1388 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 11, NOVEMBER 2003 Dispersion-Induced Ultrafast Pulse Reshaping in 1.55- m InGaAs–InGaAsP Optical Amplifiers Jian-zhong Zhang, Javier Molina Vázquez, Michael Mazilu, Alan Miller, Fellow, IEEE, and Ian Galbraith Abstract—Using the Foreman effective mass Hamiltonian, the electronic structure of the valence band and the interband dipole matrix elements in In Ga As–In Ga As P quantum-well optical amplifiers are calculated, taking into account the valence band mixing and the biaxial strain. The optical field of the amplified pulse is calculated by solving the wave equation with the computed polarization as a source term. A novel wavelet transform is introduced in analyzing the pulse chirp imposed by the optical amplifier. In the linear propagation regime, the spectrum of the amplified pulse can be either red-shifted or blue-shifted with respect to its initial center frequency, depending on the local gain dispersion spanned by the pulse spectrum. The output pulse shape can be retarded or advanced, depending on the local gain and group velocity dispersion. Furthermore, an initially unchirped pulse centered in the tail of the gain spectrum is significantly reshaped after propagating 600 m, and its spectrum is broadened and distorted considerably. In the spectral region where both gain and group velocity change rapidly, the frequency chirp for a linearly chirped input pulse is significantly weakened after propagation. Index Terms—Band structure, frequency chirp, gain dispersion, group velocity dispersion, pulse propagation, semiconductor op- tical amplifier (SOA), wavelet transform. I. INTRODUCTION O PTICAL amplification is an important ingredient in photonic technologies such as wavelength division multiplexing to overcome optical fiber transmission loss. One potential candidate for such broad-band applications is the semiconductor optical amplifier (SOA), in which the facet re- flectivities are reduced below 0.1% by the use of anti-reflection (AR) coatings, and the active region can be lengthened to have sufficient gain. Devices with active regions as long as 2 mm are available [1]. Due to their large gain bandwidth, such amplifiers can amplify subpicosecond duration pulses. The main disad- vantage of SOAs in applications for ultrafast data processing and optical communication systems is that they usually have polarization-dependent gain characteristics due to different dipole oscillator strengths of transverse electric (TE) modes and transverse magnetic (TM) modes. Some progress toward polarization-insensitive quantum-well (QW) amplifiers has been made [2]–[5] but this remains an important issue. From a theoretical viewpoint, the investigation of pulse propagation is Manuscript received November 4, 2002; revised July 8, 2003. This work was supported by the EPSRC project “The Ultrafast Photonics Collaboration.” J. Zhang, J. M. Vazquez, and I. Galbraith are with the School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, U.K. M. Mazilu and A. Miller are with the School of Physics and Astronomy, Uni- versity of St. Andrews, North Haugh, St. Andrews KY16 9SS, U.K. Digital Object Identifier 10.1109/JQE.2003.818308 also of interest, because it interconnects optical field-medium interactions, carrier dynamics, polarization dynamics, and Coulomb processes. There has been some experimental and theoretical work on pulse propagation in SOAs, but mostly devoted to the nonlinear effects on pulse amplification involving carrier dynamics [6]–[9]. Relatively few experimental measurements are performed in the linear regime, using pulses with small pulse energy compared to the saturation energy into SOAs [10]–[13]. It seems, in general, an accepted fact that in the linear propagation regime an input pulse can be amplified without any distortion as long as its spectrum lies within the amplifier bandwidth. However, this is true only when the gain and refractive index dispersion of the active medium is negligible over the region of the pulse spectrum. Indeed, in the experiments [10]–[13], the pulses were found to be amplified without much distortion as all the pulses used have durations longer than 3 ps and thus a narrow spectrum. From a practical viewpoint, the investigation of pulse amplification in the linear regime is of interest, as, for many applications such as data communications, the linear regime is the most controllable and useful for systems applications. So far, most theoretical pulse propagation studies have been focused on bulk SOAs; to the best of our knowledge, no studies on pulse propagation in the SOAs with QW structures have been reported. It is known that short pulses even in the linear regime will be modified by the amplifier. However, quantitative investigations of such modifications for QW SOAs have not been reported. The objective of this paper is to quantify how the dispersion of gain and refractive index of a QW SOA affects the temporal shape, spectrum, and frequency chirp of a propagating ultrashort pulse. As the gain and the refractive index are interrelated via the Kramers–Kronig relation, gain dispersion is accompanied by group velocity dispersion. Therefore, special attention in this work is paid to the effects on pulse amplification of the interplay between gain dispersion and group velocity dispersion. Such an investigation is of particular interest as it is based on the band structure calculations for a realistic 1.55- m QW SOA device. The physical mechanism behind frequency chirp is that different frequency components of a pulse propagate at different veloci- ties because of index dispersion, and, as a result, a time-depen- dent phase is evolved during propagation even if the input pulse has a constant phase. Microscopically, pulse propagation is de- termined by the gain and refractive index dynamics, which de- pends on the band structure; the carrier inversion and the dipole matrix elements. This paper is organized as follows. In Section II, the calcu- lation of the electronic band structure is described, accounting 0018-9197/03$17.00 © 2003 IEEE