End-fire coupling between optical fibers and diffused channel waveguides: comment Ian A White, L. D. Hutcheson, and James J. Burke University of Arizona, Optical Sciences Center, Tucson, Arizona 85721; Ian White is now with Bell Laboratories, Norcross, Georgia 30071. Received 24 March 1979. 0003-6935/79/142362-07$00.50/0. © 1979 Optical Society of America. In an earlier paper, 1 Burns and Hocker have developed a valuable tool for the calculation of all propagation effects for the modes of integrated optical dielectric waveguides. By empirically matching the fundamental mode field of the guide to symmetric Gaussian field profiles in both width (x direction) and depth (y direction), they have provided a simple and useful mathematical form for the fundamental mode field, which can then be incorporated into classical electromagnetic theory to determine the effects of irregularities, etc., on propagation in the dielectric channel. The symmetric Gaussian field profile in the x direction (width) is an excellent approximation to the exact solutions, as the evaluation of the overlap integral [Eq. (6) of Ref. 1] demonstrates. This is because of the basic symmetry of the dielectric profile in this direction. However, the strong asymmetry of the dielectric profile in depth (y axis), due predominantly to the large dielectric difference between the air and substrate, would suggest that it is more logical to seek a simple asymmetric field profile in this direction. From a wave optics viewpoint, the guided waves in the substrate would totally internally reflect from this air-substrate interface as if the interface were that of a perfectly conducting boundary (due to this large dielectric difference). The authors were obviously aware of this when they chose a zero field intensity at y = 0 (air interface) for the initialization of the numerical evaluation of the profile. A simple weighted Gaussian field profile of the form provides an excellent fit to the numerical work, where W y is defined in Ref. 1 and b is determined from the numerical work and W y . It should be noted that although this slight correction to Burns and Hocker's work does improve the field profile in the y direction, there should be little if any significant correction to their calculations of end-fire coupling between fibers and channel guides. Reference 1. W. K. Burns and G. B. Hocker, Appl. Opt. 16, 2048 (1977). 2362 APPLIED OPTICS / Vol. 18, No. 14 / 15 July 1979

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End-fire coupling between optical fibers and diffused channel waveguides: comment

Ian A White, L. D. Hutcheson, and James J. Burke University of Arizona, Optical Sciences Center, Tucson, Arizona 85721; Ian White is now with Bell Laboratories, Norcross, Georgia 30071. Received 24 March 1979. 0003-6935/79/142362-07$00.50/0. © 1979 Optical Society of America.

In an earlier paper,1 Burns and Hocker have developed a valuable tool for the calculation of all propagation effects for the modes of integrated optical dielectric waveguides. By empirically matching the fundamental mode field of the guide to symmetric Gaussian field profiles in both width (x direction) and depth (y direction), they have provided a simple and useful mathematical form for the fundamental mode field, which can then be incorporated into classical electromagnetic theory to determine the effects of irregularities, etc., on propagation in the dielectric channel. The symmetric Gaussian field profile in the x direction (width) is an excellent approximation to the exact solutions, as the evaluation of the overlap integral [Eq. (6) of Ref. 1] demonstrates. This is because of the basic symmetry of the dielectric profile in this direction.

However, the strong asymmetry of the dielectric profile in depth (y axis), due predominantly to the large dielectric difference between the air and substrate, would suggest that it is more logical to seek a simple asymmetric field profile in this direction. From a wave optics viewpoint, the guided waves in the substrate would totally internally reflect from this air-substrate interface as if the interface were that of a perfectly conducting boundary (due to this large dielectric difference). The authors were obviously aware of this when they chose a zero field intensity at y = 0 (air interface) for the initialization of the numerical evaluation of the profile.

A simple weighted Gaussian field profile of the form

provides an excellent fit to the numerical work, where Wy is defined in Ref. 1 and b is determined from the numerical work and Wy. It should be noted that although this slight correction to Burns and Hocker's work does improve the field profile in the y direction, there should be little if any significant correction to their calculations of end-fire coupling between fibers and channel guides.

Reference

1. W. K. Burns and G. B. Hocker, Appl. Opt. 16, 2048 (1977).

2362 APPLIED OPTICS / Vol. 18, No. 14 / 15 July 1979