An optical waveguide, such as an optical fiber or a dielectric slab waveguide formed on a substrate, can interact and confine optical energy in one or more waveguide modes depending on the design of the waveguide. A waveguide mode can be characterized by a number of mode parameters such as the spatial distribution of optical energy, the propagation constant, and the polarization state. Two different modes, either coexisting in the same waveguide or respectively residing in two separate waveguides, may couple with each other to exchange their energy under proper conditions. Such mode coupling can be used to perform various optical operations on guided optical waves. For example, devices like optical couplers and switches can be made by using waveguides.
Energy transfer from one optical wave to another co-propagating wave is desirable in many applications such as optical communication systems. Mode coupling between two co-propagating modes in a multimode waveguide may be used to achieve such operation. A periodic index perturbation that forms a grating along the waveguide can be used to couple the modes when the propagation constants of the two modes satisfy a Bragg-type condition. See, e.g., Yariv, Optical Electronics, Chapter 13, Saunders Publishing (1991).
For two co-propagating modes A and B to couple in a grating of a period A in the waveguide, the Bragg condition is: ##EQU1##
where .beta..sub.A, .beta..sub.B are the propagation constants for modes A and B, respectively. The power conversion may be expressed by EQU P.sub.B (Z)=P.sub.B (0)cos.sup.2 (Kz), (2)
and EQU P.sub.A (z)=P.sub.B (0)sin(Kz), (3)
where P.sub.B (0) is the power of the mode A before entering the grating and K is the coupling coefficient K between modes A and B in the grating. Hence, power exchange between modes A and B varies sinusoidally with Kz. If the interaction length z is controlled at L=.PI./(2K) or its multiples, then the power of the mode B can be completely transferred into the mode A.
However, a precise control of the grating length for such phase matching is difficult in practical devices. This may be in part due to the unavoidable variations in manufacturing the grating in the waveguide and in part due to variations in the coupling parameter (KL) caused by environmental fluctuations during operation. In addition, since the desired coupling length L=.PI./(2K) usually has a strong dependence on both the wavelength and the polarization, the above coupling device may only operate in a narrow band and can be subject to degradation in performance caused by fluctuations in polarization. Furthermore, because the difference between the propagation constants of modes A and B is usually small, the required grating period .LAMBDA.=2.PI.m/.vertline..beta..sub.A -.beta..sub.B.vertline. is large. Hence, it is difficult to make this type of grating couplers compact.