An optical ring resonator, or micro-ring resonator (MRR) is a set of waveguides in which at least one is a closed loop coupled to light input and output. The input and output can be, but are not limited to being, waveguides. Geometries 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. When light of the resonant wavelength is passed through the closed loop from the input waveguide, the light builds up in intensity over multiple round-trips owing to constructive interference and is coupled to the output waveguide. Because only a narrow wavelength range will be at resonance within the loop geometry, the optical ring resonator functions as a filter. Additionally, two or more ring waveguides can be coupled to each other to form an add/drop optical filter or to send light in a preferred direction.
Background Optical ring resonators work on the principles behind total internal reflection, constructive interference, and optical coupling.
Total internal reflection
The light travelling through the waveguides in an optical ring resonator remains within the waveguides due to the phenomenon known as total internal reflection (TIR). TIR is an optical phenomenon that occurs when a ray of light strikes the boundary of a medium and fails to refract through the boundary. 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 the boundary. 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
Interference is the process by which two waves superimpose to form a resultant wave of greater(constructive) or less(destructive) amplitude. Interference usually refers to the interaction of two distinct waves and it is a result of the linearity of Maxwell's equations. Interference could be constructive or destructive depending on the relative phase of the two waves. In maximum constructive interference, the two waves have the same phase and, as a result, interfere in a way that the resulting wave amplitude will be equal to the sum of the two individual amplitudes. As the light in an optical ring resonator completes multiple circuits around the ring component, it interferes with existing light still in the loop building up amplitude over time resulting in a set time of 100s of ns. 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.
Optical coupling
Important for understanding how an optical ring resonator works, is the concept of how the linear waveguides are coupled to the ring waveguide. When a beam of light passes through a wave guide as shown in the graph on the right, part of light will be coupled into the optical ring resonator. 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 other words, if the ring and the waveguide are brought closely together, some light from the waveguide can couple into the ring. Optical coupling is affected by three aspects
Distance Coupling length Refractive indices of the waveguide and the optical ring resonator. In order to optimize the coupling, it is usually the case to narrow the distance between the ring resonator and the waveguide. The closer the distance, the easier the optical coupling happens. In addition, the coupling length affects the coupling as well. The coupling length represents the effective curve length of the ring resonator for the coupling phenomenon to happen with the waveguide. It has been studied that as the optical coupling length increases, the difficulty for the coupling to happen decreases. Furthermore, the refractive index of the waveguide material, the ring resonator material and the medium material in between the waveguide and the ring resonator also affect the optical coupling. The medium material is usually the most important feature under study since it has a great effect on the transmission of the light wave. The refractive index of the medium can be either large or small according to various applications and purposes. To maximize power transfer from the input waveguide to the optical ring resonator, critical coupling is the target. The critical coupling shows that no light is passing through the waveguide after the light beam is coupled into the optical ring resonator. The light will be stored and lost inside the resonator thereafter. Lossless coupling is when no light is transmitted all the way through the input waveguide to its own output; instead, all of the light is coupled into the ring waveguide (such as what is depicted in the image at the top of this page). For lossless coupling to occur, the following equation must be satisfied:
| K | 2 + | t | 2 = 1 {\displaystyle |\mathrm {K} |^{2}+|t|^{2}=\mathbf {1} }
where t is the transmission coefficient through the coupler and K {\displaystyle \mathrm {K} } is the taper-sphere mode coupling amplitude, also referred to as the coupling coefficient.
Theory To understand how optical ring resonators work, we must first understand the optical path length difference (OPD) of a ring resonator. This is given as follows for a single-ring ring resonator:
O P D = 2 π r n eff {\displaystyle \mathbf {OPD} =2\pi rn_{\text{eff}}}
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