# Prism coupler

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## Resonance condition

The coupling of light into the waveguiding layer of the prism coupler is comparable to the coupling into a waveguide with the aid of a coupling prism. In both cases, the angle of incidence of the incident light must meet the condition for propagation of the light in the waveguide, i.e. the light must be totally reflected in the waveguide and the phase condition for modes must be given. If the refractive index of the waveguiding layer is the same as that of the prism, the coupling angle corresponds to the angle of propagation in the waveguide. If the refractive indices are different, they can be converted into one another with the help of Snellius' law of refraction.

Light is totally reflected at the FTIR limit, but is coupled out via the evanescent field (Frustrated Total Internal Reflection). At the outer edge of the waveguide, total internal reflection is carried out without coupling out (total internal reflection).

In contrast to the usual coupling in waveguides, the coupling prism in the prism coupler does not sit directly on the waveguide, but is separated by a coupling layer with a low refractive index. Light is totally reflected at the bottom of the coupling prism and acts on the waveguide via the evanescent field. A resonant mode is induced here, which propagates only briefly in the waveguide and then decouples it again and leaves the prism with the directly reflected light. In the case of resonance, there is also a phase jump $π$ which changes the polarization of the reflected light.

This behavior can also be simulated with the help of Fresnel's formulas for layer systems.

Since there is practically no loss of intensity in the coupling process, the angle of resonance cannot be determined by measuring the intensity of the reflected light. One therefore uses one around $π$ The analyzer is rotated in relation to the input polarization and only allows light to pass through after resonant reflection.

In the prism coupler, the resonance angles for TE and TM polarized light are clearly separated so that they can both serve as a reference for each other and the measurement is insensitive to intensity and temperature fluctuations.