Longitudinal spatial hole burning and associated nonlinear gain ingain-clamped semiconductor optical amplifiers

The longitudinal spatial hole burning (LSHB) in gain-clamped semiconductor optical amplifiers (GCSOAs) is investigated by means of a numerical model, which is based on position-dependent rate equations for the carrier density and the propagation equations for the optical power. The simulation results show that the carrier densities are nonuniformly distributed within the active layer of GCSOAs. The nonuniformity can be large, especially for high currents and optical signal powers near the saturation. It is found that the LSHB induces a gain nonlinearity, which causes interchannel cross talk when GCSOAs are used in wavelength division multiplexing (WDM) applications. In order to reduce this gain nonlinearity, two methods are analyzed: the use of low resistivity devices and the use of unbalanced Bragg mirror reflectivities     

Longitudinal spatial hole burning in a quantum-dot laser

Detailed theoretical analysis of longitudinal spatial hole burning in quantum-dot (QD) lasers is given. Unlike conventional semiconductor lasers, escape of thermally excited carriers from QDs, rather than diffusion, is shown to control the smoothing-out of the spatially nonuniform population inversion and multimode generation in QD lasers. The multimode generation threshold is calculated as a function of structure parameters (surface density of QDs, QD size dispersion, and cavity length) and temperature. A decrease in the QD size dispersion is shown to increase considerably the relative multimode generation threshold. The maximum tolerable QD size dispersion and the minimum tolerable cavity length, at which lasing is possible to attain, are shown to exist. Concurrent with the increase of threshold current, an increase of the multimode generation threshold is shown to occur with a rise in temperature. Ways to optimize the QD laser, aimed at maximizing the multimode generation threshold, are outlined     

Static frequency chirping in λ/4-phase-shifteddistributed-feedback semiconductor lasers: influence of carrier-densitynonuniformity due to spatial hole burning

An experimental and theoretical study of the effect of carrier-density nonuniformity on frequency modulation (FM) characteristics of 1.3-μm λ/4-phase-shifted distributed-feedback (DFB) lasers is discussed. The static frequency chirping is measured using a recently developed method that is free from dynamical chirping as well as thermal frequency shift. The amount of chirping shows a strong dependence on the bias current level. This is explained theoretically by considering the nonuniform carrier-density distribution due to the spatial hole burning effect     

Dynamics of spatial hole burning effects in DFB lasers

A lumped small-signal model for intensity and frequency modulation response of semiconductor lasers, including the effects of longitudinal spatial hole burning (SHB), is presented. It is shown that the laser dynamics including SHB-effects can be accurately described by three small-signal rate equations. The simplicity of the model gives new insight into SHB-effects on modulation response and cavity state stability. It is shown that SHB-effects have a cut-off frequency that depends on the carrier lifetime (including stimulated recombination) and the feedback of perturbations in the longitudinal intensity distribution during modulation     

A new DFB-laser diode with reduced spatial hole burning

An index coupled antireflection-coated distributed-feedback (DFB)-laser diode which theoretically exhibits a longitudinally uniform power density is proposed. The structure contains an amplitude modulated grating and is far more efficient in reducing spatial hole burning than multiphase-shift lasers. The laser can be expected to be single mode up to high power levels. It can be of interest when long lasers with a reduced linewidth and a flat FM response are to be used or as a laser with small modulation distortion in analog communication     

Modeling temperature effects and spatial hole burning to optimizevertical-cavity surface-emitting laser performance

Two-dimensional physical models for single-mode index guided vertical cavity surface emitting lasers (VCSELs) are developed and compared with experimental measurements on state-of-the-art devices. Starting with the steady-state electron and photon rate equations, the model calculates the above threshold light-current (LI) characteristics. Included are temperature effects, spatial hole burning effects, carrier diffusion, surface recombination, and an estimation of optical losses. The model shows that the saturation of output power in the experimental devices is due to carrier leakage over the heterojunction and not simply the shifting of the gain peak relative to the cavity mode. Using the verified model new designs are analyzed, showing that output powers greater than 15 mW and power efficiencies above 20% should be achievable with existing processing technology     

Asymmetric gain induced by longitudinal spatial carrier burning in semiconductor lasers

Nonlinear gain caused by dielectric corrugation resulting from the cavity standing wave of a lasing mode in semiconductor lasers is investigated using the perturbation approach. The results show that the nonlinear gain spectrum is asymmetric when the linewidth enhancement factor alpha not=0, and the possibility of single mode operation is greater at alpha =0.<>     

Effects of spatial hole burning on gain switching invertical-cavity surface-emitting lasers

We present a numerical study of the effects of carrier diffusion and spatial hole-burning in vertical-cavity surface-emitting lasers under gain switching. Our model includes spatial and temporal dependences of both the optical field and the carrier density. Results show that spatial hole burning places a limit on the minimum achievable pulse width. We demonstrate that spatial hole-burning tan be avoided and shorter pulses can be obtained by using an appropriate pumping geometry. We also consider the case in which the laser operates simultaneously in two transverse modes and show that transverse-mode competition induced by spatial hole burning leads to period doubling and other interesting nonlinear behavior     

Self-suppression effect of longitudinal spatial hole burning inabsorptive-grating gain-coupled DFB lasers

Longitudinal spatial hole burning (LSHB) induces degradation of longitudinal-mode stability in distributed-feedback (DFB) lasers. Measurement of frequency modulation characteristics has revealed that, in absorptive-grating gain-coupled DFB lasers, the LSHB diminishes as power increases. This anomalous behavior has been qualitatively explained by a theoretical analysis that took into account the saturable nature of the absorption of the gain-coupled grating. This LSHB suppression effect is advantageous for high-power single-longitudinal-mode operation of DFB lasers     

Er-fibre lasers: suppression of spatial hole burning by internal modulation

Spatial hole burning is suppressed in linear Er/sup 3+/ fibre lasers by two alternative modulation schemes. They move the standing wave pattern, formed by the two counterpropagating waves, along the gain medium in an oscillatory or continuous way. Output bandwidths <5 kHz result.<>     

Analytical formulation of distortion and chirp in CATV DFB lasersincluding spatial hole burning

Analytical formulas for distortions permitting the calculation of composite second order (CSO) and composite triple beat (CTB) in distributed feedback (DFB) laser diodes are given, including gain compression and longitudinal spatial hole burning (LSHB). An improved chirp expression including both effects is also proposed. Gain compression is compared to LSHB over the CATV band: LSHB effects on distortion and chirp are found to be dominant in actual CATV lasers. Nonmonotonous behavior (dips) function of frequency and bias current is verified in second- and third-order distortions in agreement with recent results     

Experimental demonstration of spatial hole burning reduction leading to 1480-nm pump lasers output power improvement

Observation of spatial hole burning reduction is reported for the first time to our knowledge on flared 1480-nm high-power InGaAsP-InP buried ridge lasers. We determined the longitudinal carrier density profile by spatially resolved spontaneous emission measurements for slightly tapered and straight active waveguides. The tapered stripe shows spatial hole burning reduction leading to 25% output power enhancement.     

Role of the conductivity of the confining layers in DH-laser spatial hole burning effects

Spatial hole burning (which has been advanced as a cause of kinking, multimode operation, self-pulsation, and other effects in double heterostructure lasers) is shown theoretically to be appreciably suppressed by highly conductive confining layers.     

Gain saturation enhancement of longitudinal hole burning viastanding wave induced wave coupling in a semiconductor laser

It is shown by a simple theoretical model that the large scale longitudinal hole burning in a semiconductor laser will enhance by about 2.6 times the gain saturation caused by the cavity standing wave induced wave coupling     

Spectral hole burning in dye solutions

Using picopulses generated by a mode-locked ruby laser, we have measured the 3-8-Å bandwidth of a hole burned in the 0-0 transition of cryptocyanine in methanol and demonstrated the inhomogeneous chatacter of this transition. The population-rate equations are written for an inhomogeneous transition with two and four energy levels interacting with continuous or pulsed excitation. Using the numerical solutions of this model together with the experimental result we determine a transverse relaxation timeT_{2} = 0.6-1ps for cryptocyanine in methanol.     

Dynamics of spectral hole burning

A model calculation is presented that describes the features of spectral-hole burning measurements performed under conditions of femtosecond transient excitation and probing. Pump-induced changes in the spectrum of probe transmittance arise not only from changes in level population (hole burning), but also from the presence of pump polarization during the probe, and from perturbations of the decay of the probe polarization. These latter effects give rise to oscillating differential transmittance spectra when the (shorter) probe pulse arrives prior to the peak of the pump noise. Only when the probe pulse follows the bulk of the pump pulse does the level population effect dominate the spectrum, so that one can observe dynamic hole-burning effects without distortion     

Detailed model and investigation of gain saturation and carrier spatial hole burning for a semiconductor optical amplifier with gain clamping by a vertical laser field

A detailed model for semiconductor linear optical amplifiers (LOAs) with gain clamping by a vertical laser field is presented, which accounts the carrier and photon density distribution in the longitudinal direction as well as the facet reflectivity. The photon iterative method is used in the simulation with output amplified spontaneous emission spectrum in the wide band as iterative variables. The gain saturation behaviors and the noise figure are numerically simulated, and the variation of longitudinal carrier density with the input power is presented which is associated with the on-off state of the vertical lasers. The results show that the LOA can have a gain spectrum clamped in a wide wavelength range and have almost the same value of noise figure as that of conventional semiconductor optical amplifiers (SOAs). Numerical results also show that an LOA can have a noise figure about 2 dB less than that of the SOA gain clamped by a distributed Bragg reflector laser.     

Spectral hole burning in erbium-doped fiber amplifiers

A new theoretical/numerical model of the spectral hole burning (SHB) effect in erbium-doped fiber amplifiers (EDFAs) is suggested. A new measurement technique for SHB measurement is developed. Experiments are conducted to identify the particular mechanism of SHB. A computer simulation program is developed using this approach. The shape and depth of the spectral hole are in accordance with the suggested theory.     

Well-barrier hole burning in quantum well lasers

The reported wide variations in the damping behavior of quantum well lasers are explained by a novel theory of nonlinear gain, well-barrier hole burning. In the model a spatial hole develops perpendicular to the active region involving carriers moving between the wells and the barrier/confinement layers. The modified rate equations describing well-barrier hole burning are presented. An analytical approximation for the nonlinear gain coefficient epsilon , valid only under certain conditions, is given. A numerical solution is given for the case of high photon densities and large capture-times. It is shown how well-barrier hole burning explains the measurements of the increased spontaneous emission from the barrier/confinement region above threshold. Various higher-than-expected damping rates reported in some quantum well lasers are shown to be consistent with the model.<>     

Numerical analysis of static wavelength shift for DFB lasers with longitudinal mode spatial hole burning

The static wavelength shift induced by longitudinal mode spatial hole burning is analyzed numerically for lambda /4-shifted DFB lasers. The effective Bragg wavelength at each bias level is introduced to clarify the contribution of nonuniformity in carrier density distribution to the lasing wavelength shift. It is shown that the wavelength shift is caused by two separate factors: by the position-dependent deviation and by the average value in the exact N/sub eq/ distribution. The former factor induces both red- and blue-shifted tuning due to the nonuniformity itself in carried density distribution, while the latter results in blue-shifted tuning due to the increase in modal gain.<>