Leaky modes of channel waveguides with uniaxial anisotropy

An exact numerical method for analyzing the propagation properties of leaky modes of inhomogeneous channel optical waveguides with a complex uniaxial diagonal permittivity tensor is developed. The method is based on solving the system of integro-differential equations formulated with respect to transversal components of the magnetic field and the longitudinal component of the electric field. Some results of investigation of leaky modes of diffused channel waveguides in LiNbO₃ and LiTaO₃ crystals are given.     

矩形芯介质波导色散关系及定向耦合器耦合长度的加权余量法计算

本文用加权余量法导出了用以计算各种条形介质波导色散关系,矩形芯双沟道耦合器耦合长度以及条载型波导色散关系的数学表达式,其精确度较其它近似方法高,且简便易行。     

Enhanced stimulated Raman scattering in slow-light photonic crystal waveguides

We investigate for the first time, to our knowledge, the enhancement of the stimulated Raman scattering in slow-light silicon-on-insulator (SOI) photonic crystal line defect waveguides. By applying the Bloch-Floquet formalism to the guided modes in a planar photonic crystal, we develop a formalism that relates the intensity of the downshifted Stokes signal to the pump intensity and the modal group velocities. The formalism is then applied to two prospective schemes for enhanced stimulated Raman generation in slow-light photonic crystal waveguides. The results demonstrate a maximum factor of 104(66,000) enhancement with respect to SOI channel waveguides.     

Gap maps, diffraction losses, and exciton–polaritons in photonic crystal slabs

A theory of photonic crystal (PhC) slabs is described, which relies on an expansion in the basis of guided modes of an effective homogeneous waveguide and on treating the coupling to radiative modes and the resulting losses by perturbation theory. The following applications are discussed for the case of a high-index membrane: gap maps for photonic lattices in a waveguide; exciton–polariton states, when the PhC slab contains a quantum well with an excitonic resonance; propagation losses of line-defect modes in W1 waveguides, also in the presence of disorder; the quality factors of photonic nanocavities. In particular, we predict that disorder-induced losses below 0.2 dB/mm can be achieved in state-of-the-art samples by increasing the channel width of W1 waveguides.     

A compact in-plane photonic crystal channel drop filter

This paper presents a novel in-plane photonic crystal channel drop filter.The device is composed of a resonant cavity sandwiched by two parallel waveguides.The cavity has two resonant modes with opposite symmetries.Tuning these two modes into degeneracy causes destructive interference in bus waveguide,which results in high forward drop efficiency at the resonant wavelength.From the result of numerical analysis by using two-dimensional finite-difference time-domain method,the channel drop filter has a drop efficiency of 96% and a Q value of over 3000,which can be used in dense wavelength division multiplexing systems.     

Improved photonic crystal directional coupler with short length

We investigate a photonic crystal (PC) waveguide coupler which is formed by two closely spaced linear waveguides in a two-dimensional triangular lattice of air holes. Our study shows that shifting one row of the air holes between the waveguides affects the dispersion curves of the guided modes and if the triangular lattice of air holes between the waveguides is replaced by a rectangular lattice, this modification results in an ultra-short coupling structure with coupling length less than 3a, where a is the lattice constant. Also, we investigate the effect of changing the radii of air holes that are adjacent to or between the waveguides on the coupling length and show that increasing the radius of air holes between the waveguides decreases the coupling length. We analyze the output spectrum of an ultra-short channel drop filter designed based on this structure.     

Simplified universal dispersion curves for channel waveguides

Simplified universal dispersion curves for graded-index diffused channel waveguides have been obtained with the new normalized WKB equation using the effective index method. It is shown that, similarly to planar guides, the propagation constant of all the guided modes of a particular channel can be obtained by two parameters, called the normalized mode orders. The dispersion relations between the propagation constant and the normalized mode order of the channel have been obtained for a number of profile shapes and waveguide dimensions.     

Channel waveguides in Ca4GdO(BO3)3 fabricated by He+ implantation for blue-light generation

Blue light at 405 nm is generated by frequency doubling of a Ti:sapphire tunable laser in He(+)-implanted channel waveguides in gadolinium calcium oxoborate crystal. A conversion efficiency of approximately 2% W(-1) cm(-2) is achieved between TM00 fundamental and TE01 harmonic modes.     

Modes of UV-written planar waveguides

The UV-induced refractive-index increase in photosensitive planar waveguides is modeled by an exponential profile. Closed-form field solutions are given and dispersion curves are calculated for TE and TM modes. Modes in air-covered waveguides can be less sensitive to the UV-written profile than modes in buried waveguides.     

Orthogonality Conditions for Leaky Modes

We consider various approaches for normalization of leaky modes of open waveguides. General properties of such modes and their relation to continuous-spectrum modes are studied. Applicability of perturbation theory for calculating the shift of mode propagation constants in the case of small variations in the waveguide structure is discussed. General relations are illustrated by an example of a waveguide in the form of a channel inside a dielectric. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 5, pp. 388–401, May 2005.     

Bragg diffraction of light in a restricted homogeneous system of tunnel-coupled waveguides

A system of tunnel-coupled rectilinear waveguides is studied. The dependence of the number of modes in this system on the number of waveguides N, the distance between the waveguides, and the number of modes in a separate waveguide is considered. It is shown that the modes of the m = N and N + 1 orders in such a system are Bragg modes; i.e., the angle between the direction of their propagation and the system axis is close to the Bragg angle. The effective refractive indices n ^* of these modes change stepwise. The step size Δn ^* is found to be dependent on the distance s between the waveguides and on the number of modes in a separate waveguide. A system of single-mode waveguides with the number of guided modes M = 34 < N = 50 is studied experimentally. It is shown that the Bragg modes of the system lie among the leakage modes of the system and have rather low losses. It is demonstrated that the localization of the Bragg modes among the leakage modes may be favorable for their selection upon light generation.     

Dielectric waveguide model for guided surface polaritons

Although surface polariton modes supported by finite-width interfaces can guide electromagnetic energy in three dimensions, we demonstrate for the first time to our knowledge that such modes can be modeled by the solutions of two-dimensional dielectric slab waveguides. An approximate model is derived by a ray-optics interpretation that is consistent with previous investigations of the Fresnel relations for surface polariton reflection. This model is compared with modal solutions for metal stripe waveguides obtained by full vectorial magnetic-field finite-difference methods. The field-symmetric modes of such waveguides are shown to be in agreement with the normalized dispersion relationship for analogous TE modes of dielectric slab waveguides. Lateral confinement is investigated by comparison of power-density profiles, and implications for the diffraction limit of guided polariton modes are discussed.     

Leakage in LiNbO3 channel H-waveguides

Attenuation of leaky modes in LiNbO₃ channel H-waveguides is studied theoretically. It is shown that leakage significantly affects the parameters of waveguides made of X-and Y-cut crystals. An approximate expression for attenuation coefficients is obtained from the solution to the scalar eigenvalue problem.     

A search-and-track algorithm for controlling the number of guided modes of planar optical waveguides with arbitrary refractive index profiles

A search-and-track algorithm is proposed for controlling the number of guided modes of planar optical waveguides with arbitrary refractive index profiles. The algorithm starts with an initial guess point in the parameter space that supports a specific number of guided modes. Then, it searches for, and tracks, the boundaries of this space or another space supporting different number of modes. It does so by monitoring the sign of a unified cutoff dispersion function. The algorithm is applied to both symmetric and asymmetric silicon-based parabolic-index waveguides. It shows that unlike asymmetric waveguides, the single-mode condition of symmetric waveguides is controlled by TM-, as opposed to TE-, polarization. This abnormal polarization control is strongest for high index contrast waveguides of sub-micrometer core sizes. The results are verified by full-vectorial beam propagation method.     

左手介质矩形波导导模和表面模的场分布

从麦克斯韦方程组出发,结合电磁场的边界条件,推导出介质矩形波导导模的一般色散方程.对普通介质矩形波导和左手介质矩形波导的导模场分布分别进行了数值模拟.通过对比两种介质矩形波导的导模场分布的模拟结果,发现左手介质矩形波导Ex22模的场分布比普通介质波导Ex00模的场更集中在波导中部.同时,根据处理普通介质矩形波导的Marcatili方法.类比得到左手介质矩形波导表面模的色散方程,并数值模拟了低阶模的场分布,结果表明,能量主要集中在波导的四个角区以及波导的边缘.     

Ultra-compact polarization beam splitter based on photonic crystal waveguides

The authors design an ultra-compact all-PC-integrated polarization beam splitter which is only composed of three waveguides: one input waveguide and two output waveguides. The input waveguide can support both TM and TE modes, but one of the two output waveguides can only support TM modes while the other can only support TE modes. So an incident beam will be separated into two different polarization beams which emerge from different output waveguides. By the simulation of finite-difference time-domain method, we know that the polarization beam splitter really works the way as we predict.     

Coupling between gaussian and guided modes at the input and output of oversized circular waveguides

The coupling between a gaussian TEMoo bearn with HE 1m modes for dielectric waveguides and TE1m and TM1m modes for metallic waveguides is analytically studied. An optimization method allows to know HE11 or TE11 modes create gaussian TEMmm bearns at the output of the waveguide.     

New method for calculating the spectra and radiation losses of leaky waves in multilayer optical waveguides

The efficiency of a new method for calculating the spectrum and attenuation coefficient of leaky electromagnetic modes is demonstrated with multilayer planar optical waveguides the guiding properties of which are determined by antiresonant reflection from the multilayer cladding (antiresonant reflecting optical waveguides) rather than by total internal reflection from the core-cladding interface as in standard optical waveguides. The new method applies to calculation of both electromagnetic modes in dielectric waveguides and electron quantum states in multibarrier semiconductor heterostructures. The characteristics of multilayer waveguides calculated by the new method are compared with published data obtained from a complex dispersion relation by the transfer matrix method. As an example, the wavelength dependence of the radiation losses for the first TE mode of a planar optical waveguide containing 52 pairs of layers is calculated.     

Quantum Zeno and Anti-Zeno Effects in the Dynamics of Non-Degenerate Hyper-Raman Processes Coupled to Two Linear Waveguides

The effect of the presence of two probe waveguides on the dynamics of hyper-Raman processes is studied in terms of quantum Zeno and anti-Zeno effects. Specifically, the enhancement (diminution) of the evolution of the hyper-Raman processes due to interaction with the probe waveguides via evanescent waves is viewed as quantum Zeno (anti-Zeno) effect. This study considers the two probe waveguides interacting with only one of the optical modes at a time. For instance, as a specific scenario, it is considered that the two non-degenerate pump modes interact with each probe waveguide linearly, while Stokes and anti-Stokes modes do not interact with the probes. Similarly, in another scenario, it is assumed both the probe waveguides interact with Stokes (anti-Stokes) mode simultaneously. The present results show that quantum Zeno (anti-Zeno) effect is associated with phase-matching (mismatching). However, it do not find any relation between the presence of the quantum Zeno effect and antibunching in the bosonic modes present in the hyper-Raman processes.