The authors give a brief historic perspective of the coupled mode theory. The development and applications of the theory in microwaves in early years and in optoelectronics and fiber optics in recent years are described. They then consider lossless coupling of two modes in time. Two coupled resonance circuits, or two coupled microwave or optical resonators, are the physical examples. The start-up of a parametric oscillator is another example. Then they look at the formal derivation of coupled mode theory and consider the more general case when the modes are not energy-orthogonal and the energies are not necessarily positive. A more detailed account of the nonorthogonal coupled mode theory developed in the last five years for optical waveguides is given. >

Coupled-mode theory

A coupled-mode theory is derived from the scalar wave equation for the interaction between forward- and backward-traveling waves in a general slowly varying coupled waveguide array containing an arbitrary number of guides with a grating overlay. The equations include the effects of nonnegligible model overlap terms and changes in modal overlap but still demonstrate power conservation. Numerical results are presented for a contradirectional track-changing filter, which show that the modifications made to the equations are significant for practical devices.

Improved coupled-mode theory for codirectionally and contradirectionally coupled waveguide arrays

Three-waveguide optical switches are analyzed by means of the coupled mode theory. Assuming that three approximate waveguides of an optical switch are identical and equally spaced, we examine the switching behavior for cases where an incident beam is launched into (1) an outer waveguide and into (2) a center waveguide. For each beam-launching case, switching voltage is applied so that the overall index profile is detuned (1) symmetrically or (2) antisymmetrically. It is concluded that only three types of optical switches out of these four configurations can perform the switching operation. We derive the switching conditions for each of three possible types and draw the corresponding switching diagrams.

Switching operations of three-waveguide optical switches

A new control algorithm for log2(N, 0, p) switching networks composed of 2 x 2 switching elements has been proposed recently. Under this algorithm, log2(N,0,p) switching networks with even number of stages are wide-sense nonblocking (WSNB) if p is the same as for the rearrangeable nonblocking (RNB) one. The considerred algorithm and WSNB conditions did not take into account crosstalk constraint, which is an important factor in photonic switching. This paper enhanced this algorithm to the case when crosstalk in the switching fabric is not allowed. WSNB conditions for this enhanced algorithm are also derived. It is shown, that the number of planes required is less than those derived earlier in other papers for WSNB multiplane banyan- type switching fabrics under crosstalk constraint. Under this algorithm, log2( N,0,p) switching networks with odd number of stages and with zero crosstalk are WSNB if p is the same as for RNB one.

A New Control Algorithm for Wide-Sense Nonblocking Multiplane Photonic Banyan-Type Switching Fabrics with Zero Crosstalk

A three-waveguide polarization independent power splitter on lithium niobate substrate

The switch characteristics of three-arm integrated optic directional couplers with both symmetric and antisymmetric drive voltages are examined. The symmetry properties of these devices, predicted by previous theory, are shown to be violated and the reasons for this are discussed in terms of scalar strong coupling coefficients normally neglected as small. It is also shown that the inclusion of modal overlaps introduces additional coupling terms and causes significant power redistribution in the bend sections. Experimental measurements for the antisymmetric configuration are presented, and it is shown that different electrode loading of the center and outer guides affects device operation. >

R.R.A. Syms

Papers

Further evidence of strong coupling effects in three-arm Ti:LiNbO/sub 3/ directional couplers