Effective Linewidth Enhancement Factor Research Articles

Feedback Sensitivity of DBR-Type Laser Diodes

It is shown theoretically that the feedback sensitivity of Distributed Bragg Reflector laser diodes with low-loss Bragg section decreases with the length of the Bragg section and also can be decreased by detuning from the Bragg peak. The effect of detuning is not only due to a change in effective linewidth enhancement factor, but also due to a change of the effective cavity length. The results can be applied also to laser diodes coupled on one side to one or more ring resonators Such lasers can have very weak feedback sensitivity.

1.3-µm passively mode-locked quantum dot lasers epitaxially grown on silicon: gain properties and optical feedback stabilization

This work reports on an investigation of the optical feedback in an InAs/InGaAs passively mode-locked quantum dot (QD) laser epitaxially grown on silicon. Under the stably-resonant optical feedback condition, experiments demonstrate that the radio-frequency linewidth is narrowed whatever the bias voltage applied on the saturable absorber (SA) is; on the other hand, the effective linewidth enhancement factor of the device increases with the reverse bias voltage on the SA, hence it is observed that such an increase influences the mode-locking dynamic and the stability of device under optical feedback. This work gives insights for stabilizing epitaxial QD mode-locked lasers on silicon which is meaningful for their applications in future large-scale silicon electronic and photonic applications requiring low power consumption as well as for high-speed photonic analog-to-digital conversion, intrachip/interchip optical clock distribution and recovery.

Mode and Lasing Characteristics for Hybrid Square-Rectangular Lasers

Whispering-gallery mode (WGM) microlasers are potential light sources for monolithic photonic integration circuits and optical interconnects. In this study, stable single-mode hybrid square-rectangular lasers (HSRLs) are reported, based on mode coupling between WGM and Fabry–Perot (FP) modes. Mode selection mechanisms are explained based on numerical results of the resonant reflection of the square microcavity and energy distributions of coupled mode in the two cavities, and the reduction of effective linewidth enhancement factor is expected as two cavities are modulated individually. HSRLs with different sizes are fabricated by contact photolithography and dry-etching techniques. For a hybrid laser with a square-side length a = 15 μm and the FP cavity length and width of L = 300 μm and d = 2 μm, stable single-mode operation with a side-mode suppression ratio up to 47 dB is obtained, and a small-signal modulation bandwidth of 13.3 GHz is realized by modulating the current of the FP cavity. The dynamic characteristics are further investigated for the hybrid laser. Furthermore, threshold currents and tunable behaviors are compared for HSRLs with a = 10, 15, and 20 μm and d = 1.5 and 2 μm.

Evaluation of Chirp Reduction in Polymer-Based Tunable External-Cavity Lasers

We evaluate the chirp reduction achievable using the detuned loading effect in the polymer-based tunable externalcavity laser (ECL) capable of operating at 10 Gb/s. In particular, we estimate the achievable linewidth enhancement factor (LEF) of this ECL considering the stable operation region increased by the nonlinear gain. The results show that, due to the nonlinear gain, we can detune the lasing mode further away from the nominal detuning limit (i.e., half of the mode spacing) by ~4 GHz for an ECL with a mode spacing of ~30 GHz under the continuous-wave (CW) operating condition. As a result of this additional detuning, the effective LEF is reduced from 1.3 to 0.8, although its material LEF is ~5. However, when we change the operating wavelength of this ECL, the minimum achievable LEF is deteriorated due to the parasitic reflection occurring at the antireflection (AR)-coated facet. For example, when the optical power reflected at the AR-coated facet is ~5% of the feedback power from the polymer Bragg grating reflector (PBR), the effective LEF is increased from 0.8 to 3.4. To verify these results experimentally, we fabricate a polymerbased tunable ECL and measure its chirp characteristics. For example, we directly modulate this ECL at 10 Gb/s and measure its effective LEF as a function of the detuned frequency. The result shows that we can reduce the effective LEF to ~1 by detuning the operating mode by 18 GHz. This value is slightly larger than that achievable under the nearly CW operating condition (i.e., 0.8) due to the chirp-induced mode hopping. We also confirm that, by optimizing the detuning condition, this ECL can be used for the transmission of a 10-Gb/s signal over 20 km of a standard single-mode fiber (SSMF) with a power penalty of <;2 dB. However, an error-free transmission cannot be achieved at some wavelengths due to the parasitic reflection. To avoid this problem, it is needed to suppress the parasitic reflection to be <;0.1% of the feedback power from the PBR.

Measurement of optical gain, effective group index and linewidth enhancement factor in 1.3 µm dilute nitride double-quantum-well lasers

The net modal gain, effective group index and linewidth enhancement factor (LWEF) in edge-emitting InGaAsN/GaAs lasers have been determined as a function of both temperature and injection current from experimentally amplified spontaneous emission spectra. The shift of the peak gain with temperature was found to be 0.49 nm/K. Values of effective group index between 3.52 and 3.59 were measured, suggesting a relatively high refractive index of 3.75 for a dilute nitride quantum well. LWEF values between 1.87 and 2.84 were measured.

Frequency noise and modulation of a four-section DBR laser

A theoretical model is presented to describe the tuning, frequency noise, and modulation characteristics of tunable DBR lasers with two active and two passive sections. Analytical expressions are derived for the intensity and frequency modulation responses, frequency noise spectrum, spectral linewidth, effective linewidth enhancement factor, and spontaneous emission rate. It is shown that a nearly flat red-shifted FM response over several gigahertz can be obtained by nonuniform current injection and modulation of the lower carrier density section in the active region. Increasing the tuning current through the passive sections enhances the FM efficiency. However, a higher FM efficiency is generally accompanied by a larger spectral linewidth. The predictions of our theoretical model are in good agreement with the available experimental data.

Spectral linewidth and FM response for a four-section DBR laser

Theoretical expressions were presented for the spectral linewidth, effective linewidth enhancement factor and FM response of a DBR laser with two active and two passive sections. It was shown that a nearly flat red-shifted FM response over several gigahertz can be obtained by nonuniform current injection and modulation of the lower-carrier-density section in the active region. However, a high FM efficiency is also accompanied by a relatively large spectral linewidth. Wavelength tuning by using the injection currents through the passive sections enhances the red-shifted FM efficiency but also broadens the spectral linewidth. In practice, linewidth broadening could be suppressed by using a large-bandgap material as the passive waveguide in order to reduce the optical confinement factor and, consequently, the tuning efficiency.

Above-threshold analysis of three-section DFB/DBR lasers with second-order gratings

An above-threshold static analysis has been performed on a three-section DFB/DBR laser with a continuous second-order grating. The laser has a center pumped section that is terminated by two unpumped grating sections. The results confirm earlier experimental observation that the laser operates with a peaked nearfield intensity distribution along the laser cavity. The values of the grating parameters and the active-section-to-total-cavity-length ratio associated with this mode of operation are obtained. They indicate good tolerance in these design parameters. The DFB/DBR laser is also found to have reduced longitudinal spatial hole burning and a smaller effective linewidth enhancement factor compared with a uniformly pumped single-section, second-order DFB laser. The introduction of asymmetry in the DFB/DBR laser results in poorer side-mode suppression compared with the symmetric DFB/DBR laser.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The optical gain coupling saturation effect on the linewidth property of complex coupled DFB lasers

The cavity length dependence of the linewidth property of complex coupled (CC) DFB lasers is investigated. In CC-DFB lasers with a fixed geometrical structure of the active region, the cavity length strongly affects the ratio of index coupling strength to the gain coupling one, which results in the variation of the effective linewidth enhancement factor /spl alpha//sub eff/. It is also found that pure gain coupled (GC) DFB lasers have the saturation characteristic in the linewidth power product, with the extension of the cavity length, These results indicate the importance of the selection of the cavity length in CC-DFB lasers. >

Large-signal dynamic behavior of distributed-feedback lasers including lateral effects

The large-signal behavior of DFB lasers is analyzed, including lateral as well as longitudinal variations in carrier density, photon density, and refractive index. The effective index method and other approximations are used to reduce the complex three-dimensional problem to one dimension. The coupled wave and carrier rate equations are then solved in a self-consistent manner. Lateral spatial carrier hole burning and lateral diffusion are found to affect the relaxation oscillation frequency and damping rate of DFB lasers, depending on their detailed structure. The effective time-averaged linewidth enhancement factor is also affected. In symmetric AR-coated /spl lambda//4 phase-shifted lasers the side mode suppression ratio can be deteriorated significantly by lateral spatial hole burning when kL is large. >

Spectral linewidth reduction in partly gain-coupled 1.55 μm strained multiple quantum-well distributed feedback laser

The effective linewidth enhancement factor αeff and the spectral linewidth Δυ are reported for the first time for a partly gain-coupled distributed feedback laser with a gain corrugation in a strained multiple quantum-well active region emitting at 1.55 μm wavelength. The αeff value is estimated to be as low as 1 and is independent of the laser cavity length L, while a decrease in the linewidth-power product ΔυPo with L has been observed, with a measured linewidth of 2 MHz at 10 mW optical output power for 300-μm-long devices. The experimental results demonstrate that a small αeff is obtained due to the strain and the gain coupling effects, while further reduction of the spectral linewidth with L is the result of longitudinal index coupling effects.

Reduced effective linewidth enhancement factor α eff of complex-coupled DFB lasers with absorptive gratings

An extended model for the calculation of alpha /sub eff/, is presented including for the first time the carrier dynamics in the absorptive grating. It is shown that for comparable carrier lifetime in the absorptive and active regions a significant reduction of alpha /sub eff/, may be achieved by the antiphase configuration of the complex coupling coefficient. >

Transfer-matrix analysis of the spectral linewidth of a partly gain-coupled MQW DFB laser

The spectral linewidth of a partly gain-coupled MQW DFB laser with a quantum-well grating is analysed using the transfer-matrix method. The effective linewidth enhancement factor and the longitudinal spontaneous emission enhancement factor are calculated by newly derived analytical expressions in terms of the transfer matrix.

Linewidth reduction of DSM lasers due to effects of composite cavity and distributed reflectors

Spectral properties of dynamic single-mode (DSM) lasers are theoretically analyzed in terms of the effects of composite cavity and distributed reflectors. Unique reduction mechanisms of adiabatic chirp and linewidth are found in distributed reflector (DR) lasers and complex-coupled (CC) (i.e., gain+index-coupled) DSM lasers, which are explained from the viewpoints of modal phase and modal gain behaviours. For CC-DSM lasers, it is shown that the arrangement of index and gain corrugation, namely, antiphase or in-phase combination, will suppress or enhance, respectively, an effective linewidth enhancement factor, alpha /sub eff/. Numerical results show that DR structures are much superior in spectral and single-mode properties to distributed-feedback (DFB) and distributed-Bragg-reflector (DBR) structures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Spontaneous emission model of surface-emitting DFB semiconductor lasers

A general spontaneous emission model is developed for surface-emitting (SE) distributed feedback (DFB) semiconductor lasers. The frequency distribution of spontaneous emission noise below lasing threshold and the spontaneous emission rate in lasing operation are formulated by using a transfer matrix method combined with the Green's function method. The effective linewidth enhancement factor is obtained from this model in terms of the elements of the transfer matrix. By way of example, the author applies the formulation to a standard SE DFB laser, and a SE lambda /4-shifted DFB laser with a distributed Bragg reflector (DBR) mirror. In particular, the author analyzes the below-threshold spectrum, the threshold current density, the differential quantum efficiency, and the spectral linewidth of these lasers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Effective linewidth enhancement factor and spontaneous emission rate of DFB lasers with gain coupling

A field rate equation governing the noise and dynamic properties of a DFB (distributed feedback) laser with gain coupling is presented. Analytic expressions for the effective linewidth enhancement factor and spontaneous emission rate are derived. It is shown numerically that the linewidth contribution from spontaneous emission can be substantially reduced in DFB lasers with gain coupling.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The influence of resonator structure on the linewidth enhancement factor of semiconductor lasers

The phenomenon of intensity-phase coupling in semiconductor lasers is studied in the linear regime in terms of an effective linewidth enhancement factor. The circumstances under which the longitudinal laser structure of a distributed feedback laser may influence this coupling are determined. For the case of uniform gain and carrier density no effect is expected from a periodic or quasi-periodic corrugation. However, when the gain layer is corrugated or a periodic gain is otherwise implemented, the influence may be considerable. It is shown that the degree of gain coupling between right- and left-travelling waves and the specific mechanism by which variations in the carrier density influence this coupling are of key importance. It is found that depending on the degree and nature of the gain coupling the effective linewidth enhancement factor may be considerably reduced or enhanced. >

Reduction of effective linewidth enhancement factor alpha /sub eff/ of DFB lasers with complex coupling coefficients

The effective linewidth enhancement factor alpha /sub eff/ of DFB lasers which have both gain and index coupling coefficients is theoretically analyzed. The unique reduction mechanism of alpha /sub eff/ due to the optical negative feedback of modal phase and modal gain in gain coupled DFB lasers was found for the first time. The numerical result showed that alpha /sub eff/ can be reduced to almost one half of the material defined linewidth enhancement factor alpha when there exists an index coupling coefficient comparable to the gain coupling coefficient. >

Influence of refractive index nonlinearities on modulation and noise properties of semiconductor lasers

The modulation response and the spectral linewidth of singlemode semiconductor lasers are analysed by taking into account the nonlinear gain and the nonlinear refractive index in the rate equations. It is shown that the effect of nonlinear gain and index can be included through an effective linewidth enhancement factor αeff that is different for frequency modulation and for spectral linewidth. The effect of the nonlinear index is particularly strong in the case of frequency modulation where αeff can become zero or even negative for lasers operating on the red side of the gain peak. In the case of laser noise, αeff causes linewidth saturation but no rebroadening at high output powers. Our results indicate that gain and index nonlinearities are not the cause of linewidth rebroadening.

Basic analysis of AR-coated, partly gain-coupled DFB lasers: the standing wave effect

A theoretical analysis of distributed feedback (DFB) lasers with mixed gain and index coupling (partly gain-coupled DFB) is given for perfect antireflection (AR) coatings. Analytical expressions for the threshold gain, facet loss, and the relative depth of the standing wave pattern are derived. At the same time the importance of the standing wave effect and its consideration by coupled mode equations is shown. For purely gain-coupled DFB lasers, simple expressions for the effective linewidth enhancement factor and the longitudinal spontaneous emission factor are derived. In addition, various approximations describing the performance of purely gain-coupled DFB lasers are given. >