Optical ring resonators
   HOME

TheInfoList



OR:

An optical ring resonator is a set of
waveguides A waveguide is a structure that guides waves, such as electromagnetic waves or sound, with minimal loss of energy by restricting the transmission of energy to one direction. Without the physical constraint of a waveguide, wave intensities de ...
in which at least one is a closed loop coupled to some sort of light input and output. (These can be, but are not limited to being, waveguides.) The concepts behind optical ring
resonator A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator ...
s are the same as those behind whispering galleries except that they use light and obey the properties behind
constructive interference In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
and
total internal reflection Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflected b ...
. When light of the
resonant Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscilla ...
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
is passed through the loop from the input waveguide, the light builds up in intensity over multiple round-trips owing to
constructive interference In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
and is output to the output bus waveguide which serves as a detector waveguide. Because only a select few wavelengths will be at resonance within the loop, the optical ring resonator functions as a filter. Additionally, as implied earlier, two or more ring waveguides can be coupled to each other to form an add/drop optical filter.


Background

Optical ring resonators work on the principles behind
total internal reflection Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflected b ...
,
constructive interference In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
, and optical coupling.


Total internal reflection

The light travelling through the waveguides in an optical ring resonator remain within the waveguides due to the
ray optics Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of '' rays''. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstan ...
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 In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
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

Interference is the process by which two waves superimpose to form a resultant wave of greater or less amplitude. Interference usually refers to the interaction of two distinct waves and it is a result of the linearity of Maxwell Equation. Interference could be constructive or destructive depending on the relative phase of the two waves. In 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 will interfere with the other light still in the loop. As such, assuming there are no losses in the system such as those due to absorption,
evanescence Evanescence is an American rock band founded in Little Rock, Arkansas in 1995 by singer and musician Amy Lee and guitarist Ben Moody. After recording independent EPs as a duo in the late 90's, and a demo CD, Evanescence released their debut s ...
, 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. There are three aspects that affect the optical coupling: the distance, the coupling length and the refractive indices between 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. One more feature about optical coupling is the critical coupling. 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: : , \Kappa, ^2 + , t, ^2 = \mathbf where t is the transmission coefficient through the coupler and \Kappa 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: : \mathbf = 2 \pi r n_\text where ''r'' is the radius of the ring resonator and ''n_\text'' is the effective
index of refraction In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
of the waveguide material. Due to the total internal reflection requirement, n_\text must be greater than the index of refraction of the surrounding fluid in which the resonator is placed (e.g. air). For resonance to take place, the following resonant condition must be satisfied: : \mathbf = m \lambda_ where ''\lambda_'' is the resonant wavelength and ''m'' is the mode number of the ring resonator. This equation means that in order for light to interfere constructively inside the ring resonator, the circumference of the ring must be an integer multiple of the wavelength of the light. As such, the mode number must be a positive integer for resonance to take place. As a result, when the incident light contains multiple wavelengths (such as white light), only the resonant wavelengths will be able to pass through the ring resonator fully. The
quality factor In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy los ...
and the finesse of an optical ring resonator can be quantitatively described using the following formulas (see: eq: 2.37 in ,or eq:19+20 in ): : \mathbf = \frac :\mathcal = \frac where ''\mathcal'' is the finesse of the ring resonator, \nu is the operation frequency, \nu_ is the
free spectral range Free spectral range (FSR) is the spacing in optical frequency or wavelength between two successive reflected or transmitted optical intensity maxima or minima of an interferometer or diffractive optical element. The FSR is not always represented ...
and \delta\nu is the full-width half-max of the transmission spectra. The quality factor is useful in determining the spectral range of the resonance condition for any given ring resonator. The quality factor is also useful for quantifying the amount of losses in the resonator as a low Q factor is usually due to large losses.


Double ring resonators

In a double ring resonator, two ring waveguides are used instead of one. They may be arranged in series (as shown on the right) or in parallel. When using two ring waveguides in series, the output of the double ring resonator will be in the same direction as the input (albeit with a lateral shift). When the input light meets the resonance condition of the first ring, it will couple into the ring and travel around inside of it. As subsequent loops around the first ring bring the light to the resonance condition of the second ring, the two rings will be coupled together and the light will be passed into the second ring. By the same method, the light will then eventually be transferred into the bus output waveguide. Therefore, in order to transmit light through a double ring resonator system, we will need to satisfy the resonant condition for both rings as follows: : \ 2 \pi n_ R_ = m_ \lambda_ : \ 2 \pi n_ R_ = m_ \lambda_ where m_ and m_ are the mode numbers of the first and second ring respectively and they must remain as positive integer numbers. For the light to exit the ring resonator to the output bus waveguide, the wavelength of the light in each ring must be same. That is, \lambda_ = \lambda_ for resonance to occur. As such, we get the following equation governing resonance: : \ \frac = \frac Note that both m_ and m_ need to remain integers. 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). Forward propagating waves in the waveguide excite anti-clockwise rotating waves in both rings. Due to the inter-resonator coupling, these waves generate clockwise rotating waves in both rings which are in turn coupled to backward propagating (reflected) waves in the waveguide.


Applications

Due to the nature of the optical ring resonator and how it "filters" certain wavelengths of light passing through, it is possible to create high-order optical filters by cascading many optical ring resonators in series. This would allow for "small size, low losses, and integrability into xistingoptical networks." Additionally, since the resonance wavelengths can be changed by simply increasing or decreasing the radius of each ring, the filters can be considered tunable. This basic property can be used to create a sort of mechanical sensor. If an optical fiber experiences mechanical strain, the dimensions of the fiber will be altered, thus resulting in a change in the resonant wavelength of light emitted. This can be used to monitor fibers or waveguides for changes in their dimensions. The tuning process can be effected also by a change of refractive index using various means including thermo-optic,N. Li, E. Timurdogan, C. V. Poulton, M. Byrd, E. S. Magden, Z. Su, G. Leake, D Coolbaugh, D. Vermeulen, M. R. Watts (2016
“C-band swept wavelength erbium-doped fiber laser with a high-Q tunable interior-ridge silicon microring cavity”
'' Optics Express'', Vol. 24, Issue 20, pp.22741-22748
electro-optic or all-optical effects. Electro-optic and all-optical tuning is faster than thermal and mechanical means, and hence find various applications including in optical communication. Optical modulators with a high-Q microring are reported to yield outstandingly small power of modulation at a speed of > 50 Gbit/s at cost of a tuning power to match wavelength of the light source. A ring modulator placed in a Fabry-Perot laser cavity was reported to eliminate the tuning power by automatic matching of the laser wavelength with that of the ring modulator while maintaining high-speed ultralow-power modulation of a Si microring modulator. Optical ring, cylindrical, and spherical resonators have also been proven useful in the field of
biosensing A biosensor is an analytical device, used for the detection of a chemical substance, that combines a biological component with a physicochemical detector. The ''sensitive biological element'', e.g. tissue, microorganisms, organelles, cell recep ...
., and a crucial research focus is the enhancement of biosensing performance One of the main benefits of using ring resonators in biosensing is the small volume of sample specimen required to obtain a given
spectroscopy Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
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. Another potential application for optical ring resonators are in the form of whispering gallery mode switches. " hispering Gallery Resonatormicrodisk lasers are stable and switch reliably and hence, are suitable as switching elements in all-optical networks." An all-optical switch based on a high Quality factor cylindrical resonator has been proposed that allows for fast binary switching at low power. Many researchers are interested in creating three-dimensional ring resonators with very high quality factors. These dielectric spheres, also called microsphere resonators, "were proposed as low-loss optical resonators with which to study cavity quantum electrodynamics with laser-cooled atoms or as ultrasensitive detectors for the detection of single trapped atoms.” Ring resonators have also proved useful as single photon sources for quantum information experiments.{{cite journal, author1=E. Engin , author2=D. Bonneau , author3=C. Natarajan , author4=A. Clark , author5=M. Tanner , author6=R. Hadfield , author7=S. Dorenbos , author8=V. Zwiller , author9=K. Ohira , author10=N. Suzuki , author11=H. Yoshida , author12=N. Iizuka , author13=M. Ezaki , author14=J. O?Brien , author15=M. Thompson , name-list-style=amp , title=Photon pair generation in a silicon micro-ring resonator with reverse bias enhancement, journal=Opt. Lett., volume=21 , issue = 23, pages=27826–27834, year=2013, doi=10.1364/OE.21.027826, pmid=24514299 , arxiv = 1204.4922 , bibcode = 2013OExpr..2127826E , s2cid=10147604 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 Four-wave mixing (FWM) is an intermodulation phenomenon in nonlinear optics, whereby interactions between two or three wavelengths produce two or one new wavelengths. It is similar to the third-order intercept point in electrical systems. Four-wave ...
and
Spontaneous parametric down-conversion Spontaneous parametric down-conversion (also known as SPDC, parametric fluorescence or parametric scattering) is a nonlinear instant optical process that converts one photon of higher energy (namely, a pump photon), into a pair of photons (namely, ...
which generate photon pairs. Ring resonators amplify the efficiency of these processes as they allow the light to circulate around the ring.


See also

*
Resonator A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator ...
*
Ring laser Ring lasers are composed of two beams of light of the same polarization traveling in opposite directions ("counter-rotating") in a closed loop. Ring lasers are used most frequently as gyroscopes ( ring laser gyroscope) in moving vessels like c ...
*
Total internal reflection Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflected b ...
*
Coupling A coupling is a device used to connect two shafts together at their ends for the purpose of transmitting power. The primary purpose of couplings is to join two pieces of rotating equipment while permitting some degree of misalignment or end mov ...
*
Filter (optics) An optical filter is a device that selectively transmits light of different wavelengths, usually implemented as a glass plane or plastic device in the optical path, which are either dyed in the bulk or have interference coatings. The optical p ...
*
Optical switch An optical transistor, also known as an optical switch or a light valve, is a device that switches or amplifies optical signals. Light occurring on an optical transistor's input changes the intensity of light emitted from the transistor's output ...
*
Coupled mode theory Coupled mode theory (CMT) is a perturbational approach for analyzing the coupling of vibrational systems (mechanical, optical, electrical, etc.) in space or in time. Coupled mode theory allows a wide range of devices and systems to be modeled as on ...


References


External links


Animation of optical ring resonator on YouTube
Optical devices Resonators