Igor V. Guryev

Photonic crystals : physics and practical modeling

to Photonic Crystals.- Fundamentals of Wave Optics.- Fundamentals of Computation of Photonic Crystal Characteristics.- Band Structure Computation of 1D Photonic Crystals.- Band Structure Computation of 2D and 3D Photonic Crystals.- Finite-Difference Time-Domain Method for PhC Devices Modeling.- Photonic Crystal Optical Fibers.- FDTD Method for Band Structure Computation.- Photonic Crystal Waveguides.- Application for Design and Simulation of Optical WDM Demultiplexer.

Improvement of characterization accuracy of the nonlinear photonic crystals using finite elements-iterative method

We investigate nonlinear one- and two-dimensional photonic crystals by applying a finite element-iterative method. Numerical results show the essential influence of nonlinear elements embedded into a quarter-wave stack and the sharp photonic crystal waveguide bend on the spectral characteristics of these structures. We compare our results with those obtained in [21] from the discrete equation method for the case of a sharp waveguide bend. The comparison shows that neglecting the nonuniform field distribution inside the embedded nonlinear elements leads to overestimation of the waveguide bend transmissivity.

Photonic density of states maps for design of photonic crystal devices

In this work, it has been investigated whether photonic density of states maps can be applied to the design of photonic crystal-based devices. For this reason, comparison between photonic density of states maps and transmittance maps was carried out. Results of comparison show full correspondence between these characteristics. Photonic density of states maps appear to be preferable for the design of photonic crystal devices, than photonic band gap maps presented earlier and than transmittance maps shown in the paper.

Characterization of all-normal-dispersion microstructured optical fiber via numerical simulation of passive nonlinear pulse reshaping and single-pulse flat-top supercontinuum

The supercontinuum (SC) generated by pumping in anomalous dispersion is sensitive to the input pulse fluctuations and pump laser’s shot noises and does not possess a single-pulse waveform, so the incident pulse becomes a noise-like train of spikes. A simple method of creating pulsed lasers with either pulse-maintaining ultrabroad SC or specially shaped pulse waveforms can be implemented using all-normal-dispersion microstructured optical fibers (ANDi-MOFs). An ANDi-MOF with a simple topology and dispersion profile maximum at 800 nm was designed using the effective index method. Its properties and suitability were characterized via numerical simulation of femtosecond parabolic pulse formation and generation of an octave-spanning pulse-maintaining SC using a generalized propagation equation. The designed ANDi-MOF is suitable for resolving both problems and allows some detuning of the pulse’s wavelength around 800 nm. However, a better choice for SC generation is pumping at or near the wavelength where the third-order dispersion becomes zero. This configuration benefits from the absence of pulse break-up under large pulse energies, which appears otherwise. The fiber can provide a low-cost method for developing supercontinuum sources and a solution to the problems of parabolic waveform formation to meet the needs of optical signal processing and pulse amplification and compression.

Formation of parabolic optical pulses in passive optical fibers

We have investigated a nonlinear pulse reshaping towards parabolic pulses in the passive normal dispersive optical fibers. We have found that pulses with parabolic intensity profile, parabolic spectrum and linear chirp can be obtained due to the passive nonlinear reshaping at the propagation distance exceeding a few dispersion lengths. These pulses preserve parabolic profile during subsequent pulse propagation in a fiber. We have examined the influence of initial pulse parameters and fiber parameters on the resulted pulse shape.

All-normal dispersion photonic crystal fiber for parabolic pulses and supercontinuum generation

We have designed an all-normal dispersion photonic crystal fiber optimized for pumping at 800 nm with initial pulses which are typical for conventional Ti:Sapphire lasers. Parabolic pulse formation and supercontinuum generation in this fiber is analyzed both in time and frequency domains.

Introduction to Photonic Crystals

Chapter 1 gives a brief introduction into the basics of photonic crystals which are a special class of optical media with periodic modulation of permittivity. We give a general idea of what photonic crystals are and then describe different kinds of photonic crystal lattices and introduce and discuss the basic terminology. Main attention is paid to the band structure, eigen states and photonic band gaps. Finally, some historical notes are given, where the first computed band structures of three dimensional photonic crystal with face-centered cubic and diamond lattices are presented as well as the band structure of inverted opal. At the end of the chapter different areas of photonic crystal applications in optical communications and lasers are given, such as waveguides, optical insulators, splitters, microresonators for spontaneous emission management, etc.

Numerical analysis for a solid-core photonic crystal fiber with tunable zero dispersion wavelengths

Here we propose a simple design for a solid-core photonic crystal fiber made of silica by keeping the golden ratio (1.618) between pitch and air hole diameter Λ /d in a subset of six rings of air-holes with hexagonal arrangement. In the case when we have a pitch equal to one micron (Λ =1 μm), we need air-holes diameters d=0.618 μm in order to obtain the golden ratio parameter (Λ/d=1.618), and achieve two zero dispersion wavelength (ZDW) points at 725 nm and 1055 nm; this gives us the possibility to use this fiber in supercontinuum generation using a laser emission close to that points. We analyzed a series of fibers using this relation and show the possibilities of tunable ZDW in a wide range of wavelengths from 725 nm to 2000 nm with low losses and small effective area. In agreement with the ZDW point needed, the geometry of the structure can be modified to the point of having only three rings of air holes that surround the solid core with low losses and good confinement mode. The design proposed here is analyzed using the finite element method (FEM) with perfectly matched layers (PML), including the material dispersion directly into the model applying the Sellmeier’s equation.

Graphics processing unit–accelerated finite-difference time-domain method for characterization of photonic crystal fibers

Abstract. In the work, we have presented the technique based on the graphics processing unit accelerated finite-difference time-domain (FDTD) method for characterization of a single-mode photonic crystal fiber (PCF) with an arbitrary refractive index profile. In contrast to other numerical methods, the FDTD allows studying the mode propagation along the fiber. Particularly, we have focused attention on the method details that allowed us to reduce dramatically the computation time. It has been demonstrated that the accuracy of dispersion obtained by the FDTD method is comparable to the one provided by the finite elements method while possessing lower computation time. The method has been used to determine the fundamental mode cut-off of all-normal dispersion PCF and to find fiber losses beyond this wavelength.

Nonlinear pulse reshaping in passive optical fibers towards quasi-parabolic waveforms

Generation and applications of the optical pulses with a parabolic intensity profile has developed into the area of dynamic research activity over recent years. Parabolic pulses can propagate remaining their parabolic profile. Particularly these pulses resist to the deleterious effect of the optical wave breaking. They are of great interest for a number of applications including the high power pulse generation, and all optical signal processing. Alternative methods of generating parabolic pulses are of especial interest in the context of non-amplification usage, such as optical telecommunications. It is found that Gaussian waveforms provide best quasi-parabolic pulses among others and within shortest distance. There is a range of soliton numbers where the shape of quasi-parabolic pulse is closest to parabolic one.