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.

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

We investigate the occurrence of instabilities related to possible transitions to chaos in specific configurations based on semiconductor lasers. Various scenarios, such as period doubling, frequency locking, quasiperiodicity, and intermittency, are observed experimentally as functions of the control parameters. These are, respectively, the current modulation, external light injection, and delayed feedback. The experimental findings are described and discussed on the basis of semiconductor-laser rate equations.

Intensity instabilities of semiconductor lasers under current modulation, external light injection, and delayed feedback

There is a direct connection between nearly degenerate four-wave mixing in a semiconductor laser and optical modulation in the laser field. It can be understood using a model of an unlocked, optically injected laser, which emphasizes the effect of the laser resonator on the optical interactions. This model correctly describes the observed spectral characteristics and their dependence on the intrinsic parameters of the semiconductor laser. This is used to develop a simple and accurate technique using a single experimental setup for the parasitic-free characterization of the intrinsic laser parameters, including the relaxation resonance frequency, the total relaxation rate, the nonlinear relaxation rate, and the linewidth enhancement factor. Other parameters, such as the spontaneous carrier lifetime, the photon lifetime, the differential and nonlinear gain parameters, and the K factor, are determined from the power dependencies of these parameters. This technique requires only two CW lasers closely matched in wavelength and is applicable to semiconductor lasers of any wavelength and any dynamic bandwidth. >

Four-wave mixing and optical modulation in a semiconductor laser

Nondegenerate four-wave mixing is measured in the 1.5 mu m traveling-wave semiconductor optical amplifier medium as a function of the pump-probe detuning frequency ranging from a few GHz to 400 GHz. It is found that two different sources are responsible for the four-wave mixing: the carrier density modulation and the nonlinear gain effect. The latter is clearly observed when the detuning frequency increases above 100 GHz. The nonlinear gain coefficient epsilon , which induces a gain grating through the pump-probe beating, is estimated to be 1.75*10/sup -23/ m/sup 3/. The change in the real refractive index associated with the nonlinear gain effect, which generates an index grating, is negligibly small. The relaxation time involved in the nonlinear gain effect is found to be less than 0.3 ps. These results support the role of the spectral hole burning rather than the carrier heating in the nonlinear gain effect. >

Observation of highly nondegenerate four-wave mixing in 1.5 mu m traveling-wave semiconductor optical amplifiers and estimation of nonlinear gain coefficient

Injection locking of a semiconductor laser can induce major changes in the modulation characteristics of the laser. A small-signal analysis using the lumped element model shows that both the frequency and damping of the characteristic resonances of the coupled complex field and free carriers (gain medium) are modified. The detuning between the injected field and the free-running oscillating field, the amplitude of the injection field relative to the free-running field, the linewidth enhancement factor, the cavity photon and spontaneous carrier decay rates, and the field enhancement of the decay rate are all key parameters in determining the changes to the modulation characteristics. For a broad range of parameters, there is simultaneous enhancement of the modulation bandwidth and stable, locked operation. The enhancement is a cavity phenomena and does not occur in a traveling wave amplifier. It requires that the frequency of the locking field be detuned from the injection-modified frequency of the cavity resonance. This causes a resonant enhancement of the modulation sideband associated with the preferred frequency of the optical cavity. Bandwidth enhancements beyond the free-running laser limit are possible over a range of injection levels and injection frequency detunings.

Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection

Intracavity nearly degenerate four‐wave mixing has been demonstrated by injecting a low intensity probe beam of frequency ω−δω inside a (GaAl)As semiconductor laser operating above threshold at the pump frequency ω. Conjugated reflectivities as high as 5000 together with a 25% energy conversion efficiency are reported with only a few milliwatt pump power. Additional peaks related to the ac stark effect have been observed at a detuning which depended on the pump power. This process could be useful for the study of instabilities occurring in lasers as well as for optical amplification in laser diodes.

Intracavity nearly degenerate four‐wave mixing in a (GaAl)As semiconductor laser

Observation of bistable reflectivity of phase conjugated signal through intracavity nearly degenerate four-wave mixing

A high‐speed and high‐gain photodetection was experimentally demonstrated in a distributed feedback semiconductor laser amplifier by detecting its forward voltage changes induced by the injection of weak intensity modulated light. Physical phenomenon involved in the photodetection stems from the reduction of quasi‐Fermi level separation through the depletion of carrier density by optical amplification. A bandwidth as wide as 500 MHz was measured together with a narrowband spectral selectivity for the amplifier biased just below the lasing threshold. The responsivity and the noise equivalent power were found to be comparable with those of the conventional detection scheme using a similar optical preamplifier and a Ge avalanche photodetector.

High‐speed and high‐gain optical amplifying photodetection in a semiconductor laser amplifier

Optical logic functions can be obtained through nearly-degenerate four-wave mixing in laser diodes operating above as below threshold. In this nonlinear mixing process the pump frequency w is given either by laser oscillation or by amplification of an external pump signal. The conjugate frequency w + δw is then obtained by intracavity nearly-degenerate four-wave mixing when a probe beam of frequency w - δw is injected through the laser diode colinearly with the pump beam. Several examples using this technique are discussed including high contrast bistable memory, AND, OR, and INV gates.

Optical Logic Functions Using Nearly Degenerate Four-Wave Mixing In Laser Diodes

Optical logic functions using nearly degenerate four -wave mixing in laser diodesBruno ThedrezGroupe Optique des Materiaux, Ecole Nationale Superieure des Telecommunications46 rue Barrault, 75634 Paris Cedex 13, FranceHisao Nakajima(10Groupe Optique des Materiaux, Ecole Nationale Superieure des Telecommunications46 rue Barrault, 75634 Paris Cedex 13, FranceRobert FreyLaboratoire d'Optique Quantique du Centre National de la Recherche Scientifique,Ecole Polytechnique, 91128 Palaiseau Cedex, Franceand Groupe Optique des Materiaux, Ecole Nationale Superieure des Telecommunications46 rue Barrault, 75634 Paris Cedex 13, FranceAbstractOptical logic functions can be obtained through nearly- degenerate four -wave mixing in laser diodes opera-ting above as below threshold. In this nonlinear mixing process the pump frequency w is given either by laseroscillation or by amplification of an external pump signal. The conjugate frequency w + Sw is then obtainedby intracavity nearly- degenerate four -wave mixing when a probe beam of frequency w - Sw is injected throughthe laser diode colinearly with the pump beam. Several examples using this technique are discussed includinghigh contrast bistable memory, AND, OR, and INV gates.IntroductionOptical bistability in passive nonlinear Fabry -Perot cavities can easily provide all optical logic func-tions. Nevertheless, losses occurring in such dissipative nonlinear devices are a limiting factor to theirserial connectivity. Obviously, the use of amplifying nonlinear media such as lasers may circumvent this di-sadvantage since amplification occurring in the laser cavity gives output signals generally more intense thanthe input signals. Among the different lasers which can be used, semiconductor lasers are very attractive dueto their compactness. Actually such devices have been considered in hybrid configurations involving both op-tical and electronical elements112.In this paper we present an all optical technique to generate logic functions in laser diodes which as aconsequence could be integrated in cascade. This all optical technique is based on intracavity nearly- degene-rate four -wave mixing and injection locking performed in laser diodes operating above or below self lasinrithreshold. In such devices digital processing is not achieved by intensity thresholding or by directional cou-pling but rather by frequency filtering.Principle of operationIn the nearly - degenerate four -wave mixing process schematized in Figure 13.'` the pump laves of frequency w(E1 (w) and E2 (w)) are generated from the laser action itself or by amplification of the external hump signalE0(w) for a laser diode operating above or below threshold respectively. The conjugate waves of frequencyw + dw

Hisao Nakajima

Papers

Intracavity nearly degenerate four‐wave mixing in a (GaAl)As semiconductor laser

Observation of bistable reflectivity of phase conjugated signal through intracavity nearly degenerate four-wave mixing

High‐speed and high‐gain optical amplifying photodetection in a semiconductor laser amplifier

Optical Logic Functions Using Nearly Degenerate Four-Wave Mixing In Laser Diodes

() Now with the Centre National d'Etude des Télécommunicatio ns,