Proceedings Volume 2994

Physics and Simulation of Optoelectronic Devices V

Marek Osinski, Weng W. Chow
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Proceedings Volume 2994

Physics and Simulation of Optoelectronic Devices V

Marek Osinski, Weng W. Chow
View the digital version of this volume at SPIE Digital Libarary.

Volume Details

Date Published: 6 June 1997
Contents: 21 Sessions, 86 Papers, 0 Presentations
Conference: Photonics West '97 1997
Volume Number: 2994

Table of Contents

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Table of Contents

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  • Progress in II-VI and III-N Materials for Semiconductor Lasers
  • Growth and Properties of Wide-Bandgap Semiconductors
  • Optical Gain in Wide-Bandgap Group-III Nitrides
  • Simulation and Modal Properties of Vertical-Cavity Surface-Emitting Lasers
  • Optical Properties and Noise in Surface-Emitting Lasers
  • Bistability and Optical Switching
  • Microcavity Physics
  • Modeling and Properties of Optical Waveguides
  • Modeling and Properties of Optical Fibers and Fiber Components
  • Optical Switches and Nonlinear Laser-Matter Interactions
  • Modulators
  • Quantum Well Physics and Simulation
  • Semiconductor Laser Modulation
  • Strained Quantum Well Lasers
  • High-Power Lasers and Amplifiers
  • External Feedback and Injection Locking
  • Many-Body Effects
  • Comprehensive Simulation of Semiconductor Lasers I
  • Comprehensive Simulation of Semiconductor Lasers II
  • Poster Session
  • Semiconductor Laser Modulation
  • Plenary Session
Progress in II-VI and III-N Materials for Semiconductor Lasers
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ZnMgSSe-based laser diodes
H. Noguchi, S. Tomiya, Shun-Lien Chuang, et al.
We summarize here recent progress in II-VI blue-green semiconductor laser diodes (LDs). ZnMgSSe quaternary alloy, a promising material for the cladding layer, has enabled us to realize a long lifetime exceeding 100h with improvements in the active layer, the electrode, and growth techniques. Studies of degradation have revealed that II-VI LDs degrade not catastrophically, but gradually with enhancement by electron-hole recombination at defect sites.
Beryllium-containing materials for II-VI laser diodes
Andreas Waag, Th. Litz, Frank Fischer, et al.
Beryllium containing ZnSe-based compound semiconductors introduce substantial additional degrees of freedom for the design of wide gap II-VI heterostructures. Interesting aspects are the lattice matching of BeTe with its high lying valence band and high p-type dopability for the growth of graded gap contacts capable of carrying high current densities, as well as the expected strengthening of quaternary beryllium compounds like BeMgZnSe as compared to the II-VI materials used on the basis of ZnMgSSe. They have a large covalency and therefore large bond energy. The covalency of BeSe e.g. is expected to be as high as the one of GaN. The fabrication of light emitting devices like LEDs and laser diodes is reported.
Self-assembled visible-bandgap II-VI quantum dots
Martin Lowisch, Michael Rabe, B. Stegemann, et al.
This paper reports on the self-assembled growth of II-VI semiconductor quantum dots by molecular beam epitaxy. The dots are formed in a highly-strained (Zn,Cd)Se film of only a few monolayer width grown on ZnSe. The formation sets on when the CD mole fraction exceeds 30 percent. We present data on the recombination and relaxation of carriers and excitons in these zero-dimensional structures as well as their interaction with phonons.
Growth and Properties of Wide-Bandgap Semiconductors
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(BAlGa)N quaternary system and epitaxial growth on (0001)6H-SiC substrate by low-pressure MO-VPE
Hideo Kawanishi, Makiko Haruyama, Toshi Shirai, et al.
GaN and their alloy systems have a potential for the application of optical devices operating in blue and ultraviolet spectral region. In this paper, the possibility of (BAlGa)N quaternary system lattice matched to (0001) 6H- SiC substrate is described for ultraviolet emitters in the view of bandgap energy, lattice-matching to substrates. The estimated bandgap energy of quaternary system is ranging from 3.9 eV to 6.1 eV. It is also discussed that the crystal growth of (BAlGa)N systems using metalorganic vapor phase epitaxy. The quaternary system lattice-matched to (0001) 6H- SiC have an advantage for the laser application operating in ultraviolet spectral region.
Epitaxial growth and properties of cubic group III-nitride layers
D. Schikora, B. Schoettger, Donat Josef As, et al.
Single-phase cubic GaN and InN layers are grown by plasma assisted MBE. The temperature-dependence of the surface reconstruction is elaborated. The structural stability of the cubic growth in dependence of the growth stoichiometry is studied by RHEED measurements and numerical simulations of the experimental RHEED patterns. Growth oscillations on cubic GaN and during the growth of GaN-InN single quantum wells are recorded at nearly stoichiometric adatom coverage. Photoluminescence reveals the dominant optical transitions of cubic GaN and InN. Using in-situ RHEED to control the surface stoichiometry it is possible to grow N-stabilized layers resulting in intrinsic p-type GaN epilayers with hole concentrations of about p equals 1 X 1013 cm-3 and mobilities of about (mu) p equals 320 cm2/Vs, respectively.
GaAs compliant substrates: a new substrate with a stretchable lattice for mismatched III-V epitaxial growth
Felix Ejike Ejeckam, Yi Qian, Shanthi Subramanian, et al.
We present the theoretical foundations and implementation methods for forming GaAs compliant substrates that have a 'stretchable' lattice to be used for high quality lattice- mismatched heteroepitaxial growth. The theoretical calculations predict an increase of several orders of magnitude in the critical thickness of a film when it is grown on another thin film that has been wafer-bonded to an angularly misaligned bulk substrate. The calculations show that the increase in critical thickness is sustained even for a 3 percent lattice mismatch between the growth and the stretchable lattice. The dependence of the growth's critical thickness on a variety of parameters are presented including the bonding energy between the compliant and bulk substrates, the lattice mismatch between the growth and compliant substrates, and the thickness of the misaligned film. Thick films of In0.35Ga0.65P were grown on the compliant substrates. Bright-field transmission electron micrographs of the growth's cross-section showed no dislocations, whereas the same films grown on bare GaAs substrates produced stacking faults and threading dislocations. The concept and technology of compliant substrates may have important applications in forming optoelectronic devices of new characteristics and wavelengths.
Optical Gain in Wide-Bandgap Group-III Nitrides
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Theoretical analysis of optical gain and exciton effect in GaN/AlGaN quantum wells
Takeshi Uenoyama, Masakatsu Suzuki
Optical gains of wurtzite GaN/AlGaN quantum wells have been studied by a first-principles calculation and the k.p method. Most of the parameters in the k.p method were determined by fitting the band structures to the first- principles calculation. Owing to the small spin-orbit splitting energies and the strong electronegativity, the large hole density of states causes the higher threshold current density of the wurtzite GaN/AlGaN quantum well lasers. Then, we have proposed a new mechanism of the optical gain for laser diodes, using a localized level and the excitonic effects. The excitonic effects enhance an oscillator strength of the optical transition. When a localized level is exist in the band-gap, the optical gain between the localized state and one of the band edge states is produced with the very small carrier density. This optical gain is enhanced by the excitonic effect a the band edges and it might show a possibility of very low threshold current density for wide-gap laser diodes.
Gain processes in blue-light-emitting quantum structures: the role of excitons and biexcitons
Hans-Juergen Wuensche, Steffen Renisch, Fritz Henneberger
Gain processes in connection with exciton localization in wide gap quantum wells ar investigated theoretically. A simulation of uncorrelated composition fluctuations in (Zn,Cd)Se as well as (Ga,In)N QWs yields considerable densities of localization sites. The localization energies calculated for representative site ensembles show that up to two excitons can be localized at every site. The bi-exciton is even stronger localized than the single exciton. A rate equation model is used for the occupation kinetics of the localize exciton-bi-exciton system. Taking further into account the fourfold spin degeneracy of the exciton state, it is shown that the localized bi-excitons provide more gain and at lower densities than localized single excitons. These results are in agreement with the experimentally detected low-density gain regime in Zn0.8Cd0.2Se QWs. Conditions for extending this gain regime up to room temperature are presented.
Optical gain of strained-layer hexagonal and cubic GaN quantum well lasers
Do-Yeol Ahn
The optical gains of strained-layer hexagonal and cubic GaN quantum wells are calculated within the multiband effective mass approximation. The 6 X 6 multiband effective-mass Hamiltonians are used to calculate the band structures of hexagonal and cubic quantum wells. Non-Markovian relaxation is taken into account in the optical gain calculation. Calculated results show that the optical gains of the cubic quantum well are larger in magnitudes than those of the hexagonal GaN quantum well over the wide range of carrier densities. The expected inferior performance of the wurzite quantum-well laser as compared with the cubic structure is mainly due to the heavier effective mass of the HH1 band of the former at the zone center.
Comparison of models for calculation of optical gain in gallium nitride
We discuss theoretical predictions for the gain spectra in GaN-based lasers from the point of view of adequate modeling, aimed at optimization of the laser structure and cavity parameters. The Coulomb enhancement effect is included, and it is shown that it leads to an increase of both the gain cross-section and the threshold current in edge-emitting lasers, due to shortening of carrier lifetime. The minimum threshold current density in such lasers with bulk active regions is estimated to be between 2 and 4 kA/cm2 at room temperature.
Prediction of low threshold current density in InGaN-AlGaN quantum wire lasers due to excitonic transitions
Wenli Huang, Faquir C. Jain
The exciton binding energies in InGaN-AlGaN quantum wire are calculated to be 30-60 meV as wire width reduces from 150 angstrom to 50 angstrom. This high binding energy results in large exciton densities, making optical transitions due to excitons dominant over free electrons and holes. Optical gain and threshold current densities in InGaN-AlGaN based multiple quantum wire lasers are computed including the effect of strain and dislocations. The calculated threshold current density for a defect free compressively-strained quantum wires laser, such as realized on sapphire or SiC substrate, are shown to yield an ultra-low threshold current density of 148 A/cm2 and 1,600 A/cm2 in the presence of dislocations. The exciton transitions assist in lowering the threshold current density which is adversely affected by the presence of dislocations and surface states. This shows an improvement over our computed value as well as the experimental data reported by Nakamura et. al. for quantum well lasers.
Simulation and Modal Properties of Vertical-Cavity Surface-Emitting Lasers
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FD-BPM modeling of vertical-cavity surface-emitting lasers
Hans Krishna Bissessur, Kenichi Iga
A self-consistent 3D model using the finite difference beam propagation method in cylindrical coordinates is presented to assess the performance of vertical cavity surface emitting lasers. It calculates the optical field pattern, output power, carrier distribution in the active layer and secondary mode excess loss. Optical diffraction and scattering are automatically included in the propagation, as well as carrier diffusion and spatial hole burning. Calculations using this model clearly show the advantage of current confinement by oxidation over proton implantation. The threshold current in oxide confined devices is predicted to reach a minimum at aperture diameters around typically 1.5 to 2.0 micrometers with a (lambda) /4 oxidized AlAs layer, compared to 12 micrometers in proton-implanted ones. The oxide thickness can still be optimized to minimize scattering losses. Tapered oxide profiles can also be considered. For current aperture diameters below 4 micrometers , single-mode behavior around threshold can be expected. Above threshold, the secondary mode rejection ratio is largely influenced by carrier diffusion which partly washes out the carrier inhomogeneity caused by spatial hole burning.
Theoretical study of electromagnetic eigenmodes of VCSELs
Dariusz W. Burak, Rolf H. Binder
The empty-cavity electromagnetic eigenmodes of vertical- cavity surface-emitting lasers, including light-vector polarization properties, are calculated from Maxwell equations in cylindrical symmetry. The electromagnetic field in each layer is expanded into local modes of the corresponding cylindrical waveguide and the vectorial transform matrix method is used to calculate the light propagation through the structure. A simplified approach for the case of uncoupled modes is also formulated. For the cavity geometry under consideration the resonant frequencies of eigenmodes predicted within the CMA agree very well with results of exact calculations. The presented method for the empty-cavity eigenmode determination may be useful for future calculations of a steady-state laser models with semiconductor material gain parameters and carriers and temperature diffusion processes taken into account.
Polarization and transverse-mode selection in birefringent vertical-cavity surface-emitting lasers
Calculations are reported of the effect of birefringence on the selection of polarization states for the case of a weekly index guided vertical-cavity surface emitting laser supporting both a fundamental and a higher-order transverse mode. The influence of the refraction index step of the waveguide on the polarization behavior of the laser is elucidated. It is found that for large refraction index steps higher-order modes can emerge which are orthogonally polarized to the dominant polarization of the fundamental mode. It is also shown that for smaller index steps polarization switching due to spatial-hole burning effects can occur. This polarization switching behavior is analyzed when current spreading effects and higher order transverse mode discrimination mechanisms are present.
Optical Properties and Noise in Surface-Emitting Lasers
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Semiclassical analysis and experimental investigations of vertical-cavity surface-emitting laser noise
Jean-Luc C. Vey, Karsten Auen, Wolfgang E. Elsaesser
Noise and amplitude squeezing performances of vertical cavity semiconductor laser are investigated theoretically and experimentally. Theoretical results based on a newly developed semiclassical model predict very good performances for VCSELs as squeezed states generator. However, they also emphasize out the strong limitation of these performances by phenomena such as thermal roll-off, polarization instabilities, gain suppression and spatial hole burning.In addition, experimental investigations have been performed with VCSELs emitting in the 770 nm range. A good correspondence between theoretical results and experiments has been found, with the additional influence of lateral modes and the polarization of the emitted light. Finally, conclusions on possible improvements and on the optimized laser parameters are drawn.
Polarization dynamics and intensity noise in VCSELs
We experimentally investigate the radio frequency noise spectrum of electrically pumped VCSELs during polarization switching. It is found that the relaxation oscillation and beating frequency of polarization modes may lock before the switching if the frequencies are comparable. We compare our experimental results with the existing models.
Coupling effect in a vertical-cavity surface-emitting laser structure observed by photoreflectance spectroscopy
P. D. Berger, C. Bru-Chevallier, Taha Benyattou, et al.
In this work we describe the possibility of photoreflectance spectroscopy to study physical effects in vertical cavity surface emitting laser structures. Photoreflectance spectroscopy has proved to be a powerful technique for non- destructive characterization of such structures prior to a full process.OUr structure is based on the GaAlAs system and is grown by GSMBE technique. The (lambda) cavity includes three 45 angstrom quantum wells. The measure of energetic position of both quantum well emission and Fabry-Perot cavity mode can be achieved by this spectrometry technique. We study here the evolution of the transition energies as a function of temperature: it exhibits an anticrossing effect when both transition arise at about the same energy. This is the proof of a coupling effect between the two oscillators which can no more be distinguished. The reflectivity shows a Rabi splitting effect at the same temperature. These phenomena are explained using a modeling of the structure reflectivity with the Abeles formalism. We take the quantum confined Stark effect into account for the active layer inside the Fabry-Perot cavity. As we consider the electric field value in the cavity, we can then deduce the photoreflectance signal. We demonstrate here the advantages of photoreflectance to observe coupling effects in microcavities.
Gain and index saturation in circular-grating distributed-feedback semiconductor lasers
Keith J. Kasunic, Mahmoud Fallahi
We report numerical results for the above-threshold spectral properties of circular-grating distributed-feedback semiconductor lasers. Our model includes a radially-varying gain and index saturation, as well as a uniformly- distributed grating loss, in the solution of the coupled- mode equations. Our results show a multi-mode spectrum for large coupling strengths, a consequence of mode competition induced by the spatially-varying gain distribution associated with the grating losses. We also find that a single-mode spectrum is possible over a limited power range.
Radiation effects in the investigation of threshold gain and threshold current of circular-grating surface-emitting lasers
Ali M. Shams-Zadeh-Amiri, Wei-Ping Huang
Circular grating surface emitting lasers have been analyzed using coupled-mode theory. Based on the assumption that the laser beam is circularly symmetric, the effect of radiation field has been properly included in deriving the coupled- mode equations. The threshold gain and threshold current of a circular grating surface emitting DBR laser has been investigated by using the new formalism.
Bistability and Optical Switching
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Polarization bistability in vertical-cavity surface-emitting lasers
We report a simple rate equation analysis taking into account the gain saturation to analyze the pitchfork bifurcation polarization bistability in laser diodes (LDs), as well as the rate equation analysis taking into account detunings of incident optical beam from the cavity resonant frequency of an LD. We show some of our experimental results displaying pitchfork bifurcation polarization bistability and the all-optical flip-flop operation in a vertical-cavity surface-emitting laser (VCSEL). We experimentally obtained the pitchfork bifurcation polarization bistability by using a trigger optical input in the VCSEL. We achieved the ultra- fast polarization bistable switching with a switching time of 7 ps by using picosecond optical trigger pulses.
Hysteresis in a directly modulated semiconductor laser
Guillermo Carpintero, F. Mancebo, Horacio Lamela, et al.
In this work we analyze numerically the dynamic behavior of directly modulated semiconductor lasers. We study the output response of the laser as the amplitude of a sinusoidal modulation current is varied at fixed bias point and modulation frequency. We show that, as in previous studies, a period doubling route to chaos can be found in the laser dynamics. Also, as in recent experiments reporting chaos in laser diodes, we have found a period tripling solution in the laser diode response.
Microcavity Physics
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Lasing modes in highly confined semiconductor microcavities
The ability to tailor the emission characteristics through use of a microcavity has become an interesting topic for fabricating improved forms of light emitters. For semiconductor light emitters the novel cavity physics also complements the technological importance, and the advanced fabrication techniques allow for mode confinement presently in the volume range of tens of cubic emission wavelengths. In this paper we discuss the mode confinement possible with Fabry-Perot semiconductor microcavities that both have extremely short cavity lengths and contain embedded dielectric regions.WHile this confinements mechanism was discovered in late 1993, it was not at first clearly understood. Today we have a much better understanding of this system, and it becomes clear that it can impact a broad range of microcavity light emitters. In addition, we discuss combining the 3D confinement of the microcavity with 3D confinement of the electronic carriers, and demonstrate room-temperature lasing from quantum dot vertical-cavity surface-emitting lasers.
Calculation of microcavity VCSEL field modes using a doubly iterative weighted index method
Michael J. Noble, John P. Loehr, James A. Lott
We generalize the weighted index method for analysis of modal structure in various devices, including vertical cavity surface emitting lasers. Our model uses a doubly iterative process to calculate the bound modes for any dielectric device with an azimuthally symmetric geometry. In order to calculate the modes we assume a separable form for the electric and magnetic vector potentials. The scalar wave equation is then solved for the axial components of electric and magnetic vector potentials. Assuming a functional form of Az equals F((rho) )G(z) and Fz equals P((rho) )Q(z) we form coupled differential equations between F((rho) ) and G(z). These equations are then iteratively solved using the coupled boundary conditions for Az and Fz. Convergence by tracking the change in the eigenfrequency for the radial and axial eigenvalue equations. Our method allows rapid calculation, compared to an analogous finite element approach, and will handle any azimuthally-symmetric geometry with piecewise-constant indices of refraction. This model is particularly well suited to the calculation of bound modes in microcavity and oxidized structures where field confinement effects can be very important. The model can also, in principle, be adapted to obtain radiative modes, and should provide a valuable tool to analyze field behavior and quantum optics effects in microcavity devices.
Modeling the lasing mode in a three-dimensionally confined Fabry-Perot microcavity
Qing Deng, Dennis G. Deppe
The lasing mode in a 3D confined Fabry-Perot microcavity with an optically thin dielectric aperture is analyzed using a quantitative model which includes accurately the boundary conditions of the cavity reflectors. The model can be applied to both guiding and antiguiding phenomena. Self- consistent calculation of the lasing field gives the eigenmode field profile, frequency, and threshold susceptibility. The analysis illustrates that the frequency is related to the lateral field distribution which is set by the lateral optical confinement of the thin dielectric aperture, the mirror reflectivity and the cavity length of the Fabry-Perot microcavity. The eigenmode frequency can be related to its loss rate.
Finite differencing of periodic structures
Jerry C. Chen, Shanhui Fan, Attila Mekis, et al.
Finite difference time domain is a powerful numerical method. We review our modeling and design of optical gratings and 2D photonic crystals, aided by the recently developed quartic perfectly matched layer boundary condition. For optical gratings with a quarter wave phase shift, we show that light can be confined in an air bridge micro-cavity. Such devices exhibit sharp transmission resonances in the stop bands. Photonic crystals also demonstrate strong localization of light so waveguides of air can be formed. In addition, even when the bending radius is zero, the transmission exceeds 0.95 percent.
Physics of excitations of a small number of quanta in microresonators
Richard Lynn Fork, Vahid R. Riasati, Darryl K. Jones, et al.
We explore the physics of excitations of a small number of quanta in microresonators. In particular, we examine this physics as it relates to the dynamics of nonlinearly coupled microlaser oscillators used to generate time resolved coherent optical wavefronts. We seek wave fronts that can be both stabilized and also rapidly reconfigured by purely electro-optic means. Novel opportunities are offered by reductions in the number of quanta needed for laser, or laser-like action; advances in microcavity nonlinear optics; densely packed arrays of microlasers; adjustable micro- optical delay lines; synchronization of pulse envelopes in physically distinct lasers; and locking of optical fields in physically distinct lasers. Quantum statistical issues could become important, but are not emphasized here. Strategies for realizing an optical analog of high repetition rate agile microwave phased array radar with true delay are examined.
Microcavity effects in an external-cavity surface-emitting laser
John V. Sandusky, Steven R. J. Brueck
We present a simple model for the variations in the wafer- normal spontaneous emission coherence length and spontaneous emission power as a function of cavity length for an external-cavity surface-emitting laser. External-cavity operation allows changing of the cavity length without affecting material properties and observation of the transition to the macrocavity domain by extending the cavity length beyond the spontaneous emission coherence length. The model smoothly describes this transition in terms of impact of an ideal Fabry-Perot cavity on the emission from a Gaussian source.
Modeling and Properties of Optical Waveguides
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Modeling tools in waveguide optics
Z. Jan Jakubczyk, Miroslaw Florjanczyk, Velko Peyov Tzolov
The beam propagation method has been widely used for waveguide optics modeling. Recently, the method has been implemented into user friendly software systems that are advanced design tools for photonic devices and integrated circuits. Considering the BPM_CAD software package, we discuss common elements of these systems including a layout editor, propagation and mode solvers, and analysis tools.
Analysis of one-way coupling between asymmetric highly multimode waveguides
In this paper, a unidirectional electrooptic modulator based on an asymmetrical highly multi-mode wavedguide coupler is proposed. The energy distribution of all the guided modes within a highly multi-mode waveguide is studied and a new conclusion is obtained. Furthermore, the whole coupling process among all the guided modes between two nonidentical highly multi-mode waveguides is analyzed and the total coupling efficiency is calculated. To achieve high switching performance in a guided-wave coupler, a larger guide is made to have a dumping effect, which can be implemented by using an absorbing material or a grating. Based on the dumping effect, the dumping process is theoretically modeled and the dumping efficiency is simulated. Not only can a high dumping efficiency of 100 percent be achieved, but a high electrooptic modulation depth more than 90 percent can also be implemented.
Polarization characterization of self-imaging GaAs/AlGaAs waveguide beamsplitters using Mueller matrix imaging polarimetry
Mueller matrix imaging polarimetry represents a novel means of characterizing the polarization effects of optoelectronic devices. The Mueller matrix contains the complete polarization properties of a sample, and can therefore be used to calculate properties such as phase retardance, polarization dependant losses and polarization crosstalk. The complete polarization properties of a series of GaAs/AlGaAs self-imaging waveguide beamsplitters were measured with an imaging Mueller matrix polarimeter. Polarization properties were mapped across high resolution images of the devices' outcoupling faces, and the uniformity of the polarization properties was measured. Properties investigated include magnitude and orientation of linear retardance, polarization dependant losses, and crosstalk between TE and TM modes.
Modeling and Properties of Optical Fibers and Fiber Components
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Improvement of the Gaussian approximation for the field of weakly guiding optical fibers
Gemma De Angelis, Gaetano Panariello, Antonio Scaglione
A set of orthonormal Laguerre-Gauss functions was used to approximate the field of the fundamental mode of a weakly guiding fiber. The parameters of the expansion were evaluated by a variational method which maximizes the mode propagation constant. It was verified that for fiber with both triangular and parabolic refractive index profile, expansion with few terms only allows to construct an accurate field approximation. The proposed approximation does not require the knowledge of the actual field of the fiber and then avoids to look for a numerical solution of the scalar wave equation. In addition, due to the elementary form of the involved functions, the parameters characterizing the fiber performance can be analytically evaluated in a closed form.
Analysis of soliton stability and interactions in a system with nonlinear gain
The soliton propagation and interaction characteristics in the presence of spectral filtering, linear and nonlinear gain are investigated. We show that, as the linear gain vanishes, the steady-state soliton amplitude and inverse duration diverge. The nonlinear gain is shown to have a significant impact on the soliton interaction when the adjacent solitons have different phases or amplitudes. In these cases, a (pi) phase difference between adjacent pulses is induced when the nonlinear gain only partially replaces the linear gain. As the linear gain vanishes, the phase difference varies continuously and the solitons oscillate only slightly around their initial time separation.
Behavior of HE1m mode wavenumbers and power flow near the cutoff frequency in absorbing fiber tapers
Leonid A. Melnikov, Elena A. Romanova
The known term cutoff denoting an abrupt transition from the guided mode to the leaky one becomes undefined when absorption losses in fiber material are taken into consideration.In order to study continuous transformation of the HE1m guided mode into the leaky one in the fiber taper with absorbing cladding we have analyzed behavior of eigenvalue equation solutions in the complex plane of transverse wavenumber of the mode in cladding. Radial profiles of cylindrical components of power flow density showing HE12 mode transformation in the fiber taper are plotted. Size of the region of cutoff is found depending on the losses in the fiber material. Caustical spatial structures are shown forming by the rays which has different directions in the radial points of transverse cross-sections of the fiber. Radial power flow is shown to form multiple cones of the power distribution in the plane parallel to the fiber axis, the number of the cones depending on the absorption losses.
Optical Switches and Nonlinear Laser-Matter Interactions
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Analysis of fully depleted differential double-heterojunction optical thyristor using MQWs and mirror layers
Jeong-Ho Lee, Byeong-Gee Kim, Young-Wan Choi
Switching characteristics of a novel PnpN optical thyristor are studied by using coupled junction model associated with current oriented method. Though the simulation method is simple, obtained quantitative results on the switching characteristics of a depleted optical thyristor (DOT) are in good agreement with reported experimental data. In this method, we can successfully explain the switching mechanism of PnpN thyristor easily. With this method we analyze our novel thyristor structure which employs multiple quantum wells (MQWs) in center light absorbing layers and bottom mirror made of quarter wavelength reflector stacks (QWRS). Simulated results show that switching characteristics of the MQWs and QWRS DOT (MQ-DOT) enhance those of previously reported structure. Considering the same device parameters such as doping concentrations and layer widths, it is expected that MQ-DOT can operate with only 55 % of the external optical power ofthe previous top-recorded PnpN structure. Keywords : DHOT, MQ-DOT, coupledjunction model, optical switching, switching characteristics
Fabrication of LD-3 polymer directional couplers
John Martin Taboada, Guohua Cao, Huajun Tang, et al.
LD-3 polymer directional couplers have the potential use as low-voltage modulators and switches. They can be integrated into module-to-module systems using currently available VLSI fabrication techniques. Modes of channel waveguides are calculated and coupling lengths are determined using BPM_CAD. We report the fabrication of LD-3 polymer directional couplers designed to operate at 1.3 micrometers .
Induced focusing in ZnSe
George G. King, Eric Donkor
We have observed induced-focusing ofa continuous wave signal from a Helium Neon laser, operating at 632.8nm, by co-propagating a chopped Argon laser, centered at SOOnm, as a pump.
FDTD simulation of optoelectronic switches
Xudong Wang, R. Jennifer Hwu
In this paper, the finite-difference time-domain (FDTD) technique is used for the full wave analysis of picosecond and subpicosecond photoconductive switches. By applying a novel voltage source formulation and the lumped-element technique, pulse generation through single switching unit in a transmission line and switches in different pulse-forming networks are simulated using the FDTD model. The simulation results agree well with the theoretical analysis and experimental data. The effects of the dispersion of the transmission line and the pulse-forming networks on ultrashort pulse formation are also studied using the FDTD simulation model.
Doppler-shifted self-reflected wave from a semiconductor
Alex Schuelzgen, S. Hughes, Nasser Peyghambarian
We report the first experimental observation of a self- reflected wave inside a very dense saturable absorber. An intense femtosecond pulse saturates the absorption and causes a density front moving into the semiconductor sample. Due to the motion of the boundary between saturated and unsaturated areas of the sample the light reflected at this boundary is red-shifted by the Doppler effect. The spectrally shifted reflection makes it possible to distinguish between surface reflection and self-reflection and is used to proof the concept of the dynamic nonlinear skin effect experimentally. Quite well agreement with model calculations is found.
Modulators
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II-VI electro-optical devices for visible-wavelength modulation
Harald Babucke, Peter Thiele, Michael Rabe, et al.
Electro-absorptive and electro-refractive modulation and switching are shown using various proof-of-concept devices at room temperature. In a multiple quantum well structure, the field-induced broadening of the confined excitons leads to a transmission change of more than 30 percent. The Pockels effect is used to modulate and switch blue-green light by means of MBE-grown ZnSe waveguides with cladding layers of (Zn,Mn)Se on n-GaAs substrates. In a retarder geometry, the strained birefringent planar waveguide demonstrates a contrast ratio larger than 80:1 at 2.485 eV. Applying the electric filed via stripe-contacts on the top cladding layer, the waveguiding for TE-polarized light can be confined in lateral direction. In the center of the lateral waveguide channel, the contrast ratio is better than 16:1 at 2.48 eV. Switching between adjacent channels is accomplished with a contrast ratio better than 5:1.
Optimization of the negative prechirping Franz-Keldysh InGaAsP bulk electroabsorption modulator
Byeong-Gee Kim, Jeong-Ho Lee, Young-Wan Choi
We perform structural optimization of negative prechirping Franz-Keldydh InGaAsP bulk electroabsorption (EA) modulator in terms of transmission change and waveguide length. For the optimization, we calculate the chirp parameter ((alpha) c) of EA modulator from the slope of n versus k curve. In the optimization process, for a given (alpha) c and modulation voltage change we calculate contrast ratio, propagation loss, optimal waveguide length, optimal transmission change varying intrinsic region thickness and bandgap wavelength. Detailed results on optimized structures are presented.
Ultrabroad-bandwidth in-line MQW GaAs/GaAlAs optical intensity modulator
Milson Tadeu Camargo Silva, Carlos Alberto de Francisco
The design and performance of three wavelength-selective optical intensity modulators integrated in-line operating near 860 nm with 8 angstrom separation based on GaAs/GaAlAs multiquantum well is reported. The device utilizes an exchange Bragg resonator embedded in a dissimilar coupled- waveguide structure in its design. Due to its unique design wavelength selectivity is obtained and the modulator presents a modulation region only 16.14 micrometers long yielding an ultrabroad bandwidth of 250 GHz for a waveguide 2.0 micrometers wide at a drive voltage of 3.0 V. In addition, the device exhibits high extinction ratio, 20 dB, low insertion loss, 2.0 dB, small size, 495 micrometers , tuning capability of 2.8 angstrom, which is 35 percent of the wavelength separation among channels, also at 3.0 V, and it is chirp-free. The in- line modulators can also be integrated with lasers, photodetectors, semiconductor optical amplifiers, etc.
Polymer-based electro-optic modulator with microwave shield for high-speed applications
Palle Geltzer Dinesen, Joern Hedegaard Povlsen
The use of a shielded microstrip-configuration for polymer- based electro-optic modulators has the advantage over an open microstrip geometry that the modulator is pacified with respect to environmental conditions. We investigate such a shielded modulator numerically. Employing the Laplace equation the quasi-TEM field distribution is calculated and by employing Wheeler's incremental rule we determine the conductor loss due to the skin effect. We demonstrate that the use of a shield in combination with a buffer layer with a low dielectric constant yields the modulator insensitive to geometrical variations. For a modulator with a wide driving electrode the maximum bandwidth may be as high as 90 GHz.
Quantum Well Physics and Simulation
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Electron escape dynamics from a biased quantum well
In this paper, a theoretical model calculating the electron escape time form a biased quantum well is presented. To solve Schroedinger equation for a quantum well under the influence of an electric field, the method of the logarithmic derivative of the wave function is used in the Green's function approach. Electron escape time is calculated by accounting for the partitioning of the total current into the thermionic emission and tunneling components. The current components are evaluated by properly accounting for the electron's group velocity and the redistribution of the density of states in the presence of an applied electric field. A comparison between this model and previously reported experimental results of the electron escape time is made, demonstrating excellent agreement.
Theory of ultrafast optical nonlinearities of uniaxially strained quantum wells
A theoretical study of ultrafast many-body effects in anisotropic semiconductors is presented. Signatures of coherent exciton-exciton interactions are identified in polarization traces in Poincare's cartesian complex plane of polarization which is used to visualize the differential polarization rotation of ultrashort light pulses due to excitons in uniaxially strained quantum wells.
Magnetoluminescence characterization of lattice matched n-type InGaAs/InAlAs/InP MQWs on InP
Eric D. Jones, Nobuo Kotera, Tomoyoshi Mishima, et al.
A knowledge of the energy-band energies and masses are important parameters for the design of semiconductor lasers and light-emitting diodes. We present results of a magnetoluminescence study on n-type InGaAs/InAlAs multiple quantum wells lattice matched to InP. From an analysis of low-temperature magnetoluminescence data, a simultaneous measurement of the in-plane conduction and valence-band masses is made. We find, assuming parabolic bands, that the conduction and valence-band masses are respectively mc approximately equals 0.069 m0 and mv approximately equals 0.061 m0, where m0 is the free electron mass. Fitting a nonparabolic conduction-band dispersion curve to the data yields a zone- center mass mc approximately equals 0.056 m0 and mv approximately 0.102 m0.
Detection of lateral composition modulation in an (InAs)n/(GaAs)n short-period superlattice on InP by magnetoexciton spectroscopy
Eric D. Jones, Joanna Mirecki-Millunchick, David M. Follstaedt, et al.
An experimental signature for detecting spontaneous lateral composition modulation in a (InAs)n/(GaAs)n short period superlattice on a InP substrate based on magnetoexciton spectroscopy is presented. We find by aligning the magnetic field in three crystallographic directions, one parallel to and the other two perpendicular to the composition modulation direction, that the magnetoexciton shifts are anisotropic and are a good indicator for the present of composition modulation.
Semiconductor Laser Modulation
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Hot carrier effects in conventional injection and tunneling injection quantum well laser diodes
Matthew E. Grupen, Karl Hess
The Minilase-II quantum well laser simulator is briefly described. Simulated modulation responses are then compared to experimental data, showing a good agreement between simulation and measurement. The simulator is also shown to distinguish between effects intrinsic to a quantum well laser and those due to external circuitry and device packaging. Next, Minilase-II is used to demonstrate the highly nonlinear effects of quantum carrier heating, including significant increases in low frequency roll off and differential gain suppressio. Finally, the simulator is used in a preliminary analysis of tunneling injection lasers. The analysis shows that tunneling injection results in less quantum carrier heating. However, the analysis also shows a decrease in the net injection of carriers into the quantum well, which offsets the decreased heating and leads to a a reduction in modulation bandwidth.
Carrier transport effects on pulse statistics of modulated quantum well lasers
Luis Pesquera, Nasreldin Mustafa, Ignacio Esquivias
We perform a theoretical study of carrier transport effects on the pulse statistics of QW lasers modulated at GHz rates for different bias levels, Ib, and modulation frequencies. The lasers considered are ultra-high speed In0.35Ga0.65As/GaAs MQW lasers with intrinsic modulation bandwidths of 40GHz. A rate-equation model, including spontaneous emission noise, which incorporates the dynamics of the unconfined carriers in the core is used. Different values of the transport/capture time, (tau) cap, and the re-emission time out of the QW's (escape time) (tau) esc, are considered to illustrate carrier transport effects. Different bias currents near threshold are considered. In this way small enough turn-on delay times and good on-off ratio are obtained.It is found that for slow modulation the laser switch-on is delayed and the timing jitter is increased when (tau) cap increases and (tau) esc decreases. These detrimental effects are reduced at high rates. However, the maximum modulation frequency decreases when (tau) cap increases. Concerning the combined dependence of turn-on time of Ib and on the modulation frequency, the results are similar to those obtained for bulk lasers when (tau) cap is not very large, even for small (tau) esc. Timing jitter becomes rather independent of the modulation frequency at GHz rates when biasing slightly below threshold. However, for large (tau) cap timing jitter increases with the modulation period. The dependence on the modulation frequency is due to the initial condition at the beginning of a pulse, that is very different from the steady state associated to Ib.
Simulation of laser sources for millimeter-wave signal generation
Phillip C. R. Gurney, Arthur J. Lowery
We present a theoretical study of a three different schemes for the generation of optical millimeter-wave signals. The models have been developed to be modular and flexible, allowing a wide range of systems and configurations to be simulated. The results show comparisons of the optical and electrical spectra of three schemes.
Modeling of semiconductor lasers by multisection digital analysis
This work presents a model for semiconductor lasers based on digital signal analysis. This model discretizes the laser cavity, sampling the electrical field along the longitudinal direction of the cavity at fixed space intervals. The discretization of the field allows us to obtain the longitudinal spectrum of the laser. For computational efficiency, the wavelength dependence of the material gain is implemented using digital filters applied to the field samples, lumped into a single cavity. Therefore, the most complex and computationally costly operation of the algorithm is performed in a single section. Even further, due to the digital nature of the filter, we can adjust any given frequency response both in modulus and phase using the theory of discrete time signal analysis. The results of this model are compared versus standard modeling methods such as integration of the rate equations with Runge-Kutta Algorithm.
Strained Quantum Well Lasers
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Amplified spontaneous emission spectroscopy of strained quantum well lasers: theory and experiment
Shun-Lien Chuang, Chih-Sheng Chang, Jeffrey R. Minch, et al.
We discuss a theoretical model for the amplified spontaneous emission (ASE) from both Fabry-Perot (FP) and distributed- feedback semiconductor lasers and show how to use the ASE spectrum to characterize important laser parameters. A systematic experimental procedure to extract optical gain, refractive-index change and linewidth enhancement factor from the spontaneous emission (SE) and ASE spectra is presented. We show good agreement between our experimental and theoretical results for strained InGaAsP quantum-well lasers. Our gain spectrum is calculated from the SE spectrum using their fundamental relationship, which avoids the nonphysical negative value below the band edge energy. This fundamental relationship is also confirmed experimentally. The electronic properties such as the band structures are calculated first, and then the optical properties such as the gain and the refractive index change induced by carrier injection. The optical properties are used to calculate the ASE spectrum which is compared directly with the experimental data, with the mirror reflectivity or the distributed-feedback effects taken into account. Our model and experimental procedures provide a rigorous approach to extract important physical parameters for strained quantum- well lasers.
Characterization and modeling of InGaAs/GaAs multiple quantum well lasers by capacitance-voltage measurements
Julia Arias, Ignacio Esquivias, Susann Buerkner, et al.
We have measured and analyzed the room-temperature capacitance-voltage (C-V) characteristics of In0.35Ga0.65As/GaAs MQW laser structures with different doping levels in the active region. Average doping densities in the well-barrier regions were directly extracted from the as- measured carrier profiles. A model for he C-V measurement, including the self-consistent solution of Poisson and Schroedinger equations, was developed. The carrier profiles obtained from the simulated C-V characteristics do not correspond to the free carrier profiles since the local charge neutrality hypothesis does not hold for QW structures. Thus, the true carrier distribution can only be determined from a full quantum-mechanical simulation of the laser structure. We have determined, form the comparison between experimental and simulated profiles, a conduction band offset (Delta) Ec/(Delta) Eg of 0.81. We have also applied C-V measurements to samples with interdiffused QWs, and obtained the characteristic interdiffusion length.
Epitaxial structure dependence of the linewidth enhancement factor in GaAs and InGaAs quantum well lasers
Jonathan Stohs, David J. Gallant, David J. Bossert, et al.
The linewidth enhancement factor, (alpha) , plays a key role in our ability to obtain spatially coherent output from high-power semiconductor lasers and amplifiers. To obtain (alpha) values, modal gain and carrier-induced refractive index change have been measured in broad-area quantum well epitaxial structures with various well depths, widths, and compositions as functions of current density.
Spontaneous-emission measurements in broad-area quantum well semiconductor lasers
Malcolm W. Wright, David J. Bossert, Gregory C. Dente, et al.
Spontaneous emission spectra have ben obtained from semiconductor quantum well lasers of varying epitaxial design. Initial measurements taken normal to the active region through the substrate and a transparent contact exhibited a modulated spectral profile dependent on the collection angle. An image model with the quantum well active region as the source and the p-side metallization as the image plane explains the observed modification and as such, presents an excellent example of a simple cavity quantum electrodynamics (QED) effect in a planar semiconductor laser. The phenomenon is made possible by the proximity of the quantum well active region to the p-side electrical contact of the device. Modification of the spontaneous emission rate and spectra can be substantial and must be accounted for if one hopes to correctly infer modal gain or carrier heating phenomena in a device using this geometry. Alternatively, to avoid the influence of the cavity QED effect, spontaneous emission can be obtained through the side wall of the device. Using this method for collection of spontaneous emission, the effect of quantum well dimensions on carrier heating in single quantum well InGaAs or GaAs active regions was also investigated. Incomplete pinning of the carrier density was observed above threshold in these samples with low duty cycle pumping.However, minimal distortion of the carrier distribution to higher energies was observed at room temperature up to current densities of 1.6 kA cm-2. Low temperature spontaneous emission spectra revealed gain suppression from carrier heating and possibly spectral hole burning in InGaAs deep and shallow quantum well lasers.
High-Power Lasers and Amplifiers
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Space-time simulation of high-brightness semiconductor lasers
Jerome V. Moloney, Robert A. Indik, Cun-Zheng Ning, et al.
A full scale simulation model, that resolves the spatio- temporal behavior of competing longitudinal mode and transverse filamentation instabilities in a wide variety of high brightness edge emitter geometries, is presented. The model is highly modular and is built on a first principles microscopic physics basis. The nonlinear optical response function of the semiconductor, computed for specific QW structures, covers the low-density absorption to high density gain saturation regimes. As an illustration of its robustness as a laser design tool, the model is applied to a monolithically integrated flared amplifier master oscillator power amplifier semiconductor laser.
Spatiotemporal dynamics in the near field of a 980-nm ridge waveguide pump laser diode
Markus O. Ziegler, E. Miltenyi, M. Muenkel, et al.
The dynamic behavior of the light output from aluminum-free 980nm ridge waveguide GaInAs/GaInAsP/GaInP pump lasers is studied in the high power regime on a picosecond time scale. Three types of the temporal evolution of the turn-on emission dynamics measured by a single-shot streak-camera can be distinguished in the near field, according to the injection current. First, at moderate pumping, the laser emission evolves through a regime of relaxation oscillations, which can be modelled by rate equations incorporating nonlinear gain. Second, at a higher current, high frequency switching between the left and right part of the active region is observed. The frequency of the switching increases proportional to the excitation current amplitude and is in the order of 10GHz. The third regime shows highly complex spatio-temporal dynamics with the coexistence of low and high frequency spatial switching and temporal pulsations. Finally, consequences of the results for applications will be discussed.
Modeling of current crowding accompanying optical filament formation in semiconductor lasers and amplifiers
An approach is developed for analysis of the current crowding induced by the optical filamentation. The criterion is proposed to estimate the suppression of the spatial hole- burning due to the current self-distribution. Numerical calculations are performed that confirm the model.
Heating of the front and rear facets of GaAlAs/GaAs edge emitting laser diodes
Uwe Menzel, Roland Puchert, A. Baerwolff, et al.
Gradual degradation and catastrophical optical damage (COD) of the facets is one of the main reasons limiting output power and lifetime of diode lasers. The facets undergo a strongly localized intense heating caused by nonradiative surface recombination of carriers. We theoretically and experimentally investigate the temperature rise at the facets of an asymmetrically coated 20-stripe GaAs/GaAlAs laser diode array. We examine the effect of the asymmetric thermal load of the facets and evaluate the role of reabsorption of photons under different conditions. It is suggested that COD occurs at the reflection-coated facet of this device.
Analytical theory of phase-locked arrays of antiguided diode lasers
A general theory of periodic diode laser arrays is developed in the approximation of an effective complex refractive index described by a step periodic function. Rigorous expressions are derived for the elements of a translation matrix. Explicit expressions are obtained for the near-field and far-field patterns of finite array modes. The concept of 2D (Gamma) -factor and the explicit expression for it are presented. Accurate analytical expressions for key parameters characterizing the resonant and adjacent array modes are obtained for the resonant structure. By using an expansion, the radiation loss versus index-step curve is well approximated near resonance by a parabola, which gives curve half-width at half intensity only 10 to 15 percent less than numerically calculated values. The analogy between the resonant arrays of antiguides and DFB lasers is discussed, and differential equations for the slowly varying envelope are derived.
Polarization sensitivity of the amplification in semiconductor optical amplifiers
Taco D. Visser, Daan Lenstra, Hans Blok
There are two main reasons which explain why in a semiconductor laser amplifier the amplification can depend on the state of polarization: (1) Waveguiding can give rise to an amplification that differs for TE polarization and for TM polarization. This can happen even if the confinement to the active layer is comparable for the two polarization states. (2) The interaction process between light and matter in a quantum well is, in general, anisotropic. This is because the electrons are confined in only one direction. So the response to an electromagnetic field will have a tensor character, rather than a scalar. We analyze these two causes and show how they can be balanced, so that the desired polarization amplification can be achieved.
External Feedback and Injection Locking
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Quasi-periodicity in semiconductor lasers
Lang and Kobayashi equations for a semiconductor laser subject to optical feedback are investigated in the limit of large delays. Be deriving slow time evolution equations, we show analytically that quasiperiodic intensities are possible and appear as a tertiary bifurcation from a periodic state.
Ultralow phase noise in multigigahertz oscillations of injection-tracked DFB lasers
Herbert Burkhard, H. Schoell
Injection of cw-light from a single-mode laser into the cavity of a second one with a frequency detuning outside the locking range leads to output power oscillations of the injected laser. The oscillation frequency and the extinction ratio can be controlled by the amount of injected power and the frequency detuning between the two noninteracting lasers. Thus a continuous tunability of the oscillation frequency is possible for frequencies ranging from < 10 GHz to > 100 GHz. A further advantage of such injection tracked oscillations is the low phase noise. Additionally the oscillations can be synchronized with external frequencies or a system clock by sideband injection locking.
Mutual entrainment in delay-coupled nonidentical semiconductor lasers
The dynamics of two mutually coupled but non-identical semiconductor lasers are studied experimentally, numerically and analytically for weak coupling. The lasers have dissimilar relaxation oscillation frequencies and intensities, and their mutual coupling strength is asymmetric. We find that the lasers may entrain to the relaxation oscillation frequency of either one of the lasers. The form of entrainment is a special form of synchronization, called localized synchronization, where one laser exhibits strong oscillations and the other one weak oscillations. We perform a bifurcation analysis to explain the mechanism of entrainment by taking advantage of the inherently large parameters in a semiconductor laser, the linewidth enhancement factor (alpha) and the ratio of the carrier and photon lifetime T.
Many-Body Effects
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Incorporating many-body effects into modeling of semiconductor lasers and amplifiers
Cun-Zheng Ning, Robert A. Indik, Jerome V. Moloney, et al.
Major many-body effects that are important for semiconductor laser modeling are summarized. We adopt a bottom-up approach to incorporate these many-body effects into a model for semiconductor lasers and amplifiers. The optical susceptibility function computed from the semiconductor Bloch equations (SBEs) is approximated by a single Lorentzian, or a superposition of a few Lorentzians in the frequency domain. Our approach leads to a set of effective Bloch equations. We compare this approach with the full microscopic SBEs for the case of pulse propagation. Good agreement between the two is obtained for pulse widths longer than tens of picoseconds.
Experimental study of physical parameters of semiconductor lasers
Gleb E. Shtengel, Paul A. Morton, Rudolf F. Kazarinov, et al.
We discuss various experimental methods for measurements of the optical gain, transparency wavelength and optical loss. We discuss existing methods as well as newly developed. It is also shown how this set of measurements allows for characterization of other laser parameters, such as linewidth enhancement factor, differential gain, and wavelength chirp. We illustrate how these techniques are used for improving the laser performance for different applications.
Theory of momentum orientation relaxation in semiconductors
Rolf H. Binder, Hilding Sigurd Koehler, Nai-Hang Kwong, et al.
We present numerical results for charge-carrier relaxation processes by carrier-carrier scattering in various semiconductor structures. Common to all examples is the aspect of anisotropy. Our results are based on a generalized quantum Boltzmann equation. Specifically, we solve the Kadanoff-Bayn equations for the relevant two-time Green's function. The systems under consideration are bulk GaAs with anisotropically photo-excited electrons and hexagonal CdS.
Comprehensive Simulation of Semiconductor Lasers I
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Physical models and numerical simulation of modern semiconductor lasers
Z-.M. Li
Simulation of modern semiconductor lasers requires the inclusion of complex physical models as well as sophisticated numerical analysis techniques in 2/3 dimensions. Using DFB lasers and VCSEL's as examples, we describe our physical models for strained quantum wells, spatial hole burning effects, carrier transport, thermal effects, and multiple lateral and longitudinal modes. Numerical approaches used to integrate various physical models are also discussed.
Simulation of semiconductor quantum well lasers
Muhammad A. Alam, Mark S. Hybertsen, R. Kent Smith, et al.
A 2D bulk and quantum well laser simulation tool, based on the Bell Laboratories electron device simulator PADRE, has been developed. PADRE contains a suite of robust programs for obtaining self-consistent solutions of the Drift Diffusion equations. To this suite has been added programs for calculating the optical intensity inside the laser, the capture and emission rates between bound and free carriers, the interaction between the confined carriers and the optical field, and a set of ne, powerful schemes for obtaining rapid convergence of the nonlinear equations of the model. This paper describes the augmented program in its present form, gives examples of its present abilities and limitations, and discusses some illustrative results to show features of the simulation tool.
Spectral domain modeling of distributed feedback lasers
In this paper a.d.c. spectral model of the DFB laser is described. The description is based on the coupled wave theory for corrugated optical waveguides. The analysis is carried out in the spectral domain for a continuum of wavelengths. As such, the model is inherently capable of capturing the effects of all the longitudinal lasing and non-lasing modes.
Comprehensive Simulation of Semiconductor Lasers II
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Simulation of GaInP laser diode structure
Peter Blood, Damian Foulger, Peter M. Smowton, et al.
We have simulated the current flow and potential through visible emitting (AlGa)InP quantum well lasers by a self- consistent finite element solution of the current continuity equations and Poisson's equation linked to a state-broadened calculation of recombination and optical gain in the well. We have used this to investigate the influence of the complete device structure, and in particular the p-cladding layers, on the temperature dependence of threshold current and the external differential efficiency. The aim of the paper is to demonstrate the influence of the whole device structure on the characteristics of GaInP lasers.
Modeling of the linewidth enhancement factor in multiple quantum well InGaAsP-based lasers
Mark S. Hybertsen
A microscopic model of the gain and refractive index change in multi-quantum well lasers is applied to study the linewidth enhancement factor. The following issues in the model are studied: the lineshape used to broaden the gain, band gap renormalization, self consistent band bending and carrier spill out into the separate confinement layers. The application of the model to laser design issues is illustrated through consideration of the influence of well strain and barrier band gap. Comparison is made to experiment.
Calculation of Auger recombination in long-wavelength lasers
The understanding and evaluation of the Auger coefficient, C, and its variation with band structure is essential for accurate device modeling of long wavelength quantum well devices. We have developed a calculation of the Auger coefficient C for both 'band-to-band' processes, which involve strict k-selection rules, and 'k-relaxed' processes, where the strict k-selection rule is relaxed by momentum from phonons. To identify which process is dominating in 1.5 micrometers QW devices we have compared hydrostatic pressure measurements of the lasing threshold current with theoretical predictions for each process. We find that the 'k-relaxing' models are in good agreement with experiment as a function of pressure while the 'band-to-band' processes overestimate the reduction of the non-radiative component of the threshold current with pressure. Based on these results, we predict the threshold current for a number of well characterized 1.5 micrometers QW devices in the literature with a variety of strains and well widths.
Poster Session
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Wavelength tuning and intensity noise in diode laser butt coupling
Yakov S. Sidorin, Pentti Karioja, Dennis G. Howe
Coherent optical feedback into a continuously operating diode laser causes optical output power fluctuations as well as a spectrum shift. This spectrum shift can be accounted for by solving the boundary value problem for the optical field. We choose another method, in which the change of the nonlinear laser characteristics and the optical properties of the oscillation cavity versus the effective reflectance of Fabry-Perot etalon formed by the laser output mirror and an external reflector is described by a phenomenological model. We consider a high power laser diode with significant external feedback from the entrance facet of a butt-coupled fiber and explain the wavelength variations of up to 15 nm versus laser-to-fiber separation that we observed experimentally. The longitudinal mode spectrum of the butt- coupled laser diode is characterized as well.
Theoretical calculation of turn-on delay time statistics of lasers under PRWM
Luis Pesquera, Jose Revuelta, Angel Valle, et al.
In this work we present a new combined analytical and numerical method to obtain the turn-on delay time probability distribution P((tau) ) of single-mode semiconductor lasers under pseudorandom work modulation (PRWM) of the injection current. The laser is descried by stochastic rate equations that include the effect of the spontaneous emission noise. The method allows the calculation of P((tau) ) for lasers biased below and above threshold, and for different modulation frequencies. For bias currents below threshold the method is based on the same assumptions that the theory already developed for the periodic modulation regime. When the laser is biased above threshold a new method is introduced to obtain P((tau) ) in the periodic modulation case. Under PRWM the turn-on time probability distribution is shown to satisfy an integral equation, and the kernel is obtained by numerical integration of the deterministic laser rate equations. In this way the numerical simulations of the stochastic rate equations is avoided. Then large computational times are not necessary to obtain P((tau) ). The results obtained with this method are in good agreement with the numerical simulations of the stochastic rate equations. These results show, in agreement with previous numerical results, that turn-on time statistics for laser diodes modulated in the GHz range is very different under periodic and PRWM regimes. In the periodic regime timing jitter is rather independent of the bias current. Under PRWM timing jitter becomes larger when biasing above threshold that when biasing below threshold. This large jitter is related to a bimodal P((tau) ) due to pattern effects. A bias slightly below threshold suppresses these patterns effects making the laser response almost independent of previous input bits. The method developed in this work can be used to obtain the bit error rate as a function of the transmission distance for different bias currents and bit rates.
Effect of strain on the Auger recombination processes in type-II heterostructures with QWs
Aleksey D. Andreev, Georgy G. Zegrya
Auger recombination processes in type II heterostructures with strained quantum wells (QW) have been studied theoretically. It is shown that in type II QW there are two channels of electron and hole recombination. During the Auger recombination processes these two channels interfere destructively, which results in decrease of the Auger matrix element and the AR rate. During radiative recombination process one of these recombination channels is the dominant. It is shown that the Auger recombination rate essentially depends on strain. It is demonstrated that under certain conditions the Auger recombination rate can be suppressed by choosing the optimal value of strain.
Modeling of master oscillator-power amplifier (MOPA) semiconductor lasers
Monolithically integrated flared amplifier master oscillator power amplifier (MFA-MOPA) semiconductor lasers are studied theoretically using a high resolution computational model which resolved times and longitudinal and transverse space dependencies and includes Lorentzian gain and dispersion spectra. The simulations show that, by altering the linear flare of the power amplifier into a nonlinear, trumpet- shaped flare, the dynamic stability range of the MOPA is increased by a factor of 3. This enables the MOPA to maintain a stable, nearly diffraction limited output beam for higher currents before the onset of transverse instabilities, large beam divergence and facet damage due to filamentation. Thus the MOPA will be able to emit an output beam of significantly higher power and brightness.
Two coupled semiconductor lasers in transient regime: equivalent circuit analysis
In this paper, the first large-signal circuit model for laterally coupled semiconductor laser structures is presented. The present work gives application to the study of the transient regime of two coupled semiconductor lasers. The model includes both the electrical and optical characteristics of the device. The circuits elements that compose the model can be differentiated in two very different groups: on one hand, we have obtained circuit elements that describe the lasing processes in a single emitter. This elements coincide with already developed models for the single emitter. On the other hand, new circuit elements that account for the coupling terms have appeared. Also, a new variable has been modeled, the phase difference between the emitters. We will test our model by comparing the results obtained with the circuit model with those obtained by direct integration of the rate equations with standard numerical integration methods. Further indications on how to use the same approach with more complex structures will be given.
Reflectivity of two-dimensional waveguide facets using the vector free space radiation mode method
Martin Reed, Phillip Sewell, Trevor Mark Benson, et al.
In this work the proven free space radiation mode (FSRM) method is extended to determine the polarization dependent reflectivity of a guided mode in a 2D waveguide incident at an arbitrary angle onto a facet. The FSRM method is an attractive semi-analytical method which is fast, simple and accurate and has previously been successful in cross sectional analyses, propagation and 1D facet problems. The method is applicable to a wide variety of practical buried structures with small lateral index variations. Novel 2D results for the reflectivity of polarized and vector modes at a n angled facet are provided.
Gain spectra and optical transition probability in doped quantum well heterostructures
Alexander A. Afonenko, Valerii K. Kononenko, Ivan S. Manak
In the work we investigated the influence of the dimensional quantization on the probability of optical transitions with no k-selection rule. It is shown that calculations of the recombination rate and gain coefficient will be inaccurate if they are performed with using the probability of optical transitions determined for bulk semiconductors. Successive examination of radiative transitions with no the k-selection rule leads to a qualitative coincidence of the dependence of the spontaneous recombination rate on the quantum well width with the results obtained in the model of direct transitions.With the suppression of the constant injection efficiency the inversion current value is practically independent of the quantum-well layer thickness. Various approaches for the calculation of the spontaneous recombination rate are discussed.
Avalance photodetectors with an electrically isolated guard ring
Babatunde Odubanjo, Chen-Show Wang, Wen I. Wang
A 2D finite difference method is employed to demonstrate the effectiveness of the use of guard rings in reducing surface electric field along the semiconductor/insulator interface of planar avalanche photodetectors (APDs). Results from our modeling indicate a 20 percent edge field reduction in doubly-diffused devices as compared to singly-diffused p+n- junctions. The introduction of guard rings and double diffusion process is shown to provide an extra degree-of-freedom in the design of APDs, thus improved device characteristics against breakdown fields.
Numerical modeling of light beam propagation in nonlinear waveguide media: effects of misalignment and inhomogeneous broadening
Leonid A. Melnikov, Vladimir L. Derbov, Aleksey I. Bychenkov, et al.
Using the modified generalized method of moments the equation of motion are derived for the parameters of a misaligned astigmatic Gaussian beam with torsion in an axially symmetric nonlinear medium. Nontrivial features of beam dynamics are revealed in a parabolic waveguide with Kerr nonlinearity. Peculiarities of near-resonance self- action of an axial beam depending upon the Lorentz-to- Doppler linewidth ratio are analyzed numerically.
Coherent state of Wannier-Mott excitons: transformations of nonlinear spatial structures
Yuri I. Balkarey, Alexander S. Cohen, Mordukh I. Elinson, et al.
Nonlinear structures of a coherent state of Wannier-Mott excitons sustained by resonant optical pumping in semiconductors are investigated both theoretically and numerically. The structures can originate from both instability with respect to spatial periodic stratification and finite amplitude disturbances, when initial homogeneous state is stable with respect to the small fluctuations. Spectrum of collective excitations and stability of the structures are discussed. Transformations of structures are demonstrated.
Investigation of the processes of propagation and diffraction of light in periodic mediums with sinusoidally modulated coupling coefficient
Galina I. Manankova, Victor I. Sokolov
The processes of propagation, interaction and diffraction of electromagnetic waves in periodic mediums with sinusoidally modulated coupling coefficient, which is provided by biharmonic multiple (pi) -phase shifted Bragg grating, are investigated theoretically. The applicability of biharmonic grating for improving the transmission characteristics of narrowband wavelength-selective optical filters is discussed.
Semiconductor Laser Modulation
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Large-signal analysis of self-pulsating laser diodes
Michael J. Adams, Chanjira Sinthanayothin
A semi-analytical large-signal model has been developed for self-pulsation in laser diodes containing saturable absorbers. The model yields an explicit expression for the frequency of self-pulsation as a function of current and other device parameters. Predictions from the model are compared with the results of numerical simulations. Conditions for the regions of self-pulsation and bistability are also derived, and shown to be more general than those of previous treatments.
Plenary Session
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Present status of short-wavelength group-III nitride-based laser diodes
Shuji Nakamura
The continuous-wave (CW) operation of InGaN multi-quantum- well-structure laser diodes (LDs) was demonstrated at room temperature (RT) with a lifetime of 35 hours. The threshold current and the voltage of the LDs were 80 mA and 5.5 V, respectively. The threshold current density was 3.6 kA/cm2. Longitudinal modes with a mode separation of 0.042 nm were observed under CW operation at RT. When the temperature of the LDs was varied, large mode hopping of the emission wavelength was observed. The peak wavelength also showed mode hopping toward higher energy with increasing operating current. Each single-mode laser emission was located at a peak of each periodic subband emission. These periodic subband emissions probably result from the transitions between the subband energy levels of the InGaN quantum dots formed from In-rich regions in the InGaN well layers. The carrier lifetime and the threshold carrier density were estimated to be 10 ns and 2 X 1020/cm3, respectively. The beam full width at half- power values for the parallel and the perpendicular near- field patterns were 1.6 micrometers and 0.8 micrometers , respectively. Those of the far-field patterns were 6.8 degrees and 33.6 degrees, respectively.
Physics of semiconductor microcavities and microcavity lasers
The optical properties of semiconductor microcavity systems are studied theoretically on the level of a fully quantum mechanical nonequilibrium theory. The normal mode coupling of the exciton and cavity resonances is investigated for various excitation conditions. Transmission, reflection, photoluminescence, and lasing characteristics are analyzed using the full quantum electrodynamic theory.