Carrier-induced Index Change Research Articles

Free-carrier-induced nonlinear dynamics in hybrid graphene-based photonic waveguides

We develop from first principles a theoretical model for infrared pulse propagation in graphene-covered hybrid waveguides. We model electron dynamics in graphene by Bloch equations, enabling the derivation of the nonlinear conductivity and of a rate equation accounting for free-carrier generation. Radiation propagation is modeled through a generalized nonlinear Schr\"{o}dinger equation for the field envelope coupled with the rate equation accounting for the generation of free carriers in graphene. Our numerical simulations clearly indicate that unperturbed Kerr solitons accelerate due to the carrier-induced index change and experience a strong self-induced spectral blueshift. Our numerical results are fully explained by semianalytical predictions based on soliton perturbation theory.

Performance Evaluation of Integrated Semiconductor Ring Laser Gyroscope

We present a mathematical analysis and comparison of the performance of integrated on-chip semiconductor ring laser gyroscope (SRLG) fabricated using GaAs/AlGaAs and InP/InGaAsP technologies. The performance parameters of the gyro are modeled in terms of fundamental material, waveguide, and resonator parameters. In addition to this, influence of phenomena specific to semiconductor lasers such as nonlinear coupling, spatial hole burning, gain grating formation, and carrier induced index change on the gyro performance is also included. The analysis helps in identifying critical parameters, which must be optimized to improve the gyro performance.Best achievable performance of integrated SRLG is calculated, and design modifications are suggested to enhance it for high-performance military applications.

Index-Antiguiding in Narrow-Ridge GaN-Based Laser Diodes Investigated by Measurements of the Current-Dependent Gain and Index Spectra and by Self-Consistent Simulation

The threshold current density of narrow (1.5 {\mu}m) ridge-waveguide InGaN multi-quantum-well laser diodes, as well as the shape of their lateral far-field patterns, strongly depend on the etch depth of the ridge waveguide. Both effects can be attributed to strong index-antiguiding. A value of the antiguiding factor R = 10 is experimentally determined near threshold by measurements of the current-dependent gain and refractive index spectra. The device performances are simulated self-consistently solving the Schr\"odinger-Poisson equations and the equations for charge transport and waveguiding. Assuming a carrier-induced index change which matches the experimentally determined antiguiding factor, both the measured high threshold current and the shape of the far-field pattern of lasers with shallow ridges can be reproduced theoretically.

Self-frequency blueshift of dissipative solitons in silicon-based waveguides

We analyze the dynamics of dissipative solitons in silicon on insulator waveguides embedded in a gain medium. The optical propagation is modeled through a cubic Ginzburg-Landau equation for the field envelope coupled with an ordinary differential equation accounting for the generation of free carriers owing to two-photon absorption. Our numerical simulations clearly indicate that dissipative solitons accelerate due to the carrier-induced index change and experience a considerable blueshift, which is mainly hampered by the gain dispersion of the active material. Numerical results are fully explained by analytical predictions based on soliton perturbation theory.

Static and Dynamic Modeling of Circular Grating-Coupled Distributed Feedback Lasers

A computer model is developed to analyze the steady-state and transient responses of circular grating-coupled distributed feedback (CGC DFB) lasers. The model solved the time-dependent coupled-mode equations and carrier rate equation self-consistently by using a modified time-domain finite-difference method. The nonuniform distributions of carrier concentration and refractive index are taken into calculation. Using the model, the temporal and spatial variations of electric field and carrier concentration of the CGC DFB lasers are examined. It is found that the laser performance would be underestimated if the carrier-induced index change is ignored in the calculation. On the other hand, it is noted that the output power and resonant oscillation frequency as well as damping rate of the lasers could be maximized simultaneously by an optimal design for the grating.

Performance Optimization of a Reconfigurable Waveguide Digital Optical Switch on InGaAsP–InP: Design, Material, and Carrier Dynamics

The design and performance of an InGaAsP-InP 1 times 2 reconfigurable waveguide digital optical switch (RW-DOS) actuated by carrier-induced refractive index modulation is described. Using a device model based on the two-dimensional beam propagation method, we present an analysis of the role of material bandgap, carrier lifetime, and waveguide design on the switch performance. The model results are compared with experimental measurements of carrier-induced index change and switching performance for RW-DOS devices and test structures fabricated in InGaAsP alloys with waveguide core compositions of Q = 1.2, Q = 1.3, and Q = 1.4 mum. We discuss compromises between power consumption, switching speed, and propagation loss. The optimized InGaAsP-InP devices exhibited better than 25-dB switching contrast ratio and require less than 20-mA drive current.

Effect of Index Variation in Active Layer on Transverse Mode for Vertical-Cavity Surface-Emitting Lasers

The distribution of carrier density in an active layer of a vertical-cavity surface-emitting laser (VCSEL) produces a refractive index distribution, affecting the transverse-mode behavior of the VCSEL causing high-order-mode lasing. To achieve high-power fundamental-mode operation, we investigated the reduction in this effect by elongating the cavity. Experimental data show that the high-order mode started lasing immediately above a threshold in a lambda-cavity VCSEL with an active area large than 10 µm in diameter. By introducing a long monolithic cavity, high-order-mode lasing was suppressed. Theoretical results clearly show that such high-order-mode suppression is achieved because the effect of carrier-induced index change in the active layer is reduced by elongating the cavity.

Butt-jointed DBR laser with 15 nm tunabilitygrown in three MOVPE steps

InGaAsP/InP butt-jointed, buried ridge DBR lasers, exhibiting a record 15 nm tuning range, have been realised using only a three-step MOVPE process. The highest number (38) ever reported of regularly spaced wavelength channels is obtained from a two-section DBR laser, in which the passive waveguide was optimised in terms of carrier-induced effective index change and active-passive coupling efficiency.

Optimization of the carrier-induced effective index change in InGaAsP waveguides-application to tunable Bragg filters

A model for the refractive index of InGaAsP and its dependence on the carrier density is presented. Full transport calculations for electrons and holes in heterostructures, including temperature effects, are used to show that the maximum injected carrier density is limited by electron heterojunction leakage for low-cladding doping and by recombination in the tuning layer for high-cladding doping. With the effective index method, we can then compute the maximum propagation constant change as a function of the waveguide geometry. Thermal effects are important only in the case of poor heatsinking. Using these results, we can estimate a maximum tuning range of more than 15 nm for optimized Bragg reflection gratings.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Strong increase of the derivative of the carrier-induced index change of semiconductor lasers at low injected carrier density

The carrier-induced index change of a semiconductor laser was measured for injected carrier density ranging from 3 * 10/sup 16/ cm/sup -3/ to 2 * 10/sup 18/ cm/sup -3/. A strong nonlinear behavior between index change and carrier density is observed. The derivative of the index change versus carrier density at low carrier density can be 15 times larger than the derivative of the index change at high carrier density. >

The sublinear relationship between index change and carrier density in 1.5 and 1.3 mu m semiconductor lasers

The carrier-induced index change was measured using a novel injection-reflection technique in combination with differential carrier lifetime data. The observed relation between index change and injected carrier density at bandgap wavelength is nonlinear and is approximately given by delta n/sub act/=-6.1*10/sup -14/ (N)/sup 0.66/ for a 1.5- mu m laser and delta n/sub act/=-1.3*10/sup -14/ (N)/sup 0.68/ for a 1.3- mu m laser. The carrier-induced index change for a 1.3- mu m laser at 1.53- mu m wavelength is smaller and is given by delta n/sub act/=-9.2*10/sup -16/ (N)/sup 0.72/. >

Theory and experiment of the parasitic-free frequency response measurement technique using facet-pumped optical modulation in semiconductor diode lasers

The letter describes the theory and experiment of the newly developed parasitic-free frequency response measurement technique using facet-pumped optical modulation on diode lasers. It was found that the modulation damping rate depends on the relative position of the pump laser wavelength with respect to the Fabry–Perot resonance wavelength of the laser under study. This effect is fully explained in terms of the carrier-induced index change. For multilongitudinal mode lasers, it is shown experimentally and theoretically that the damping rate and frequency response measured by this technique give the intrinsic frequency response corresponding to direct current modulation only if the cavity lengths of pump and probed lasers are equal, and then only if the pump laser wavelength coincides with the Fabry–Perot transmission maximum or minimum of the probed laser.

Spectral shift and distortion due to self-phase modulation of picosecond pulses in 1.5 μm optical amplifiers

Picosecond pulses are observed to exhibit large frequency shifts (∼50 GHz) and spectral distortion on propagation through semiconductor laser optical amplifiers. The spectral changes are shown to result from self-phase modulation occurring due to the carrier-induced index changes that invariably accompany gain saturation. An analytic model for pulse amplification is presented by including the self-phase modulation effects. Its predictions are in good agreement with the experimental results.

Characterisation of single-mode channel waveguides from far field measurements

A method for the experimental characterisation of single mode channel waveguides using their far field radiation pattern is proposed. It is shown that if the substrate and cover refractive indices are known (which is true in most cases) then the core refractive index and the core dimensions, and hence the aspect ratio can be predicted by the far field patterns of the fundamental modes. The present method should find application in the characterisation of elliptical core fibers and in predicting the carrier induced index changes in diode-lasers.

Gain nonlinearities in semiconductor lasers: Theory and application to distributed feedback lasers

The gain spectrum in semiconductor lasers is affected by the intensity-dependent nonlinear effects taking place due to a finite intraband relaxation time of charge carriers. We obtain an analytic expression for the nonlinear gain in multimode semiconductor lasers using the density-matrix formalism. In general, the nonlinear gain is found to consist of the symmetric and asymmetric components. The asymmetry does not have its origin in the carrier-induced index change, but is related to details of the gain spectrum. The general expression for the nonlinear gain is used to discuss the range of single-longitudinal-mode operation of distributed feedback lasers. It is also used to obtain an analytic expression for the self-saturation coefficient and to compare the predicted value to the experimental value for both GaAs and InGaAsP lasers. The agreement between the theoretical and the experimental values supports the hypothesis that spectral hole burning is the dominant mechanism for the gain nonlinearities in semiconductor lasers.

Longitudinal mode behavior and tunability of separately pumped (GaAl)As lasers

A three-segment laser, when separately pumped, shows both frequency switching and continuous tuning with a modulation current applied to the middle segment. The wavelength changes are attributed to gain peak shift with the carrier concentration and carrier-induced index change. A total wavelength change of 61 Å, a continuous tuning range of 4.1 Å, and a tuning rate of −0.74 Å/mA are obtained. The laser may be useful in optical FM fiber communication.

The carrier-induced index change in AlGaAs and 1.3 µm InGaAsP diode lasers

The carrier-induced index change has been measured for a large number of broad-area AlGaAs and 1.3 μm InGaAsP diode lasers. The observed index change with injected carrier density is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-(1.2 \pm 0.2) \times 10^{-20}</tex> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> for AlGaAs lasers and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-(2.8 \pm 0.6) \times 10^{20}</tex> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> for 1.3 μm lasers. The index change at threshold varies from -0.03 to -0.06 for AlGaAs lasers and from -0.04 to -0.10 for InGaAsP lasers. This variation is correlated with the carrier density at threshold, which depends on active layer thickness and doping level. For the first time, the observed index change is compared to the carrier density found from differential carrier lifetime measurements. This accurate determination of the carrier density represents a significant improvement over previous studies.

Relationship between carrier-induced index change and feedback noise in diode lasers

An improved theoretical analysis of single-mode diode laser dynamics reveals that feedback-induced intensity pulsations and frequency modulation are consequences of the carrier-dependent modal refractive index of the laser cavity. A stability criterion based on injection-locking theory indicates that gain-guided diode lasers are more likely to exhibit feedback-induced pulsations than are index-guided devices. Numerical simulation of feedback-induced noise is shown to be in excellent agreement with previously reported experimental data.

Relationship Between Carrier-Induced Index Change and Feedback Noise in Diode Lasers

An improved theoretical analysis of single-mode diode laser dynamics reveals that feedback-induced intensity pulsations and frequency modulation are consequences of the carrier-dependent modal refractive index of the laser cavity. A stability criterion based on injection-locking theory indicates that gain-guided diode lasers are more likely to exhibit feedback-induced pulsations than are index-guided devices. Numerical simulation of feedback-induced noise is shown to be in excellent agreement with previously reported experimental data.

Carrier-induced index change in AlGaAs double-heterostructure lasers

A large carrier-induced index change is reported for conventional 8 μm-stripe oxide-isolated AlGaAs double-heterostructure lasers. At threshold, the index change of the active layer is −0.05 to −0.07, which is a factor of 5 to 10 larger than previously reported. It is accompanied by an even greater change in dispersion. These effects cannot be explained by a free-carrier effect, and are most likely caused by a carrier-induced shift of the absorption edge.