Two-dimensional theory of distributed feedback semiconductor lasers

A theory which takes account of the two dimensional waveguide structure of the distributed-feedback (DFB) laser is presented. Laser threshold conditions in the case of no external reflections are calculated for a three-layer model in which one cladding layer has a periodically changing dielectric constant. In contrast with the coupled-wave theory the threshold conditions are found to be asymmetric with respect to the Bragg frequency. The longitudinal mode which lies below and nearest the Bragg frequency has the lowest threshold gain. The difference between the threshold gains of the two adjacent longitudinal modes straddling the Bragg frequency has a maximum as a function of the coupled strength of the grating     

Modeling of distributed feedback semiconductor lasers withaxially-varying parameters

A numerical model that is capable of predicting important laser characteristics such as the threshold gain and the gain margin between the main and side modes for a distributed-feedback (DFB) semiconductor laser of arbitrary complexity is described. The method consists of solving the coupled-mode equations with axially varying parameters iteratively until the boundary conditions at the two facets are satisfied. The numerical model is applied to two DFB laser structures. In the case of a multiple-phase-shift DFB laser the results show that such devices can have a more uniform axial distribution than that of a conventional quarter-wave-shifted DFB laser while maintaining sufficient gain margin between the main and side modes. In the case of a dual-pitch DFB laser it is shown that the incorporation of a slightly different grating period (~0.1%) over a small section can provide a gain margin that is comparable to that achieved in quarter-wave-shifted DFB lasers     

Analysis and optimum design of distributed feedback lasers usingcoupled-power theory

Based on coupled-power theory, the analysis and optimum design of distributed feedback (DFB) lasers are discussed. It is shown that the lowest threshold and the elimination of spatial hole burning in antireflection-coated index-coupled/gain-coupled/complex-coupled DFB lasers can be achieved by properly choosing DFB laser parameters such as the phase shift value, variations of the grating along the cavity, etc. It is also shown that coupled-power theory is simple and provides an easy approach to analytical understanding of the physical mechanisms crucial for the optimum design of DFB lasers     

Analysis of the spontaneous emission rate of multiple-phase-shift distributed feedback semiconductor lasers

A general expression for the spontaneous emission rate of multiple-phase-shift DFB semiconductor lasers is given using the transfer matrix based on the Green's function method. The spontaneous emission rate for coupled phase-shift DFB lasers is calculated.<>     

Time-dependent semiclassical theory of gain-coupled distributed feedback lasers

A semiclassical treatment of the time-dependent behavior of a gain-coupled, distributed feedback laser (DFL) has been developed. This treatment takes into account the field propagation within the DFL, and is therefore capable of predicting its behavior even for extremely short pump pulses. Comparisons are made to existing steady-state and transient theories where they are valid, showing good agreement, and new predictions are made of the behavior in the short pump pulse regime. It is found that the emitted pulse duration is dominated by the transit time through the pumped region. By studying the evolution of the field distribution inside the cavity, insight can be gained into the operation of the DFL. The effect of spatial hole burning in a gain-coupled DFL is treated and found to be small.     

Analysis of ridge-waveguide distributed feedback lasers

An analysis concerning the coupling efficiency and the threshold current density is presented for a ridge-waveguide distributed feedback laser. Particular attention is paid to the grating efficiency that is different under and beyond the ridge region because of different lateral environments and generally different corrugation depths. The threshold current density and its optimization are discussed for 1.55 μm InGaAsP lasers after considering the design parameters, such as the ridge width and the layer thicknesses. Both the TE and TM modes are considered. A narrow ridge helps to reduce the device threshold if the grating under the ridge is absent or is partially washed out during the ridge-overgrowth procedure.     

Gain-coupled distributed feedback semiconductor lasers with anabsorptive conduction-type inverted grating

A gain-coupled (GC) distributed feedback (DFB) semiconductor laser with an absorptive conduction-type-inverted grating is proposed. Devices based on GaAlAs/GaAs materials are fabricated using two-step OMVPE. By inverting the conduction type of the absorptive region, threshold current is lowered by 10 mA, which is to compensate for the threshold increase due to extra absorption. In addition, nonlinear output property associated with the saturable nature of the absorption is eliminated. An ultralow chirping capability under gain switching high speed modulation and the narrow linewidth nature of this laser are experimentally studied     

Wavelength-tunable organic semiconductor lasers based on elastic distributed feedback gratings

Wavelength-tunable organic semiconductor lasers based on mechanically stretchable polydimethylsiloxane(PDMS)gratings were developed. The intrinsic stretchability of PDMS was explored to modulate the period of the distributed feedback gratings for fine tuning the lasing wavelength. Notably, elastic lasers based on three typical light-emitting molecules show comparable lasing threshold values analogous to rigid devices and a continuous wavelength tunability of about 10 nm by mechanical stretching....     

High external feedback resistance of laterally loss-coupled distributed feedback quantum dot semiconductor lasers

External optical feedback effects on quantum dot (QD) laterally loss-coupled (LLC) distributed feedback (DFB) lasers are reported for the first time in this letter. The critical external feedback ratio that causes coherence collapse of the QD DFB is measured to be -14 dB. No spectral broadening at this feedback level is observed within the 0.06-nm resolution of the optical spectrum analyzer (OSA). Self-homodyne measurements also confirm that the rebroadened linewidth of the QD DFB under -14-dB feedback is still much smaller than the feedback-free linewidth. Under 2.5-Gb/s modulation, eye-diagram measurements show that the signal-to-noise ratio starts to degrade at a feedback ratio of -30 dB in the QD LLC-DFB, about 20 dB higher than a typical quantum-well DFB at the same output power and extinction ratio.     

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.     

Multiple-waveguide distributed feedback lasers

Coupled wave theory is used to examine the performance of lasers formed from an array of coupled stripe waveguides with a grating overlay. It is found that such lasers exhibit inherent longitudinal mode discrimination, and, if the number of coupled guides is small, inherent transverse mode discrimination as well. The conditions for such selectivity are examined in detail, and it is shown that the correct grating distribution to use is one in which the grating fills the overlap region between the coupled guides.     

Chaos in semiconductor lasers with optical feedback: theory andexperiment

The authors present a detailed theoretical and experimental investigation of the nonlinear dynamics of a semiconductor laser with optical feedback. The results show that the coherence collapsed state is a chaotic attractor and that chaos is reached for increasing feedback level through a quasi-periodic route interrupted by frequency locking. Furthermore, the coexistence of two attractors, associated with the same external cavity mode, but having different relaxation oscillation frequencies, is demonstrated and explained     

Analysis of distributed feedback lasers using optical low-coherencereflectometry

The analysis of distributed feedback (DFB) lasers by optical low-coherence reflectometry (OLCR) shows the appearance of additional more or less periodic minima in the reflectogram. These do not reflect local minima of the reflectance, but are rather due to multipath interference effects caused by spectral filtering of the white light source by the laser under test. It is shown that the coupling coefficient of the laser can be determined from the period of these minima     

Analysis of DFB semiconductor lasers with external optical feedback

A theoretical analysis of the sensitivity of DFB semiconductor lasers to external optical feedback is presented. Numerical simulations allow the authors to determine the optimum facet reflectivity, for a given κL value, to minimise the sensitivity to external optical feedback     

Tunable two-segment distributed feedback lasers

The authors describe a two-segment distributed feedback laser at 1.3 mu m with a tuning range of 12.8 AA (209 GHz) and an FM response of 7 GHz/mA. The observed tuning behaviour is in qualitative agreement with an earlier theoretical model. Such two-segment DFB lasers are useful in frequency-multiplexed, frequency-modulated optical networks.<>     

High-power single-mode simplified antiresonant reflecting opticalwaveguide (S-ARROW) distributed feedback semiconductor lasers

Simplified antiresonant-reflective-optical-waveguide distributed-feedback semiconductor lasers based on Al-free InGaAs-InGaAsP-InGaP materials are reported for the first time. Devices with 6.5-μm-wide emitting apertures operate single-frequency (λ=0.968 μm) and single-spatial-mode to 157-mW continuous-wave output power. The full-width at half-maximum of the lateral far-field pattern is 4.5°, in excellent agreement with theory. Relative intensity noise values as low as -154 dB/Hz are measured between 500 MHz and 8 GHz     

Principles of distributed feedback and distributed Bragg-reflector lasers

Wave propagation in periodic waveguides is analyzed by decomposing the eigen Bloch waves into traveling-wave components. It is shown that the principal components consist of a primary forward wave, a primary backward wave, and their Bragg-scattered secondary waves. One important parameter is the coupling constantsdue to Bragg scattering, which relates the secondary wave to the respective primary wave. Laser threshold condition is then obtained by applying the continuity of tangentialEandHat the two boundaries. The results thus obtained are general and applicable to thin-film lasers with various waveguide structures. The laser threshold condition of thin-film Bragg lasers is expressed in terms of two effective reflection coefficients for easy comparison with conventional lasers. For appreciable reflection, a significant change either in the propagation constant or in the coupling constant is required. Two basic types of thin-film Bragg lasers are distributed-feedback (DFB) lasers in which Bragg scattering is confined to the active medium and distributed-Bragg-reflector (DBR) lasers in which Bragg scattering is limited to regions beyond the active medium. The threshold gain, frequency control, and mode selectivity for both types are analyzed and the analyses are applied to GaAs and Nd lasers. It is shown that DBR lasers should have a lower threshold gain and a better mode selectivity than DFB lasers. For distributed-feedback effect to play a significant role in thin-film Bragg lasers, the product kLintmust be greater than unity whereKis the distributed-feedback coefficient and Lintis the interaction length. Advantages for having periodic structures outside the active medium so as to relax constraints onkand Lintare also discussed.     

Antisymmetric taper of distributed feedback lasers

In a distributed feedback (DFB) laser with spatial index modulation, an antisymmetric taper of the feedback parameter,k, removes the threshold degeneracy, which is characteristic of uniform structures, and leads to one mode of particularly low threshold. Exact solutions are presented for the special case of an antisymmetric step ofk. An approximate perturbation method is developed which gives simple expressions for the threshold gains, and externalQ's of some tapered distributed feedback structures. The method is tested against two exact solutions, the uniform, and the stepped-kDFB laser. It is shown that the threshold of the stepped-kDFB laser is the lowest of any structure with an antisymmetric taper and a prescribed maximum value of|k|.     

Groove-cell analysis of distributed feedback lasers

The propagation of waves in a groove cell is analyzed. This propagation is a function of transfer matrix, which contains the gain, together with the phase constant, the length of a groove cell, and the groove reflection coefficient. When the transfer matrix is cascaded the transmission of an optical field and the reflection coefficient of a distributed feedback structure can be determined even with unequal grooves and any groove number. With the help of an eigenvalue equation the threshold gain and phase constant of the resonator modes are determined for a symmetrical laser. The increase of threshold gain is demonstrated for an inhomogeneous laser with changed mean value of effective refractive index along the laser length. Bloch waves exist in a long grating (or a closed loop) of periodic grooves     

Optical feedback on self-pulsating semiconductor lasers

Weak optical-feedback effects on the statistical properties of self-pulsations in narrow-stripe semiconductor lasers are analyzed using Lang-Kobayashi-type equations. The self-pulsation features are compared with the characteristics of excited relaxation oscillations. We determine the operating regime in which the randomizing effect of spontaneous-emission noise destroys pulse coherence. In this regime, only phase-insensitive effects of optical feedback are possible, and optimum jitter reduction is achieved with delay times of the order of an integer-odd multiple of the free-running pulsation period. In the high-pump operating regime, interpulse coherence is retained and the optical-feedback phase is shown to be instrumental for pulse-jitter control. Our results show that for cavity lengths up to 10 cm, variations on the order of half an optical wavelength induce jitter variations of one order of magnitude