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Mode Coupling

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Definition: a concept for describing and calculating light propagation in certain situations, e.g. involving nonlinear interactions

German: Modenkopplung, Kopplung zwischen Moden

The concept of mode coupling is very often used e.g. to describe the propagation of light in some waveguides or optical cavities under the influence of additional effects, such as external disturbances or nonlinear interactions. The basic idea of coupled-mode theory is to decompose all propagating light into the known modes of the undisturbed device, and then to calculate how these modes are coupled with each other by some additional influence. This approach is often technically and conceptually much more convenient than, e.g., recalculating the propagation modes for the actual situation in which light propagates in the device.

Some examples of mode coupling are discussed in the following:

Technically, the mode coupling approach is often used in the form of coupled differential equations for the complex excitation amplitudes of all the involved modes. These equations contain coupling coefficients, which are usually calculated from overlap integrals, involving the two mode functions and the disturbance causing the coupling. Typically, the applied procedure is first to calculate the mode amplitudes for the given light input, then to propagate these amplitudes based on the above-mentioned coupled differential equations (e.g. using some Runge–Kutta algorithm), and finally (if required) to recombine the mode fields to obtain the resulting field distribution.

An important physical aspect of such coherent mode coupling phenomena is that the optical power transferred between two modes depends on the amplitudes which are already in both modes. A consequence of that is that the power transfer from a mode A to another mode B can be kept very small simply by strongly attenuating mode B. In this way, mode B is prevented from acquiring sufficient power to extract power from mode A efficiently, so that mode A experiences only little loss, despite the coupling.


[1]A. W. Snyder, “Coupled-mode theory for optical fibers”, J. Opt. Soc. Am. 62 (11), 1267 (1972)
[2]H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers”, J. Appl. Phys. 43 (5), 2327 (1972)
[3]A. Yariv, “Coupled-mode theory for guided-wave optics”, IEEE J. Quantum Electron. QE-9, 919 (1973)
[4]H. Haus et al., “Coupled-mode theory of optical waveguides”, J. Lightwave Technol. 5 (1), 16 (1987)
[5]W. P. Huang et al., “Optical wavelength filter with tapered couplers”, IEEE Photon. Technol. Lett. 3 (9), 812 (1991)
[6]R. Paschotta et al., “Nonlinear mode coupling in doubly-resonant frequency doublers”, Appl. Phys. B 58, 117 (1994)
[7]W.-P. Huang, “Coupled-mode theory for coupled optical waveguides: an overview”, J. Opt. Soc. Am. A 11 (3), 963 (1994)
[8]N. Matuschek et al., “Exact coupled-mode theories for multilayer interference coatings with arbitrarily strong index modulations”, IEEE J. Quantum Electron. 33 (3), 295 (1997)
[9]R. Paschotta, “Beam quality deterioration of lasers caused by intracavity beam distortions”, Opt. Express 14 (13), 6069 (2006)
[10]A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers”, Opt. Express 19 (11), 10180 (2011)
[11]A. W. Snyder and J. D. Love, Optical Waveguide Theory, Chapman and Hall, London (1983)

See also: modes, fibers, waveguides

Categories: fibers and other waveguides, methods

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