## Ball lens reflections by direct solution of Maxwell`s equations

Description:
Ball lenses are important for many applications. For example, ball lenses can be used to match the mode of a laser diode (LD) to a single mode fiber (SMF), essential for low-loss, high bit rate communication systems. Modeling the propagation of LD light through a ball lens presents a challenge due to the large angular divergence of the LD field (typically > 20{degrees} HWHM) and the subsequent significant effect of spherical aberration. Accurately calculating the reflected power is also difficult, but essential, since reflections as small as {minus}30 dB can destabilize the LID. A full-wave analysis of this system using, e.g., a finite-difference time-domain method is not practical because of the size of the ball lens, typically hundreds of wavelengths in diameter. Approximate scalar methods can give good results in some cases, but fail to calculate reflected power and miss polarization effects entirely. The authors` approach exploits the fact that the scattering of an arbitrary electromagnetic beam from a sphere is an exactly solvable problem. The scattering of a plane wave from a sphere is a classical problem which was solved by Mie in 1908. More recently, various workers have considered the scattering of a Gaussian beam from a sphere and its numerical implementation for other applications. To the authors knowledge, this is the first time this approach has been applied to a problem in optical design. They are able to calculate reflection and transmission accurately with modest computational effort.

Date:
February 15, 1995

Creator:
Ratowsky, R.P.; Deri, R.J. & Kallman, J.S.

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