Self-consistent analysis of side-mode suppression in gain-coupledDFB semiconductor lasers

Based on a set of spatially dependent multimode rate equations derived from Maxwell's equations, a self-consistent analysis of gain-coupled distributed feedback (DFB) lasers is developed. By introducing the modal net gain into the coupled wave equations, we also obtain a closed form formula of the side-mode suppression ratio (SMSR) for DFB lasers. It is shown that, associated with the distributed feedback, the longitudinal spatial hole burning, and the nonlinear gain compression effects, gain coupling produces significant effects on the SMSR of DFB lasers     

Distributed feedback lasers in chiral media

The combined effects of chirality and gain (or loss) on wave propagation and coupling in periodic structures is investigated here. The focus is on distributed feedback (DFB) lasers in a transversely unbounded periodic slab with spatially modulated electromagnetic parameters. The analysis uses a coupled-mode approach employing a canonical physical model of chiral materials to predict the effects of modulated chirality admittance on DFB lasers. Results for DFB laser behavior in chiral media are compared and contrasted to that in achiral media. It is found that, under certain circumstances, the electric and magnetic field coupling, which is characteristic of chiral materials, results in a lower threshold gain for DFB lasers in media with a given index of refraction and characteristic impedance. It is also found that chiral index-coupled or gain-coupled DFB lasers exhibit the same spectral mode properties as achiral DFB lasers     

Traveling wave analysis of semiconductor lasers: modulationresponses, mode stability and quantum mechanical treatment of noisespectra

We present a traveling wave analysis of a general class of semiconductor lasers, which includes multisection DFB/DBR lasers and gain-coupled DFB lasers. The analysis leads to new semianalytic expressions for the small-signal IM and FM modulation responses, the intensity and FM noise spectra, and the linewidth. The expressions are given in terms of solutions to four coupled linear homogeneous differential equations and can easily be evaluated numerically. We also derive a stability parameter σ, for which σ<0 indicates that the mode is unstable with respect to small-scale fluctuations. The noise spectra are derived from semiclassical calculations as well as from calculations based on quantized fields, and we discuss the limitations of the semiclassical approach. The formalism of the quantum mechanical treatment has a built-in relationship between the relative intensity noise and the noise of the injection current. This relationship is discussed and illustrated by numerical examples     

Side-mode suppression mechanism of gain-coupled DFB lasers with periodically etched quantum wells

The effect of the gain and index coupling on the side-mode suppression ratio (SMSR) is studied for gain-coupled DFB lasers with periodically etched quantum wells. An accurate expression for the SMSR based on the amplified spontaneous emission model is used with the local-normal-mode transfer-matrix method. The mechanism for the strong single-mode stability of the gain-coupled DFB lasers is explained by the difference between the effective gain and loss of the Bloch waves in the grating structures. This new view clearly shows the advantage of the gain-coupled DFB lasers in terms of single-mode stability.     

Improvement of single-mode gain margin in gain-coupled DFB lasers

Using the Bloch-wave analysis, this paper investigates the effect of the gain grating on the single-mode condition in DFB lasers. Various factors affecting the threshold gain of gain-coupled DFB lasers are analyzed in some detail. It is shown for the first time that unequal section lengths in the gain grating can have a significant effect on the single-mode gain margin of gain-coupled DFB lasers, especially when the linewidth enhancement factor α_M is large, because the long and shortwavelength Bloch waves are in phase and in antiphase with the index grating of DFB lasers, respectively     

Relaxation oscillation frequency of DFB lasers with gain coupling

Using the spatially-dependent rate equations based on the Green's function analysis, we investigate the dependency of the relaxation oscillation frequency on the complex coupling coefficient and other parameters of gain-coupled DFB lasers by simultaneously considering spatial-hole-burning, gain saturation and gain compression. An explicit expression for the relaxation oscillation frequency for DFB lasers including the longitudinal spatial effects has been obtained. It is found that antiphase gain-coupling significantly enhances the local effective differential gain in the gain-coupled DFB laser and hence increases the relaxation oscillation frequency. We have also shown for the first time that the modal linewidth enhancement factor α_M plays an important role in determining the relaxation oscillation frequency of gain-coupled DFB lasers, especially when the built-in index coupling is weak     

Spatial hole burning effects in distributed feedback lasers

The effects of spatial hole burning in a steady-state distributed feedback (DFB) laser are examined by numerically solving the coupled mode equations that describe the system. An approximate solution for the gain above threshold is derived and compared to the exact solution. It is shown that the self-induced grating that arises due to spatial hole burning significantly reduces the mode discrimination of index-coupled DFB lasers. This makes it difficult for these lasers to maintain single-longitudinal-mode behavior above threshold. However, it is found in addition that bulk-modulated (gain-coupled) DFB lasers do not lose their mode selectivity above threshold, indicating that these lasers may be better choices for narrow-linewidth operation     

Transfer-matrix dynamic model of partly gain-coupled 1.55 μm DFBlasers with a strained-layer MQW active grating

A dynamic model for partly gain-coupled 1.55 μm MQW DFB lasers consisting of etched strained-layer multiquantum wells is presented. For the modulation and noise characteristics of DFB lasers, analytical expressions which take into account both the longitudinal distribution of laser parameters and carrier transport effects are derived for the first time using the transfer-matrix method. As a numerical example, the relaxation oscillation frequency is compared to experimental results, and reasonable agreements are obtained between the theory and experiment     

Gain-coupled DFB lasers versus index-coupled and phase shifted DFBlasers: a comparison based on spatial hole burning corrected yield

A statistical yield analysis is presented for gain- and index-coupled distributed feedback (DFB) laser structures, allowing a comparison of their single longitudinal mode (SLM) yield capabilities. For the yield calculations, the threshold gain difference and the longitudinal spatial hole burning (SHB) are taken into account. By comparing the experimental and theoretical yield of index-coupled DFB lasers, the significance of SHB for correct yield predictions is illustrated. For the purpose of comparison, yield calculations for various λ/4-shifted DFB lasers (with low facet reflectivities) are presented. The most emphasis, however, is on partly gain-coupled DFB lasers. Estimations of practical gain coupling coefficient values for gain and for loss gratings are discussed     

Extraction of gain parameters for truncated-well gain-coupled DFBlasers

An amplified spontaneous emission transfer matrix model for prediction of the subthreshold spectral output of distributed-feedback (DFB) lasers was developed and fitted to the spectra of truncated-well gain-coupled DFB lasers using a least-squares-fitting algorithm. Modal gains for the high- and low-gain segments of the truncated-well DFB lasers were extracted, and their evolution as a function of injection current was examined. Results explain the tendency for the truncated-well gain coupled DFB lasers to have higher yields of single-frequency lasers and larger sidemode suppression ratios than are expected from simple considerations     

External feedback sensitivity of partly gain-coupled DFBsemiconductor lasers

External optical feedback sensitivity of partly gain-coupled DFB semiconductor lasers has been analyzed in above threshold operation regime. Both the longitudinal spatial hole burning and the nonlinear gain compression have been taken into account. A comparison has been made among λ/4-shifted, pure index-coupled and partly gain-coupled DFB laser diodes. Even though pure index-coupled and partly gain coupled DFB lasers exhibit similar sensitivity to external optical feedback at the threshold, however, gain grating can reduce the feedback sensitivity when the lasers operate well above the threshold specially when the κL parameter is high     

Transient side-mode suppression in gain-coupled DFB lasers

Based on the spatially dependent multimode rate equations, we investigate the transient side-mode suppression in the gain-coupled distributed feedback (DFB) lasers. A simplified but accurate multimode dynamic analysis of gain-coupled DFB lasers is developed. To first order of perturbation approximation, the study includes various spatial effects, such as the distributed complex coupling, the nonuniform carrier distribution, and the nonlinear gain compression. It is found that gain coupling introduces high decay rates and low dynamic differential gains for the side modes, which effectively suppress their transient fluctuation and shorten the rise time of the transient side-mode suppression ratio (SMSR)     

Effect of in-phase and antiphase gain coupling on high-speedproperties of MQW DFB lasers

Effect of in-phase and antiphase gain-coupling on high-speed properties is studied for MQW DFB lasers with periodically truncated quantum-wells. The enhancement of modulation bandwidth due to antiphase gain-coupling is found significantly suppressed, and gain-coupled DFB lasers with high κL are preferred for large modulation bandwidth due to the presence of linear gain saturation in MQW lasers     

Large-signal dynamic model for gain-coupled DFB lasers based on the transmission-line laser model

New scattering matrices are developed for the transmission-line laser model (TLLM) to enable the dynamics of gain-coupled DFB lasers to be studied. The resulting model is able to simulate large-signal transient responses and spectral characteristics of gain-coupled DFB semiconductor lasers, and gives threshold gains in excellent agreement with analytical formulations.<>     

Performance comparison of gain-coupled and index-coupled DFBsemiconductor lasers

Comprehensive numerical simulations with the transmission-line laser model (TLLM) are used to compare the behavior of gain-coupled DFB lasers with index-coupled DFB lasers fabricated from identical materials. These simulations compare slope efficiency, threshold current, spectra, small-signal modulation bandwidth, maximum-intrinsic modulation bandwidth, large-signal transient response and chirp, relative-intensity-noise (RIN) spectra, and feedback sensitivity for coherence collapse. In most cases gain-coupled lasers with additional index coupling have better performance than index-coupled lasers for a given material. However, high-coupling factor index-coupled lasers do have lower threshold currents, lower RIN levels, and lower sensitivity to external feedback than gain-coupled lasers, although spatial hole burning in these devices can be disadvantageous     

Effects of structural parameters on the external optical feedbacksensitivity in DFB semiconductor lasers

External optical feedback sensitivity in distributed feedback (DFB) semiconductor lasers is analyzed with special attention to phase-shifted and complex-coupled lasers. The effects of various structural parameters such as coupling strength, facet reflectivity, and corrugation phase angle on external optical feedback sensitivity are studied. The λ/4 phase-shifted index-coupled DFB laser exhibits low external optical feedback sensitivity for large index-coupling coefficient and high facet reflectivity. Pure gain-coupled DFB lasers perform better than the phase-shiftless uniform index-coupled DFB lasers but worse than λ/4 phase-shifted index-coupled lasers with high coupling strengths. External optical feedback sensitivity of complex-coupled lasers depends significantly on the index-to-gain coupling ratio, the phase between the index and gain gratings, and the total coupling     

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     

Enhanced maximum intrinsic modulation bandwidth of complex-coupled DFB semiconductor lasers

DFB lasers with complex (gain and index) coupling are shown to have reduced K-factors, that is increased maximum intrinsic modulation bandwidths, compared with pure gain-coupled lasers. The K-factor is shown to be dependent on the ratio and phase of the index coupling to the gain coupling. Appropriate choice of the ratio of index coupling to gain coupling can triple the maximum intrinsic modulation bandwidth of the laser.<>     

Effective linewidth enhancement factor and spontaneous emissionrate 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     

Electromagnetically induced distributed feedback intersubband lasers

We propose a method to coherently generate uniform and phase-shifted complex-coupled (CC) semiconductor distributed feedback (DFB) lasers based on intersubband transitions in n-doped quantum-well structures. This is done by utilizing infrared-induced coherent optical processes in these structures including resonant enhancement of refractive index of the conduction intersubband transitions and generation of laser-induced transparency and gain without inversion. We show that these coherent phenomena can generate electromagnetically induced gratings where the index and gain/loss perturbations and their relative phases can be manipulated using an infrared laser beam. This allows us to coherently control optical feedback in a waveguide structure, switching from a case where there is no feedback in the absence of the infrared laser to the case where different types of CC optical feedbacks are generated as this field is properly adjusted. These include generation of gain and index perturbations (partly gain-coupled DFB laser), pure index corrugation (index-coupled DFB laser), and loss and index perturbations (loss-coupled DFB laser). We study these feedback mechanisms in the cases where the optically induced gratings are uniform along the cavity or have a /spl pi//2 phase shift. We discuss mode characteristics of such electromagnetically induced DFB intersubband lasers and find out how here the gain- and index-coupled DFB lasers are associated, respectively, with gain without inversion and laser-induced transparency in the conduction intersubband transitions of quantum-well structures.