Optical ring resonators

An optical ring resonator is a set of waveguides in which at least one is a closed loop coupled to some sort of light input and output.

The concepts behind optical ring resonators are the same as those behind whispering galleries except that they use light and obey the properties behind constructive interference and total internal reflection.

Additionally, as implied earlier, two or more ring waveguides can be coupled to each other to form an add/drop optical filter.

Given that the angle of incidence is larger than the critical angle (with respect to the normal of the surface) and the refractive index is lower on the other side of the boundary relative to the incident ray, TIR will occur and no light will be able to pass through.

For an optical ring resonator to work well, total internal reflection conditions must be met and the light travelling through the waveguides must not be allowed to escape by any means.

Interference usually refers to the interaction of two distinct waves and it is a result of the linearity of Maxwell Equation.

As such, assuming there are no losses in the system such as those due to absorption, evanescence, or imperfect coupling and the resonance condition is met, the intensity of the light emitted from a ring resonator will be equal to the intensity of the light fed into the system.

The reason for this is the phenomenon of the evanescent field, which extends outside of the waveguide mode in an exponentially decreasing radial profile.

In order to optimize the coupling, it is usually the case to narrow the distance between the ring resonator and the waveguide.

The medium material is usually the most important feature under study since it has a great effect on the transmission of the light wave.

[3] For lossless coupling to occur, the following equation must be satisfied: where t is the transmission coefficient through the coupler and

must be greater than the index of refraction of the surrounding fluid in which the resonator is placed (e.g. air).

The quality factor and the finesse of an optical ring resonator can be quantitatively described using the following formulas (see: eq: 2.37 in,[4] or eq:19+20 in,[5] or eq:12+19 in [6]): where

A system of two ring resonators coupled to a single waveguide has also been shown to work as a tunable reflective filter (or an optical mirror).

In this context, the utilization of nested ring resonator cavities has been demonstrated in recent studies.

[8][9] These nested ring resonators are designed to enhance the quality factor (Q-factor) and extend the effective light-matter interaction length.

This would allow for "small size, low losses, and integrability into [existing] optical networks.

"[10] Additionally, since the resonance wavelengths can be changed by simply increasing or decreasing the radius of each ring, the filters can be considered tunable.

[11] The tuning process can be affected also by a change of refractive index using various means including thermo-optic,[12] electro-optic [13] or all-optical [14] effects.

Electro-optic and all-optical tuning is faster than thermal and mechanical means, and hence find various applications including in optical communication.

Optical ring, cylindrical, and spherical resonators have also been proven useful in the field of biosensing.,[15][16][17][18][19] and a crucial research focus is the enhancement of biosensing performance [20][21][22][23] One of the main benefits of using ring resonators in biosensing is the small volume of sample specimen required to obtain a given spectroscopy results in greatly reduced background Raman and fluorescence signals from the solvent and other impurities.

Resonators have also been used to characterize a variety of absorption spectra for the purposes of chemical identification, particularly in the gaseous phase.

[24] Another potential application for optical ring resonators are in the form of whispering gallery mode switches.

[10] Many researchers are interested in creating three-dimensional ring resonators with very high quality factors.

[26] Many materials used to fabricate ring resonator circuits have non-linear responses to light at high enough intensities.

This non-linearity allows for frequency modulation processes such as four-wave mixing and Spontaneous parametric down-conversion which generate photon pairs.

A computer-simulated ring resonator depicting continuous wave input at resonance.
Total internal reflection in PMMA
A pictorial representation of the coupling coefficients
Visualization of: how the light from a point source is guided by a waveguide, how the waveguide is coupled to a ring resonator, and how the ring resonator is in turn coupled to another waveguide.
A transmission spectra depicting multiple resonant modes ( ) and the free spectral range .
A double ring resonator with rings of varying radii in series showing the relative intensities of light passing through on the first cycle. Note that the light passing through a double ring resonator would more often travel in multiple loops around each ring rather than as pictured.
Optical mirror (reflector) made of a double ring system coupled to a single waveguide. Forward propagating waves in the waveguide (green) excite anti-clockwise traveling waves in both rings (green). Due to the inter-resonator coupling, these waves generate clockwise rotating waves (red) in both rings which in turn excite backward propagating (reflected) waves (red) in the waveguide. The reflected wave exists only in the part of the waveguide to the left of the coupling point to the right ring. [ 7 ]
Nested Cavity Configuration: Light undergoes multiple round trips within the nested cavity, the number of which is approximately determined by the product of the round trips within the main cavity and the nested cavity. [ 8 ] [ 9 ]