Analysis Of Pulse Propagation Research Articles

Abundant Exact Travelling Wave Solutions for a Fractional Massive Thirring Model Using Extended Jacobi Elliptic Function Method

The fractional massive Thirring model is a coupled system of nonlinear PDEs emerging in the study of the complex ultrashort pulse propagation analysis of nonlinear wave functions. This article considers the NFMT model in terms of a modified Riemann–Liouville fractional derivative. The novel travelling wave solutions of the considered model are investigated by employing an effective analytic approach based on a complex fractional transformation and Jacobi elliptic functions. The extended Jacobi elliptic function method is a systematic tool for restoring many of the well-known results of complex fractional systems by identifying suitable options for arbitrary elliptic functions. To understand the physical characteristics of NFMT, the 3D graphical representations of the obtained propagation wave solutions for some free physical parameters are randomly drawn for a different order of the fractional derivatives. The results indicate that the proposed method is reliable, simple, and powerful enough to handle more complicated nonlinear fractional partial differential equations in quantum mechanics.

ANALYSIS OF ULTRAHSORT LASER PULSES PROPAGATION IN MEDIUM: LITHARGE GLASS SF56A

Propagation of an ultra-short lasers pulses in a linear optical medium consisting of free space, dispersive media. However, analytical methods have the limitations of not being able to handle arbitrary pulse profiles. Also, closed form solutions are often obtained after certain levels of approximations. This has motive a few studies based on the use of numerical simulation techniques in the analysis of pulse propagation. In view of the recent advance in ultra-short pulse propagation, a strong need is felt for developing a numerical formalism capable of performing such a complete analysis of the issues involved in pulse propagation.
 This allows us to analyze the pulse in the time-frequency domain at any arbitrary plane. With this tool, we investigate the spectral and temporal evolution of ultra-short pulses at any arbitrary propagation distance.

Quadruple Gaussian Laser Beam Profile Dynamics in Collisionless Magnetized Plasma

This paper presents an investigation of self-focusing of a quadruple Gaussian laser beam in collisionless magnetized plasma. The nonlinearity due to ponderomotive force which arises on account of nonuniform intensity distribution of the laser beam is considered. The nonlinear partial differential equation governing the evaluation of complex envelope in the slowly varying envelope approximation is solved using a paraxial formalism. The self-focusing mechanism in magnetized plasma, in the presence of self-compression mechanism will be analyzed in contrast to the case in which it is absent. It can be observed that, in case of ponderomotive nonlinearity, the self-compression mechanism obstructs the pulse self-focusing above a certain intensity value. The effect of an external magnetic field is to generate pulses with smaller spot size and shorter compression length. The lateral separation parameter and the initial intensity of the laser beam play a crucial role on focusing and compression parameters. Also, the three-dimensional analysis of pulse propagation is presented by coupling the self-focusing equation with the self-compression one.

Analysis of pulse propagation through multilayer plasmonic waveguides in the quasi-bound mode region

We present a numerical analysis of surface plasmon dispersion and the nonlinear nature of wave propagation on different smooth waveguides with lossy noble metal films. We also analyze the effective parameters that can affect the dispersion behavior of a thin dielectric slab waveguide embedded in a symmetric metal film. Three kinds of metal (silver, gold, and copper) with Johnson–Christy constants have been utilized in waveguides. Four kinds of dielectric material (air, Teflon, FR-4, and silicon) have been employed in the insulator layer of the metal–insulator–metal waveguide. The dispersion curve of the metal–insulator–metal waveguide with different metal and dielectric arrangements has been studied numerically. By multi-nominal fitting of dispersion curves, we have derived the nonlinear properties of Gaussian (chirped) wave propagation, dispersion length, and pulse broadening through a three-layer plasmonic waveguide. A comparison of three-layered plasmonic waveguides with different guiding layers has been accomplished. Simulation results have shown that dispersion curves with a larger peak and a quasi-bound mode cause the Gaussian waves to be dispersed and broadened during longer traveling distances. The achieved results serve an impressive function in the design of optical switches and delay lines.

Pulse propagation of photon-added coherent states in waveguides with side-coupled nonlinear cavities

We present a theoretical analysis of pulse propagation in a waveguide with a side-coupled Kerr nonlinear cavity. As a specific application, we demonstrate how the nonlinearity has a profound influence on transport properties of a photon-added coherent state. We find that the fields provided by the coherent states facilitate a tunable nonlinearity on the few-photon level, allowing for a robust gating of single photons.

Frequency-Dependent Formulations of a Drude-Critical Points Model for Explicit and Implicit FDTD Methods Using the Trapezoidal RC Technique

A Drude-critical points (D-CP) model for considering metal dispersion is newly incorporated into the frequency-dependent FDTD method using the simple trapezoidal recursive convolution (TRC) technique. Numerical accuracy is investigated through the analysis of pulse propagation in a metal (aluminum) cladding waveguide. The TRC technique with a single convolution integral is found to provide higher accuracy, when compared with the recursive convolution counterpart. The methodology is also extended to the unconditionally stable FDTD based on the locally one-dimensional scheme for efficient frequency-dependent calculations.

Design and optimization of fiber optical parametric oscillators for femtosecond pulse generation

In this paper, we use a genetic algorithm and pulse-propagation analysis to design and optimize optical parametric oscillators based on soft-glass microstructured optical fibers. The maximum parametric gain, phase-match, walk-off between pump (1560 nm) and signal (880 nm) pulses, signal feedback ratio and signal-pump synchronization of the cavity are optimized. Pulse propagation analysis suggests that one can implement a fiber optical parametric oscillator capable of generating approximately 200-fs pulses at 880 nm with 43% peak-power conversion, high output pulse quality (time-bandwidth product approximately 0.43) and a wavelength tuning range that is limited only by the glass transmission windows.

Modeling photonic crystal fiber for efficient soliton pulse propagation at 850 nm

We numerically investigate the dynamics of soliton propagation at 850 nm in chloroform filled liquid core photonic crystal fiber (LCPCF) by using both finite element method (FEM) and split step Fourier method (SSFM). We propose a novel chloroform filled PCF structure that operates as a single mode at 850 nm featuring an enhanced dispersion and nonlinearity for efficient soliton propagation with low input pulse energy and low loss over small distances. We adopt the projection operator method (POM) to derive the pulse parameter equations which clearly describes the impact of fourth order dispersion on the pulse propagation in the proposed PCF. To analyse the quality of the pulse, we perform the stability analysis of pulse propagation numerically and compare our results of the newly designed chloroform filled PCF with that of standard silica PCF. From the stability analysis, we infer that the soliton pulse propagation in modified chloroform filled PCF is highly stable against the perturbation.

Self-phase modulation effects and pulse propagation in gain-guided fibers

We present a theoretical analysis of pulse propagation and self-focusing in a gain-guided (GG) fiber amplifier. A weak pulse is launched in the GG fiber when the input pulse reaches a critical power the pulse begins to collapse in the transverse direction. By using different input powers the transmission characteristics are changed. We add coupling to a single-mode fiber at the output end and study pulse dispersion and energy.

Slow light pulse propagation in dispersive media

We present a theoretical and numerical analysis of pulse propagation in a semiconductor photonic crystal waveguide with embedded quantum dots in a regime where the pulse is subjected to both waveguide and material dispersion. The group index and the transmission are investigated by finite-difference-time-domain Maxwell–Bloch simulations and compared to analytic results. For long pulses the group index (transmission) for the combined system is significantly enhanced (reduced) relative to slow light based on purely material or waveguide dispersion. Shorter pulses are strongly distorted and depending on parameters broadening or break-up of the pulse may be observed. The transition from linear to nonlinear pulse propagation is quantified in terms of the spectral width of the pulse. To cite this article: T.R. Nielsen et al., C. R. Physique 10 (2009).

Slow light in quantum dot photonic crystal waveguides

A theoretical analysis of pulse propagation in a semiconductor quantum dot photonic crystal waveguide in the regime of electromagnetically induced transparency is presented. The slow light mechanism considered here is based on both material and waveguide dispersion. The group index ng for the combined system is significantly enhanced relative to slow light based on purely material or waveguide dispersion.

Refractive index and wave vector in passive or active media

Materials that exhibit loss or gain have a complex-valued refractive index $n$. Nevertheless, when considering the propagation of optical pulses, using a complex $n$ is generally inconvenient---hence the standard choice of real-valued refractive index, i.e., ${n}_{s}=\text{Re}(\sqrt{{n}^{2}})$. However, an analysis of pulse propagation based on the second-order wave equation shows that use of ${n}_{s}$ results in a wave vector different to that actually exhibited by the propagating pulse. In contrast, an alternative definition ${n}_{c}=\sqrt{\text{Re}({n}^{2})}$, always correctly provides the wave vector of the pulse. Although for small loss the difference between the two is negligible, in other cases it is significant; it follows that phase and group velocities are also altered. This result has implications for the description of pulse propagation in near resonant situations, such as those typical of metamaterials with negative (or otherwise exotic) refractive indices.

Time domain UTD-PO solution for multiple building diffraction for UWB signals

A time domain (TD) solution for the analysis of the multiple-diffraction is presented. This proposed solution is based on representation of the inverse Laplace transform of the corresponding frequency domain solution, as it is given by a hybrid of UTD-PO solutions. The TD results can be applied in pulse propagation analysis when multiple-diffraction has to be considered.

Three-dimensional FDTD method for optical pulse propagation analysis in microstructured optical fibers

We propose a three-dimensional (3D) finite-difference time-domain (FDTD) method to analyze the pulse propagation characteristics in microstructured optical fibers (MOFs). The computation domain size is greatly reduced by adopting the technique of moving problem space. The propagating pulse is virtually held in the buffer cell of the problem space as simulation continues. This method is capable to investigate the temporal evolution of the propagating pulse. Spectral information can be obtained by Fourier analysis. As an example, the influence of the kerr nonlinearity on the optical pulse propagation in a Lorentz dispersive MOF is demonstrated. The model is also used to simulate the nonlinear interactions between the pump spectral broadening and third harmonic generations in a highly nonlinear fused silica nanowire with good agreement with the generalized nonlinear envelop equation (GNEE) model.

FDTD analysis of pulse propagation on microstrip line and an exponentially parallel plate antenna produced by photoconductive switches applied bias voltage

AbstractThe d'Alembents formula with one free end was used to understand the pulse produced by photoconductive semiconductor switch (PCSS) and propagating in microstrip‐line at the bias voltage. A total reflection border was given for keep the steady electric field in order that the propagation of pulse in the microstrip line could be analyzed by finite time difference domain method. The reflection parameter of this border was computed. The border and a simple model of photoconductive switches were used to analyze the process of pulse transmitting in the microstrip line. The electric field distributions at the different time were given. The experiment result has proven that there is excellent agreement between the simulated and measured version of pulse output. An exponentially parallel plate antenna loaded with dielectric using PCSS was designed and analyzed. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 168–172, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23035

Theoretical Investigation of Carrier Envelope Phase Dependence of All-Optical Poling with the Third- and Higher-Order Nonlinear Processes

Dependence of efficiency in all-optical poling with nonlinear processes, up to eighth order, is considered. The explicit form of the nonlinear susceptibility that is responsible for the poling is derived, which shows both CEP and phase mismatch dependence. On the basis of an analysis of pulse propagation in a nonlinear material, it is shown that one can identify the order of nonlinearity that is relevant to the poling process, relying on current technology of CEP stabilization and thin-film growth.

Pulse propagation in adiabatically coupled photonic crystal coupled cavity waveguides

A rigorous analysis of pulse propagation in planar photonic crystal (PhC) coupled cavity waveguides (CCWs) of finite length is reported. Conventional PhC waveguides, formed by a single line defect, are used at both interfaces of the CCW. An adiabatic taper based on progressively varying the radii of the spacing defects between cavities is used to achieve flat transmission bands with respect to the butt coupling case. The influence on the main parameters of the propagated pulse such as group delay, full width at half maximum and pulse attenuation are investigated for both the adiabatic and butt coupling cases. Furthermore, the Fabry-Perot formula has been used for modeling the pulse propagation along the CCW of finite length, which permits to analyze a large range of parameters avoiding the huge computation time requirements of finite-difference time-domain simulations.

An analytical formula for the mean differential group delay of randomly birefringent spun fibers

Polarization-mode dispersion (PMD) is a serious impairment for high-bit-rate optical telecommunication systems. It is known that spinning the fiber during the drawing process drastically reduces the PMD. However, the analysis of pulse propagation through a randomly birefringent spun fiber is still at an early stage. In this paper, we derive an analytical formula for the mean differential group delay of a periodically spun fiber with random birefringence. We model the birefringence with fixed modulus and a random orientation under the condition that the spin period is shorter than the beat length. Finally, we numerically compare the analytical results with those given by the random-modulus model of birefringence, and we obtain good agreement as long as the short-period assumption is satisfied.

Discrete orthogonal Gauss–Hermite transform for optical pulse propagation analysis

A discrete orthogonal Gauss–Hermite transform (DOGHT) is introduced for the analysis of optical pulse properties in the time and frequency domains. Gaussian quadrature nodes and weights are used to calculate the expansion coefficients. The discrete orthogonal properties of the DOGHT are similar to the ones satisfied by the discrete Fourier transform so the two transforms have many common characteristics. However, it is demonstrated that the DOGHT produces a more compact representation of pulses in the time and frequency domains and needs less expansion coefficients for a given accuracy. It is shown that it can be used advantageously for propagation analysis of optical signals in the linear and nonlinear regimes.

Statistical analysis of pulse propagation driven by polarization-mode dispersion

The linear propagation of pulses driven by random polarization-mode dispersion is considered. Analytical expressions are derived for the probability-density functions of the pulse width, timing displacement, and degree of polarization. The study is performed in Stokes space, and frequency correlation between modes is shown to play an important role in it.