Amplified-spontaneous-emission spectrum of the radiation field in surface-emitting DFB lasers

In this paper, the authors calculate the amplified-spontaneous-emission spectrum of the radiation field in surface-emitting distributed feedback (DFB) lasers. The response of the laser cavity to the Langevin noise source in the frequency domain is obtained using the newly developed Green's functions for the slowly varying amplitudes of the guided waves. The authors show that the power spectra from the surface and the edge are different, and this discrepancy is due to excitation of the radiation field by the interference between the counter-propagating waves inside the cavity. This feature can be properly exploited in the design of surface-emitting DFB lasers for optical communications.     

Mode analysis of DFB SE lasers

This paper presents theoretical results on mode characteristics of surface-emitting (SE) lasers utilizing an active second-order grating section. Based on a coupled-mode approach, longitudinal modes and the associated space-harmonic transverse modes are calculated via a numerical technique. From these, the lasing-mode spectrum, near- and far-field patterns of the radiation mode, and the surface-emission power efficiency are obtained. Effects of the substrate reflector and the grating parameters are also investigated. Finally, comparisons are made with conventional, edge-emitting DFB lasers. The results indicate that with a suitable choice of structural parameter values, DFB SE lasers can be made to possess both the spectral discrimination of the conventional DFB lasers and the advantages of SE lasers at the same time and also that the second lowest longitudinal mode may be preferred over the fundamental longitudinal mode for many applications due to its symmetric field distribution     

Dynamic analysis of radiation and side-mode suppression in asecond-order DFB laser using time-domain large-signal traveling wavemodel

In this paper, we have developed a relatively simple algorithm to calculate the large-signal dynamic response of DFB lasers by solving the time-dependent coupled wave equations directly in the time domain. The spontaneous emission noise, longitudinal variations of carrier (hole burning) and photon densities as well as that of the refractive index are taken into consideration. To demonstrate the power of this straightforward algorithm, the model shows how the side-mode suppression ratio in devices with high κL and a λ/4: phase shift is significantly affected by the radiation in the second-order DFB laser. The time-dependent radiation pattern in grating-coupled surface-emitting lasers is also calculated for the first time     

Second-order distributed feedback lasers with mode selection provided by first-order radiation losses

We present a theoretical study of the effect of radiation losses on the mode selectivity of DFB lasers with second-order gratings. For a second-order grating, interference of the radiation due to first-order diffraction of oppositely propagating guided waves cancels the radiation loss at one of the edges of the spectrum gap. This provides threshold gain discrimination of order 10 cm^-1against one of the two dominant modes occurring near the edges of the gap. This should allow fabrication of DFB lasers with properties that are nearly independent of the positions of the facets relative to the grating corrugations, which are uncontrolled. By applying antireflection coatings to the two ends, differential quantum efficiencies close to those of conventional Fabry-Perot lasers should be achievable.     

Optically pumped surface-emitting DFB GaInAsP/InP lasers with circular grating

The lasing action in surface-emitting DFB lasers with circular grating (SE-CG DFB) is reported for the first time. 1.283 mu m laser oscillation is demonstrated by optical pumping. The threshold pumping power density is estimated to be 16.2 kW/cm/sup 2/. The pulsed output power is more than 25 mW.<>     

Above-threshold analysis of second-order circular-grating DFBlasers

The behavior of second-order circular-grating DFB lasers in the above-threshold regime are analyzed. The formulation uses the standing wave method for treating lasers with second-order gratings. The effects of spontaneous emission and the variation of carrier and photon densities in the radial direction are included in a self-consistent fashion in the model. In particular, we examine the output power emitted from the surface of the laser, the near-field, and the far-field pattern of the laser as a function of the injected current     

The effect of die bonding distributed feedback lasers

The effect of die-bonding-induced strain on the output spectra of gain-coupled distributed feedback (DFB) diode lasers was investigated. Bonding strain affects the in situ diffraction grating in DFB lasers and manifests itself as changes in the output spectrum. It is shown in this paper that such changes are observed in DFB lasers by comparing the spectra before and after die bonding. In addition, it was also observed that upon die bonding the lasing mode can, in some cases, flip from one side of the stopband to the other. This flip was modeled using a probability-amplitude transfer-matrix DFB laser model that included a bonding-induced perturbation of the pitch of the Bragg grating along the length of the cavity. The nonuniform strain perturbation of the pitch of the grating was determined from a finite element method simulation of a die bonded laser chip and correlated well with the strain that was deduced from measurements of the degree of polarization of photoluminescence from bonded chips.     

Effects of radiation loss on the performance of second-order DFBsemiconductor lasers

The effects of radiation loss on the performance of second-order distributed-feedback (DFB) semiconductor lasers with a symmetrical grating are analyzed systematically. The threshold gains of the two lowest modes, the differential quantum efficiency, and the spectral linewidth are calculated as a function of the complex coupling coefficient. The comparison is also made between a conventional DFB and a quarter-wave phase-shifted DFB laser. It is shown that the effects of radiation loss are different in these two laser types. In addition, a simple approximate expression for threshold gain is derived. By way of example, a DFB laser with a rectangular grating is analyzed. It is shown that the performance of a second-order DFB laser is not sensitive to the grating pitch over a fairly wide range, provided that it is close to the pitch which gives the maximum coupling coefficient     

Radiation patterns of higher azimuthal order spatial modes from aconcentric-circle-grating waveguide cavity using the volume-currentmethod

We calculate the surface-emitted scattered radiation from a concentric-circle-grating waveguide cavity. The full vector form of the scattered radiation is calculated using the volume-current method, where the index perturbation caused by the grating is represented as an induced-current driving term in the free-space wave equation for the scattered field. We show intensity patterns and field vector plots for a range of azimuthal modes besides the previously reported fundamental mode, and we find excellent agreement with the observed emission patterns and field polarization from concentric-circle-grating surface-emitting semiconductor lasers     

Transfer-matrix formulation of spontaneous emission noise of DFBsemiconductor lasers

A unified formulation of the spontaneous emission noise in semiconductor DFB (distributed feedback) lasers is presented by using a transfer-matrix approach. Analytical expressions for the noise power per unit frequency bandwidth below threshold and the spontaneous emission rate into the lasing mode are obtained based on the Green's function method. Three DFB laser structures are analyzed: (1) a standard DFB structure with facet reflectivities, (2) a multisection DFB structure composed of n sections which models a phase-shifted DFB laser and a multielectrode (tunable) DFB laser, and (3) a periodic layered DFB structure which models a surface-emitting DFB laser. It is shown that the spontaneous emission noise of a complicated DFB laser structure can be calculated easily by the transfer matrix of each section of the structure and its derivative to frequency     

Axial profile of grating coupled radiation from second-order DFBlasers with phase shifts

Axial profiles of the grating-coupled radiation field emitted in a direction normal to the surface of distributed-feedback (DFB) lasers with phase-shifted second-order corrugation are theoretically analyzed. The profiles are calculated for nonreflecting DFB lasers with the following phase shifts: λ/4 shift, two λ/8 shifts, and two 3λ/8 shifts. It is demonstrated that the radiation field can be controlled by changing the phase shifts. This result suggests a new method for modulating the surface emission of a DFB laser     

Above-threshold analysis of loss-coupled DFB lasers: threshold current and power efficiency

The threshold current and power efficiency of loss-coupled DFB lasers have been calculated numerically using an above-threshold model. Compared with perfectly AR-coated devices, lasers with asymmetric facet coatings have substantially lower threshold current. However, significantly higher front-facet power efficiency is only possible at small grating-coupling coefficients. In particular, the range of loss-coupling coefficients for higher efficiency becomes narrower with larger grating duty cycle and larger index-coupling coefficient. These results can be explained by the interdependence of the reflectivity and extra loss associated with loss-coupled gratings.     

Analysis and design of combined distributed-feedback/Fabry-Perotstructures for surface-emitting semiconductor lasers

We propose combined distributed-feedback/Fabry-Perot (DFB/FP) structures for surface-emitting semiconductor lasers. The analysis is based on coupled-wave equations modified for surface-emitting lasers. The proposed structures, which exhibit enhanced resonance due to a matching between the gain and field distributions resulting in a reduced threshold compared with simple FP structures, are formed by placing the DFB structure between two DBR mirrors of an FP resonant cavity and introducing phase layers between the DFB region and the mirrors. It was found that the periodic-gain structures are a special case of the combined DFB/FP structures in which the index coupling effect is assumed to be negligible due to a small fill factor or a small refractive-index difference. The effect of complex (gain and index) coupling on the design and the threshold characteristics of the structures is clearly illustrated. Some important design considerations that were neglected in the previous papers are addressed     

Gain clamping in semiconductor optical amplifiers with second-order index-coupled DFB grating

A systematic investigation of gain-clamped semiconductor optical amplifiers (GC-SOAs) based on the second-order index-coupled DFB gratings is carried out by way of simulation. In particular, we focus on the main effects of the radiation loss caused by the first-order diffraction of the gratings on the amplifier performance. The magnitude of the total complex coupling coefficient is the main factor to determine the level of gain clamping. We demonstrate that a high-performance GC-SOA can be realized by using purely loss-coupled second-order DFB gratings with more relaxed tolerance on grating strength and period. It is shown that, in the presence of weak reflection-related coupling, the parasitic radiation loss associated with the second-order grating always helps to expand the linear amplification region and to reduce the longitudinal spatial hole burning along the cavity. Further, we demonstrate through comparison that the GC-SOAs have higher saturation power and much shorter carrier lifetime than the conventional SOAs. An improved design by longitudinal variation of the grating duty cycle is proposed such that the noise performance of the amplifier can be enhanced without much sacrifice on the linear amplification regime.     

Second-order distributed feedback polymer laser based on holographic polymer dispersed liquid crystal grating

We report on the fabrication and characterization of a second-order distributed feedback (DFB) polymer laser based on a holographic polymer dispersed liquid crystal (HPDLC) transmission grating. The fine organic grating is fabricated on top of the homogeneous conjugated polymer layer in a one-step process. The device shows surface-emitting, single mode laser emission with a threshold of 13.3 μJ/cm², and the working characteristics merely degrade after 10 months of storage in ambient atmosphere. We further explain the dependence of threshold on pumping length, and demonstrate the small refractive index modulation of this all-organic grating is sufficient to maintain efficient DFB laser action. This simple working structure, combined with large processing area provided by the holographic polymerization technique, is extremely promising in realizing ultra-low cost plastic lasers.     

Spontaneous emission model of surface-emitting DFB semiconductorlasers

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 λ/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     

中红外可调谐量子级联激光器研究进展

量子级联激光器(QCL)是中红外波段重要的激光光源,其中,可调谐中红外量子级联激光器具有单纵模、频率可调谐的优点,成为目前研究的热点。可调谐中红外量子级联激光器主要通过分布反馈(DFB)光栅、分布布拉格反射(DBR)光栅、外腔衍射光栅等方法实现。本文介绍了中红外量子级联激光器的基本原理,分别归纳、总结了近年来DFB、DBR可调谐量子级联激光器以及外腔可调谐量子级联激光器的研究进展,讨论了各种可调谐方法的优缺点。最后,对可调谐量子级联激光器的发展趋势进行了展望。     

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 second-order gratings

The results of an analysis of second-order gratings used as distributed Bragg reflectors in surface-emitting lasers are presented. The gratings provide reflection, output coupling, and power transmission to other gain segments for purposes of injection locking. The analysis determines these quantities for arbitrary-shaped grating teeth and includes the presence of a substrate reflector to reduce the radiated power in that direction. The reflector is shown to be effective, but only if it can be precisely positioned. Examples illustrating variations in dimensions, tooth shapes and heights, waveguide loss, and detuning are included. Second-order, square gratings, whose conventional coupling coefficient is identically zero, exhibit substantial reflectivity which is primarily produced by the radiation reaction. The analysis also forms the basis for calculating the far-field grating coupled radiation patterns