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     

Effective-index matrix analysis of distributed feedbacksemiconductor lasers

A method is developed for calculating the threshold gain in distributed feedback (DFB) semiconductor lasers consisting of a four-layer waveguide. Each corrugation region is expressed by a transfer matrix comprising the complex effective index, and the threshold calculation is reduced to the matrix multiplication. It is found that a periodic variation of the effective gain and loss induced by the modulation of the optical confinement factors gives rise to the threshold gain difference between the two adjacent modes on both sides of the Bragg frequency in standard DFB lasers without facet reflections. The absorption loss in the guiding layer increases the amplitude of the gain modulation, resulting in the increase of the threshold gain difference     

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     

Longitudinal mode behaviors of 1.5 µm range GaInAsP/InP distributed feedback lasers

Longitudinal mode behaviors of asymmetric structure distributed feedback buried heterostructure (DFB-BH) lasers are examined theoretically and experimentally. A 1.5 μm range GaInAsP/InP DFB-BH laser was fabricated by a three-step LPE growth process. We measured the stopband in the spectrum of the DFB laser. It was found that no resonance mode emission occurred in the gain spectrum and its spectrum was asymmetric with respect to the Bragg wavelength. Most of the lasing power concentrated on the DFB mode adjacent to the stop-band which was determined by the Bragg condition. The measured spectrum was explained by the calculated results of the coupled wave theory with external reflectors. The asymmetric spectrum was caused by the relative position of the cleaved facet on the corrugation grating. It was shown that the asymmetric structure DFB laser, which consisted of two end facets with different reflection coefficients, gives a stable single longitudinal mode. There was no mode jump up to 2.3 times threshold. At a modulation depth of 100 percent, the ratio of the highest nonlasing mode intensity to the lasing DFB mode was estimated to be -16.0 dB.     

The symmetry of the amplified spontaneous emission spectrum incomplex-coupled DFB lasers

We present relations between facet reflections and coupling coefficient for the amplified spontaneous emission (ASE) spectrum of a complex-coupled, an index-coupled, and a gain-coupled distributed feedback (DFB) laser to have a mirror image with respect to the Bragg wavelength. We show that the ASE spectrum of a complex-coupled DFB laser cannot be symmetric in general with respect to the Bragg wavelength. The index-coupled and gain-coupled DFB lasers can have symmetric ASE spectrum for some values of the phase of the facet reflection coefficient that are determined     

High-temperature single-mode operation of 1.3-μm strained MQWgain-coupled DFB lasers

Single-mode and high-power operation at temperatures up to 120°C has been achieved in 1.3-μm strained MQW gain-coupled DFB lasers. A stable lasing wavelength is maintained due to a large modal facet loss difference of the two Bragg modes, which is provided by the gain-coupling effect. A very low temperature dependence of the threshold current has been obtained by detuning the lasing wavelength to the long wavelength side of the material gain peak at room temperature, which effectively compensates the waveguide loss at higher temperatures. An infinite characteristic temperature T_o can be realized at certain ranges of temperature depending on the detuning value     

Theoretical analysis of external optical feedback on DFB semiconductor lasers

The effect of external optical feedback on resonant frequency, threshold gain, and spectral linewidth of distributed feedback (DFB) semiconductor lasers is theoretically analyzed. The analysis applies to any type of laser cavity formed by a corrugated waveguide limited by partially reflecting facets. It is shown that the sensitivity to optical feedback on a facet is closely related to the power emitted through this facet. Numerical results on wavelength selectivity and on sensitivity to optical feedback are given for conventional DFB lasers having an AR-coated facet and for quarter-wave-shifted (QWS) DFB lasers with AR-coatings on both facets. Both laser types are found to be more sensitive to optical feedback on their AR-coated facet than Fabry-Perot lasers for lowkL. On the other hand, QWS-DFB lasers are found to be relatively insensitive to optical feedback for largekL.     

Effect of mirror facets on lasing characteristics of distributed feedback InGaAsP/InP laser diodes at 1.5 µm range

The effect of mirror facets on lasing properties of distributed feedback (DFB) InGaAsP/InP laser diodes was studied theoretically and experimentally. A DFB laser with a window region was found to be suitable to examine the effect of mirror facets. The effective reflectivity of a window structure was calculated to be very small, typically as small as 0.03 percent for a few tens of micrometers of the window region. These small effective reflectivities were experimentally confirmed. Three kinds of DFB lasers, i.e., a double-window (DW), a single-window (SW), and a Fabry-Perot (FP), were discussed. Two modes with a separation corresponding to a so-called stopband appeared in a DW-DFB laser, in which almost no reflection at both ends was estimated. On the other hand, the threshold and the resonant wavelength of an SW- and an FP-DFB laser were found to be sensitive to the phases of corrugation at the facets. It turned out, however, that the mirror facet contributed to the single-mode operation due to an asymmetric resonant spectrum and to the reduction in the threshold. Although a low-threshold-current FP-DFB laser was experimentally obtained, the coincidence between the gain peak and the Bragg wavelengths was essential in this type. The SW-DFB laser seemed the most promising among the three types in terms of the stability of the single-mode 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.     

Laterally coupled strained MQW ridge waveguide distributed-feedbacklaser diode fabricated by wet-dry hybrid etching process

The fabrication and the characteristics of the laterally coupled GaInAsP-InP quantum-well ridge waveguide distributed-feedback (DFB) lasers are presented. The electron beam (EB) lithography and the wet and dry hybrid etching technique have been used to fabricate the deep grating structures for the DFB lasers on and beside the sidewalls of the narrow ridge waveguide. The threshold current was 18.5 mA at 20°C, and the sidemode suppression ratios (SMSRs) were ensured to be more than 40 dB for as-cleaved devices with various cavity lengths. The continuous-wave output powers of over 15 mW/facet have been observed, while transverse and longitudinal modes have remained in single mode at this output level     

Transfer matrix analysis of the amplified spontaneous emission ofDFB semiconductor laser amplifiers

Analytical expressions are derived for the amplified spontaneous emission of a DFB (distributed-feedback) semiconductor laser amplifier with reflective cavity ends. The analysis is extended to a multisection DFB structure including a phase-shifted DFB semiconductor laser amplifier. It is shown that the spontaneous emission power per unit frequency bandwidth emitted from one facet is proportional to the transmission gain and to a quantity which at threshold becomes the inverse of the differential quantum efficiency of the other facet. The analysis is applied to two practical cases: (1) calculation of emission spectra of a DFB semiconductor laser biased below the threshold, and (2) assessment of the signal-to-noise ratio performance of DFB semiconductor laser amplifiers     

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     

Instability of coherence in semiconductor laser due to externalfeedback in hybrid-integrated optical waveguide components

The coherence instability of oscillation-frequency shift and spectrum-linewidth fluctuation of a distributed feedback (DFB) semiconductor laser due to reflected feedback from input or output facets in a butt-coupled waveguide device is theoretically analyzed. A low-loss butt-coupling method between a semiconductor laser and a waveguide device for hybrid-integrated optical components used in coherent optical-fiber systems is presented. The calculated results indicate that (1) the coherence instability of the DFB lasers is sensitive to external optical feedback, (2) feedback from the waveguide input facet affects the laser frequency and gain shifts, and (3) feedback from the output facet intensifies the linewidth fluctuations     

Design and realization of InGaAs/GaAs strained layer DFB quantumwell lasers

Optical waveguiding in an InGaAs/GaAs strained-layer distributed feedback (DFB) quantum well laser is investigated using the one-dimensional shooting method presented. The numerical approach is used to optimize the waveguide geometry and to calculate the corrugation period and the coupling factor for the integrated Bragg grating. The quantum well DFB structure designed according to the numerical calculations for an emission wavelength of 982 nm was realized for the first time entirely by molecular beam epitaxy (MBE) growth. Thus, side-mode suppression ratios of 49 dB, threshold currents of 7 mA and quantum efficiencies of 0.4 mW/mA were achieved     

Quasi-periodic complex-coupled distributed-feedback structures withan exponential-like gradient of coupling

We investigate theoretically the linear properties of quasi-periodic complex-coupled distributed-feedback (DFB) structures in which the coupling constants experience a longitudinal variation along the propagation axis according to an exponential-like relationship (exp, sh, ch, ···). The results of the simulations are in good accordance with what could be expected at first sight from the particular form taken in this case by the coupled-wave equations. In particular, the gradient of coupling can provide a shift, either of the apparent average absorption (respectively, gain) or of the detuning from Bragg resonance, depending upon its exact form, Moreover, we show that this shift is asymmetric with respect to the direction of propagation, leading to a nonreciprocal behavior in reflection. We extend our analysis up to the laser modes at threshold     

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.     

Gain margin analysis of distributed feedback lasers for bothtransverse electric and magnetic modes

A theoretical analysis of the gain margin with both transverse electric (TE) and transverse magnetic (TM) modes in distributed feedback (DFB) lasers of second-order gratings and various structural parameters is presented. Though the dominant mode is usually a TE mode, one of the TM modes often becomes the secondary mode with the second lowest threshold and seriously affects the single-mode characteristics of DFB lasers. To design DFB lasers with a large gain margin, proper amounts of facet reflectivity for both polarizations and control of the spatial phase of the grating at the facet are required     

A strained-layer InGaAs-GaAs asymmetric cladding gain-coupled DFB laser with titanium surface gratings by metalorganic chemical vapor deposition

A single growth step ridge waveguide InGaAs-GaAs distributed feedback (DFB) QW laser with second-order Ti surface gratings is described. The Ti gratings introduce a periodic variation of the loss in the cavity to promote single frequency emission. The device operates on single longitudinal and lateral modes, with a threshold current of 27.9 mA and more than 30 dB of side-mode suppression.     

Analysis of TE/TM mode selectivity in DFB lasers with a phase-shift region

In phase-shift distributed feedback (DFB) lasers, there is limited suppression of the TM mode despite extremely large submode suppressibility. The TE/TM mode selectivity of a DFB laser structure with a nonuniform waveguide region as the phase shifter is analyzed. Calculations of the threshold gain difference between the TE and TM modes are performed using the effective index method and the coupled-wave theory. It is found that the TM mode suppressibility can be doubled by optimizing the dimensions of the phase-shift region. This structure overcomes the TM mode problem.<>     

A distributed feedback ridge waveguide quantum well heterostructurelaser

A method for incorporating distributed feedback in a ridge waveguide laser by means of lateral gratings and a single growth step is discussed. The necessary Bragg condition for distributed feedback is satisfied by etching gratings along the ridge in the top confining layer of the laser on either side of the contact stripe. Both Fabry-Periot modes and a single emission peak away from the peak of the gain profile are observed in lasers with cleaved facets. The Bragg reflection emission peak does not shift with increasing drive current, which is characteristic of a distributed-feedback (DFB) laser