Phase-amplitude Coupling Factor Research Articles

Fuzzy logic approach to Henry factor for distributed feedback laser case

In this study, a simple approach for intelligent modeling of the Henry factor (\alpha-alpha parameter, antiguiding factor, phase-amplitude coupling factor) or the so-called linewidth enhancement factor, which is an actual analysis and design parameter for semiconductor laser diodes and optical communication systems, is proposed based on the fuzzy logic (FL) phenomenon. The proposed FL-based model easily computes the Henry factor in terms of different wavelengths and injection current levels (i.e. the inputs of the model). The experimental data belong to a distributed feedback laser, obtained from amplified spontaneous emission spectra, which is among the techniques required for the characterization of semiconductor lasers. For the Henry factor, the suggested method's approximation provides predictions within the accuracy level of 95%--99.99%.

Numerical analysis of SOA performance over a wide optical bandwidth in a CO-OFDM transmission system

We present a numerical analysis of the impact of the optical amplification by semiconductor optical amplifiers (SOAs) in a Coherent Optical-Orthogonal Frequency Division Multiplexing transmission link at 100 Gb/s. The numerical modeling of SOA is developed to be able to simulate all of nonlinear effects of the SOA, particularly four-wave mixing effect. This model is integrated into a co-simulation platform to perform a simulation at a system level. Error Vector Magnitude (EVM) measurement is given with respect to the number of subcarriers and phase-amplitude coupling. We show also the dependence of the EVM at the signal wavelength by performing our simulations on a wide optical bandwidth, taking into account the main parameters of the SOA—such as the phase-amplitude coupling factor, the saturation power and the noise figure—that influence the non-linear effects.

Classical theory of laser linewidth

The classical theory of light fluctuations rests on the intuitive concept that jumps between atomic states occur at independent times when the optical field has a prescribed value. The statistical properties of phase-noise sources are obtained in the present paper by applying this principle to detuned atoms. Formulae for amplitude and phase fluctuations coincide with quantum-theory results even when ‘non-classical’ states of light are generated. Theories employing semiclassical or quantum concepts are reviewed. We consider particularly the linewidth of laser oscillators operating below and above threshold when the atomic polarization cannot be adiabatically eliminated. Quantum-theory results by Lax (1966) are recovered from classical theory in a straightforward manner. More general results are given for dispersive loads, applicable to external-cavity lasers and relevant to gain guidance. It is emphasized that the K-factor as calculated by Petermann is applicable only below threshold. When more than one emitting element is present, population rate equations need to be considered and the linewidth decreases when the pump fluctuations are suppressed. The role of gain compression relating to semiconductor lasers is discussed. It is shown that at low and moderate powers gain compression reduces the effective phase-amplitude coupling factor, α. But at high power a number of mechanisms contribute to linewidth rebroadening. One of them is the statistical (quasi-thermal equilibrium) fluctuation of the refractive index. General concepts applicable to broadband light are outlined in an appendix.

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

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 laser's phase-amplitude coupling factor alpha. An experimental measurement of the alpha factor that relies on this formula is discussed.

Optimum conditions for soliton launching from chirped sech^2 pulses

Simple and exact analytical formulas are derived for the optimum power and width of chirped sech2 pulses that maximize the energy transfer to the fundamental soliton. The maximum achievable energy transfer is shown to be equal to 2/(1+1+α2), normalized relative to the initial pulse energy, where α is the laser phase-amplitude coupling factor. The critical values of the α factor for the fundamental soliton are given simply in terms of the normalized pulse amplitude A by αcr = (4A2 − 1)1/2.

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 laser's phase-amplitude coupling factor alpha. An experimental measurement of the alpha factor that relies on this formula is discussed.

Measurement of the effective phase-amplitude coupling factor /spl alpha//sub eff/ of high speed semiconductor optical amplifier modulator

A semiconductor optical amplifier has been used as an external modulator. The large signal response has shown a 3-dB bandwidth of 3.1 GHz when the amplifier was saturated by the input optical wave. Moreover, the effective phase-amplitude coupling factor, which is a typical parameter of a semiconductor optical amplifier, was measured to be 8.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Propagation of single-mode 1.5-μm gain-switched semiconductor laser pulses in normally dispersive fibers

The behavior of gain-switched semiconductor laser pulses propagating in normally dispersive fibers is analyzed both theoretically and experimentally. A simple gain switch model is analytically derived from rate equations including gain compression effects in order to predict the instantaneous optical intensity and frequency during the pulse. A great deal of attention is given to the phase equation. It is shown that carrier dependence of the phase-amplitude coupling factor /spl alpha/ must be taken into account to accurately describe experiments. By means of an Er/sup 3+/ doped amplifier, nonlinear propagation of such pulses in normally dispersive fibers is experimentally studied for various peak powers up to 3.2 W. Large Kerr-induced spectrum narrowing is demonstrated together with the production of pulses of adjustable width from 3 to 12 ps. Corresponding time-bandwidth products measured between 0.4 and 0.8 are close to the Fourier transform limit. These results are successfully compared to theory by means of computer simulation involving both the gain-switch model and the nonlinear propagation in the fiber. >

Phase-amplitude coupling factor of single-mode gain-switched InGaAsP laser diodes

The phase amplitude coupling factor ( alpha -factor) of gain-switched InGaAsP laser diodes is deduced from chirp measurements. A tunable laser scheme makes it possible to obtain the wavelength dependence of alpha over approximately 40 nm. The alpha -values are found to be higher than those deduced from spontaneous emission spectra below threshold. It is shown that the difference is explained by the dependence of alpha with carrier density. Time-resolved measurements of spontaneous emission during pulse buildup reveal that the carrier density at maximum can be 1.5 times higher than the threshold carrier density. Experimental evolutions of alpha are well reproduced by calculations. >

Very narrow-linewidth (70 kHz) 1.55 μm strained MQW DFB lasers

A linewidth as narrow as 70 kHz together with a linewidth-power product of 0.2 MHz.mW have been achieved on 1450 μm long compressively strained quantum well uniform DFB lasers. The results are achieved through a reduction of the phase-amplitude coupling factor, which is measured to be 1.7 times lower than in unstrained devices.

Gain compression and phase-amplitude coupling in GaInAs quantum well lasers with three, five and seven wells

The gain compression and phase-amplitude coupling factors are measured along with the differential gain in GaInAs/GaInAsP quantum well lasers with three, five and seven wells. Results are compared with those obtained for a conventional bulk laser of the same quaternary material. The ultimate modulation bandwidth deduced from the measurements is shown to increase with the number of wells. For the seven well laser, the ultimate modulation bandwidth is found to reasonably approach that obtained for the bulk laser while the phase-amplitude coupling factor is 2.6 times smaller.

Evaluation of semiconductor optical parameters for laser diodes

The small-signal modulation and noise properties (electrical voltage, optical power and phase) of laser diodes depend on ten real parameters relating to the semiconductor material employed. Among these, the phase-amplitude coupling factor α is of particular importance. These parameters are evaluated for GaAs at 0.87μm, GaInAsP at 1.55 μm and InAsSb at 3.87 μm at room temperature. Revised expressions for the optical gain are used. The light-hole contribution, the plasma effect and band-gap shrinkage are taken into account. The latter leads to a significant reduction of α, particularly below the peak-gain frequency. The α-factors for the three materials listed above are found to be, respectively, 2.9, 3.85 and 8.3 for conventional diodes.

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

A Green's 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.

Multielement laser-diode linewidth theory

A simple formula is presented for the linewidth-power product of multielement laser diodes, under the condition that the active elements are submitted to the same field. The theory is particularly applicable to laser diodes incorporating two thin active layers of different composition. Such diodes can be modeled by two active conductances in parallel with a linear admittance. If the injected current exhibits full shot noise, the laser linewidth is given by the same expression as for a single active element, except that alpha and alpha(2) must be replaced by their average values weighted by the injected bias currents, where alpha denotes the phase-amplitude coupling factor. The same result is applicable to conventional index-guided laser diodes.