Enhanced gain and narrow linewidth of an optical cavity by the Doppler effect in a four-level atomic system

Abstract

A scheme for high gain and narrow linewidth of an optical cavity with a four-level atomic system is proposed by the Doppler effect via active Raman gain (ARG) process. Atomic motion leads to Doppler frequency shift which induces constructive interference for the linear susceptibility. The enhanced normal dispersion greatly narrows the cavity linewidth, and the amplified gain gives rise to a high cavity transmission. Simulation results show that the cavity linewidth based on ARG is about one order of magnitude narrower than that based on electromagnetically-induced transparency under the same conditions, and the cavity transmission intensity could be enhanced by nearly 30 times.     

Chirped self-healing Airy pulses compression in silicon waveguides under fourth-order dispersion

Abstract

We present the compression of Airy pulses in silicon-on-insulator (SOI) waveguides under the fourth-order dispersion (FOD) using the variational approach that involves Rayleigh’s dissipation function (RDF). All the pulse characteristics are under the influence of the two-photon and the frequency-carrier absorptions. In a quasi-linear approximation, the pulse compression conditions induced by the interaction of the group-velocity dispersion (GVD), the chirp and the FOD are derived. In the nonlinear case, the self-phase modulation (SPM), the two-photon absorption (TPA) and the free-carrier absorption (FCA) reduce the length of compression in a propagation regime of normal GVD, positive chirp and a negative value of FOD. The TPA reduces the maximal power reached than the SPM while the FCA rather increases its value. These results are confirmed in the general case where they all interact with the linear dispersion terms of the SOI waveguide.     

Influence of nonlinear coupling of pulses on spatio-temporal compression

Abstract

Properties of a novel configuration of an optical (spatio-temporal) pulse compressor, that is based on a Kerr-type planar waveguide into which two pulses are simultaneously launched, are studied. It is assumed that the pulse which is the subject of the compression propagates in the anomalous dispersion regime, while the auxiliary pulse is in normal dispersion. The best parameters of the proposed compressor are obtained when duration of the auxiliary pulse is so large that this dispersion can be neglected, while energy of the second pulse is above the threshold of first-order soliton generation. It is observed that in such a configuration the compression occurs simultaneously with the generation of a soliton-like solution. It is argued that the proposed configuration with two simultaneously propagating pulses has advantages over the configuration with a single pulse, namely the maximal compression factor and the optimal length of the compressor is, respectively, more than 3 times larger and, at least, 10 times greater than the corresponding values of the compressor with a single pulse. It is also demonstrated that such a compressor can be considered as a universal device, since its operation depends only slightly on the initial parameters of the pulse subject to the compression.     

Effect of intensity dependent higher-order dispersion on femtosecond pulse propagation in quantum well waveguides

We have studied theoretically the dispersion of ultrafast coherent pulses in GaAs/AlGaAs quantum well waveguide structures as a function of optical intensity. Semiconductor Bloch equations are used to obtain the polarization induced in the medium due to an incident Gaussian electromagnetic beam. The partial differential equation describing the pulse propagation in the presence of group velocity dispersion is used to analyze the role of higher-order dispersion on femtosecond pulse propagation in the waveguide. Due consideration has been given to the intensity dependent optical susceptibility of the medium. The results of the numerical analysis manifest significant influence of higher-order dispersion on femtosecond pulse propagation over short waveguide distance.     

Bright solitary waves in high dispersive media with parabolic nonlinearity law: The influence of third order dispersion

Abstract

We find exact bright solitary wave solutions of a cubic-quintic nonlinear Schrödinger equation describing the propagation of extremely short pulses. Particular cases are discussed. The influence of third order dispersion is numerically investigated, showing the pulse stability for relative low values of the third order dispersion coefficient. When propagation at the zero dispersion point is considered the pulses are always unstable.     

Effect of material dispersion on the focusing of isodiffracting ultrashort pulses by a lens

Abstract

Based on the Fourier transform, the focusing of isodiffracting ultrashort pulses by a lens is studied, where the material dispersion of first, second and higher order is taken into account, respectively. Numerical calculation results for spatial and temporal intensity distributions, photon flux and energy density of focused isodiffracting ultrashort pulses are given and illustrated. It is shown, compared to the dispersion-free case, that the first-order dispersion leads to a broadening of the pulse form, photon flux and energy density, and a decrease of their peak values. The second-order dispersion results in a further broadening of the pulse form and photon flux, and a further decrease of their peak values, whereas the higher-order dispersion plays a relatively minor role.     

Bloch Wave Analysis of Dispersion and Pulse Propagation in Pure Distributed Feedback Structures

Abstract

The excitation and behaviour of monochromatic and pulsed optical Bloch waves in pure distributed feed-back structures are discussed and analysed. The Bloch wave approach, based on a detailed knowledge of the natural optical modes of the periodic structure, is complementary to the more commonly used coupled-wave approach. The inter-relationship between dispersion, field micro-structure and group velocity is discussed, and the effects of group-velocity and higher-order dispersion on pulse propagation treated. Questions about the usefulness of DFB structures for dispersion correction and soliton formation are addressed.     

High-stability time-domain balanced homodyne detector for ultrafast optical pulse applications

Abstract

Low-noise, efficient, phase-sensitive time-domain optical detection is essential for foundational tests of quantum physics based on optical quantum states and the realization of numerous applications ranging from quantum key distribution to coherent classical telecommunications. Stability, bandwidth, efficiency, and signal-to-noise ratio are crucial performance parameters for effective detector operation. Here we present a high-bandwidth, low-noise, ultra-stable time-domain coherent measurement scheme based on balanced homodyne detection ideally suited to characterization of quantum and classical light fields in well-defined ultrashort optical pulse modes.     

Group Velocity Dispersion of Ring Cavities with Lateral and Angular Dispersive Elements

Abstract

A general formalism for the calculation of group velocity dispersion of laser cavities containing elements with angular or lateral dispersion is developed. This formalism is applied to the cavity of a ring laser with one prism and to a cavity with two antiparallel prisms. The calculated results are in agreement with experimental findings for such lasers.     

Cubic-quintic saturable nonlinearity effects on a light pulse strongly distorted by the fourth-order dispersion

Abstract

We analyze a useful process able to safeguard the fundamental soliton light pulse stability in a strongly perturbed environment by the fourth-order dispersion (FOD). This optical pulse propagation is described by the nonlinear Schrödinger equation (NLSE) with cubic–quintic saturable nonlinearities. Some pulse parameters, called collective variables (CVs) such as amplitude, temporal position, width, chirp, frequency shift and constant phase are obtained analytically. Numerical evolution of CVs and their stability are studied under a typical example to verify our analysis.     

Dispersion effects on the interaction of Airy beams and dark solitons

We simulate and analyse an Airy pulse coupled with a dark soliton in a single-mode fibre by solving the non-linear Schrödinger equation (NLSE). Simulations show that the group velocity parameter β₂₂ has a huge impact on the interaction between the Airy pulse and the dark soliton. At some values of β₂₂, a bright soliton arises from the Airy pulse. The intensity of the bright soliton reaches a maximum when β₂₂ takes a certain value. Meanwhile, the transmission distance and the primary energy of the Airy pulse are affected by the different values of β₂₂. However, when the Airy pulse propagates in a linear medium, varying the value of β₂₂ has only a slight impact on the interaction, and no bright soliton detaches from the Airy pulse. In brief, the dispersion effect has a large impact on the interaction of Airy pulses and dark solitons in a non-linear medium; however, dispersion has a lesser impact on interactions in a linear medium.     

Optical solitons in some SIT type equations

Abstract

In this paper, we consider the SIT type equations with group velocity dispersion, Kerr nonlinearity, higher order dispersion, self-steepening and pumping effects and analyse the dynamics of ultra short pulse propagation in nonlinear resonant fibre. The nature of the pulse propagation is governed by the nonlinear Schrödinger-Maxwell Bloch (NLS-MB) type equations. Considering the isospectral and non-isospectral eigen value parameter, we generate the soliton solutions through the Bäcklund transformation method.     

Vibrational instability of the charged interface of immiscible electrically conductive liquids

This paper shows that, in an electrostatic field normal to the flat interface of two viscous electrically conductive liquids, an oscillatory instability of the interface with periodically increasing amplitude can be produced when the electrical conductivity of the upper liquid is substantially greater than that of the lower one. Results are obtained by numerical analysis of the dispersion equation. Pis’ma Zh. Tekh. Fiz. 23, 32–36 (November 12, 1997)     

Periodic and solitary wave solutions for ultrashort pulses in negative-index materials

Abstract

We present a detailed analysis for the existence of dark and bright solitary waves as also fractional-transform solutions in a nonlinear Schrödinger equation model for competing cubic–quintic and higher-order nonlinearities with dispersive permittivity and permeability. Parameter domains are delineated in which these ultrashort optical pulses exist in negative-index materials (NIMs). For example, dark solitons exist for the case of normal second-order dispersion, anomalous third-order dispersion, self-focusing Kerr nonlinearity, and non-Kerr nonlinearities, while the bright solitons exist for the case of anomalous second-order dispersion, normal third-order dispersion, self-focusing Kerr nonlinearity, and non-Kerr nonlinearities. This is contrary to the situation in ordinary materials.     

Novel high gain regimes of spatio-temporal modulational instability for a single-cycle pulse in metamaterials

We derive a generalized expression for the spatio-temporal modulational instability (MI) gain in a metamaterial incorporating linear dispersion terms up to fourth order and nonlinear dispersion terms up to second order and study the influence of the varying input pulse widths and carrier frequency on MI gain. For a single-cycle pulse we have found new regimes of spatio-temporal MI, symmetrically located with respect to the central gain maximum at q?=?0 (q being the transverse spatial frequency of the perturbation). The gain in these new branches of MI is much higher compared to the central branch.     

Block pulse function analysis of time‐varying and non‐linear networks

Abstract

General methods are developed for the analysis of linear and non‐linear networks by the use of the block pulse functions, which are related to the Walsh functions by a linear transformation. For both cases, piecewise‐constant solutions are obtained. For the time‐varying systems, the piecewise‐constant solutions are obtained by the solution of a set of recurrence linear algebraic equations. For the nonlinear systems, a set of recurrence nonlinear algebraic equations has to be computed successively. Illustrative examples are accompanied by the exact or numerical solutions for comparison.     

Soliton propagation in nonlinear optics with higher-order effects

Abstract

We consider the nonlinear wave propagation in a single-mode dielectric waveguide. Considering the envelope equation by Kodama and Hasegawa, which consists of the higher-order terms in the form of higher-order dispersion and dissipation, we investigate the conditions for which the system admits soliton-type pulse propagation through Painlevé analysis. We also present N-soliton solutions.     

Evaluation of laser drilling of holes in thermal barrier coated superalloys

Abstract

Laser drilling of precise holes in thermal barrier coated Ni based superalloys has been studied. The interplay between various hole geometrical features such as hole shape, taper, barrelling, undercut, etc. and laser parameters such as pulse energy, pulse width and pulse repetition rate have been examined. The hole diameters are seen to follow a linear dependence on the incoming laser power densities for pulse width up to 2·0 ms. However, such a linear dependence was not observed for a pulse width of 3·0 ms. It was found that high pulse energy and short pulse width (high power density) gave crack free recast layer, whereas low pulse energy and longer pulse width (low power density) gave microcracks in the heat affected layer of superalloy. The significant barrelling observed in IN718 material at low power density values is due to multiple reflection of the incident beam from the cavity in combination with plasma formation at the evaporation front and trapping of the incident radiation causing excessive heating in that region.     

Study of dispersion compensation in femtosecond lasers

Abstract

We present a formal analysis of dispersion compensation in femtosecond lasers and provide a detailed examination of the relevant features in Ti: sapphire and Cr: LiSAF lasers. It is shown that the essential of dispersion compensation up to the fourth order consists of searching for the solutions of a group of three linear equations. With the use of a prism pair, complete compensation of both the second- and the third-order dispersion corresponds to solving two of the three equations with the prism separation and the intraprism beam path length as variables. Owing to the limitations on the practically achievable prism separation and the intraprism path length in a laser set-up, only some of these solutions are physically meaningful; hence both zero second- and third-order cavity dispersion may be realized merely within a certain specific spectral range. The fourth-order dispersion, however, cannot be completely compensated for in this case unless a third control variable is introduced. It is also shown that the dominant parameter in determining the spectral region where dispersion is minimized is the difference between the ratio of the third-order dispersion to the second-order dispersion of the laser rod and that of the selected prism pair material. This also explains the major differences between Ti: sapphire and Cr: LiSAF lasers in terms of dispersion compensation.