Sourabh Roy

Modeling the Dispersion of the Nonlinearity in Slow Mode Photonic Crystal Waveguides

Nanophotonic structures enabling the engineering of linear dispersion are often exploited for nonlinear processing. However, the dispersion of the nonlinear response has been generally overlooked, also because of the difficulty of accurately taking this effect into account. Here, we first show the necessity of considering the nonlinear dispersion and then propose a simplified approach through which the modeling can be performed. As an example, we consider waveguides in which a large group index and low group velocity dispersion are achieved at the same time by modifying a single design parameter, i.e., an asymmetric translation of the hole rows closest to the core. It is shown that the dependence on the wavelength of the normalized Bloch mode overlap integrals for self-phase modulation (SPM) can be interpolated by a four-parameter formula that is similar to the Morse potential. The parameters can be related to specific properties of the nonlinear SPM coefficient, which in the specific case depends on the translation parameter, by simple linear and exponential functions. Cross-phase modulation and four-wave mixing coefficients can then be derived from the self-phase one, through a geometric mean, slightly corrected to account for the interacting wave detuning, and the complete modeling of nonlinear dispersion is achieved.

Determining Properties of Fabricated Index-Guiding Photonic Crystal Fibers Using SEM Micrograph and Mode Convergence Algorithm

We develop a method for modeling properties of fabricated (realistic) air-silica photonic crystal fibers (PCFs). Our approach involves extracting the transverse refractive index (RI) profile of the drawn PCF from its scanning electron micrograph on which is operated a precise and fast mode-analysis recipe based on a finite difference (FD) field convergence scheme. From the digitized scaled RI distribution, we evaluate propagation characteristics of guided modes of PCFs, examining modal shapes, birefringence, dispersion, and other relevant properties. Naturally, our true-structure study of PCFs using FD algorithm exhibits results that are more close to measured data, establishing its practicality as compared with idealized-structure modeling. To demonstrate the efficacy of our method, we investigate some application-specific experimentally drawn PCFs, well known for their study in the literature. The key results that fairly predict experimental measurements are presented. Besides modeling fabricated fibers, this analysis will be very useful to realize PCFs with targeted specifications using feedback of estimation and characterization of trial fabrications.

Modeling the tapering effects of fabricated photonic crystal fibers and tailoring birefringence, dispersion, and supercontinuum generation properties

The effects of tapering fabricated air-silica photonic crystal fibers (PCFs) by tailoring the key modal and nonlinear properties of PCFs have been studied by analyzing the tapered structure using a finite difference mode calculation algorithm. The process of tapering is simulated through repeatedly redefining the geometry of the fiber cross section in a progressively tapered dimension preserving the shape. We tested the performance of the analysis by evaluating the modal characteristics, namely, the mode-effective area, birefringence, dispersion, nonlinearity, and supercontinuum properties of some well-known PCF examples under successive tapered conditions. Tapering, as an additional parameter, is seen to improve birefringence of a typical high-birefringence PCF by 1 order of magnitude. The analysis also estimates the extent of tapering that is required to achieve a target amount of evanescent field that has potential applications in an evanescent field sensor. Our investigation with tapered PCF structures includes tailoring dispersion properties and increasing nonlinearity, which leads to broader and lower threshold supercontinuum generation. The analysis should, therefore, be useful as a ready technique for taper analysis of any arbitrary structure PCF and also in PCF-preform (stacking structure) analysis, which can provide preestimates of properties in a targeted dimension of the final PCF before drawing.

Narrowband optical parametric gain in slow mode engineered GaInP photonic crystal waveguides.

We predict narrowband parametric amplification in dispersion-tailored photonic crystal waveguides made of gallium indium phosphide. We use a full-vectorial model including the dispersive nature both of the nonlinear response and of the propagation losses. An analytical formula for the gain is also derived.

Parametric Gain and Conversion Efficiency in Nanophotonic Waveguides With Dispersive Propagation Coefficients and Loss

Nanophotonic waveguides can be engineered in order to exhibit slow mode propagation thereby enhancing the nonlinear responses. In such waveguides, loss and nonlinear coefficients are strongly wavelength dependent, a property that must be considered when the signal to pump detuning is large. Exact formulas for the parametric gain and conversion efficiency, accounting for the dispersion of losses and nonlinearity, are derived here. They can be applied to any waveguide presenting such features; in particular they have been calculated for a III-V semiconductor photonic crystal waveguide, where narrow- and broad-band amplification are predicted. The asymmetry of losses causes major asymmetries in the gain and conversion efficiency, which are no longer simply related as in the case of waveguides in which loss do not depend on the wavelength.

Analysis of Nonlinear Multilayered Waveguides and MQW Structures: A Field Evolution Approach Using Finite-Difference Formulation

In this paper, we present a method of analyzing nonlinear multilayered-planar waveguides and multiple-quantum-well structures. The method is based on scalar and semi-vectorial solutions of Helmholtzs equation devised with a mode-field convergence technique in a finite-difference grid. The approach is general, simple to formulate, and applicable to any arbitrary structures with Kerr-like/non-Kerr-like nonlinearities for determining guided mode characteristics of both TE and TM polarizations and the dispersion relations. We analyze a number of known waveguide structures reported in the literature to test the accuracy and establish the efficacy of the algorithm as a useful analysis recipe for modeling and understanding the modal properties of such nonlinear multilayered waveguides.

Parametric gain in dispersion engineered photonic crystal waveguides.

We present a numerical simulation of parametric gain properties in GaInP PhC dispersion engineered waveguides in which the group velocity dispersion crosses zero twice and where the pump and the signal are 100 ps pulses. The simulations use the M-SSFT algorithm which incorporates dispersive nonlinear coefficients and losses. We concentrate on narrow band parametric gain which occurs for pump wavelengths in the normal group velocity dispersion regime. The effects of structural details, of pump wavelength and of losses are carefully analyzed.

Dual-pump parametric amplification in dispersion engineered photonic crystal waveguides

This paper describes a numerical simulation of narrow band parametric amplification in dispersion engineered photonic crystal waveguides. The waveguides we analyze exhibit group velocity dispersion functions which cross zero twice thereby enabling many interesting pumping schemes. We analyze the case of two pulsed pumps each placed near one of the zero dispersion wavelengths. These configurations are compared to conventional single pump schemes. The two pumps may induce phase matching conditions in the same spectral location enabling to control the gain spectrum. This is used to study the gain and fidelity of 40 G bps NRZ data signals.

Narrowband optical parametric amplification measurements in Ga 0.5 In 0.5 P photonic crystal waveguides

We report the first demonstration of narrowband parametric amplification in a chip scale semiconductor waveguide. A dispersion engineered, Ga0.5In0.5P photonic crystal waveguide with a dispersion function that exhibits two zero crossings was used with a pulsed pump placed in the normal dispersion regime while a tunable probe was scanned on either side of the pump. A peak conversion efficiency of -10 dB was obtained with a peak pump power of only 650 mW. The narrowband nature of the gain spectrum was clearly demonstrated.

Dual POF and prism sensor for liquid concentration measurement based on hysteresis area

An intensity modulated Fiber optic prism based liquid concentration sensor is proposed. The sensing principle is based on total internal reflection (TIR) inside the prism which gets modulated in the vicinity of liquid as a function of refractive index. The precise movement of sensor head in liquids, gives rise to a hysteresis curve which is considered as a measure of liquid concentration. Different liquid concentrations of Sucrose, Saline solution (NaCl) and Glycerin are taken for the study. The sensor exhibits sensitivity of 371.16, 2133.25 and 1501.89 Sucrose, Saline water and Glycerin solutions respectively.