the c-axis 57 is transverse to the waveguide length and parallel to the substrate plane. Four mutually parallel electrodes 51, 52, 53 and 54 each being in width less than one-fourth of the width a are located symmetrically with respect to the waveguide width on waveguide face 56. For clarity, electrodes 52 and 53 are discussed first.
Slender stripe electrodes 52 and 53 are deposited slightly displaced on either side of center plane 15. When a potential difference V is impressed across them, a curved electric field 48, which is parallel to the c-axis 57 at center plane 15, produces a maximum electrooptic effect on the even modes where their energy is greatest, near the center of waveguide 55. The effect on the odd modes, however, is negligible when only electrodes 52 and 53 are employed. Thus, such a configuration is analogous to that of FIG. 2 in its operation and is fully operative to produce a nonuniform but bilaterally symmetric refractive index increase or decrease centered along center plane 15.
In an additional advantageous feature, however, electrodes 51 and 54 are included in the embodiment illustrated in FIG. 7 such that fields 47 and 49 of opposite direction to field 48 are created. Means for maintaining the four electrodes at spatially alternating relative electrical potentials are provided in the form of appropriate connections either by wires as shown or by deposited end connections to the electrodes as interdigitated electrodes. A voltage source such as the combination of batteries B, potentiometer P, and switch S1, provides interruptable or pulsed control for the device 50. The voltage source can as shown have one pole connected to electrodes 51 and 53 in common and have the other pole connected to electrodes 52 and 54 in common. In this manner the refractive index can be increased near the center of the waveguide but decreased along two parallel zones displaced laterally therefrom.
Then, the odd modes which carry most of their energy in the regions between electrodes 51 and 52 and electrodes 53 and 54 are electrooptically influenced in their propragation in an opposite manner to the even modes without significantly counteracting the effect of electrodes 52 and 53 on the even modes. The result is that the even modes and odd modes are differentially affected as groups so as to produce a differential π phase shift between the even and odd modes with a much smaller voltage being required and hence less energy.
The above qualitative description of the principles of the inventive modulator/switch is presently supplemented by a mathematical description which will serve to present these principles more rigorously.
Consider a multimode slab waveguide as in FIGS. 1 and 2 of width a, thickness b, and refractive index n at wavelength λ. The substrate thickness is designated b' when b' is different from b. The waveguide propagation constants β (β = (2πn)/λ in an extended volume of index n) of the lower-order modes which are far from cutoff can be approximated by ##EQU1## p and q being integer mode designations. For modes far away from cutoff, (λp << 2an and λq << 2bn), the following further approximation is also valid: ##EQU2## Consider the case where only one variation occurs across the thickness of the waveguide (q = 1). The remaining modes then have propagation constants βpl which differ by ##EQU3## where pi and pj are distinct positive integer values of p.
The phase shift for mode pq in a length L of the waveguide is βpq L. The differential phase shift between modes is Δβpq L, which for q = 1 and by rearranging equation (3) is given by ##EQU4##
If it be possible to find some length or lengths L where the modes are reconstructed in phase with each other, that is, in the same phase relationship as they occur at the input end of the waveguide, then the length of waveguide 3 at which light energy exits on the same side as the side on which it entered is determined. This occurs when
Δβpl L = 2πm, m being an integer (5)
corresponding to each pair pi and pj. Any length L which is an integer multiple of 8a2 n/λ will satisfy condition (5) as can be seen by inspection of equation (4). As will be shown next, light energy exits on the opposite side from which it enters at odd multiples of half the length 8a2 n/λ for which light exits on the same side at which it enters.
As suggested in FIG. 3, any input distribution of light energy in waveguide 3 can be analyzed as a set of modes, the even modes being symmetric with respect to center plane 15 and odd modes being antisymmetric. As shown in FIGS. 4 and 5, a mirror image of the input from an energy point of view can be produced when either the even modes are all reversed in sign or the odd modes are all reversed in sigh. This occurs when there is a 180� or π phase shift between consecutive modes such that
Δβpl L = πm, m being an odd integer when pi = pj + 1. (6)
When condition (6) is satisfied, all the even modes are in phase with each other, since for them pi = pj + 2 so Δβpl L = 2πm. All the odd modes are also in phase with each other, since for them also pi = pj + 2 and Δβpl L = 2πm. But as between the even and odd modes there is a sign reversal and hence a mirror image is produced when condition (6) is satisfied.
Condition (6) can indeed be satisfied because if ##EQU5##
Δβpl L = π [(pj +1)2 - pj 2 ](8)
Δβpl L = π(2pj +1) (9)
which satisfies the condition (6) since 2pj +1 is odd for all pj. Moreover, inspection of equation (8) shows that Lc = (4a2 n)/λ is the least critical length at which the light energy exits from the opposite side from the one it entered. Of course, 2Lc = (8a2 n)/λ is the expression for the least critical length multiple at which the light energy exits from the same side as the one it entered. That odd multiples of Lc all act like Lc and even multiples of Lc all act like 2Lc is readily seen by considering each multiple as corresponding to lengths Lc in series shunting the light beam from side to side with each Lc.
If electrodes are placed on either side of the waveguide so as to uniformly change the refractive index of the entire waveguide, a form of switch can be conceived which operates by changing the effective critical length L. Given a maximum refractive index change Δnmax obtainable in a given structure as by electrooptic means, the effective length L must be changed from an even to odd multiple m (or vice versa) of (4na2)/λ. This corresponds to the condition ##EQU6## If (.sup.Δn i max)/n is on the order of 10-4, then m = 104, which means that very long waveguide lengths are required in such a hypothetical switch.
In the present invention, however, the need for such long lengths is eliminated by using electrodes which are small enough compared to the waveguide in order to differentially affect the propagation of the even and odd modes in the guide itself by presenting different refractive indices to them.
For modes of the same polarization (all TE or all TM) and with voltage applied let ne denote the effective refractive index in the waveguide for the even modes, and let no denote the effective refractive index for the odd modes. In the absence of applied voltage, ne and no are both equal to the refractive index n of the waveguide for the modes, but when voltage is turned on the difference between ne and no becomes significant. The phase φe = βL for the even modes is (compare equation (1)) ##EQU7## and the phase shift for the odd modes is ##EQU8## In addition to the phase shift introduced by differencing the waveguide terms in the square brackets with respect to p, as previously discussed, there is now required a 180� or π phase shift between the even and odd modes introduced by Δn = ne - no, and the following equation results: ##EQU9## Equation (14) satisfactorily approximates the phase shifting contribution of the slender electrode or electrodes since the contribution to the phase shift resulting from a change in n from the terms in the square brackets is relatively smalll. Solving equation (14) for Δn yields ##EQU10## This Δn is the effective refractive index change needed in order to cause light of wavelength λ to switch from one side to the other of the output end of a multimode waveguide of an appropriate length L.
Assume the modulator/switch of FIGS. 1 and 2 designed for use with a helium-neon (He-Ne) laser source with λ = 0.633 micrometers, a = 50 micrometers, n = 2.4 and length equal to only one critical length so that ##EQU11## Then
L ≅ 38 millimeters.
Substituting equation (16) into (15) ##EQU12##
Δn = 8.35 � 10-6
This effective level of Δn is relatively easily obtained by the electroopic effect and is much smaller than the value Δnmax assumed at first hereinabove.
If the thickness b = 10μm for substrate 3, then the switching voltage V required is related to an ideal voltage V' where ##EQU13## when the standard electroopic effect formula involving the r33 coefficient is employed. For LiNbO3 r33 is 31 � 10-12 (meters/volt). Because the electrode 9 causes a refractive index change over only a portion of the waveguide cross-section, a voltage correction factor of a/2w is applied. When w = 1/4a, the correction factor is 2.
Substituting in (18) and applying a correction factor of 2 yields
V = 0.8 volt.
The device is of a type such that when voltage is off light incident in branch 5 of FIG. 1 exits through branch 8. With voltage on, the light exits from branch 7, and the device acts as a switch. If light is incident at both branches 5 and 6, reversing switch action is achieved. When one but not both of branches 5 and 6 carries incident light a unipolar voltage between 0 and 0.8 volts peak-to-peak can modulate the light output at branch 7.
The length dimension of the switch of Example I can be reduced even more by reducing the width a to 20 micrometers, with thickness b remaining at 10 micrometers, and electrode width w being 5 micrometers.
Using equations (16), (17) and (18),
L = 6.1 millimeters
Δn = 52.2 � 10-6 (effective value)
V = 4.8 volts (with correction factor of 2)
It is apparent that there is an inverse proportionality between the length L and switching voltage V required. For most purposes, a width a less than 50 microns is preferable so as to keep the length L small enough for practical devices (less than 1 centimeter), and the thickness b is preferably less than about 25 microns or one-half the width a so as to readily permit waveguide branches with an aspect ratio a/2b of at least 1.0 and so as to allow switching voltages V to fall in an advantageous range.
For integrated optics applications it is preferable to have length L be as short as possible without increasing V to impractically high values. Also, the capacitance of the modulator/switch should be low so that the electrode voltage can have a high modulation rate or very short risetime. Use of integrated optics sources based on technology in the gallium arsenide (GaAs) - gallium aluminum arsenide (GaAlAs) system makes a wavelength λ of 0.85 micrometers or longer preferable.
In accordance with the invention it has been discovered that the length L for the modulator/switch can in fact be even shorter than L = 4na2 /λ. This unexpected resut has been found in spite of the fact that 4na2 /λ is the minimum length for single-image self-imaging in a passive multimode waveguide.
The operation of such a reduced-length modulator/switch is explained as follows. Recalling equation (4) ##EQU14## When L = 2na2 /λ, ##EQU15## In general the relation pi = pj + 2 defines all modes which are even in symmetry (even modes) when pj is an odd integer and all modes which are odd in symmetry (odd modes) when pj is an even integer. Substituting this relation into equation (20) yields ##EQU16##
Δβpl L = 2π (pj + 1) (23)
Equation (23) shows that the even modes are all in the same phase relationship to each other after propagation through L = 2na2 /λ as they were at the input end because Δβpl L is a multiple of 2π regardless of pj. Equation (23) shows that the odd modes are also reconstructed in original phase relative to one another.
As between the even modes (pj an odd integer) and odd modes (pi = pj + 1), however, ##EQU17## Equation (25) shows that the relative phase of the even and odd modes is always an odd multiple of (π/2). Moreover, it can be seen that equation (25) shows that the odd modes as a group are offset by -90� or -π/2 from the even modes as a group because (π/2) (2pj + 2) is a multiple of 2π for all odd integer pj and so (π/2) (2pj + 1) must indicate a constant offset of -π/2.
Thus, adding a phase shift of + π/2 electrooptically generates a single self-image in a half-critical-length multimode waveguide 3, and adding a phase shift of -π/2 electrooptically generates the inverted or switched single self-image in the waveguide. A bipolar modulating or switching voltage can readily provide this dual polarity π/2 phase shift.
Accordingly, a switching of the image occurs when the applied voltage is switched from one polarity to the opposite polarity. And when the applied voltage is zero, power is split between the two output ports. Thus, a highly advantageous component is obtained for use in integrated optics switching arrays because it doubles as a switch and as a 3db coupler. As a modulator this element utilizes an AC (alternating) modulating voltage requiring no DC (direct) bias or offset to amplitude modulate light leaving each output branch 7 and 8.
The parameters of this Example III embodiment are as follows:
L = 2na2 /λ, and (26)
using an LiNbO3 substrate with n = 2.2, a = 20 micrometers, b = 10 micrometers, w = 5 micrometers, and λ = 0.85 micrometers the length of the multimode waveguide required is L = 2.1 millimeters.
The integer multiples of this half-critical length are also usable, of course. In particular, the integer multiples between 1 and 4 inclusive, i.e., 2.1 mm, 4.2 mm, 6.3 mm and 8.4 mm are all under 1 centimeter and can be of interest for integrated optics applications by virtue of their relatively miniature dimensions.
In order to calculate Δn in the half-critical length embodiment, reference is made to the discussion relating to equation (14). However, only a � π/2 phase shift for either set of modes in the half-critical length embodiments is required to modify the - π/2 offset, so ##EQU18## With
L = 2na2 /λ, ##EQU19## Substituting the example values for n, a, and λ yields an effective value of refractive index change
Δn = � 1 � 10-4.
The voltage required is (after correction) ##EQU20##
V = � 12 volts.
Assuming a permittivity ε in LiNbO3 of 30 times the permittivity εo of free space, a top electrode width w of 5 micrometers and capacitance given by ##EQU21## yields
C = 0.27 picofarad.
The power required for modulation purposes at frequency f and V = 12 volts is calculated to be
P = 1/2 CV2 f. (31)
P = 20 microwatts at 1 megahertz.
The peak electric field strength in the embodiment is
E = (V/b) (32)
E = 12000 volts per centimeter.
This value is well below the breakdown voltage in LiNbO3 which is of the order of 100,000 volts per centimeter.
The modulation depth or extinction ratio obtainable in the invention is higher to the extent that the even and odd modes are differentially effected. Since higher order modes of both types have significant energy in any location in which the electrodes may be placed, an estimate of the modulation depth or extinction ratio can be derived by assuming that only a few low order modes are correctly affected, and then calculating the ratio of unintended energy on one output side to the energy leaving the other side. When such a calculation is performed assuming three modes sin x, c1 sin 2x, and c2 sin 3x with c1 and c2 being chosen to minimize the ratio, an extinction ratio of 22.9 dB is obtained, a value satisfactory in both modulator and switch applications. However, modulator applications do not necessarily require as high a ratio as is advantageous for switches.
The modulator/switch of FIG. 6 is fabricated with a = 20 micrometers, b = 10 micrometers, and identical electrode widths w suitably being between 1 and 5 micrometers. w is assumed to be 2.5 micrometers for the calculations. Again L = 2na2 /λ = 2.1 centimeters in LiNbO3 at λ = 0.85 micrometer. The operating voltage remains approximately � 12 volts because the same index change Δn is still required, this time for the odd modes. The capacitance C is about the same as for a single electrode 9 having a width of 5 micrometers since two electrodes 41 and 42 having w = 2.5 micrometers are used. So C = 0.27 picofarad.
The modulator/switch of FIG. 7 is fabricated in LiNbO3 with a = 20 micrometers, b = 2 micrometers, b' = 10 micrometers, and electrode widths of 3 micrometers or less spaced apart 2 micrometers when the 3 micrometer width is used. The electrodes clear the edges of the waveguide by 1 micrometer on either side. An indium gallium arsenide phosphide (InGaAsP) laser source of 1.20 micrometer radiation is employed.
L = 2na2 /λ = 1.5 millimeters.
It should be recognized in the calculation of the refractive index change Δn that the embodiment at any one time increases the refractive index for one set of modes, say even, and reduces it for the other set of modes, say odd. Thus, the effective index change, here call Δ1 n, in the LiNbO3 for the embodiment of FIG. 7 is actually only one-half that required in other previously described embodiments of the invention. ##EQU22## Substituting the n, a and λ for this Example V embodiment yields
Δ1 n = � 1 � 10-4
The voltage V is calculated assuming an effective spacing between the electrodes for electric field purposes equal to the center-to-center spacing d of 5 micrometers. The uncorrected voltage V' is taken to be ##EQU23## Applying a voltage V correction factor of a/2d yields ##EQU24## Substituting values,
V = � 6.0 volts.
The maximum electric field strength E is the ratio of 6 volts to the electrode spacing of 2 micrometers, so E = 30,000 volts per centimeter. This value is well under the breakdown strength of LiNbO3 previously mentioned. Varnish may be applied if required to protect the electrodes from breakdown in air.
The capacitance of the embodiment is estimated as if there are three parallel capacitors with parallel plates of width w = 3 micrometers spaced at d = 5 micrometers. Using ε = 30εo, and L = 1.5 millimeters with the equation ##EQU25## and substituting values yields
C = 0.72 picofarads.
The modulation power from equation (31) with the C and V of this Example V is P = 13 microwatts at 1 megahertz.
A substrate bearing one or more modulator/switch devices of the type shown in FIG. 1 is suitably coupled to one or more optical fibers by means of a butt optical joint such as is suggested in U.S. Pat. No. 3,976,358 to G. H. B. Thompson. For instance, the branch including waveguides 5 and 6, can be coupled to input optical fibers. Of course, the relatively narrow waveguides must frequently lead together to waveguide 3 from a spacing perhaps several times the width a of waveguide 3 so that larger optical fiber diameters may be accommodated. Then light incident through each optical fiber is able to enter an appropriate side of waveguide 3 through one of the waveguides 5 or 6.
FIGS. 8 and 9 show an alternative means of coupling to the optical fibers which prevents the outside diameter of the optical fibers from being a constraint on design. Briefly, this approach uses a pair of separating mirrors or prisms at each end of a multimode waveguide 60 for coupling into optical fibers located transverse to the waveguide.
As shown in FIG. 8, a multimode waveguide 60 having electrodes 61 and 62 connected by conductors 76 and 77 to a source of voltage V operates as a multimode waveguide modulator/switch in the manner previously discussed. Waveguide 60 is made from a slab of LiNbO3 polished down to suitable thickness. Separating prisms 71 and 72 are respectively brought by micromanipulation and cemented to right and left sides of an input end of the waveguide 60. Also, the prisms 71 and 72, which have oblique reflecting surfaces oriented at an angle sufficient to provide total internal reflection, are cemented to the cores 64 and 66 of two input fiber waveguides 63 and 65. The input fibers are essentially in the same plane as waveguide 60 and collinear with respect to each other. The fibers are also approximately perpendicular to the length of waveguide 60. Similarly, separating mirrors 73 and 74 located at an output end of the waveguide 60 are cemented to the waveguide and to cores 68 and 70 of the fiber waveguides 67 and 69 which form an output medium for the device. The entire assembly of waveguide 60 with electrodes 61 and 62, mirrors 71 through 74 and optical fibers 63, 65, 67 and 69 is potted for mechanical strength in epoxy or other suitable medium 75, which has a sufficiently low refractive index compared to the separating prisms and waveguide 60 to permit total internal reflection therein.
Light entering the multimode switch 80 through optical fiber 63 via core 64 passes into prism 71 and is reflected into the left side of the input end of waveguide 60. The light energy so introduced propagates in even and odd modes through waveguide 60 and if the voltage V is suitably selected, the light exits from the right side of the output of lower end of waveguide 60, enters the prism-shaped separation element 74 and is reflected and coupled into the core 70 of output optical fiber 69. At another voltage V, or perhaps no voltage, the light is equally coupled to both separation elements 73 and 74 and exits approximately equally through output fibers 67 and 69. At still another voltage V the light as a whole essentially exits through the left side of the output end of waveguide 60 and is entirely coupled to and carried away by optical fiber 67.
Light entering through both optical fibers 63 and 65 simultaneously, bearing distinct modulations, can be simultaneously introduced by means of the prism assembly including elements 71 and 72 so as to propagate in even and odd modes in the waveguide 60. At one voltage V, waveguides 64 and 66 are respectively coupled to waveguides 67 and 69, and at another voltage V waveguides 64 and 66 are respectively coupled to waveguides 69 and 67 in reverse manner. Alternatively, at still another voltage or no voltage at all the light in waveguides 64 and 66 can be combined so that equal amounts of both input modulations exit via light waves from waveguide fibers 67 and 69 due to a 3db coupler action.
Thus, the assembly of FIG. 8 permits its use as a discrete optical fiber voltage-controlled component having uses as an amplitude modulator, switch, multiplexer and demultiplexer. When it is desirable to control the polarization of the input light, optical fibers having an elliptical or other polarization-conserving cross-section may be used.
FIG. 9 shows an end profile view of the optical multimode switch of FIG. 8. Optical fibers 67 and 69 having cores 68 and 70 are butted against prisms 73 and 74, the oblique faces of which appear as adjacent squares in FIG. 9. Epoxy 75 encapsulates the entire assembly including waveguide 60 behind prisms 73 and 74. A source of voltage V is conductively coupled via conductors 76 and 77 to narrow stripe 62 and wide electrode 61 on opposite faces of the multimode waveguide. The electrode 61 need not necessarily be a thin evaporated deposit as suggested in FIG. 9, but may alternatively be a metallic pedestal 77 terminating in a tip 61. The tip may be either equal in width to the waveguide 60 or even wider for suitably substantial mechanical support.
The embodiments of the invention hereinabove described are to be considered as being only illustrative and not exhaustive. Many embodiments of the invention can be fashioned utilizing appropriate materials, shapes and dimensions so as to fully realize the utility of the invention by application of its principles.
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