Analytical model of a semiconductor optical amplifier

The spatial dependence of the material gain is introduced in the model of a semiconductor optical amplifier. Analytical expressions of the profiles of the carrier density, spontaneous emission, and amplified fields are obtained for amplifiers with arbitrary facet reflectivities. The nonuniformity of the carrier density is demonstrated in the case of low facet reflectivities. The model predicts the output saturation power and gain ripple, with good agreement with experimental results in resonant and traveling-wave amplifiers. Very low-gain ripple measured in low facet reflectivities amplifiers is explained by the model. A comparison with the uniform gain model shows that important deviations can occur in the case of low facet reflectivities. It is also shown that with the currently achievable low facet reflectivities, the maximum available gain is limited by spontaneous emission     

Analysis of the phase-amplitude coupling factor and spectrallinewidth of distributed feedback and composite-cavity semiconductorlasers

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     

Diagnostics of asymmetrically coated semiconductor lasers

The authors present a simple diagnostic procedure for lasers that have a priori unknown facet reflectivities. The most important laser parameters that can be extracted are the cavity decay rate Gamma /sub c/ (equal to the inverse of the photon lifetime), the mirror loss coefficient alpha /sub m/ identical to -1/2 L In R/sub 1/R/sub 2/, the internal loss coefficient alpha /sub i/, the facet reflection coefficients R/sub 1/ and R/sub 2/, the spontaneous emission factor n/sub sp/, and the differential gain xi /sub l/. The authors have verified the procedure by applying it to lasers with a priori known facet reflection coefficients, these lasers were weakly index guided (VSIS and CSP types).<>     

Fundamental limits of sub-ps pulse generation by active modelocking of semiconductor lasers: the spectral gain width and the facetreflectivities

The authors present a numerical simulation of active mode locking of a semiconductor laser amplifier (SCLA) in an external cavity, which includes the finite spectral gainwidth. This is shown to be essential for introducing a lower limit of the pulsewidth, although the gain linewidth is about a factor of 10-50 broader than the inverse pulsewidth. This numerical treatment consistently explains the experimental findings that even SCLA facet reflectivities as low as 10 ^-4 lead to trailing pulses with an intensity almost of the same order of magnitude as the leading one. This theory makes detailed predictions about the influence of the facet reflectivities, the spectral gainwidth, and the injection current on the picosecond pulse generation     

Deposition and measurements of electron-beam-evaporated SiOx antireflection coatings on InGaAsP injection laser facets

In situ-monitored electron-beam-evaporated nonstoichiometric silicon monoxide (SiO_x) antireflection coatings on 1.5-μm laser facets are described. Reflectivities of 0.05% are demonstrated on devices with one facet coated, and mean reflectivities of 0.07% are demonstrated for traveling-wave amplifiers with both facets coated. The polarization-dependent reflectivities were measured at several wavelengths for both device types and were found to be broad-band (R <0.1% over an approximate wavelength range of 400 Å). The reflectivities obtained using measurements of the noise and gain spectra were compared. The use of the noise spectrum was found to underestimate the reflectivities, especially in measurements of the wavelength-dependent reflectivity over a wide wavelength range and in measurements of devices with both facets coated (traveling-wave amplifiers)     

Accuracy of Fabry-Perot method of semiconductor laser gain measurement

The Fabry?Perot (FP) method of semiconductor laser gain measurement, first proposed by Hakki and Paoli (1975), is widely used. It is based on the measurement of the FP resonances excited by spontaneous emission. Its validity rests on the assumption that a single mode is significant. We show, using a simplified laser model, that this assumption is valid only when the power mirror reflectivity is very small, or near the laser oscillating frequency. For example, the error is in the order of 20% when the power facet reflectivities are equal to 37% and the modal gain is unity. These results apply to both index-guided and gain-guided lasers.     

Photonic switching modules designed with laser-diode amplifiers

Photonic switching elements are designed from semiconductor optical amplifiers and passive couplers with fiber-to-fiber unity gain and low crosstalk. Designs for a 2×2 and an asymmetric 2×3 element, and several designs for 4×4 elements, are presented. While most amplifier analyses have stressed the importance of ultralow facet reflectivities for high-gain operation, with protection against external reflections with optical isolators, modest facet reflectivities are satisfactory for these elements. It is also shown that substantial amounts of external reflection can be tolerated. The various architectures are compared according to amplifier count, blocking characteristic, broadcast potential, noise power (amplified spontaneous emission), and fault tolerance     

Transfer-matrix formulation of spontaneous emission noise of DFBsemiconductor lasers

A unified formulation of the spontaneous emission noise in semiconductor DFB (distributed feedback) lasers is presented by using a transfer-matrix approach. Analytical expressions for the noise power per unit frequency bandwidth below threshold and the spontaneous emission rate into the lasing mode are obtained based on the Green's function method. Three DFB laser structures are analyzed: (1) a standard DFB structure with facet reflectivities, (2) a multisection DFB structure composed of n sections which models a phase-shifted DFB laser and a multielectrode (tunable) DFB laser, and (3) a periodic layered DFB structure which models a surface-emitting DFB laser. It is shown that the spontaneous emission noise of a complicated DFB laser structure can be calculated easily by the transfer matrix of each section of the structure and its derivative to frequency     

Facet reflectivity of a spot-size-converter integratedsemiconductor optical amplifier

Traveling-wave type semiconductor optical amplifiers (SOAs) integrated with a spot-size-converter (SSC) are extensively studied for improvement of coupling efficiency with single-mode fibers and for cost reduction in packaging. In this paper, the structural dependence of the SSC on effective facet reflectivity R_eff is investigated theoretically and experimentally. It is shown that, not only sufficient mode-conversion in the SSC region, but also the introduction of angled facets, are essential for reducing R_eff. A small gain ripple (less than 0.1 dB) in an amplified spontaneous emission (ASE) spectrum, fiber-to-fiber gain of 26 dB, and saturation output power of 7 dBm are observed for the fabricated SOA, which consists of a window length of 20 μm, facet angle of 7°, and anti-reflection coated facet of less than 1% reflectivity     

Analytical model of a superluminescent diode

Using a set of traveling wave rate equations ,a superluminescent diode with a low facet reflectivity is studied .Analytical expressions of the distribu-tions of carrier density ,forward-and backward-propagation photon densities,and gain are obtained at different facet reflectivities.It is shown that the high nonuni-form carrier distribution is evident in the case of low facet reflectivity.The results can serve as useful guides in understanding emission mechanism of superlumi-nescent diodes.     

Analytical model of a superluminescent diode

ＡｎａｌｙｔｉｃａｌｍｏｄｅｌｏｆａｓｕｐｅｒｌｕｍｉｎｅｓｃｅｎｔｄｉｏｄｅＭＡＤｏｎｇｇｅ；ＳＨＩＪｉａｗｅｉ；ＧＡＯＤｉｎｇｓａｎ（Ｄｅｐｔ．ｏｆＥｌｅｃ．Ｅｎｇ．，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ１３００２３，ＣＨＮ）Ａｂｓ...     

Pulse buildup dynamics of an actively mode-locked laser diode arrayin the external cavity

Dynamic pulse evolution characteristics of an actively mode-locked laser diode array in the external cavity have been investigated. Numerical calculations based on modified traveling-wave rate equations reproduce experimentally observed pulse and spectral width evolution and show that the buildup time is about 45 round-trips. We have also performed a theoretical analysis to understand which of the laser operating parameters would affect the buildup dynamics. It is shown that either higher dc bias current or larger radiative recombination coefficient (which is inversely proportional to the excited-state lifetime) will render the laser exhibiting shorter steady-state pulse width and faster evolution to the steady state. Other parameters affecting the buildup, but to a lesser extent, include the radio-frequency (RF) modulation current, spontaneous emission coefficient, and gain coefficient. The power reflectivities of the output mirror and the antireflection coated diode facet, on the other hand, have little effect on the pulse width and buildup time for single pulse generation     

Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers

A theory of spontaneous emission noise is presented based on classical electromagnetic theory. Unlike conventional theories of laser noise, this presentation is valid for open resonators. A local Langevin force is added to the wave equation to account for spontaneous emission. A general expression is found relating the diffusion coefficient of this force to the imaginary part of the dielectric function. The fields of lasers and amplifiers are found by solving the wave equation by the Green's function method. The lasing mode is a resonant state associated with a pole in Green's function. In this way, noise in lasers and amplifiers is treated by a unified approach that is valid for either gain guiding or index guiding. The Langevin rate equations for the laser are derived. The theory is illustrated with applications to traveling wave and Fabry-Perot amplifiers and Fabry-Perot lasers. Several new results are found: optical amplifier noise increases inversely with quantum efficiency; spontaneous emission into the lasing mode is enhanced in lasers with low facet reflectivities; and the linewidth of a Fabry-Perot laser with a passive section decreases as the square of the fraction of the cavity optical length that is active.     

Nearly degenerate four-wave mixing in laser diodes subject tostrong probe injection power

Nearly degenerate four-wave mixing (FWM) in above-threshold laser diodes with symmetric or asymmetric facet reflectivities, subject to strong probe injection power, is investigated theoretically, taking into account the effects of pump depletion, carrier diffusion, gain saturation, gain compression, total power dependence of the gain and coupling coefficients as well as the longitudinal dependence of the nonlinear interaction. It is shown that the reflectivity efficiencies of probe and conjugate waves demonstrate significantly different behaviors for strong probe injection power, compared to small probe injection power, and a greater than 3 dB enhancement of reflectivity efficiencies can be achieved in an asymmetric laser diode, compared to a symmetric laser     

Analytic description of a homogeneously broadened injection laser

Analytic expressions for modeling the steady-state spectral output of homogeneously broadened lasers are presented. The expressions define the laser output in terms of the pumping rate, resonator reflectivities, arbitrary gain, spontaneous emission, and saturation profiles for each mode. To derive the analytic expressions the laser is idealized as a homogeneously broadened amplifier contained by a plane-parallel Fabry-Perot resonator. Rate equations are used to describe the interaction of the laser-mode intensities and population inversion over an infinitesimal section of the amplifier and differential equations describing the amplification of the modes as they pass through the gain section are deduced. Exact analytic solutions to these differential equations are found. These solutions, along with the boundary conditions imposed by the resonator, are used to specify completely the output of the laser. The model predicts a single-pass intensity gain which increases exponentially with pumping below threshold and saturates above threshold. An interesting result is that for a laser which is symmetric, an analysis which takesI^{+} = I^{-} = I, whereI^±are intensities traveling in the ± direction, gives results identical to an analysis which explicitly considers bothI^{+}andI^{-}, irrespective of the resonator mirror reflectivities. The predictions of the model are compared to the spectral output and single-pass intensity gain of a GaAs diode laser and found to be in good agreement. The laser model may be generalized in a straightforward manner to include feedback, compound cavities, and optical amplifiers.     

半导体光放大器啁啾特性分析

改进了分析行波半导体光放大器啁啾特性的理论模型,其中考虑了有限的端面反射率和自发辐射。理论研究表明,这些因素的引入将减小光放大器附加到放大光脉冲上的非线性频率啁啾。     

Yield analysis of non-AR-coated DFB lasers with combined index and gain coupling

The threshold gain difference for DFB lasers with various degrees of gain coupling and different strengths of facet reflectivities is calculated as a function of the random phases between grating and facet reflectivities. From this, the yield for single mode behaviour is determined. It is shown that even for cleaved facets a relevant improvement in terms of threshold gain difference is obtained by introducing a small fraction of gain coupling.<>     

Amplified spontaneous emission effects in semiconductor laseramplifiers

The analysis presented provides a quantitative method for predicting semiconductor laser amplifier performance in the presence of ASE (amplified spontaneous emission). It indicates that in order to increase the fraction of pump power that contributes to the amplification of the input laser field relative to that spent in overcoming internal losses, an amplifier should operate at as high an excitation level as possible. This may mean operating an amplifier above its free-running oscillation threshold. A limitation to the maximum pump power is the increase in ASE. With too high an excitation, ASE dominates over the amplified input laser field, resulting in a quenching of the amplifier gain, efficiency and coherence. ASE effects may be mitigated by increasing the input laser intensity, decreasing the amplifier facet reflectivities, or, in some cases, tuning the master oscillator so that it is resonant with the amplifier. The analysis indicates that minimizing the facet reflectivity is the most effective way to circumvent ASE limitations to power scaling semiconductor laser amplifiers     

Analysis and application of theoretical gain curves to the design of multi-quantum-well lasers

Gain/current curves for a single quantum well are calculated. The optimum well number, cavity length, threshold current, and current density of multi-quantum-well (MQW) lasers are derived in terms of this gain curve. The limiting performance of MQW lasers is found to be better than that of graded refractive index (GRIN) lasers, assuming comparable efficiencies and spontaneous emission linewidths. The optimum threshold current for an MQW laser with a 7 μm cavity and 90 percent facet reflectivity issim50 muA/μm.     

Length dependence of threshold current in multiple quantum welllasers

The threshold current density of single-quantum-well lasers increases at short laser lengths more rapidly than for multiple-well lasers. Using microscopic gain calculations, these differences are shown to be a natural consequence of the nonlinear gain/current relation associated with high electron concentrations in thin wells. The threshold current shows a minimum that depends on facet reflectivities and number of wells