Modeling of Tuning of Microresonator Filters by Perturbational Evaluation of Cavity Mode Phase Shifts
TL;DR: In this article, a perturbational expression for changes in the cavity propagation constants due to slight modifications of the cavity core refractive index is derived, which permits us to analytically calculate shifts in the spectral response of the 2-D resonators.
Abstract: Microresonator filters, which are realized by evanescent coupling of circular cavities with two parallel bus waveguides, are promising candidates for applications in dense wavelength-division multiplexing. Tunability of these filters is an essential feature for their successful deployment. In this paper, we present a framework for modeling of tuning of the microresonators by changes in their cavity core refractive index. Using a reciprocity theorem, a perturbational expression for changes in the cavity propagation constants due to slight modifications of the cavity core refractive index is derived. This expression permits us to analytically calculate shifts in the spectral response of the 2-D resonators. Comparisons of the resultant shifts and spectra with direct simulations based on a coupled mode theory show satisfactory agreement.
Citations
More filters
TL;DR: In this paper, the spectral characteristics of a ring resonator made of Si photonic wires are modeled using mode expansion of supermodes of the directional coupler, and the influence of the coupling coefficient, loss factor and waveguide dispersion on the spectral features are analyzed in detail.
Abstract: The spectral characteristics of a ring resonator made of Si photonic wires are modeled using mode expansion of supermodes of the directional coupler. The influence of the coupling coefficient, loss factor and waveguide dispersion on the spectral features are analyzed in detail. The model is then compared with the experimental data of a ring resonator designed for sensing purposes. The model that includes a wavelength dependence on coupling length reproduces the large variations of the envelope of the experimental spectrum, when coupling coefficient cover its full range from 0 to 1. Fitting parameters explain the details of the experimental spectrum and contribute to the sensor optimization, as well as illustrating general guidelines for ring resonator design.
36 citations
Cites background from "Modeling of Tuning of Microresonato..."
...Although often mentioned in theoretical works [27], a large confusion seems to persist in the recent literature, especially for ring resonator made of high index contrast material....
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TL;DR: In this article, the resonant frequency shift characteristic of tunable resonators is theoretically analyzed, and it is shown that the frequency shift range is dependent on the configurations and tuning methods of couplers.
Abstract: Ring resonators integrated with tunable couplers are useful devices in integrated optics systems. The resonant frequency shift characteristic of tunable resonators is theoretically analyzed. It is shown that the resonant frequency shift range is dependent on the configurations and tuning methods of couplers. It provides an analytical explanation of the frequency shift effect by the phase transmission method and the coupled-mode theory (CMT) of asymmetric waveguides. Optimized designs of different kinds of tunable couplers are discussed in order to improve the resonant frequency stability. Moreover, the intensity–phase relationship induced by the resonant frequency shift effect is also discussed, and a more efficient configuration of optical sensors using phase modulation is proposed.
14 citations
01 Jan 2010
TL;DR: In this article, an ab initio frequency domain model of circular micro-resonators, built on the physical notions that commonly enter the description of the resonator functioning in terms of interaction between fields in the circular cavity with the modes supported by the straight bus waveguides, is discussed.
Abstract: This chapter discusses an ab initio frequency domain model of circular microresonators, built on the physical notions that commonly enter the description of the resonator functioning in terms of interaction between fields in the circular cavity with the modes supported by the straight bus waveguides. Quantitative evaluation of this abstract model requires propagation constants associated with the cavity/bend segments, and scattering matrices, that represent the wave interaction in the coupler regions. These quantities are obtained by an analytical (2-D) or numerical (3-D) treatment of bent waveguides, along with spatial coupled mode theory (CMT) for the couplers. The required CMT formulation is described in detail. Also, quasi-analytical approximations for fast and accurate computation of the resonator spectra are discussed. The formalism discussed in this chapter provides valuable insight into the functioning of the resonators, and it is suitable for practical device design.
9 citations
Cites background from "Modeling of Tuning of Microresonato..."
...for purposes of the evaluation of fabrication tolerances, o r for predicting the effects of tuning mechanisms [8, 51]....
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01 Jan 2008
5 citations
References
More filters
TL;DR: In this article, light transmission through a curved dielectric rod of rectangular cross section embedded in different dielectrics is analyzed in closed-form, though approximate form, in three ranges: (i) small cross section guides such as a thin glass ribbon surrounded by air; making its width 1 percent of the wavelength, most of the power travels outside of the glass; the attenuation coefficient of the guide is two orders of magnitude smaller than that of glass; and the radius of curvature that doubles the straight guide loss is around 10,000Λ.
Abstract: Light transmission through a curved dielectric rod of rectangular cross section embedded in different dielectrics is analyzed in closed, though approximate form. We distinguish three ranges: (i) Small cross section guides such as a thin glass ribbon surrounded by air—Making its width 1 percent of the wavelength, most of the power travels outside of the glass; the attenuation coefficient of the guide is two orders of magnitude smaller than that of glass, and the radius of curvature that doubles the straight guide loss is around 10,000Λ. (ii) Medium cross section guide for integration optics—It is only a few microns on the side and capable of guiding a single mode either in low loss bends with short radii of curvature or in a high Q closed loop useful for filters. Q's of the order of 108 are theoretically achievable in loops with radii ranging from 0.04 to 1 mm, if the percentage refractive index difference between guide and surrounding dielectric lies between 0.1 and 0.01. (iii) Large cross section guides—They are multimode and are used in fiber optics. Conversion to higher order modes are found more significant than radiation loss resulting from curvature.
699 citations
"Modeling of Tuning of Microresonato..." refers background in this paper
...Due to high Q and compactness of these filters, they are explored for dense wavelength-division multiplexing in integrated optics [2]–[4]....
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TL;DR: In this article, micro-ring wavelength filters and resonant modulators using polymer materials at 1300 nm and 1550 nm are analyzed, designed, and demonstrated, and they are integrated with vertically coupled input and output waveguides.
Abstract: Micro-ring wavelength filters and resonant modulators using polymer materials at 1300 nm and 1550 nm are analyzed, designed, and demonstrated. The rings are integrated with vertically coupled input and output waveguides. The devices are fabricated using optical lithography. Filters with a finesse of 141 and free spectral range of 5 nm at 1300 nm and finesse of 117 with a free spectral range (FSR) of 8 nm at 1550 nm are demonstrated. Ring resonators with a Q as high as 1.3 /spl times/ 10/sup 5/ at 1300 nm are demonstrated. The filters can be temperature tuned at the rate of 14 GHz//spl deg/C. Resonant ring modulators, which use an electrooptic polymer, are demonstrated. The resonance wavelength voltage tunes at the rate of 0.82 GHz/V. The modulators have a bandwidth larger than 2 GHz. Using the resonant modulator, and open eye diagram at 1 Gb/s is demonstrated.
597 citations
TL;DR: A photonic device based on a high-finesse, whispering-gallery-mode disk resonator that can be used for the detection of biological pathogens and formulas are presented that allow the sensitivity of the device to be quantified and that show that, under optimum conditions, as few as 100 molecules can be detected.
Abstract: We describe a photonic device based on a high-finesse, whispering-gallery-mode disk resonator that can be used for the detection of biological pathogens. This device operates by means of monitoring the change in transfer characteristics of the disk resonator when biological materials fall onto its active area. High sensitivity is achieved because the light wave interacts many times with each pathogen as a consequence of the resonant recirculation of light within the disk structure. Specificity of the detected substance can be achieved when a layer of antibodies or other binding material is deposited onto the active area of the resonator. Formulas are presented that allow the sensitivity of the device to be quantified and that show that, under optimum conditions, as few as 100 molecules can be detected.
451 citations
"Modeling of Tuning of Microresonato..." refers background in this paper
...This perturbational viewpoint is often employed for microresonator-based biosensors and chemosensors [9], [10]....
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Book•
31 Oct 1991
TL;DR: In this article, the weak guidance approximation of waveguides embedded in a low-index medium is described, where the waveguide can be interpreted as an anisotropic waveguide.
Abstract: 1. Basic Concepts. Maxwell equations. Normal mode theory. Scattering matrices. Coupled mode theory. Variational techniques. 2. Modes of Optical Waveguides - I. The weak guidance approximation. Waveguides embedded in a low index medium. Step-index slab waveguides. Step-index circular fibers. Weakly guiding anisotropic waveguides. 3. Modes of Optical Waveguides - II. Graded slabs or fibers. 3-D planar waveguides. Numerical methods for arbitrary cross-sections. Leaky modes. 4. Perturbation Techniques. Modal expansion method. Variational techniques. Reciprocity techniques. Global perturbation methods. Applications. 5. Non-Uniform Systems. Local mode expansions. Bent waveguides. Bent and twisted waveguides. Non-uniform curvatures. 6. Discontinuities. Excitation of a guided mode through a junction. Abrupt discontinuities. Bibliography. Index.
272 citations
"Modeling of Tuning of Microresonato..." refers background or methods in this paper
...By applying Lorentz’s reciprocity theorem [14] in polar coordinates to (Ep,Hp, p) and (E,H , ), one obtains...
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...In [14], a similar expression for the change in the propagation constant for bulk uniform permittivity perturbations of straight waveguides is derived by means of a variational principle....
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...Similar expressions for the induced changes in propagation constants of modes supported by straight waveguides are well known [14]....
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TL;DR: In this paper, an improved coupled-mode equation for parallel dielectric waveguides was derived by using a newly found relationship that connects the propagation constants of the individual guides to the coupling coefficients via an overlap integral that measures the guides' proximity.
Abstract: An improved version of coupled-mode equations for parallel dielectric waveguides has been derived by using a newly found relationship that connects the propagation constants of the individual guides to the coupling coefficients via an overlap integral that measures the guides' proximity. The four parameters of these new coupled equations are simple functions of essentially one single quantity: the asynchronism of the individual guides properly normalized.
254 citations