Principles for modal waves in guided wave optics

Abstract

The geometrical optics theory of modal waves propagating along optical waveguides is described. The theory is general and thus applicable to the general classes of inhomogeneous waveguides including aniso‐tropic media. This paper points out that the light ray, which is the fundamental concept in geometrical optics, is to be definable as the energy ray and the wave‐normal ray. The variational principles valid for these two definitions are explained. The energy ray is the well‐known ray that shows the path of energy transport. The wave‐normal ray is defined to be the locus of the wave‐normal vectors perpendicular to the wavefronts. The variational principles that describe these two rays are different, and therefore the ray equations for both rays are different in anisotropic media. The former is known as Hamiltonian optics, but the latter is not yet established as geometrical optics. It is pointed out that the latter should be used to describe the geometrical behaviors of guided modes and the propagation of modal waves without any logical contradiction. Optics describing guided modes in terms of the wave‐normal rays is called guided wave optics, and some differences from Hamiltonian optics are discussed using several examples.

Geometrical Optics of Guided Waves in Waveguides

“…Each gives complete information on the wave mechanism of propagation in time-space domain. Basic rules that constitute different ray configurations in the medium environment are deduced from different variational principles [4,5]. These are outlined in this section.…”

“…Nevertheless, the geometrical rules for dynamical waves can be derived from the stationary rules obtained above. To show this, we first note [5] that the path of a wavepacket in time domain coincides with the path of a beam wave which is a "spatial wavepacket" of stationary wavelets in space. The path of the spatial wavepacket can be determined as follows by complex ray techniques [35,[38][39][40][41][42].…”

“…It is the purpose of the present Chapter to give a brief review of the recent development of the stationary optics described in terms of wave-normal rays [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], and thus it is not the purpose to give a selfcontained paper that provides the full theory the readers can follow. The wave-normal ray description is useful for modal waves in visible and invisible regions.…”