refraction of the core of the fiber and N2 is the index of refraction of the cladding of the fiber. Although the preceding formula is acceptable for multimode fiber, the use of single-mode fiber can result in significant computation errors. A more accurate method when working with single-mode fiber is to treat the output of the fiber as a gaussian source. Then the NA can be computed as NA = 21/MFD, where 1 is the wavelength of light expressed in terms of micrometers. According to the optics literature, the resulting NA value computed for single-mode fiber can be up to a third smaller than the value listed by some fiber manufacturers. When selecting a lens, a good rule of thumb to follow is to select optics with an NA at least 50 percent greater than the waveguide to be collimated. Doing SO can result in over 99 percent of transmission flow- ing through the optics. Coupling Considerations Once a light beam is collimated, you need to consider the coupling of the beam into a fiber or waveguide. In doing SO you need to consider the spot diameter (SD) of the focused beam and its NA. The focused SD should be less than or equal to the MFD of the waveguide, while the NA of the focused beam should not exceed the NA of the waveguide. If you know the focal length f of the lens, you can compute the SD and numerical aperture for the focused beam NA B as follows: = f DA X MFD fiber Team-Fly® Light Sources and Detectors If you are using multimode fiber, you should select a lens that pro- vides values for SD and NA B less than or equal to 70 percent of the maxi- mum allowable values. In addition, you should not attempt to focus the spot on an area less than 30 percent of the core of the fiber, as this could cause burning of the end of the fiber. While it is possible to find a range of focal length lenses that satisfy the previously listed computa- tions, when working with single-mode fiber, only one focal length will satisfy spot size and numerical aperture requirements. Alignment Considerations Once you select collimating and f