Above-threshold mode discrimination in external reflector andphase-shifted DFB lasers

The longitudinal mode discrimination above threshold in both distributed feedback lasers with one external reflector and those with phase-shifted grating structures is studied. By numerically solving a pair of coupled mode equations, it is shown that when these types of lasers have nonsaturable index coupling, they lose their mode discrimination at powers only a few times the saturation power of the medium due to the effects of spatial hole burning     

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     

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     

增镀光学薄膜改善DFB激光器的光谱特性

利用增镀光学薄膜的方法,有效地将原来处于双模工作的１．３μｍＤＦＢ激光器变为单模工作的激光器．选择的增镀膜层起到了抑制边模的作用．从而改变了激光器的模式特性．实验表明,增镀光学薄膜技术可望成为改善ＤＦＢ激光器单模成品率的一种辅助方法     

Lateral and longitudinal mode discrimination in index-guidedcircular ring semiconductor lasers

We present the first analysis of the mode structure and thresholds of index-guided ring lasers, and on longitudinal mode discrimination of X-junction-coupled ring lasers. Submilliampere thresholds can be achieved with single-lateral-mode ring lasers having small refractive index steps. In addition, strong longitudinal mode discrimination can be obtained with ring lasers of different cavity lengths coupled via an X junction     

Modeling of short, single-frequency, fiber lasers in high-gainfiber

Grating gain must be accounted for when designing single-frequency fiber lasers which utilize intracore, erbium-doped, Bragg reflectors for cavity feedback, and mode selectivity. A closed-form solution, derived through coupled mode theory for the spectral reflectivity of an intracore Bragg phase grating in an amplifying fiber is derived and applied to the design of single-mode fiber lasers. Both analytical and experimental results are presented     

Simulation Analysis of Higher Order Laterally-Coupled Distributed Feedback Lasers

Laterally-coupled distributed feedback (LC-DFB) lasers use a lithographic fabrication step to define the distributed feedback grating, avoiding subsequent regrowth. Using higher order gratings can enhance the lithographic tolerance for lower resolution patterning, yielding lasers more amenable to fabrication. We show that LC-DFB lasers with higher order gratings, although requiring a higher threshold gain than those of first-order, provide a degree of longitudinal mode discrimination. Incorporating radiating partial waves, we have calculated modified coupled-mode coefficients for various duty cycles, grating orders, and grating geometries using a two-dimensional finite-element method. The modified coupled-mode equations were solved with and without a $lambda /4$ phase shift. The phase shift, while beneficial for first-order gratings, was found to generally diminish laser performance for lasers with higher order gratings.      

Single-lobe symmetric coupled laser arrays

We propose a new high-power laser in which an array of N lasers is coupled to another of N + 1 lasers through Y-junctions. The field distributions of the eigenmodes in the N-array are identical to those of the supermodes in the evanescently coupled laser array. The threshold gain for the lowest-order mode is much lower than the higher-order modes. This strong mode discrimination will enable very high-power single-lobe operation.     

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.     

光纤光栅外腔半导体激光器的理论和实验分析

从耦合模理论出发,结合激光原理,研究了光纤光栅外腔半导体激光器(FBG-ECL)的理论模型．得到光纤光栅反射率的解析解。利用速率方程理论讨论FBG-ECL的高频响应特性。根据等效腔模型．讨论了耦合系数对FBG-ECL阈值特性的影响。指出存在最佳光纤光栅反射率．使得激光器不仅功率输出大,而且边模抑制比高。最后实测了不同反射率情况下激光器的激射光谱。     

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.     

Pb1-xSnxSe/Pb1-x-yEuySnxSe corrugated diode lasers

The design, fabrication, and testing of distributed Bragg reflector (DBR), distributed feedback (DFB), and grating coupled emission (GCE) Pb_1-xSn_xSe/Pb_1-x-yEu_ySn _xSe double heterostructure stripe geometry molecular-beam-epitaxy (MBE) grown diode lasers are discussed. The DBR and DFB lasers are the first Pb-salt corrugated lasers to operate in CW (continuous) mode at temperatures above that of liquid nitrogen. For the GCE lasers, a narrow far field distribution of ~5° was obtained for the first time     

Enhancement of the Mode Area and Modal Discrimination of Microchip Lasers Using Angularly Selective Mirrors

Angularly selective mirrors (ASMs) are proposed as a means to expand the mode area and modal discrimination of microchip lasers. ASMs used as output couplers selectively reflect incoming k vectors over a narrow angular range, while they transmit more inclined components. The eigenvalue problem of a microchip resonator equipped with a Gaussian ASM is solved analytically in the paraxial optics approximation using the ABCD matrix formalism. The narrow angular distribution of the reflected beam produces, through the laws of diffraction, a significant increase of the mode size and improved transverse mode discrimination, at the expense of higher oscillation threshold due to larger output coupling losses. Simulations performed using the parameters of Yb³⁺-doped YAG material show that one order of magnitude increase of the mode area can reasonably be achieved without causing overheating and thermal fracture. ASMs can be directly deposited on the active material in the form of a resonant grating mirror. This technology involves only planar batch processes that retain the mass production advantage of microchip lasers. The significant increase of brightness of microchips expected from this innovation will give rise to more effective and more compact devices and new applications.     

A new DFB-laser diode with reduced spatial hole burning

An index coupled antireflection-coated distributed-feedback (DFB)-laser diode which theoretically exhibits a longitudinally uniform power density is proposed. The structure contains an amplitude modulated grating and is far more efficient in reducing spatial hole burning than multiphase-shift lasers. The laser can be expected to be single mode up to high power levels. It can be of interest when long lasers with a reduced linewidth and a flat FM response are to be used or as a laser with small modulation distortion in analog communication     

Polarization optical bistability induced by TM mode injection to aDFB laser with complex coupled coefficient

A novel method is proposed to produce an optical bistability by using a dynamically stable complex coupled DFB (CC-DFB) laser with TM mode injection. In this paper polarization optical bistabilities are analyzed in detail using coupled mode equations and rate equations for the CC-DFB lasers considering the longitudinal hole burning and carrier dependent complex coupling coefficients. Several parameters reflecting the physical features of a complex coupled DFB laser are discussed. It is shown that for a CC-DFB laser the polarization bistability induced by the TM mode injection is much stronger for the antiphase of complex coupling than that for the in-phase. In addition, the influences of initial coupling condition for gain grating structure on the optical bistability are also investigated considering both cases of the antiphase and in-phase     

Realization of dot DFB lasers

Dot lasers with first-, second- and third-order gain coupled distributed feedback (DFB) gratings have been realized by low damage dry etching in combination with wet chemical etching and epitaxial over-growth. This technique allows above room temperature (RT) operation of dot DFB lasers with dot diameters down to 85 nm. The laser spectra show the expected emission of gain coupled DFB lasers. Threshold current densities between 1.1 kA/cm/sup 2/ and 2.6 kA/cm/sup 2/ could be obtained depending on size of the active region. An improvement in T/sub 0/ could be demonstrated comparing 0-D/1-D/2-D lasers on the same wafer. Based on the dot grating geometry improvement of the side mode suppression ratio (SMSR) was observed for broad-area dot DFB lasers.     

Highly efficient grating-coupled surface-emitters with single outcoupling elements

We demonstrate highly efficient grating coupled surface emitting lasers with single-grating outcouplers. An outcoupling efficiency of 94% into air was achieved using a nonresonant rectangular second-order grating in combination with a multilayer reflector below the waveguide. This resulted in an external differential quantum efficiency as high as 50%, comparable to that of conventional edge-emitting lasers, limited by absorptive loss in the passive grating sections. The lasers have separated oscillators and outcouplers, which facilitates the fabrication of surface emitters that possess beam-shaping capabilities through holographic wavefront conversion.     

Asymmetric twin-waveguide 1.55-μm wavelength laser with adistributed Bragg reflector

We demonstrate a single frequency, 1.55 μm wavelength laser based on an asymmetric twin-waveguide structure using a single growth step and a simple fabrication process. The external Bragg grating is formed on the passive ridge waveguide, optically coupled to the twin-guide gain section using a low loss, tapered mode transformer. The grating is produced by near-field holographic printing using a phase mask. Output powers >11 mW in a small-spot waveguide with a side-mode suppression ratio >40 dB and a slope efficiency of 0.11 W/A are obtained under pulsed operation. These performance characteristics are comparable to conventional, nonintegrated, conventional discrete DBR lasers, although the twin-waveguide design is compatible with photonic integrated circuits such as monolithic transmitters and WDM coherent receivers     

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.     

Influence of standing waves on DFB lasers including saturableabsorptive gratings

The influence of standing waves on the performance of distributed feedback (DFB) lasers is investigated, whereby local changes of the wavenumber as induced by gain compression or inhomogeneous saturation of an absorptive grating are incorporated into the coupled wave equations. With the help of this model, it is shown that gain compression ultimatively limits the maximum output power for monomode operation. As compared to in-phase complex-coupled lasers, it is shown that the worse monomode capability of antiphase complex-coupled lasers is related to the better stability properties of these lasers. Additionally, a characteristic interaction between the saturable absorptive grating and the optical field is found, which furthermore reduces the maximum monomode output power of antiphase complex-coupled lasers with saturable absorptive gratings