Philippe Gallion

Quantum phase noise and field correlation in single frequency semiconductor laser systems

The influence of quantum phase fluctuations which affect single frequency semiconductor lasers in various coherent detection systems is discussed in terms of photocurrent autocorrelation and spectral density functions. The general treatment given in this paper can be applied in diverse practical cases and points out the problems of phase correlation and phase matching between the two mixed optical beams. In the more general case the photocurrent spectrum is found to be composed of discrete and quasi-Lorentzian parts whose energies and spectral spreads are discussed as a function of the laser line width, the phase matching and the phase correlation between the two coherently combined fields.

Analysis of the phase-amplitude coupling factor and spectral linewidth of distributed feedback and composite-cavity semiconductor lasers

A Greens function approach to the analysis of semiconductor lasers is formulated in a form suitable for complex cavity structures. Both the spontaneous emission rate and the effective phase-amplitude coupling factor can be accurately evaluated. For distributed-feedback (DFB) lasers, the spontaneous emission rate is strongly dependent on both the facet reflectivities and the grating coupling coefficients. The effective phase-amplitude coupling factor depends on the wavelength detuning from the gain maximum. The calculated linewidth of DFB lasers differs considerably from previous calculated results and gives better agreement with experimental results. For composite-cavity lasers, the frequency dependence of the equivalent reflectivity has a strong impact on the phase-amplitude coupling factor and the spontaneous emission rate. Distributed Bragg reflector (DBR) lasers are investigated as an example of a composite-cavity structure. >

Phase Correlation and Linewidth Reduction of 40 GHz Self-Pulsation in Distributed Bragg Reflector Semiconductor Lasers

In this paper, self-pulsation (SP) in a distributed Bragg reflector (DBR) semiconductor laser without a saturable absorber is experimentally and theoretically investigated. Detailed experimental characterizations of the SP DBR laser are reported in the optical and radio-frequency domains. Phase correlation between the longitudinal modes selected by the DBR mirror has been experimentally demonstrated. A theoretical model based on coupled rate equations for three modes has been developed to study the time evolution of phases and amplitudes of the modes. The carrier density modulation, resulting from the beating between adjacent longitudinal modes generates four-wave mixing (FWM) and is responsible for mutual injection locking, leading to passive mode-locking. The calculated power spectral density of the frequency noise derived from the model is in agreement with experimental results and proves that the phases of the longitudinal modes are identically correlated through the FWM process in this type of SP lasers

Performance improvement of 10 Gb/s standard fiber transmission systems by using the SPM effect in the dispersion compensating fiber

The use of dispersion compensating fibers (DCFs) has now emerged as the most practical technique to compensate for the chromatic dispersion in the long-haul, optically amplified standard fiber (1.3 /spl mu/m zero dispersion) transmission systems. We investigated the effects of self phase modulation (SPM) in the standard fiber and the dispersion compensating fiber (DCF) in a repeaterless 10 Gb/s transmission system. We show that the SPM in the DCF reverses the spectral broadening in the standard fiber. We further show that the DCF length which offers the widest eye margin decreases as the launching power into the DCF is increased while the ISI penalty remains the same. This results in an increased signal-to-noise ratio (SNR) and hence improvement of the system performance.The use of dispersion compensating fibers (DCFs) has now emerged as the most practical technique to compensate for the chromatic dispersion in the long-haul, optically amplified standard fiber (1.3 μm zero dispersion) transmission systems. We investigated the effects of SPM in the standard fiber and the DCF in a repeaterless 10 Gb/s transmission system. We show that the SPM in the DCF reverses the spectral broadening in the standard fiber. We further show that the DCF length which offers the widest eye margin decreases as the launching power into the DCF is increased while the ISI penalty remains the same. This results in an increased signal-to-noise ratio (SNR) and hence improvement of the system performance.

Optical injection locking and phase-lock loop combined systems

Optical injection locking and optical phase-lock loops have been used for laser synchronization. The use of a combined optical injection locking and phase-lock loop system is proposed here. We have taken into account the modification of the slave laser phase response induced by the injection locking to calculated the phase-error signal spectrum and the phase-error variance for an optical injection locking and phase-lock system. They show that this system presents both a wide locking range, given by the optical injection locking action, and a low phase error for low frequencies, given by the optical phase-lock loop action. These results can improve the system tracking capability and decrease the final phase-error variance compared with those in isolated systems.

Modulation properties of an injection-locked semiconductor laser

The modulation properties of an injection-locked semiconductor laser are investigated using the rate equation formalism. Intensity and phase modulations (IM and PM) are analyzed throughout the locking range where the locked laser is stable. The relaxation oscillation resonance in the IM and PM frequency responses can be dramatically reduced by tuning the injected power and the frequency difference between the master laser and the free-running slave laser. The power spectra under direct modulation are derived throughout the stable locking range. The spreading of the harmonics of the modulated locked laser is strongly affected by the frequency detuning, the injected power, and the injected current modulation. Measurements illustrating the theoretical results are also presented. >

Semiconductor laser dynamics beyond the rate-equation approximation

Starting from the density-matrix equations, we have obtained a new set of generalized macroscopic Maxwell-Bloch equations for semiconductor lasers which can be used to study ultrafast phenomena at femtosecond time scales where the conventional rate equations are no longer valid. The band-structure details are included in these Maxwell-Bloch equations through two parameters κ and ζ which can be determined numerically by using their definitions or obtained experimentally by fitting the measured data. In the limit of ultrafast intraband relaxation (the rate-equation approximation), these equations reduce to the conventional rate equations. As an illustration of the usefulness of the new Maxwell-Bloch equations we have obtained the analytic expressions for several important laser parameters such as the differential gain, the linewidth enhancement factor and the nonlinear gain coefficient, in terms of the parameters κ and ζ when the semiconductor laser is operating continuously (the cw operation). The results obtained from these analytic expressions agree with those obtained numerically from the density-matrix equations under steady-state conditions by integrating over the density of states.

A generalized approach to optical low-coherence reflectometry including spectral filtering effects

In the interpretation of optical low-coherence reflectometry measurements, the reflectivity of the device under test is in general supposed to be with a slow dependency on optical wavelength. However, recent research aims at investigating strongly wavelength-dependent devices, such as fiber Bragg gratings and semiconductor lasers. In this paper, a general theory including spectral filtering effects is developed. It appears as a generalization of previously reported results only valid under special conditions.

Time-bandwidth product of chirped sech 2 pulses: application to phase-amplitude-coupling factor measurement

An exact analytical expression for the time-bandwidth product DeltatDeltaf of chirped sech(2) pulses is derived. The relation can be expressed by DeltatDeltaf = 0.1786 arcosh(cosh pialpha + 2) as a function of the lasers phase-amplitude coupling factor alpha. An experimental measurement of the alpha factor that relies on this formula is discussed.

Phase correlation between longitudinal modes in semiconductor self-pulsating DBR lasers

Phase correlation leading to self-pulsation (SP) in semiconductor distributed Bragg reflector (DBR) lasers is investigated experimentally and theoretically. Under proper biasing conditions, the laser oscillates with three main modes and we observe that each two-modes beating provides SP with identical spectral linewidth. Under the same operating conditions, the measured spectral linewidths of the beating modes are much larger than the linewidth of the self-pulsating signal. These results demonstrate the natural occurrence of passive mode-locking (PML) and phase correlation in semiconductor DBR lasers. A model based on multimode coupled-wave rate equations, including four-wave mixing (FWM), is developed to describe PML and SP in the gain region of the laser cavity. This model demonstrates that the existence of phase correlation between longitudinal modes is due to FWM.