iber- optic couplers with differences in the housing, lenses, and laser output coupling method diode fiber supported. The cou- pler shown uses both a collimating lens and a focusing lens with locking screws to fas- screw focusing ten the coupler collimator lens together. Light Sources and Detectors then the characteristics of the collimated beam are given by the follow- ing formulas: BD = 2xfxNA where MFD and NA are the mode field diameter and numerical aper- ture of the waveguide while BD and DA represent the beam diameter and full-divergence angle of the collimated beam. The BD and focal length of the lens are expressed in millimeters. In comparison, the DA is expressed in milliradians, where 1 mrad is 0.057° while the MFD is expressed in micrometers. As shown in Figure 4.14, large waveguides do not collimate well. For example, suppose you attempt to collimate a 500-um-core fiber with a 5-mm-focal-length lens. In this situation the divergence angle becomes 500 um/5 mm or 100 mrad. Since 1 mrad is 0.057°, the DA becomes 5.7°, which may not be much better than what you started with prior to the collimating process. Mode Field Diameter and Numerical Aperture Considerations A second point that warrants attention is how the NA and MFD are defined. Laser manufactures define their beams in terms of gaussian Figure 4.14 Fiber The operation of a fiber collimator. Beam Diameter (BD) Divergence Angle (DA) = MFD/f focal length of the lens Numerical Aperature of the waveguide MFD = Mode Field Diameter Chapter Four beam characteristics. As a result, the beam size of a laser diode is defined at the point where its intensity drops to 13.5 percent of its peak intensity of 1/e2. Laser diode manufacturers refer to this as full-width at half-maximum (FWHM) levels. If you are coupling a laser diode to multi- mode fiber, you can use the core diameter as the MFD and the refrac- tive indices of the fiber's core and cladding to compute the fiber's NA. To do SO, you would use the following formula: NA = VN2-N2 where N 1 is the index of 