Coupled-mode Theory Analysis Research Articles

Coupled mode theory analysis for circular photonic crystal ring resonator-based add-drop filter

A two-dimensional circular photonic crystal ring resonator (PCRR)-based add-drop filter (ADF) is designed for ITU-T G.694.2 eight-channel coarse wavelength division multiplexing systems. The resonant wavelength and pass-band width of the ADF are 1491 and 13 nm, respectively. Close to 100% of coupling and dropping efficiencies and a 114.69 quality factor are observed through simulation. Then the coupled mode theory (CMT) analysis of circular PCRR-based ADF is attempted to compare obtained CMT response into simulated finite difference time domain method response. The overall size of the device is much smaller; that is, 11.4×11.4 μm, which is highly suitable for photonic integrated circuits and all optical photonic network applications.

All-Optical Switches Based on Multiple Cascaded Resonators With Reduced Switching Intensity-Response Time Products

The general nonlinear behavior of multiple cascaded resonators is analyzed by using the coupled-mode theory in time and then compared to a single resonator from the viewpoint of optical bistable operation. Our analysis reveals that from the perspective of switching intensity, the multiple resonator structure is more advantageous than the single resonator with an equivalently increasing quality factor. It is also shown that a switching intensity-response time product, suggested as a performance metric for optical bistable devices, decreases linearly as the number of cascaded resonators increases. The effect of coupling n resonators is equivalent to a single resonator device with n-time increased quality factor in terms of the performance metric. The coupled-mode theory analysis is confirmed by a numerical study of the bistable operation of one-dimensional photonic crystal resonator structures using the finite-difference time-domain method.

Slow-light dispersion properties of multiatomic multiband coupled-resonator optical waveguides

In this paper, we investigate the dispersion properties of a multiatomic coupled-resonator optical waveguide (CROW), and show the existence of band-dependent group velocities in its slow-light bands. By including the next-nearest-neighbor coupling terms in a coupled-mode theory (CMT) analysis for the structure, we explain the physical origin of the band-dependent group velocities in terms of the modification of molecular mode-coupling strengths, and also derive the criteria for complete band separation and perfect intermode intensity overlap. Our results imply that when estimating the performance of a multiwave slow-light device, the band dependency of group velocities must also be considered in addition to the conventional CROW dispersion. Numerical analysis with a photonic crystal platform shows excellent agreement with theory.

Improving the imaging intensity of a photonic crystal flat lens by an antireflection method

In this paper, a two-dimensional photonic crystal (PC) consisting of a triangular lattice of silicon rods in air is studied theoretically. Equal-frequency contours (EFCs) analysis shows that this PC structure exhibits an effective refractive index n eff = −1 at a normalized frequency ω = 0.30 × 2 π c / a . A superlens effect is demonstrated using this PC structure by the finite-difference time-domain (FDTD) simulation. An antireflection layer (ARL) is introduced into the PC slab surface in order to achieve a high-intensity image. Two point sources imaging process is also simulated both in the case of a perfect PC structure and in the case of a PC structure with an ARL. The results show that the method of introducing the ARL into the PC surface is effectual for improving both the intensity of the image and the capability of the super-resolution of two sources, which are in accord with the coupled-mode theory analysis. Theoretical study implies that the surface defect modes play an important role in enhancing the transmitted intensity of energy flow.

Optical Forces in Hybrid Plasmonic Waveguides

We demonstrate that in a hybrid plasmonic system the optical force exerted on a dielectric waveguide by a metallic substrate is enhanced by more than 1 order of magnitude compared to the force between a photonic waveguide and a dielectric substrate. A nanoscale gap between the dielectric waveguide and the metallic substrate leads to deep subwavelength optical energy confinement with ultralow mode propagation loss and hence results in the enhanced optical forces at low input optical power, as numerically demonstrated by both Maxwell's stress tensor formalism and the coupled mode theory analysis. Moreover, the hybridization between the surface plasmon modes and waveguide modes allows efficient optical trapping of single dielectric nanoparticle with size of only several nanometers in the gap region, manifesting various optomechanical applications such as nanoscale optical tweezers.

Improving unrestricted imaging quality of a triangular lattice photonic crystal slab by modifying surface configuration

We propose a photonic crystal (PC) structure only by replacing square lattice [Luo et al. (2002) [12]] with triangular lattice to obtain an unrestricted imaging. Equal-frequency contours (EFCs) analysis shows that this triangular lattice two-dimensional PC exhibits an effective isotropic refractive index n eff=−1 at a normalized frequency ω=0.291×2 πc/ a. Imaging quality of this triangular lattice PC slab involving both power intensity and full-width at half-maximum intensity of the image is studied using the finite-difference time-domain (FDTD) simulation. In order to achieve a high-quality image, an appropriate surface termination is chosen. In addition, by adjusting the surface air-hole radius of the PC slab, the imaging quality can be further improved. Coupled-mode theory analysis shows that the optimized surface termination and the adjusted surface air-hole can excite two kinds of surface modes that can couple with the Bloch wave in the PC. With the help of these surface modes, both the intensity of image and the super-resolution capacity of this triangular lattice PC slab can be improved greatly.

Cavity mode control in side-coupled periodic waveguides: Theory and experiment

We demonstrate that the modes of coupled cavities created in periodic waveguides can depend critically on the longitudinal shift between the cavities. In the absence of such shift, the modes feature symmetric or antisymmetric profiles, and their frequency splitting generally increases as the cavities are brought closer. We show that the longitudinal shift enables flexible control over the fundamental modes, whose frequency detuning can be reduced down to zero. Our coupled-mode theory analysis reveals an intrinsic link between the mode tuning and the transformation of slow-light dispersion at the photonic band-edge. We illustrate our approach through numerical modeling of cavities created in arrays of dielectric rods, and confirm our predictions with experimental observations.

Coupled mode theory analysis of mode-splitting in coupled cavity system

We analyze transmission characteristics of two coupled identical cavities, of either standing-wave (SW) or traveling-wave (TW) type, based on temporal coupled mode theory.Mode splitting is observed for both directly (cavity-cavity) and indirectly (cavity-waveguide-cavity) coupled cavity systems. The effects of direct and indirect couplings, if coexisting in one system, can offset each other such that no mode splitting occurs and the original single-cavity resonant frequency is retained. By tuning the configuration of the coupled cavity system, one can obtain different characteristics in transmission spectra, including splitting in transmission, zero transmission, Fano-type transmission, electromagnetically-induced-transparency (EIT)-like transmission, and electromagnetically-induced-absorption (EIA)-like transmission. It is also interesting to notice that a side-coupled SW cavity system performs similarly to an under-coupled TW cavity. The results are useful for the design of cavity-based devices for integration in nanophotonics.

Imaging properties of a two-dimensional photonic crystal with rectangular air holes embedded in a silicon slab

Abstract We investigate the superlensing effect of a two-dimensional (2D) triangular photonic crystal (PC) slab consisting of rectangular air holes in silicon. An analysis of equal-frequency contours (EFCs) shows that geometric parameters of the PC element shape can greatly change the shape of EFCs, thus change the effective phase index of the PC structure. Moreover, an effective negative refractive index n eff = −1 can be obtained at a normalized working frequency of 0.30 × 2 π c / a by adjusting the width of the rectangular air holes. Imaging capacity of this PC slab involving both the power intensity and full width at half-maximum of image is studied by the finite-difference time-domain (FDTD) method. In order to achieve a high-quality image, an appropriate surface termination of the PC slab is chosen. Coupled-mode theory analysis shows that the optimized surface termination can excite two kinds of surface modes which can couple with the Bloch wave in the PC. With the help of these surface modes, both the intensity of image and the super resolution capacity for the PC slab lens can be improved greatly.

Diffraction engineering of multimode waveguides using computer-generated planar holograms

The self-imaging property in multimode waveguides is related to the waveguide widths and lengths. By engineering the diffraction properties of multimode waveguides, we propose a scheme to design devices with reduced self-imaging lengths at a fixed width. Using computer-generated planar holograms, the coupling coefficients between the guided modes are adjusted to generate the desired diffraction properties. Calculations based on the coupled-mode theory are presented. Devices are designed based on a silicon-on-insulator (SOI) platform. Beam propagation simulations are used to verify the coupled-mode theory analysis.

High spatial resolution imaging in a clipping Kagomé lattice photonic crystal

In this paper, a two-dimensional Kagomé lattice photonic crystal (PC) made of GaAs ( ɛ = 12.96) dielectric rods in air is considered. This Kagomé lattice PC has an effective refractive index n eff = −1 at a low normalized frequency ω = 0.187 × 2 πc/ a. Imaging quality and the capability of the super-resolution of two point sources are studied for a superlens made of such PC structure. In order to achieve a high quality image and to improve the spatial super-resolution of two sources, a clipping Kagomé lattice PC is designed. Results simulated by finite-difference time-domain method show that imaging quality and super-resolution of two sources can be enhanced greatly as the perfect Kagomé lattice structure are superseded by the clipping Kagomé lattice structure. Coupled-mode theory analysis gives an explanation why the clipping structure is superior to the perfect one for both the imaging quality and the capability of the super-resolution of two sources. This clipping Kagomé lattice PC structure would be widely used in optical devices and integrated circuit.

Purcell effect in nonlinear photonic structures: a coupled mode theory analysis

We develop a coupled mode theory (CMT) model of the behavior of a polarization source in a general photonic structure, and obtain an analytical expression for the resulting generated electric field; loss, gain and/or nonlinearities can also be modeled. Based on this treatment, we investigate the criteria needed to achieve an enhancement in various nonlinear effects, and to produce efficient sources of terahertz radiation, in particular. Our results agree well with exact finite-difference time-domain (FDTD) results. Therefore, this approach can also in certain circumstances be used as a potential substitute for the more numerically intensive FDTD method.

Prediction and suppression of strong dispersive coupling in microracetrack channel drop filters

For a four-port microracetrack channel drop filter, unexpected transmission characteristics due to strong dispersive coupling are demonstrated by the light tunneling between the input-output waveguides and the resonator, where a large dropping transmission at off-resonance wavelengths is observed by finite-difference time-domain simulation. It causes a severe decline of the extinction ratio and finesse. An appropriate decrease of the coupling strength is found to suppress the dispersive coupling and greately increase the extinction ratio and finesse, a decreased coupling strength can be realized by the application of an asymmetrical coupling waveguide structure. In addition, the profile of the coupling dispersion in the transmission spectra can be predicted based on a coupled mode theory analysis of an equivalent system consisting of two coupling straight waveguides. The effects of structure parameters on the transmission spectra obtained by this method agree well with the numerical results. It is useful to avoid the strong dispersive coupling region in the filter design.

All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures

We analyze the resonant linear and nonlinear transmission through a photonic crystal waveguide side-coupled to a Kerr-nonlinear photonic crystal resonator. First, we extend the standard coupled-mode theory analysis to photonic crystal structures and obtain explicit analytical expressions for the bistability thresholds and transmission coefficients which provide the basis for a detailed understanding of the possibilities associated with these structures. Next, we discuss limitations of standard coupled-mode theory and present an alternative analytical approach based on the effective discrete equations derived using a Green's function method. We find that the discrete nature of the photonic crystal waveguides allows a geometry-driven enhancement of nonlinear effects by shifting the resonator location relative to the waveguide, thus providing an additional control of resonant waveguide transmission and Fano resonances. We further demonstrate that this enhancement may result in the lowering of the bistability threshold and switching power of nonlinear devices by several orders of magnitude. Finally, we show that employing such enhancements is of paramount importance for the design of all-optical devices based on slow-light photonic crystal waveguides.

Section-wise-exact coupled-mode theory of waveguide quasi-phase-matched second-harmonic generation

We derive exact mathematical expressions for both the amplitude and phase evolution of optical waves due to linear and nonlinear interactions in a waveguide device and propose a section-wise-exact coupled-mode theory analysis for quasi-phase-matched second-harmonic generation in the waveguide. Section-wise-exact coupled-mode theory is readily applicable to nonuniform quasi-phase-matched gratings and can be useful as a quantitative method in their analysis and design. Using the method, several numerical results are presented for second-harmonic generation in periodically poled LiNbO/sub 3/ channel waveguides. In addition, we introduce a split-step method which takes propagation losses into account and which can include linear and two-photon absorption and waveguide losses.

Circularly symmetric distributed feedback semiconductor laser: An analysis

We analyze the near-threshold behavior of a circularly symmetric distributed feedback laser by developing a coupled-mode theory analysis for all azimuthal modes. We show that the equations that describe the low-order azimuthal modes are, to a very good approximation, the same as those for the one-dimensional (linear) distributed feedback laser. We examine the behavior of higher-order azimuthal modes by numerically solving the exact coupled-mode equations. We find that while a significant amount of mode discrimination exists among radial (longitudinal) modes, as in the one-dimensional distributed feedback laser, there is a much smaller degree of discrimination among azimuthal modes, indicating probability of multimode operation. Despite the multimode behavior, we find that the frequency bandwidth associated with modes that do lase ought to be smaller than the spacing between Fabry-Perot modes of a typical semiconductor laser. This laser is an excellent candidate for a surface-emitting laser—it should have a superb quality output beam and is well-suited for array operation.

Mode Propagation in a Nonuniform Cylindrical Medium (Correspondence)

A simplified form of the coupling coefficient C(/spl beta//sub p/, /spl beta//sub q/) resulting from a coupled mode theory analysis of wave propagation in a nonuniform medium is derived. It is found for most situations of interest that C(/spl beta//sub p/, /spl beta//sub q/) is proportional to 1/(/spl beta//sub p/-/spl beta//sub q/) and the power transfer between two modes is proportional to 1/(/spl beta//sub p/ - /spl beta//sub q/)/sup 4/. /spl beta//sub p/ and /spl beta//sub q/ are the two different modal propagation constants. For a dielectric rod C(/spl beta//sub p/, /spl beta//sub q/) is a simple line integral around the rod boundary. Approximate forms are presented for optical waveguides.