K. Nakkeeran

Nearly chirp- and pedestal-free pulse compression in nonlinear fiber Bragg gratings

We demonstrate almost chirp- and pedestal-free optical pulse compression in a nonlinear fiber Bragg grating with exponentially decreasing dispersion. The exponential dispersion profile can be well-approximated by a few gratings with different constant dispersions. The required number of sections is proportional to the compression ratio, but inversely proportional to the initial chirp value. We propose a compact pulse compression scheme, which consists of a linear and nonlinear grating, to effectively compress both hyperbolic secant and Gaussian shaped pulses. Nearly transform-limited pulses with a negligibly small pedestal can be achieved.

A mathematical approach to Integral Resonant Control of second-order systems

Systems with colocated sensor-actuator pairs exhibit an interesting property of pole-zero interlacing. Integral Resonant Control (IRC) exploits this property to result in superior damping performance over multiple resonant modes by prescribing an adequate feed-through term to swap the pole-zero interlacing to a zero-pole one - thus enabling a simple integral feedback controller to add substantial damping to the system. Over the past few years, the IRC has proved extremely popular and versatile and has been applied to damp the resonance in a variety of systems. So far, a simulation-based manual search has been used to determine the three main parameters of the IRC scheme namely: (i) feed-through term, d, (ii) integral gain, k and (iii) resulting damping, ζ. In this paper, a full quantification of the effect of feed-through term on second-order colocated systems as well as a mathematical formulation for the relation between the feed-through term, integral gain and achievable damping are presented. These results add to the current understanding regarding the behaviour of colocated systems and facilitate the IRC design for a specified damping.Systems with colocated sensor-actuator pairs exhibit the interesting property of pole-zero interlacing. Integral resonance control (IRC) exploits this property by changing the pole-zero interlacing to zero-pole interlacing. The unique phase response of this class of systems enables a simple integral feedback controller to add substantial damping. Over the past few years, IRC has proven to be extremely versatile and has been applied to a wide variety of systems whose dominating dynamics of interest can be accurately modeled by second-order transfer functions. To date, a manual approach has been employed to determine the parameters of the IRC scheme, namely the feed-through term and the integral gain. In this paper, the relationship between the feed-through term, integral gain, and achievable damping is derived analytically for undamped/lightly damped second-order systems. The relationship between damping controller and an outer servo loop is also derived. These results add to the current understanding of colocated systems and automate the design of IRC controllers with a specified damping and tracking bandwidth. The presented results are applied to design and implement a damping and tracking controller for a piezoelectric nanopositioning stage.

Efficient Pulse Compression Using Tapered Photonic Crystal Fiber at 850 nm

By using appropriate self-similar scaling analysis, we delineate the generation of linearly chirped solitary pulses in photonic crystal fiber (PCF) at 850 nm to obtain the short pulses with large compression factor and minimal pedestal energy when compared to adiabatic compression scheme. The dispersion and nonlinearity varying nonlinear Schrödinger equation aptly models the pulse propagation in such a PCF. The analytical results demand that the effective dispersion must decrease exponentially while the nonlinearity must increase exponentially in the PCF. Thus, based on the analytical results, we propose the new design of tapered PCF by varying the pitch and diameter of the air hole. We adopt the projection operator method to derive the pulse parameter equations which indeed very clearly describe the self-similar pulse compression process at different parts of the PCF structures. As we are interested in constructing compact compressor, we also introduce another designing of PCF by filling chloroform in the core region. The chloroform filled tapered PCF exhibits low dispersion length for efficient pulse compression with low input pulse energy over small propagation distances.

Transmission and stability of solitary pulses in complex Ginzburg-Landau equations with variable coefficients

A class of complex Ginzburg–Landau (CGL) equations with variable coefficients is solved exactly by means of the Hirota bilinear method. Two novel features, elaborated in recent works on the bilinear method, are incorporated. One is a modified definition of the bilinear operator, which has been used to construct pulse, hole and front solutions for equations with constant coefficients. The other is the usage of time- or space-dependent wave numbers, which was employed to handle nonlinear Schrodinger (NLS) equations with variable coefficient. One-soliton solutions of the CGL equations with variable coefficients are obtained in an analytical form. A restriction imposed by the method is that the coefficient of the second-order dispersion must be real. However, nonlinear, loss (or gain) is permitted. A simple example of an exponentially modulated dispersion profile is worked out in detail to illustrate the principle. The competition between the linear gain and nonlinear loss, and vice versa , is investigated. T...

Modeling Self-Similar Optical Pulse Compression in Nonlinear Fiber Bragg Grating Using Coupled-Mode Equations

Nearly pedestal-free optical pulse compression using self-similar chirped optical solitons near the photonic bandgap (PBG) structure of nonlinear fiber Bragg gratings (NFBGs) with exponentially decreasing dispersion is investigated using the generalized nonlinear coupled-mode equations (NLCMEs). The full dispersion characteristics and the effect of PBG are included. We find that the ratio of the frequency detune of the pulses center frequency from the Bragg frequency of the NFBG to coupling coefficient of the NFBG is an important design parameter of the NFBG optical pulse compressor. We carried out a comprehensive study on the effect of the ratio of frequency detune to coupling coefficient, grating length, initial chirp, initial dispersion, and initial pulsewidth on the self-similar optical pulse compression. We also studied the compression of both the hyperbolic secant and Gaussian-shaped pulses and the effect of variation in the initial pulsewidth on the optical pulse compression.

Dissipative Solitons in Coupled Complex Ginzburg-Landau Equations

Pulse propagation in inhomogeneous nonlinear media with linear and nonlinear gain and loss, described by a system of nonlinearly coupled complex Ginzburg–Landau equations (CGLEs) with variable coefficients, is considered. Exact solitary pulse (SP) solutions are obtained analytically, for special choices of variable coefficients of the nonlinear gain/loss terms, by a modified Hirota bilinear method. The solutions include space- or time-dependent wave numbers, which imply dilatation or compression of the SPs. Stability of the solutions is tested by means of direct simulations, which demonstrate that, in many cases, the SPs are stable against perturbations.

Suppression of sideband frequency shifts in the modulational instability spectra of wave propagation in optical fiber systems

In standard optical fibers with constant chromatic dispersion, modulational instability (MI) sidebands execute undesirable frequency shifts due to fiber losses. By means of a technique based on average-dispersion-decreasing dispersion-managed fibers, we achieve both complete suppression of the sideband frequency shifts and fine control of the MI frequencies, without any compromise in the MI power gain.

Ultrashort pulse train generation using nonlinear optical fibers with exponentially decreasing dispersion

We propose and numerically demonstrate a simple method to generate a high-repetition-rate ultrashort pulse train. We show that the nonlinear propagation of a prechirped dual-frequency signal through a fiber with exponentially decreasing dispersion will give rise to a train of noninteracting solitons at a high repetition rate.

Generation of a Train of Ultrashort Pulses Near-Infrared Regime in a Tapered Photonic Crystal Fiber Using Raised-Cosine Pulses

We consider an optical pulse propagating in a tapered photonic crystal fiber (PCF) wherein dispersion as well as nonlinearity varies along the propagation direction. The generalized nonlinear Schrödinger equation aptly models the pulse propagation in such a PCF. The design of the tapered PCF is based on the analytical results, which demand that the dispersion decrease exponentially and the nonlinearity increase exponentially. In this paper, we adopt the generalized projection operator method for deriving the pulse-parameter equations of the Lagrangian variation method and the collective variable method. Besides, we consider another pulse profile called raised cosine (RC), which is aimed at replacing the conventional hyperbolic secant pulse. From the detailed results, we infer that the initial RC pulse evolves into a hyperbolic secant pulse. Further, in order to minimize the input power requirement, we employ the idea of replacing the solid core in the PCF with chloroform. In addition to the single pulse compression, we also investigate the possibility of multisoliton pulse compression. Here, we consider eight chirped hyperbolic secant pulses as input and generate a train of ultrashort pulses at 850 nm based on the chirped multisoliton pulse compression. In a similar way, we extend this pulse compression with eight RC pulses.

Ultra-short pulse propagation in birefringent fibers—the projection operator method

We examine the propagation of ultra-short optical light pulses in dispersion-managed birefringent fiber transmission systems, in which the pulse dynamics is governed by the coupled higher-order nonlinear Schrodinger equations with higher-order linear and nonlinear optical effects. We derive the equations of motion in terms of pulse parameters such as amplitude, temporal position, width, chirp, frequency and phase, using a projection operator method, and we obtain the spatial dynamical behavior of picosecond and femtosecond pulse parameters. From our detailed analysis, we show that the stimulated Raman scattering has a strong impact on the pulse dynamics.