Presented here is a new approach for analysis of the so-called holey photonic crystals—a class of electro-optical components, in which periodicity of air holes in dielectric media is used for confinement of light. This class includes several kinds of microstructured fibers, semiconductor lasers etc. Accurate evaluation of optical characteristics of those devices is usually a complicated problem due to the large dimensions and the fine structure of their refractive index distribution. Furthermore, usually, only numerical solutions for this class of optical components are available. The overwhelming majority of the physical models, suitable for analysis of holey photonic devices, proceed from the “natural” assumption: the devices are considered as arrays of air holes, surrounded by dielectric material. In this work we propose another model. Namely, we treat them as arrays of dielectric spots (waveguides), embedded in the air (cladding material). This model allows utilization of the extended coupled-mode theory (a relatively new approach designed for analysis of infinite arrays of coupled waveguides and previously considered inapplicable to holey optical components) for calculations of the latter. In this sense, we present a new method for analysis of holey photonic crystals. On the one hand, our method allows analytical evaluation of some optical characteristics of holey optical components (such as the number of photonic bands and bandwidth). On the other hand, accurate numerical computation of the photonic band structure of the holey photonic devices, incorporating a large number of holes, can be done with this technique on a timescale of several minutes.

Standard Coupled-Mode Theory (Standard CMT) is a well-known approach for analysis of coupling and propagation of guided modes in multiwaveguide systems. In order to analyze propagation of EM fields these systems, Standard CMT solves 1st order differential matrix equation (Standard CMT equation). Analytical solution for this equation currently exists only for the multiwaveguide systems with dielectric function, homogeneous along the optical axis (z-axis). Coupled-mode analysis of the devices, whose dielectric function varies along the optical axis (e.g. photonic components with integrated optical gratings) till now, is only available with numerical techniques. In this work, we propose the general Analytical solution for Standard CMT equation, including the case of dielectric function, inhomogeneous in the z-direction. This solution represents an effective analytical tool for fast and accurate analysis, design and optimization of a variety of photonic components, whose principles of operation are based on the variation of their dielectric function along the optical axis.

Standard Coupled-Mode Theory (Standard CMT), developed for analysis of guided modes in arrays of coupled parallel waveguides, was extended to include analysis of arbitrary optical beams (AB-CMT). This extension bypasses some characteristic limitations of the coupled-mode formalism, existed so far, and thus offers an effective tool for fast and accurate computations of optical beams in the variety of waveguiding devices, matching the model of parallel waveguides (including, but not limited by modern photonic micro-devices). AB-CMT combines analytical capabilities and high computational accuracy with numerically stable algorithms and low time- and resource consumption. Our computations show the close agreement between the results, acquired with AB-CMT, and those received with the well established Beam Propagation Method (BPM), served as the benchmark.

We present a new, coupled-mode formalism based, Analytical approximation for photonic array modes in 2D electro-optical components, based on photonic crystal lattices (arrays of identical coupled waveguides / lasers) and superlattices (periodic sequences of different coupled waveguides / lasers). The two most popular configurations (square and hexagonal lattices and superlattices) are considered. Our approximation is applicable for the components, in which light propagates along the optical axis of the device. This approach allows for a very fast, simple and accurate analytical evaluation of the EM fields in 2D photonic devices.

Coupled Mode Theory (CMT) is a well-established formalism, which is widely used in the computation of the optical characteristics of photonic devices, matching the model of array of parallel waveguides [1]-[6]. In particular, it is applicable to 2D photonic crystal devices (i.e. arrays of coupled waveguides / phased laser arrays), in which light propagates along the optical axis of the component. So far, CMT applications were limited to devices, in which the refractive index of the core of a solitary element is higher than that of the clad. Thus, photonic devices, based on periodic arrays of holes and utilizing gap guidance mechanism or combination of total internal reflection and gap guidance (e.g. majority of photonic crystal fibers (PCF), several kinds of modern thresholdless lasers [7]-[8]), were unavailable for CMT analysis. In this work, we show, the best of our knowledge for the first time, how the coupled-mode formalism can be applied to holey photonic crystal devices.

A new analytical approximation for photonic array modes is presented. We consider the specific class of one-dimensional (1D) photonic crystals (encompassing large arrays of coupled identical planar waveguides, large arrays of identical phase-locked lasers, etc.), in which light propagates along the optical axis of the device. Approximate analytical expressions for the array modes (both spatial distribution and propagation constants) become available. This approach allows a fast, simple, and accurate analytical evaluation of the electromagnetic field in 1D photonic crystal devices.

Based on the recently proposed time-dependent coupled mode theory (TD CMT) for parallel waveguides, we present an analysis of three advanced photonic micro-devices: micro-interferometer, 90-deg bent, and a tunable beam splitter. An accurate analysis of these devices with commercial software may take many hours, whereas the TD CMT needs only minutes with little sacrifice of accuracy. (C) 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). [DOI:10.1117/1.OE.51.5.054001]

A combination of erbium (Er), ytterbium (Yb), and neodymium (Nd), in fiber amplifiers, is examined. This combination extends the pumping wavelength spectrum by creating a new pumping path. Furthermore, the Nd addition enables pumping the amplifier from within the amplifier center, and thereby decreases the amplified spontaneous emission at the amplifier ends. A mathematical model is presented relating the excited population density, the signal power along the amplifier, the energy transfer among the ions, and the amplified spontaneous emissions. The study compares the amplifier characteristics of Er-Yb-Nd co-doped amplifier with a traditional Er-Yb amplifier for various combinations. The new configuration adds flexibility into the amplifier design. By properly selecting its parameters, one can increase the output signal power and decrease the amplified spontaneous emission, to comply with various requirements.

Relaxation oscillations and gain switching of erbium-doped waveguide ring lasers (EDWRLs) are studied using numerical simulations based on time-dependent rate-propagation equations. The counter-directional wave suppression is analyzed for different waveguide ring cavity configurations and pumping schemes. It is shown that the counter-directional wave suppression in unidirectional EDWRLs undergoes relaxation oscillations synchronously with oscillating power. It is also shown that the suppression in the first spike is maximal, so the gain switching technique provides the most favorable conditions for unidirectional lasing. Furthermore, for the one-end-pumped gain-switched EDWRL, highly unidirectional operation is possible with no intracavity elements included. In this case the counter-directional wave suppression considerably exceeds its steady-state value. The gain-switched suppression caused by intracavity elements is close to the steady-state value.

An approximate perturbation based method for fast calculation and investigation of complex-shaped two-dimensional photonic crystals is presented. Both E- and H-polarizations are analyzed. Useful analytical formulas for calculating the dispersion relations are developed. The accuracy of the approximations is examined against numerical calculations, showing good match for a wide range of photonic crystal parameters. The present approach can be useful for the investigation of various physical effects inside photonic crystal structures as well as for the design of new photonic crystal devices.

Coupled mode theory for parallel waveguides is extended to include temporal variations of both the dielectric function of the photonic array and the input optical power. This formulation can be very useful for the design and comprehensive analysis of modern photonic devices, such as two-dimensional photonic crystals, represented by arrays of parallel waveguides. In the special case of a time-dependent input signal, but stationary dielectric constant, analytical solutions exist for the extended formulation. The accuracy and computer time of the formulation's numerical solutions are examined against finite difference time domain and time-dependent beam propagation analyses of waveguide arrays. (C) 2010 Optical Society of America

A mathematical approach is presented that is based on coupled-mode theory (CMT); it is extended to infinite perfect photonic structures and combined with the supercell method for analysis of infinite photonic crystals with introduced point (0D) and linear (1D) defects. This approach shows a strong advantage over most existing techniques in regards to time and consumption of resources, and thus allows one to quickly analyze operational characteristics of different photonic devices [photonic crystal fibers (PCFs), phased arrays of VCSELs, etc.] over a wide range of physical parameters. (C) 2009 Optical Society of America

An approximate analytical approach for calculating the dispersion relations of two-dimensional photonic crystals, which was earlier developed for E-polarization, is extended for H-polarization (which is usually problematic for analytical treatment, because of field discontinuities). Useful analytical formulas, for calculating the dispersion relations and the magnetic fields, are developed. We show that the presented approach and the derived expressions provide a good approximation for a wide range of photonic crystal parameters. The results are also compared with accurate numerical calculations to check the validity of the approximations. This approach provides not only a fast way for photonic crystal calculations, but it also can be useful for the investigation of various physical effects as well as for the design and analysis of new photonic crystal devices.

Gain switching of unidirectional erbium-doped waveguide ring lasers is studied using numerical simulations based on the time-dependent rate-propagation equations. The counter-directional wave suppression is analyzed for different waveguide ring cavity configurations and pumping schemes. It is shown that for the one-end pumped gain-switched erbium-doped waveguide ring laser, highly unidirectional operation is possible with no intra-cavity elements included. In this case the counter-directional wave suppression considerably exceeds its steady-state value. If the unidirectional operation is caused by the deliberately introduced intra-cavity elements, the gain-switched suppression remains close to the steady-state value.

The dispersion relation for two-dimensional photonic crystals with rectangular geometry is analyzed, using analytical techniques. Both E-polarization and H-polarization are considered. By comparing with accurate numerical calculations, we show that the presented approach, with its derived expressions, can be used as a good approximation for various photonic crystals with a wide range of parameters. The degenerate bands, anticrossing effect and band gap creation can be analyzed, using the presented method. This approach provides not only a fast way for photonic crystal calculations, but also can be employed for investigating various physical effects, as well as for the design and analysis of new photonic crystal devices.

Coupled-mode theory (CMT) is widely used in the analysis of optical systems, such as arrays of parallel waveguides, coupled resonator optical waveguides (CROWs) and phase-locked arrays of VCSELs. In this work, we combined vectorial CMT equations for finite arrays with the concept of Bloch waves. Thus, we extended CMT analysis to the case of infinite perfect photonic structures: arrays of identical waveguides and photonic crystal superlattices. Next, we combined extended CMT with so-called Supercell method for the analysis of infinite photonic crystals with point and linear defects. It has found that this approach can provide very fast and accurate evaluation of finite, but large, 2D photonic crystals, both perfect and with introduced irregularities.

Coupled-mode theory (CMT) is extended to the case of infinite 2-D photonic arrays, made of periodically repeated identical groups of different waveguides (supercells). Born-Karman boundary conditions, applied to the CMT equations for this system, are used to compute the photonic band structure. This method was found to be more efficient and much less resource-consuming than the existing approaches, for the analysis of finite large-sized arrays.

Coupled-mode theory, developed for several parallel waveguides, is extended to the case of infinite 2-D photonic crystals. Periodic boundary conditions, applied to a system of coupled identical waveguides, are used to compute the photonic band structures. This approach is shown to be more efficient than the usual numerical methods when tested on finite, but large-sized, arrays. Photonic crystals made of single-mode and multimode waveguide arrays are examined

We investigate omnidirectional reflection from higher-order gaps in one-dimensional photonic crystals. Moreover, we present a designing criterion for omnidirectional reflection from several distinct gaps simultaneously, using only a single photonic crystal with a constant period. We show that for practical values of photonic crystals parameters, several relatively large omnidirectional gaps may be obtained. As an example, we demonstrate an omnidirectional reflector that exhibits two distinct wide omnidirectional ranges at near-infrared wavelengths. This omnidirectional reflector that operates in several ranges of wavelengths may have various potential applications.