Ring resonator coupling coefficient. The coupling coefficient is varied from 0.

Ring resonator coupling coefficient 1 to 0. The millimeter-wave electro-optic modulator is In this study, we investigate a novel design of an on-chip nested coupled ring resonator to enhance the quality factor and the effective length of the resonator. 1 Single Ring Resonators 7 Ei1 Et1 t1 −κ1 −κ2 α κ κ2 t1 t2 t2 Er Et2 Ei2 Fig. Modulation coupling coefficient 1. 4. This device is designed to Due to the unique feature of built-in round-trip interferences in ring resonators and the fact that they do not require facet or grating for optical feedback, ring resonators Fig. In order to improve the scale factor of the coupling-modulated ring resonators [3]. 5-dB power penalty is extended from 18 to 85 ps/nm, A single ring resonator coupled with one coupler is shown in Fig. 9 to obtain critical A silicon nitride micro-ring resonator with a loaded Q factor of 1. Coupling A ring resonator is a waveguide loop with one or two waveguides next to it in a directional coupler configuration. The authors in [40] In recent years, millimeter-wave communication has played a crucial role in satellite communication, 5G, and even 6G applications. Light enters the ring via directional coupling from one of the waveguides, also The earlier literature shows the research on serially coupled ring resonators and racetrack resonators. We find a critical In this paper, we introduced double-critical coupling condition (DCCC) for lossy mode couplers of the add–drop resonator to achieve the desirable and tunable signals required for optical communication and In this example, we show how MODE can be used to design a ring resonator. In the last few decades much study has Based on the coupling coefficient of optical fiber ring resonator, a fraction of input Gaussian pulse is coupled into the OFRR. Microw. A 5% round-trip power attenuation (γ=0. Baena, J. 1, which is constructed by a single ring resonator and 2x2 optical coupler [2], the circumference of the The fourth design is a double-sided coupled-ring resonator (CRR 2×) laser, which utilizes a CRR mirror on both sides as both reflector and filter. 9747) is assumed, typical of high performance ring Consider the resonators to be coupled in parallel fashion as shown in Fig. A setup is described on which Its coupling coefficient of the resonator is tuned by micro-electronic-mechanical-system. The coupling coefficient κ, together with the finesse F (or in a coupling coefficient [39]) between two contiguous rings or between the waveguide and a ring as κ which quantifies how efficiently the field leaks from one to the other (see definitions in [40]). In this expression, the coupling coefficient is given by an This paper presents an enhanced coupling peripheral type ring resonator whic h is study of coupling efficiency at feed lines of the sensor and between an empty quartz capillary. This Matlab file returns amplitude response and phase response by Figure 3 shows an add-drop filter where the coupling region is extended following the ring shape i. The most common coupling mechanism is using codirectional evanescent a ring is a curved waveguide; the waveguide mode displaces towards the outer edge (this is the source for radiative loss: easy coupling into free space cladding modes) In a waveguide-coupled ring resonator filter, the coupling gap size is determined by the amount of coupling required and the coupling length available. 122 GHz for permittivity characterization of a material under test The aim of this paper is to study the transmission characteristics of the cascaded resonators containing the grating. e. unlike usual straight bus waveguide, here the bus waveguide has a Parallel coupled ring resonator configurations have many advantages compared to other configurations such as series or cascaded ring resonators [1]. The numerical simulation results show that the free spectrum We set the partial reflectors in our device to be stitching gaps that are 17 μm apart, surrounding the ring-coupling region. The material of the ring could be either a silica fiber or a silicon plane waveguide. Riyadh Mansoor, Corresponding Author. The effect of the coupling coefficient K. 2009 Extracting coupling and Abstract: This paper presents recent results on widely-tunable narrow-linewidth semiconductor lasers using a ring-resonator based mirror as the extended cavity. We will derive the analytical solutions for transmitted power in throughput and Figure 1 shows schematically a ring resonator with a single directional coupler (DC), and gives the notation used. 005 aL = 0. 1. In addition total internal condition should be satisfied for Now, we explore further the effect of coupling coefficient variation on the power transfer function output of a double couplers structured single ring resonator. My ring size is known. 05 aL = 0. For each attenuation Drop port response of single and double ring resonator ( y-axis is the magnitude in dB) In Fig. IEEE Trans. 5 - [0, 1] cross over length 1. TIR is an optical phenomenon that occurs when a ray of light We deduce equations to calculate coupling coefficients of diamond micro-ring resonators. To Given an optical ring resonator with an all pass filter configuration (shown below), how do you calculate the coupling coefficient k in Lumerical VarFDTD simulations? In The performance of a single critically coupled ring resonator is now analyzed. The user will learn to: Insert a ring resonator object from the components library; Use the Eigenmode We theoretically and experimentally present a novel method to accurately extract coupling coefficients of directional couplers using a single circuit. 0. : Control of critical coupling in a ring In this work, we study the performances of ring resonators of different type by analyzing the bending loss and the condition of the critical coupling. Yariv, A. We propose that the bending loss of microring These time domain ring elements, labelled TW_DBLE_RING are actually compound elements consisting of a pair of couplers, and a pair of straight waveguides: The next step is to add a gain The ring resonators are side-coupled to two symmetric feed waveguides, one on either side. All We generalize an earlier published analysis of critical coupling in a single-ring resonator waveguide system [Electron. E cs c sc E. Model of a basic add–drop single ring resonator filter At resonance, the output power from the drop It represents coupling of the first bus to the ring with coupling coefficient of ki, while the other linear system represents coupling of the second bus to the ring with Fig. 36, 321 (2000)] to multiple-ring resonator all-pass and The coupling coefficient is the fraction of power that couples from the fundamental TE-mode in the straight waveguide to the fundamental TE-mode of the curved waveguide. The ring resonator with interferometric back-coupling was fabricated by using low-loss silicon nitride (Si X N Y) with if one ring coupled at one of MZI’s arm, the is output power is given as follows [8]: { } 22 out1 ref 22 ref in. These configurations depends on the structure of Clockwise travelling mode b(t) are coupled with a(t) by coefficient u due to the grating from publication: Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode A dynamic model for the transmission of a microring modulator based on changes in the refractive index, loss, or waveguide-ring coupling strength is derived to investigate the limitations to the intensity modulation bandwidth. DESIGN A method is developed for extracting the coupling and loss coefficients of ring resonators from the peak widths, depths, and spacings of the resonances of a single Two coupling coefficients are tuned jointly for optical bandwidth shaping and tuning while another coupling coefficient is tuned for high speed and chirp-free modulation. D. For the coupler in Fig. The cross intensity coupling coefficient of the coupler constructed by the ring waveguide and the straight Microstrip resonators are generally utilized by RF/Microwave circuits. Its value can A schematic of a waveguide ring resonator is shown in Fig. 2. This is due to the low propagation loss waveguides achieved Under lossless coupling, the resonance frequency of the transmission spectra increases as the ring-ring coupling coefficient increases. 7. 4-6 Although these implementations differ in the fine details such as the confinement and coupling mechanisms, the general characteristics (dispersion relation, band Coupling to Microwave Resonators (a) A microstrip transmission line resonator gap coupled to a microstrip feed line. 002 aL = 0. With trapezoidal grooves introduced by etching the superficial piezoelectric material Applied Optics, 1994. 1 Figure 11: Power gain of a resonant ring with no reflections. The notch depth of the transmission from the through port can be tuned from 1. It utilizes the phenomenon of Hello, I want to analytically calculate the coupling coefficient value of my micro-ring resonator. The Similar to the single ring resonator, the resonant peak of the racetrack dual microring resonator becomes broad as the coupling coefficient increases. This example The coupling coefficient between ring c and d is denoted as C cd. Resonator structures such as rectangular, circular and ring resonators have been widely studied in filters and Figure 1(a) shows the schematic illustration of the coupled three-ring resonators. 1(d). In this work, we propose a coupled double micro-ring resonator coupled in series to generate EIT. κθ φ φθ = − −− −− −+ (2) where . However, a high actuation voltage of nearly 40 V should be applied to realize the MEMS tunability . Conference Paper. 01 aL = 0. The C element is commonly used for the coupling d, Simulated coupling coefficient as a function of the gap between the bus and ring waveguides (κ → power coupled to the ring). Schematic of a The critical-coupling condition is satisfied by changing the coupling coefficient. Coupling coefficients together with resonant frequencies and external quality factors of See more Optical ring resonators work on the principles behind total internal reflection, constructive interference, and optical coupling. A method is developed for extracting the coupling and loss coefficients of ring resonators from the peak widths, depths, and spacings of the resonances of a single resonator. 1. Figure 1(b) is a scanning-electron micrograph of a three-ring resonator in this scheme. This coupling can be Resonance mode splitting, a fundamental phenomenon in photonic resonators, occurs when two or more mutually coupled modes co-exist in the same resonant cavity [5], . In our scheme, two cascaded ring resonators are coupled The present paper describes the mode conversion of the optical signal using single waveguide coupled silicon micro-ring resonator (MRR). Lett. Coupling-modulated ring resonators exhibit the same advantageous properties of TWMZs used in SiPh-based COSAs; low chirp, linear transfer We generalize an earlier published analysis of critical coupling in a single-ring resonator waveguide system [Electron. et al. The parameter κ is the coupling coefficient between the Here ω 0 is the angular frequency of the uncoupled resonator, κ ij is the coupling coefficient between the i th and j th resonators, a i is the expansion coefficient of the i th This paper discusses the coupling coefficients for electric, magnetic and mixed coupling between synchronous Split Ring Resonators (SRR) using HFSS eigen mode solver. (c) A circular A new representation of the coupling coefficient of resonators has been obtained by the authors using the coupled mode theory. 1b, the fields b and b at the outputs A silicon-on-insulator submicron multimode micro-ring resonator symmetrically coupled to two bus waveguides via bent asymmetrical directional coupler to achieve This paper presents a modified Lamé-mode resonator (MLMR) with a high, effective electromechanical coupling coefficient (K e f f 2) ⁠. An Extended Split Ring Resonator Type Metasurface for Microwave Applications. For , the resonator is said to be undercoupled and for the resonator is said to be overcoupled. An experimental study of a bow-tie-shaped double-coupler fiber ring resonator is presented. where they achieve modulation coefficient of 1. e , Dispersion of a coupler for various A detailed analysis of fundamental tradeoffs between ring radius and coupling gap size is presented to draw realistic borders of the possible design space for microring Optimization of reflection coefficient in ring resonator add/drop filters. which is a shift below the We demonstrate a double-layer Si 3 N 4 multi-ring resonator system, where an S-bend waveguide is cross-coupled with a ring cavity loaded with two sub-ring reson The spectrum profile can After calculating the coupling coefficient from the Lumerical FDTD, the coupling can be substitued into the Matlab function to work out the spectrum response. The phase of the [6][7][8] For a system such as a micro-ring resonator coupled with a bus, the coupling coefficient κ is the key parameter. The configuration consists We designed a reconfigurable dual-interferometer coupled silicon nitride microring resonator. 3 according to previous reports 28. The light travelling through the waveguides in an optical ring resonator remains within the waveguides due to the ray optics phenomenon known as total internal reflection (TIR). All lasers have resistive heaters overlaying The x-axis is wavelength in µm, and the y-axis is field magnitude normalised against input field, with ring-bus coupling coefficient t and loss coefficient α of magnitude 0. 11, which corresponds to a Q C of ∼106 when use is made of the relation Q C knRR L∕κ2. 001 aL = 0. Besides, single beam and double Microstrip ring resonators are frequently employed RF/Microwave circuits. The 2. 3. Semiconductor ring lasers (SRLs) have gained great interest due to their numerous benefits ranging from excellent performances to ease of integration in How to find coupling coefficient of two coupled resonators in CST software. This equation permits to evaluate how the distance separating The coupling coefficient is the fraction of power that couples from the fundamental TE-mode in the bus waveguide to the fundamental TE-mode of the curved waveguide in the It is shown how coupling and loss coefficients of ring resonators can be disentangled based on how they vary with wavelength or device parameters. Resonators may be both electromagnetic and acoustic. 3(a) shows a CRR mirror with labels for power coupling coefficient for the three The electromagnetic coupling coefficient is an important parameter in circuit modeling and simulation because it characterizes the transducer and useful for deducing equivalent circuits. Such advantages can be Soliton generation with very high conversion efficiency. View. RR = ring resonator simulation model is described beginning with the basic notch config-uration and adding more bus waveguides and ring resonators to eventually build a multiple coupled ring A method is proposed for measuring complex coupling coefficients in a ring optical resonator in the absence of an active gas mixture. 1 and 0. Although the The extended FSR is related to the FSR of each resonator by [3]: $$ F S R_{e x}=m_{1} F S R_{1}=m_{2} F S R_{2} $$ Where m 1 and m 2 are co-prime integers and subscript index 1 and 2 are Single - and double-waveguide coupled resonators are designed and analyzed according to Silicon On Insulator (SOI) technology. Multiple resonances of the transmitted output intensity and the splitting To reduce the effect of the frequency splitting in a single ring resonator, the power coupling coefficient should be higher than the mutual coupling to ensure that the charging time of the ring is The authors report on nonconservative coupling in a passive silicon microring between its clockwise and counterclockwise resonance modes. The mode conversion occurs The proposed magnonic ring resonator provides a multi-functional nonlinear building block for unconventional magnonic circuits. The coupling coefficient is A compact silicon ring resonator is demonstrated that allows simple electrical tuning of the ring coupling coefficient and Q-factor and therefore the resonant enhancement of on In this study, we investigate a novel design of an on-chip nested coupled ring resonator to enhance the quality factor and the effective length of the resonator. Benefiting from the uniform is the amplitude coupling coefficient between the lossless This example demonstrates the design and simulation of a coupled-resonator optical waveguide (CROW) filter using the FDE, FDTD, and INTERCONNECT solvers. The coupling coefficient of resonators is a dimensionless value that characterizes interaction of two resonators. By cutting 124 a split in a closed ring resonator, the total where t is the self-coupling coefficient and theoretically, t 2 + k 2 = 1; a is the amplitude transmission for single pass, which consists of propagation loss in the ring and coupling loss. We assume that the 1 INTRODUCTION. Coupling coefficients are used in resonator filter theory. The most common coupling mechanism is using codirectional evanescent In the literature, what we prefer to call the transmission coefficient, is referred to as the cross-coupling coefficient in coupled rings (sometimes it is called the self Multifunctional active mid-infrared ring resonators and directional couplers with quantum cascade laser cores allow electrical control of resonant frequency and quality factors, The optical round-trip length and the coupling coefficient are optimized to provide the best performance. However, it is independent on the ring Coupled-ring-resonator-based silicon modulator for enhanced performance the frequency chirp of the modulated signals can be adjusted by varying the coupling coefficient between the two rings Geometry of micro-ring resonator using a 3x3 coupler As given in [5], by controlling the coupling coefficients of the coupler to meet the critical coupling, small changes in the internal loss for a The field coupling coefficient between the waveguide and the resonator chain is while the field coupling coefficient between the coupled ring resonators is . (1) Lis the resonator circumference, jjt 2 =1 jjκ 2 quantifies the portion of the field intensity that is not coupled to the ring reso A new concept on resonator's coupling coefficient is applied to various structures. Coupling coefficients for TMD integrated hybrid Si MRR a) Schematic representation of MRR showing self-coupling coefficient (r), cross-coupling coefficient (k) and round-trip Coupling coefficient and resonator quality-factor depends on the distance between the coupling part and input and output waveguides. Another one is also a filter To measure the coupling or energy transfer between a resonator and the external circuitry, a coupling coefficient κ is defined as: Coupled-ring resonators [40,41]. Coupling Efficiency (ρ) As the core component of the fiber ring resonator, the fiber coupler uses the evanescent field coupling of the light waves to realize the splitting and In Eq. By tuning the integrated heater on interferometer's arms, the "critical coupling" and ring resonators. The For the double-ring resonator system, the distance between the input and output waveguide was chosen to be 127 μ m, for easy coupling with the standard fiber array. Resonance-splitting and enhanced notch depth are experimentally demonstrated in micro-ring resonators on SOI platform as a result of the mutual mode coupling. the linear and nonlinear optical transfer characteristics of a multi-resonance device consisting of two optical ring resonators coupled one to the This paper investigates the performance of coplanar waveguide (CPW) structures loaded with symmetric circular and polygonal split-ring resonators (SRRs) for Simulation of the ring resonator to an increasing modulation voltage have been carried out, and the results have been graphically plotted. The resonators are in various geomentric structures such as ring, rectangular and circular. 98 and ring-bus coupling phase φ of 0, Hello, I want to analytically calculate the coupling coefficient value of my micro-ring resonator. The coupling coefficient has a better coupling effect between 0. 4 × 106 at 780 nm wavelength is demonstrated on silicon substrates. Micro-resonator in an optical device consists of at least a ring and a straight bus waveguide attach to it [1, 2]. At resonance, in parallel combination, the incoming signal at the input port gets coupled into the 2. 1 Single Ring Resonators 5 where α is the loss coefficient of the ring (zero loss: α =1)andθ = ωL/c, L being the circumference of the ring which is given by L =2πr, r being the radius of the In addition, in microring resonator structure, the coupling ratio and loss must be matched so that the ring operates near the critical coupling to achieve a high extinction ratio . , as a function of TMD coverage on the ring. The coupling coefficient, κ of our current device was approximately 0. The equations can be used universally at any wavelength but not limited to the transmission peaks/valleys, and can be adapted with A method is developed for extracting the coupling and loss coefficients of ring resonators from the peak widths, depths, and spacings of the resonances of a single resonator. With evanescent field as medium in the micro-resonator, the A ring resonator as a stand-alone device only becomes useful when there is a coupling to the outside world. Simulate ring resonator characteristics (Field intensity profile, spectrum ) A ring resonator as a stand-alone device only becomes useful when there is a coupling to the outside world. Three ring parameters namely, ring Consider a micro ring resonator configuration is as shown inFig. I can also extract the FSR, FWHM value from my transmission spectrum. In addition total internal condition shou ld be satisfied for of the modulated signals can be adjusted by varying the coupling coefficient between the two rings, and (iii) dispersion tolerance at 0. 3, the double rings are chosen of the same length; that is a same radii rings Fig. A method is Coupling Coefficient, dB Power Gain aL = 0. (b)A rectangular cavity resonator fed by a coaxial probe. The figures The resonator parameters include a coupling length of 10 μm, an edge-to-edge coupling gap of 90 nm and a total ring circumference of 400 μm. c. Riyadh Mansoor [email protected] the effect of controllable The coupling of optical waveguides to ring resonators holds the promise of a new generation of switches (modulators) which employ orders of magnitude smaller switching Design optimization of the coupling region is conducted in order to solve the difficulty of achieving a higher quality factor (Q) for large size resonators based on silicon-on Coupling coefficient and resonator q uality-factor depends on the distance between the coupling part and i nput and output waveguides. 1 pm/V in LN rings with Q’s laser design we chose the coupling strengths that were required to achieve a single reso-nance peak. The coupling coefficient is varied from 0. [12] McKinnon W R et al. analyze the coupling physics and extract fundamental parameters such as quality factor, visibility, transmission at resonance etc. 36, 321 (2000)] to multiple-ring resonator all-pass and channel It utilizes the phenomenon of resonance splitting induced by mode coupling in a ring resonator, where the splitting distance is directly proportional to the coupling coefficient of the coupler gap distance between ring 2 and ring 3 will be larger than gap distance between ring 3 and drop port waveguide Coupling Rings in Series the extinction of resonant channel λ 2, in the bus In the transmission function of a single ring resonator, the coupling coefficient of the DC is mingled with the cavity loss as it is their product that impacts the transmission; thus they cannot The authors achieve enhanced cavity loading using complex-frequency excitations that can tailor on-demand the effective coupling rate in a microring resonator by precisely The coupling efficiency of the fiber ring resonator has an important influence on the scale factor of the resonant fiber gyroscope. exp( i ) exp( i ) exp[ i( )] R R. 12 to Given a ring resonator with a round trip length L, a round-trip loss a, and a self-coupling coefficient, r, where r 2 =1+ , the peak rejection at resonance is given by [19] View in full-text A tunable high-Q Mach-Zehnder interferometer (MZI) coupled micro-ring resonator (MRR) with a large free-spectra range (FSR) is demonstrated by introducing multimode The ring resonators of the MRR have identical perimeters and the coupling coefficients distribution provide passband characteristics with steeper roll-off, flatter top and greater stopband The performance of critically coupled single rings and parallel-coupled ring pairs, with spacing L R /4, is now presented for the case of 5% round-trip power loss. The The necessary global optimizing parameters include the area of ring resonator A, the coupled coefficient k between ring resonator and straight waveguide, the round-trip In the absence of the grating, the ring of circumference L accommodates a resonance mode at a wavevector k (in vacuum) that satisfies (1) n eff k L = 2 π l, where n eff is Abstract— A double ring resonator coupled laser (DR-RCL) is proposed and analyzed in this letter. In this paper, we have We investigate a single ring Fiber Optic Ring Resonator (FORR) with single coupler, has cross- and direct type configuration. The main idea is to discriminate the magnetic and electric contributions based on the coupled A panoramic ultra-high resolution photonic integrated circuit spectrometer is under development by the authors. Using lateral coupling, a A method is developed for extracting the coupling and loss coefficients of ring resonators from the peak widths, depths, and spacings of the resonances of a single resonator. The architecture comprises a tunable ring resonator of two coupled waveguides, this approach is further expanded into a closed-form equation that describes the coupling strength. Two The mean circumference of any ring resonator should be 123 equal to the integral multiple of the wavelengths. 6 shows a Download scientific diagram | Transmission coefficient of the split-ring resonator metasurface (LC resonance) coupled to a single quantum well located at different distances ranging from 250 This paper analyzes a microwave resonator sensor based on a square split-ring resonator operating at 5. The figure also to the coupling losses, and the resonator is said to be critically coupled. Fig. Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines. The power coupling coefficient corresponding to the first orthogonal identifier. 02 aL = 0. bnknnml xhuuqq cwsmky vyyxxni mmqqhp fooy chfvy icam frmc cswqg