Govind P. Agrawal

Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers

Amplification of ultrashort optical pulses in semiconductor laser amplifiers is shown to result in considerable spectral broadening and distortion as a result of the nonlinear phenomenon of self-phase modulation (SPM). The physical mechanism behind SPM is gain saturation, which leads to intensity-dependent changes in the refractive index in response to variations in the carrier density. The effect of the shape and the initial frequency chirp of input pulses on the shape and the spectrum of amplified pulses is discussed in detail. Particular attention is paid to the case in which the input pulsewidth is comparable to the carrier lifetime so that the saturated gain has time to recover partially before the trailing edge of the pulse arrives. The experimental results, performed by using picosecond input pulses from a 1.52- mu m mode-locked semiconductor laser, are in agreement with the theory. When the amplified pulse is passed through a fiber, it is initially compressed because of the frequency chirp imposed on it by the amplifier. This feature can be used to compensate for fiber dispersion in optical communication systems. >

Nonlinear optical phenomena in silicon waveguides: Modeling and applications

Focus Serial: Frontiers of Nonlinear Optics Several kinds of nonlinear optical effects have been observed in recent years using silicon waveguides, and their device applications are attracting considerable attention. In this review, we provide a unified theoretical platform that not only can be used for understanding the underlying physics but should also provide guidance toward new and useful applications. We begin with a description of the third-order nonlinearity of silicon and consider the tensorial nature of both the electronic and Raman contributions. The generation of free carriers through two-photon absorption and their impact on various nonlinear phenomena is included fully within the theory presented here. We derive a general propagation equation in the frequency domain and show how it leads to a generalized nonlinear Schrodinger equation when it is converted to the time domain. We use this equation to study propagation of ultrashort optical pulses in the presence of self-phase modulation and show the possibility of soliton formation and supercontinuum generation. The nonlinear phenomena of cross-phase modulation and stimulated Raman scattering are discussed next with emphasis on the impact of free carriers on Raman amplification and lasing. We also consider the four-wave mixing process for both continuous-wave and pulsed pumping and discuss the conditions under which parametric amplification and wavelength conversion can be realized with net gain in the telecommunication band.

Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers

The theory of nondegenerate four-wave mixing (NDFWM) in semiconductor lasers and amplifiers is presented with particular emphasis on the physical processes that lead to population pulsations. In the case of nearly degenerate four-wave mixing, modulation of the carrier density at the beat frequency Ω of the pump and probe waves creates a dynamic population grating whose effectiveness is governed by the spontaneous carrier lifetime τs. Such a grating affects both the gain and the refractive index of the probe wave. In particular, the probe gain exhibits features analogous to those observed in a detuned atomic system arising from the optical Stark effect. Both the gain grating and the index grating contribute to NDFWM, with the dominant contribution coming from the index grating. For detunings such that Ωτs ≫ 1, population pulsations correspond to modulation of the intraband population arising from spectral hole burning. Our results show that NDFWM is then limited by the phase-mismatch effects governed by the transit time τ rather than by the intraband population-relaxation time T1. Significant NDFWM is expected to occur for detunings up to about 300 GHz for typical transit-time values of 3 psec in semiconductor lasers.

Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing

It is shown that the transmission spectrum of a fiber Bragg grating can be tailored by incorporating single or multiple phase-shift regions during the fabrication process. Phase shifts open up narrowband transmission windows inside the stop band of the Bragg grating; transmitted wavelength can be changed by adjusting the amount of phase shift. As a specific application, we discuss how phase-shifted Bragg gratings can be used to make an all-fiber demultiplexer for multichannel lightwave systems.<<ETX>>

Impact of two-photon absorption on self-phase modulation in silicon waveguides

We study the effects of two-photon absorption on the self-phase modulation (SPM) process in silicon waveguides while including both free-carrier absorption and free-carrier dispersion. An analytical solution is provided in the case in which the density of generated carriers is relatively low; it is useful for estimating spectral bandwidth of pulses at low repetition rates. The free-carrier effects are studied numerically with emphasis on their role on the nonlinear phase shift and spectral broadening. We also consider how the repetition rate of a pulse train affects the SPM process.

Soliton fission and supercontinuum generation in silicon waveguides.

We show through numerical simulations that silicon waveguides can be used to create a supercontinuum extending over 400 nm by launching femtosecond pulses as higher-order solitons. The physical process behind continuum generation is related to soliton fission, self-phase modulation, and generation of Cherenkov radiation. In contrast with optical fibers, stimulated Raman scattering plays little role. As low-energy (approximately 1 pJ) pulses and short waveguides (<1 cm) are sufficient for continuum generation, the proposed scheme should prove useful for practical applications.

Ultrabroadband parametric generation and wavelength conversion in silicon waveguides

We show that ultrabroadband parametric generation and wavelength conversion can be realized in silicon waveguides in the wavelength region near 1550 nm by tailoring their zero-dispersion wavelength and launching pump wave close to this wavelength. We quantify the impact of two-photon absorption, free-carrier generation, and linear losses on the process of parametric generation and show that it is difficult to realize a net signal gain and transparent wavelength conversion with a continuous-wave pump. By investigating the transient dynamics of the four-wave mixing process initiated with a pulsed pump, we show that the instantaneous nature of electronic response enables highly efficient parametric amplification and wavelength conversion for pump pulses as wide as 1 ns. We also discuss the dual-pump configuration and show that its use permits multiband operation with uniform efficiency over a broad spectral region extending over 300 nm.

Gain nonlinearities in semiconductor lasers: Theory and application to distributed feedback lasers

The gain spectrum in semiconductor lasers is affected by the intensity-dependent nonlinear effects taking place due to a finite intraband relaxation time of charge carriers. We obtain an analytic expression for the nonlinear gain in multimode semiconductor lasers using the density-matrix formalism. In general, the nonlinear gain is found to consist of the symmetric and asymmetric components. The asymmetry does not have its origin in the carrier-induced index change, but is related to details of the gain spectrum. The general expression for the nonlinear gain is used to discuss the range of single-longitudinal-mode operation of distributed feedback lasers. It is also used to obtain an analytic expression for the self-saturation coefficient and to compare the predicted value to the experimental value for both GaAs and InGaAsP lasers. The agreement between the theoretical and the experimental values supports the hypothesis that spectral hole burning is the dominant mechanism for the gain nonlinearities in semiconductor lasers.

Line narrowing in a single-mode injection laser due to external optical feedback

The effect of external optical feedback on the linewidth of a single-mode injection laser is considered theoretically. A set of three rate equations with Langevin noise sources is used to obtain the power spectrum. If the high-frequency structure in the power spectrum is ignored, the line shape is Lorentzian and exhibits broadening or narrowing depending on the external-cavity phase shift. Particular attention is paid to the line narrowing after including the effect of carrrier-induced index changes.

Gaussian beam propagation beyond the paraxial approximation

The propagation of a Gaussian beam in a homogeneous, isotropic, local, linear, and nonmagnetic dielectric medium is studied using the angular spectrum representation for the electric field. The electric field associated with the Gaussian beam inside the dielectric medium consists of the paraxial result and higher-order non-Gaussian correction terms. It is shown that the second-order correction term satisfies an equation consistent with the recent work of Lax, Louisell, and McKnight. Numerical results showing the corrections to the paraxial approximation are presented.