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.     

Analysis of radiation mode effects on oscillating properties of DFBlasers

The effects of radiation mode on the oscillating properties of distributed feedback (DFB) lasers with second-order corrugations are analyzed for designing a new type of DFB laser. A formulation based on the transfer matrix technique is applied to calculating Streifer's ζ-terms added to the coupled-wave equations. These terms represent the effects of radiation and evanescent modes. This formulation greatly simplifies the analysis of distributed resonance along multilayered waveguide structures with arbitrary-shaped second-order corrugations. The effects of vertical resonance are also incorporated into the formulation. Various types of DFB lasers with phase-shifted second-order corrugations are analyzed using this method. It is found that the phase shift and the blaze of the corrugations greatly affect the longitudinal mode selectivity. A new phase-shift DFB laser structure with two complementary blazing regions connected at the shift is proposed. It is demonstrated that this structure has small radiation loss resulting in low-threshold performance despite employing second-order corrugations     

Improved coupled mode analysis of corrugated waveguides and lasers

Corrugated waveguides and lasers in resonant and non-resonant situations are analyzed by an improved coupled mode theory based on a set of the coupled mode equations for guided modes and radiation continuum. The distributed feedback (DFB) coefficient and the radiation loss coefficient are given in closed forms. The formulation can be applicable to arbitrarily shaped gratings and multilayer waveguide structures. The accuracy of the theory is examined by comparing it with Tamir's exact calculation for a nonresonant situation and also with Streifer's one for a DFB structure. Reasonable accuracy is obtained by the proper choice of the unperturbed waveguide parameter. The dependence of the two coefficients on the grating depth, the grating period, the guide layer thickness, and the refractive index difference between core and cladding layers is obtained for all Bragg orders up to the fourth, and for four typical grating shapes, namely, for rectangular, sinusoidal, symmetric triangular, and sawtooth gratings. Both the threshold gain of DFB lasers utilizing higher order Bragg reflection and the output coupling efficiency of grating beam couplers are also calculated for these parameters. A new multilayer structure for controlling the radiation loss is proposed and analyzed. This structure is suitable for the suppression of the radiation loss in DBR reflectors as well as for the improvement of the output coupling efficiency in grating beam couplers.     

DFB光纤激光器最佳输出特性研究

采用传输矩阵法,对影响DFB掺铒光纤激光器输出功率的耦合因子、光栅长度进行了研究,数值分析了不同谐振腔损耗下最佳输出功率所对应的最佳光栅长度及耦合因子的变化。结果表明,在设计光纤激光器时,根据光纤光栅的制作损耗,优化光栅长度及耦合因子可以使光纤激光器的输出实现最佳化。这些结论对基于光纤激光器的结构优化具有指导意义。     

Analysis of TM-polarized DFB laser structures with metal surfacegratings

An analysis of distributed feedback (DFB) laser structures with metallized surface grating structures in TM polarization is presented. The modal properties of these structures are described using coupled-mode theory where the coupling coefficients are derived from rigorously computed on-resonant Floquet-Bloch solutions of the waveguide grating problem. Based on this theory, first- and second-order DFB quantum cascade laser structures operating at a wavelength of 10 μm are investigated numerically. We show that, utilizing a metal stripe grating structure, second-order laser structures are feasible showing efficient surface emission, whereas radiation into the substrate is strongly suppressed. The fraction of stimulated emission power being emitted via the surface can be as high as 17.5% whereas a low threshold gain of 20 cm^-1 is maintained     

Nonlinear analysis of a dielectric distributed feedback laser withcomplex coupling coefficient

An approximate analysis of the nonlinear operation of DFB a dielectric laser with complex coupling coefficient is presented, An expression relating the small signal gain to the output power and the system parameters, including the spatial hole burning effect, is obtained. It is shown that the gain grating, the loss grating, and the higher order Bragg grating all contribute to laser operation above the threshold in a different manner. Moreover, it is possible to achieve a “negative” gain effect in the partly gain-coupled structure operating above the threshold, which depends on the output power level, the distributed loss level and the spatial hole burning effect     

A new method for the calculation of the emission spectrum of DFBand DBR lasers

A method based on transmission matrices that allows the emission spectra of arbitrarily complicated semiconductor laser structures to be computed below and above threshold has been developed. These can include active and passive periodic or uniform sections. As examples, the authors compute the emission spectra of a normal distributed feedback (DFB) laser, a DFB laser with a λ/4 phase shifter, and a surface-emitting distributed Bragg reflector (DFB) laser. To do that, Petermann's method for calculating the spontaneous emission coupling coefficient has been extended to the case of a periodic waveguide. It is shown how the spontaneous emission, when treated correctly, can be used to measure the coupling coefficient of the grating in a DFB laser with a λ/4 phase shifter     

高成品率DFB激光二极管的设计及制备

设计并制作了一种新型分布反馈(DFB)光栅激光二极管结构.采用传输矩阵法模拟得到了不同光栅耦合因子、不同结构下随机相位对归一化阈值增益差和性能参数分布的影响;对高于阈值增益情况下激光二极管的特性进行了分析,结果表明随着激光二极管偏置电流的增加,光场平坦因子和归一化阈值增益差几乎保持不变,激光二极管单模稳定性好;模拟得到了光谱随偏置电流的变化,不同偏置电流下光谱的边模抑制比均大于40 dB.采用全息光刻技术结合普通光刻技术制备了新型DFB光栅.相比于均匀光栅激光二极管,新型DFB光栅激光二极管性能参数一致性更好、成品率更高,成品率达到80％以上.     

Influence of a nonuniform coupling coefficient on the static andlarge signal dynamic behavior of Bragg-detuned DFB lasers

A time domain model is used to study the large signal dynamics of general Bragg-detuned cavities. Such structures, in which the grating pitch is spatially nonuniform so that a distributed phase shift is produced along the cavity, are often called corrugation-pitch-modulated distributed feedback lasers (CPM-DFB). Furthermore, by introducing a longitudinally dependent coupling coefficient κ, a corrugation-pitch-modulated distributed-coupling-coefficient DFB laser (CPM-DCC-DFB) with quite different spectral properties can be realized. We present in this paper a comparison between these two kinds of components. It is shown that an adequate profile of the coupling coefficient (stronger coupling at the center of the cavity) in a CPM-DCC-DFB structure can help to achieve better steady-state singlemode operation with respect to conventional CPM-DFB lasers (uniform coupling coefficient). However, in CPM-DCC-DFB lasers, side modes are liable to be excited during the turn-on transient interval, thus imposing a limitation to the modulation depth requirement     

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.     

低掺杂铒纤上分布反馈布拉格光纤激光器的制作

采用准分子激光器成功地在低掺杂普通铒纤上制作出5 cm的光纤光栅分布反馈布拉格(DFB)激光器,铒纤的峰值吸收率为5 dB/m,在100 mW,980 nm抽运光条件下,光纤激光器的输出功率为50μW,边模抑制比为50 dB。使用耦合模理论分析了一段5 cm带相移的分布反馈布拉格光纤激光器输出光强同腔内损耗及相移量的关系,计算结果表明,光纤腔内的损耗对激光器的输出具有非常重要的影响,大的损耗对应获得最大功率的光栅耦合强度相应减小,因此,在低掺杂铒纤上制作分布反馈布拉格激光器必须正确估计光纤激光器的腔内损耗,选择合适的光栅耦合强度,可以获得较大的输出功率。     

The effect of complex coupling coefficients on distributed feedback lasers

The effect of complex coupling coefficients on the performance of distributed feedback (DFB) lasers is studied. The physical origins of a complex coupling coefficient are specified, and its relation with gain or loss mechanisms which occur inside the laser is discussed. Numerical results are presented for the oscillation frequencies, threshold gains, and intensity patterns of the longitudinal modes of the DFB laser.     

Threshold condition of DFB semiconductor lasers by thelocal-normal-mode transfer-matrix method: correspondence to thecoupled-wave method

An analytical expression for the threshold condition of DFB semiconductor lasers is derived based on the local-normal-mode transfer-matrix method (TMM). The threshold condition is expressed in terms of an equivalent reflection coefficient of a DFB laser structure and a Bloch-wave propagation constant. It is shown that the TMM threshold condition can reproduce the one which is derived by the coupled-wave method (CWM) under certain conditions. It is also shown that the CWM can predict very accurately the spatially averaged values of the threshold modal gain and the detuning frequency which are obtained by the TMM if the coupling coefficient in the CWM is replaced by the TMM coupling coefficient     

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.     

The design assessment of λ/4 phase-shifted DFB laserstructures

A detailed nonlinear model of the performance of single-frequency laser structures operating both below and above threshold is discussed. Arbitrary series combinations of uniform pitch grating, linearly-chirped pitch grating and plane guide sections can be analyzed-taking longitudinal-mode spatial hole burning into account. The material properties of each section of a device structure can be specified. The output power from each end of the laser and the emission wavelength, and the longitudinal intensity, carrier density, and relative permittivity profiles are predicted as a function of drive current above threshold for each lasing mode. The linewidth is also estimated while allowing for the nonuniform longitudinal distribution of spontaneous emission into the mode in a physical manner. The model was used to provide the data with which to trade off the numerous interacting performance parameters of a λ/4 phase-shifted DFB (distributed-feedback) laser. The design options are then summarized     

Above-Threshold Spectrum of the Radiation Field in Surface-Emitting DFB Lasers

This paper addresses the above-threshold analysis of the amplified spontaneous emission spectrum of the radiation field in surface-emitting distributed feedback (DFB) lasers with a second-order grating. To the best of the authors' knowledge, this paper is the first report in this regard. The analysis takes advantage of the time- and frequency-domain approaches. The essence of this method is obtaining the spectrum of the laser power using the fields in the frequency domain, whereas the above-threshold carrier distribution inside the cavity is obtained by the finite-difference time-domain approach. The use of this approach can be justified by the fact that the wave equations in the time and frequency domains are related by the Fourier transform. Applying this method to the surface-emitting DFB lasers with a second-order grating, the authors will demonstrate that excitation of the radiation field by the interference between the counter-propagating waves inside the cavity provides additional filtering mechanism, which makes the side-mode suppression ratio of the power emitted from the surface different than that from the edge. More importantly, it is shown that the interesting features of a properly designed quarter-wave phase-shifted surface-emitting DFB lasers with a second-order grating can be exploited in the design of transmitters for optical communications     

Analysis of TE and TM modes in DFB lasers by two-dimensional theory

The two-dimensional theory of a distributed feedback (DFB) laser (which was previously presented and applied to the analysis of the laser threshold conditions for the transverse-electric (TE) mode in a simple three-layer waveguide structure) is developed to treat both TE and transverse-magnetic (TM) modes in a four-layer waveguide structure with a thin grating layer, which more closely reflects actual DFB laser structure. The differences between TE and TM modes for the dispersion relations and the laser threshold conditions are clarified. The effects of the waveguide structure (including grating layer thickness, refractive indexes of layers, coupling constant, and corrugation period) on the threshold gains and the gain differences between the two longitudinal modes on both sides of the Bragg frequencies are studied in detail for both TE and TM modes     

Analysis of optical-injected distributed feedback lasers using complex optical low-coherence reflectometry

A theoretical and experimental investigation of reflectograms obtained for a distributed feedback (DFB) semiconductor laser using a phase-controlled high-resolution optical low-coherence reflectometer was carried out, yielding the effective group refractive index and its variation above threshold, the cavity internal loss, as well as the grating coupling factor of a multiquantum-well DFB laser. In addition, direct measurements of the injection-induced complex-modal index changes are presented for the first time.     

High-Power Distributed Feedback Laser Diodes Emitting at 820nm

通过将二级光栅直接刻在脊形波导AlGaInAs/AlGaAs DFB激光器的无铝光波导层上,实现了波长约为820nm,单面功率为30mW的单纵模激光器.由于采用无铝光栅,保证了二次外延质量,从而得到较好的器件性能.激光器的阈值电流为57mA,斜率效率约为0.32mW/mA.