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H. Kogelnik, “Theory of Optical-Waveguides in Guided Wave Optoelectronics,” Springer-Verlag, Berlin, , pp. H. Kogelnik, “Theory of dielectric waveguides,” in Integrated Optics,T. Tamir, Ed. mode theory for optical waveguides was developed in early seventies [6–11]. optics. This chapter is devoted to the theory of these waveguides. Other chapters of .. which is taken from KOGELNIK and RAMASWAMY.

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For full-text searches, use our search page. The concept of mode coupling is very often used e. 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. 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 theorg 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 waveghides based on the above-mentioned coupled differential equations e.

Instead of using coupled-mode theory, which is based on simplifying assumptions which are not always well fulfilledone can also study mode coupling phenomena with numerical beam propagation. This method is computationally more intense, but can generate more detailed insight.

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The field evolution has been calculated with numerical beam propagation, and the local mode powers have been obtained from the results using overlap integrals with the mode functions as obtained from a mode solver applied to the bare fiber. 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. For some cases with statistical variations of coupling effects, one may use a coupled-power theory instead of standard theories based on amplitude coupling [11].

If you like this article, share it with your friends and colleagues, e.

Light-propagation and imaging in planar optical waveguides

Sorry, we don’t have an article for that keyword! Mode Coupling Waveguidea concept of mode coupling is very often used e. Some examples of mode coupling are discussed in the following: An optical fiber may have several propagation modes, to be calculated for the fiber being kept straight.

If the fiber is strongly bent, this can introduce coupling e. Bend losses can be understood as coupling to non-guided wavegujdes thus lossy modes.

Fiber Bragg gratings FBGs can be understood is fibers which are equipped with additional means for mode coupling — for example, for reflecting light with short period gratings or for coupling to modes guided modes or kohelnik modes propagating in the same direction with long period gratings. Nonlinear interactions in a waveguide can also couple the modes as calculated for low light intensities to each other.

This picture can serve e. In high-power fiber amplifiers, a mechanism has been identified which can couple power from the fundamental fiber mode into higher-order modes [12].


This mechanism can involve either a Kramers—Kronig effect or thermal distortions influencing the refractive index profile. This leads to a strong loss of beam quality above a certain pump power level.

Optical resonators cavities can exhibit various kinds of mode coupling phenomena. For example, aberrations of the thermal lens in the gain medium of a solid-state bulk laser couple the modes of the laser resonatoras calculated without these aberrations.

In this situation, however, not all involved modes are necessarily resonant at the same time.

Guided-wave optoelectronics – Theodor Tamir – Google Books

This means then that the amplitude contribution which is fed e. This nonresonant nature of the coupling means that the coupling will in general have a small effect — which is essential for laser operation with high beam qualitysince otherwise aberrations would strongly excite higher-order modes, having a higher beam parameter product.

Strong resonant coupling can occur in certain situations, involving frequency degeneracies of resonator modes. Evolution of mode powers in a long-period fiber Bragg grating, which couples light from the injected fundamental mode radiation into higher-order modes.

Light-propagation and imaging in planar optical waveguides – IOPscience

This diagram has been taken from a case study on beam propagation in fiber devices. B 58, [7] W. Express 14 13[10] M. Express 19 26B [12] A. Express 19 11[13] A. RP Services and Tools. B 58, A 11 3 Express 14 13 Express 19 26B Express 19 11 ,