Laser Threshold Condition Research Articles

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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Reduction of lasing threshold current density by the lowering of valence band effective mass

In present day semiconductor lasers, there is a serious asymmetry between the very light conduction band mass and the very heavy valence band mass. Under laser threshold conditions, the hole occupation remains classical even while the electrons are degenerate. This results in a significant penalty in terms of threshold current density, carrier injection level, and excess Auger and other nonradiative recombination. We propose a combination of strain and quantum confinement to reduce the valence band effective mass and to lessen the laser threshold requirements.

On the Vibronic Laser Theory

A theoretical model is presented which accounts for the electron-phonon interaction and for the vibrational level structure of a solid-state laser device. In particular, the laser threshold condition is derived and discussed.

Influence of optical feedback on laser frequency spectrum and threshold conditions

The steady state behavior of the external cavity operated laser has been analyzed, taking into account multiple reflections. The effect of optical feedback is included in the phase- and gain-conditions by a factor which is shown to have a simple geometrical representation. From this representation it is easily seen how the laser frequency spectrum and the threshold gain depend on external parameters such as distance to the reflection point and the amount of optical feedback. Furthermore, by inserting a variable attenuator in the external cavity and measuring the threshold current versus transmittance we have simultaneously determined the photon lifetime and the absolute amount of optical feedback. For the laser considered we found the photon lifetime \tau_{p} = 1.55 ps.

Band-to-band Auger effect in GaSb and InAs lasers

Band-to-band Auger recombination for a semiconductor laser is studied theoretically. Auger recombination calculation method is formulated, which may be applicable to a semiconductor with any injected carrier density. Using the formulated equation, injected carrier density dependence, and the temperature dependence of the Auger lifetime for GaSb and InAs are calculated. The temperature dependence of Auger lifetime and the upper limit of the quantum efficiency under laser threshold condition are also discussed. Calculated result shows that Auger recombination affects cw room-temperature operation for an InAs laser considerably.

GaAs-Al&amp;lt;inf&amp;gt;x&amp;lt;/inf&amp;gt;Ga&amp;lt;inf&amp;gt;1-x&amp;lt;/inf&amp;gt;As strip buried heterostructure lasers

A new laser structure, the strip buried heterostructure (SBH) laser, using an active strip on a low-loss waveguide is described, theoretically analyzed, and experimentally characterized under both pulsed and CW operations. The waveguiding properties and laser threshold conditions are analyzed using the effective refractive index approximation. The calculated results agree fairly well with measured results. Pulsed output powers as high as 400, 230, and 130 mW/mirror without AR coating have been obtained at "catastrophic" mirror failure for SBH lasers with 10, 5, and 3 μm strips, respectively. Throughout this entire current injection range, stable transverse mode operation and excellent linearity and symmetry in light-current characteristic from each mirror were obtained. Intermodulation products were measured for 5 μm strip SBH lasers. At an average power of 4 mW and modulation depth of 80 percent, the third-order component was about 48 dB below the fundamental. Excess noise above threshold was not present. For SBH lasers with efficient injection current confinement and active strip area of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">380 \times 10 \mu</tex> m, pulsed and CW current thresholds were about 74 and 85 mA, respectively. The average external quantum efficiency was about 45 percent. CW operation has been achieved at a heat-sink temperature as high as 115°C. The current threshold has an exponential variation with temperature exp ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T/T_{0}</tex> ) where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_{0} = 110</tex> K. For SBH lasers with strip widths <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sim5 \mu</tex> m, stable fundamental mode oscillation in both transverse directions was observed up to 9 times threshold. Far-field beam divergences of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8-10\deg</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">26-30\deg</tex> were obtained in directions parallel and perpendicular to the junction plane, respectively. Single-longitudinal-mode operation up to twice threshold was obtained for SBH lasers with strip widths <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lsim5 \mu</tex> m under both pulsed and CW operations. Relaxation oscillation and self-pulsation were not observed for SBH lasers with clean transverse modes in pulsed response up to current injection levels as high as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4 \times I_{th}</tex> . For these particularly good diodes, self-pulsation was not observed before aging under CW operation in preliminary experiments. Aging studies have not yet been performed. Densely packed monolithic linear arrays of SBH lasers with center-to-center spacing of 15 μm were also studied. They exhibited similar laser characteristics as in single SBH lasers, but with increased maximum pulsed output power/mirror, approximately ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">310 \times N</tex> ) and ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">150 \times N</tex> ) mW for arrays with ∼10 and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sim4 \mu</tex> m strips, respectively. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> is the number of lasers in the array. Spectral behavior of these arrays was also studied as a function of injection current and temperature.

Application of the Injection Laser as a Reference Source in Cryogenic Interferometry

An Ali_xGaxAs, injection laser has been employed as a reference source in a rapid scan cryogenic interferometer spectrometer. The interferometer was designed to operate at 20°K with a scan velocity of 1 cm/sec and a spectral resolution of 2 cm-1. The slide velocity control and sampling requirements for a continuous drive interferometer are discussed and those properties which are needed in choosing and calibrating an injection reference laser are given. The relative advantages and limitations of an injection reference laser are given and are related to the laser's spectral purity, threshold condition, power efficiency, and beam pattern.

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 constant s due to Bragg scattering, which relates the secondary wave to the respective primary wave. Laser threshold condition is then obtained by applying the continuity of tangential E and H at 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 kL int must be greater than unity where K is the distributed-feedback coefficient and L int is the interaction length. Advantages for having periodic structures outside the active medium so as to relax constraints on k and L int are also discussed.

Frequency- and time-dependent gain characteristics of dye lasers

The approach used by McCumber for treating phonon-terminated lasers is applied to investigate the gain properties of dye lasers and is extended to include effects arising from population buildup in the triplet-level system and associated triplet-triplet absorptive losses. The gain is expressed in terms of time-dependent excited-state populations and spectral emission and/or absorption functions. For a given optical-pump pulse, a computer program is used to solve rate equations for the populations up to threshold and to calculate the gain as a function of time and frequency. The gain varies with frequency over the broad fluorescence bands characteristic of dye molecules and with time until the threshold for laser action is reached. Experiments using rhodamine 6G verify the predicted dependence of the laser frequency and time of threshold on cavity Q and demonstrate laser frequency tuning by adjusting the opening time of an intracavity Q switch. No variation of laser frequency is expected for fluorescing molecules exhibiting large Stokes shifts; this is observed for 7-hydroxycoumarin. Computer calculations of the gain for anthracene and rhodamine B illustrate the dependence of gain properties on the rate of intersystem crossing and triplet-triplet absorption. An estimate of the rate of intersystem crossing for rhodamine B in methanol is obtained from a comparison of predicted and observed laser threshold conditions. Requirements for achieving flashlamp-pumped laser action are shown to depend upon both flashlamp and dye properties and are analyzed using the above approach.