Modern Semiconductor Lasers. Isabel Reis

Transcription

1 Modern Semiconductor Lasers Isabel Reis University Stuttgart Advanced Seminar 23rd June 2016 Supervisor: Dr. Michael Jetter

2 Today, lasers are used in a wide range of important applications and especially semiconductor lasers have become an integral part in latest technology and the world s life. As laser revenues have shown, this year, the market sectors of communication and optical storage segments continue to comprise the largest section in laser sales with material processing not far behind. These are followed by the usage in lithography, in lasers for scientific and military markets and in instrumentation and sensoring. Entertainment, displays and image recording segments continue to be small - yet important - laser categories. In particular, semiconductor lasers are one of the most popular optical coummunication light sources for data transmission enabling modern Internet. In addition, these are used in optical digital recording and are consequently characterizing the world s laser revenue significantly. What enabled the appearance of modern semiconductor lasers in the last decades is the availability of both sophisticated multilayered bandgap-engineered semiconductor structures of high compactness and high-power operations as a response to the rising demand. The combination of rapid progress in desired properties and requirements characterize semiconductor lasers to be the lasers of the future. Theoretical Basics - Atomic Lasers The term laser is an acronym for light amplification by stimulated emission of radiation emphasizing the theoretically predicted statement by Einstein in 1917 that the amplification relies on stimulated emission.[1] In general, lasers are characterised by three elements, the pump source, the active medium required to obtain gain and the feedback. Feedback is usually provided by two mirrors. Although these criteria are valid for all lasers, it is necessary to distinguish between atomic and semiconductor lasers, as in atomic lasers the active medium is described by discrete eigenstates whereas in the case of semiconductor lasers the band structure is taken into account. Absorption, stimulated and spontaneous emission The occupation of either states or bands is an indicator if lasing is possible or not. The desired carrier population inversion is based on the processes of absorbing and emitting photons, mathematically defined by a balance equation. A transition from a lower energetic level E 1 to higher energy E 2 by annihilation of a photon of energy hν is named absorption, reversed by emitting a photon is called emission.[2] Each process is illustrated in figure 1. The occupation of the energy levels is given by N 1, respectively N 2. The following Figure 1: Depicted are the processes of absorption, spontaneous and stimulated emission. rate equations consists of the occupation, the Einstein coefficients A and B and in the case of absorption and stimulated emission of the energy density u(ν) of the surrounding electromagnetic field. The latter does not characterize the spontaneous emission, as it is a statistically distributed process with 1

3 polarization, phase and direction of the emitted photon not determined in advance. The significant process for lasing is the stimulated emission, since one photon out of the radiation field invokes the emission of a photons and the decay into a lower energy state of itself. Both photons are having equal properties, the same energy and momentum, leading to an increase of radiation. In total the balance equation of the occupation densities and photons can be derived to dn 1 /dt = dn 2 /dt = N 1 B 12 u + N 2 B 21 u + N 2 A 21. In thermal equilibrium, the occupation densities can be approximated by the Boltzmann distribution N 2 N 1 = g 2 g 1 ( exp ( exp E 2 k B T E 1 k B T ) ) = g 2 g 1 exp ( ) E, k B T where k B represents the Boltzmann factor and g 1, g 2 the weighting of degeneracy. Carrier population inversion As the unit of identical two-level-systems is considered, a population inversion indicates a higher particle density in the upper level and the process of emission dominates the induced absorption. The sufficient condition is given by N 2 g 2 > N 1 g 1. Since in thermal equilibrium E 2 > E 1 is valid, the inversion condition is just guaranteed if the thermal equilibrium is distorted.[2] This is achieved by continuous energy supply by either optical or electrical pumping. For instance, pumping may be based on excitation through scattering or injection of charge carriers respectively. Additionally, the coherent, induced emission has to dominate the spontaneous one, as the latter arbitrary process can evoke incoherent noise by the superposition with induced emission. Laser Systems If a radiation field is emitted into a two level system, as shown in figure 2, both absorption and stimulated emission occur. As the probabilities of exciting atoms from the ground state and of bringing excited atoms down to the ground state again are equal, it is only possible to reach an equality in occupation for the two levels. Figure 2 depicts, in a three level system a population inversion between the energy levels E 3 and E 2 is feasible if the lifetimes of staying in a level follow the relation τ 2 τ 3. The transition between E 3 Figure 2: The two-level-, three-level- and four-level-system and E 2 is usually based are visualized. Both the pump beam, the lifetimes on non-radiation transmission. To obtain inversion and the transition for lasing operation are shown. the ground state has to be depopulated by half of its total amount. This drawback of a high pump energy is not given in a four-level-system. In a four-level-systems, the amplification of radiation is evoked between the energy levels E 2 and E 1. The belonging lifetimes fulfill the following conditions τ 2 τ 3 und τ 2 τ 1. Speaking pictorially, a rapid relaxation from the energy level E 3 to E 2 and from the level E 1 to E 0 are required. The latter is necessary since atoms are not allowed to stay in E 1 when continuous wave operation is requested and reabsorption prohibited. In figure 2 the schematics are visualized. 2

4 Semiconductor Lasers In general, most of the semiconductor lasers are p-n-diodes. The gain mechanism in the active layer is based on population inversion and light generation due to the recombination of holes and electrons injected by the p- and n-sides, known as cladding layers, of a p-njunction. Thus, the emission wavelength is determined by the band gap and the lasing material. The process of recombination can be induced by optical or electrical pumping. Through cleaved polished facets optical feedback is supplied as illustrated in figure 3. A homojunction diode laser is build up of one type of semiconductor material. Because of a low overlap of the small gain region with the spacial laser mode and a high threshold current density requiring a pulsed operation of the laser at room temperature, these are not suitable for applications. The excessive absorption losses due to the spreading of the laser mode in the cladding regions lead to the development of double heterostructure diode Figure 3: The figure depicts a homojunction diode laser. It is taken from [3] lasers providing a four level system, as they consist of different materials.[4] In figure 4 a AlGaAs/GaAs heterostructure laser is demonstrated. GaAs with a lower band gap and higher refractive index forms the active layer, while AlGaAs with a lower refractive index and higher band gap defines the doped cladding layers. In order to obtain a nonequilibrium in carrier distribution, the heterostructure diode can be biased in forward direction. With the resulting shape of the conduction and valence band, the charge carriers are confined to the GaAs layer generating a degenerated electron and hole gas. After waiting for the thermalization to end, quasi-fermi levels are established in both the conduction and valence band. Subsequently, the injected electrons and holes are able to recombine under emission of photons. Consequently, to be efficent the active layer is made of a direct semiconductor. Further progress can be achieved by confining the carriers into a quantum well. The structure is known as separated confined heterostructure (SCH) in which an additional layer, the waveguiding layer, is inserted between the cladding and active region. As the energy of the well depth is larger than the thermal energy, all carriers are likely to stay in the well. In addition, the overlap between the optical mode and gain region is quite strong and absorption in cladding layers almost negligible. Prerequisites of Lasing Operation As mentioned in the previous section, carrier population inversion can be achieved if a high-intensity light beam is supplied else the p-njunction can be forward biased. Afterward the injection of charge carriers, the system is described by the quasi-fermi levels EF ν and Ec F lying in the valence and conduction band respectively. The inversion is mathematically formulated by a higher probability of being in the conduction band compared to the valence band, f(e = E c ) > f(e = E ν ), following the Fermi-Dirac statistics. 3

5 Figure 4: A heterostructure diode laser made of AlGaAs/GaAs is shown. The four-level-system is highlighted. It is taken from [5]. Net gain mechanism Analogically to atomic lasers, the processes of absorption, spontaneous and stimulated emission as radiative band-to-band transitions are essential to describe the net gain mechanism. The rate equations are formulated by the Einstein coefficients, the density distribution of the conduction D c and the valence band D ν and the Fermi-Dirac statistics. Exemplarily, the spontaneous rate equation R spon is explained. It is independent of the emitted photon density n phot (E 2 E 1 ) as there is no interaction of the photon with others. Consequently, besides the Einstein coefficient A 21 merely the density distribution of the occupied states in the conduction band D c (E 2 E c ) and the unoccupied ones in the valence band D ν (E ν E 1 ) are required. Both are combined with the corresponding Fermi-statistic f 2 and (1 f 1 ) respectively. In total, the rate equations are given by R spon = A 21 D c (E 2 E c )f 2 D ν (E ν E 1 )(1 f 1 ) R abs = B 12 n phot (E 2 E 1 )D ν (E ν E 1 )f 1 D c (E 2 E c )(1 f 2 ) R stim = B 21 n phot (E 2 E 1 )D c (E 2 E c )f 2 D ν (E ν E 1 )(1 f 1 ). The net gain is the difference between the absorption and stimulated emission process. Likewise the absorption does, the rate of stimulated emission depends on the photon density n phot (E 2 E 1 ).The ratio between the absorption and stimulated emission rate is expressed by R abs = f 1(1 f 2 ) exp R stim f 2 (1 f 1 ) = ( E2 E c F k B T exp ( E1 E ν F k B T ) ( hν (E c ) = exp F EF ν ) k B T where EF c and Eν F are the quasi-fermi levels and k B is the Boltzmann factor. At thermal equilibrium and EF c = Eν F the exponential function is greater than 1 and the absorption process dominates. However, for photons with energies larger than the band gap, (EF c Eν F ) > hν > E g, lasing operation can be achieved. The gain is zero if EF c Eν F = E g is fulfilled, leading to transparency.[4] Resonant Cavity in Semiconductor Lasers There is a variety of possibilities to provide positive feedback. Mostly, a Fabry-Pérot resonator is employed in edge-emitting diode lasers by cleaving the facets. Then, the mode propagates in a dielectric waveguide with an effective refractive index determined by the indices of the waveguide core and claddings. The laser is likely to oscillate at a frequency that matches a longitudinal mode supported by the resonator. The reflectivity of the cleaved facets can be modified by any dielectrical coating.[3] Without coating 32% reflectance is feasible, since the refractive index of a semiconductor material is roughly n 3.[4] ), 4

6 Threshold Gain Beyond transparency, the semiconductor laser is able to provide positive optical gain although it is still superposed by loss effects. The threshold gain defines the equilibrium of internal and external losses, determining the beginning of lasing. Mathematically, it can be derived by the following consideration: The output power P rt of the optical mode after a round trip is given by P rt = P 0 R 1 R 2 exp(2l(g α i )), where α i represents the internal loss per unit length, g the volume gain per unit length, L the cavity length, R 1, R 2 the front respectively rear reflectivity and P 0 the initial power. Since the gain should compensate the loss after ( a roundtrip, meaning P rt = P 0, the threshold condition is given by g th = α i + 1 ln 1 2L R 1 R 2 ). The first term is marked by the mentioned free-carrier absorption losses and scattering in the semiconductor material and therefore a material parameter defining the quality. The second represents the end loss of the cavity. Confinements What is required is the reduction in the threshold gain and an increase in the laser efficiency by optical and carrier confinement. The waveguiding and confinement are based on two different approaches, the gain-guided and index-guided lasers. As shown in figure 5, the installation of a narrow stripe in the laser geometry is the most common technique to avoid transverse multimodes and to bound the charge carriers to an area within the active region. Injecting current through an aperture in a dielectric layer leads to a nonuniform current density and carrier concentration profile. The resulting gain profile produces a guiding effect in the active layer as amplification is just evoked within the stripe width.[6] It is difficult to produce single transverse mode operation in a gainguided laser unless one goes to a very narrow stripe of 2 µm allowing the current to spread significantly into the cladding layers. Consequently, for single transverse mode output index-guided optical cavities with at least one nonuniform layer are designed. The modification in structure leads to an effective step in the index profile.[3] Stongly-index-guided lasers are known as buried heterostructures in which the active layer is Figure 5: Taken from [3], a stripe geometry laser for gainguiding is illustrated. By modification of at least one layer an index-guided laser is designed. buried on all sides in higher bandgap materials with lower refractive index creating a high index step along the active layer. Optical confinement is accomplished by change in the refractive index. As mentioned, in a SCH thight optical confinement is optimized by additional waveguiding layers surrounding the active zone. For instance, the refractive index profile and confined optical mode of a SCH structure with a quantum dot layer centered in the active region is illustrated in figure 6. The strength in confinement is defined by the optical confinement factor Γ determining the ratio of the light intensity of the lasing mode within the active region to the total intensity over all space. The product of Γ and the gain coefficient g represents the modal gain as the ratio of the transverse dimension of the active layer to the cavity mode. Furthermore, carrier confinement is accompanied by an increase in the carrier density i. e. due to a small active layer. In the shown SCH both confinements are considered and respected. Typically, the thicknesses of carrier-confining active layers are 0,1 0,2 µm in double heterostructures and about 10 nm in QWs.[4] 5

7 Gain in Semiconductor Lasers With optical and carrier confinement, the possibility to optimize the lasing system is given. Positive gain is achieved beyond the point of transparency. If the carrier density N has not reached the threshold yet, N N th, the losses dominate the gain and lasing is still unfeasible. What is required is an increase in the carrier density. At the moment, when the carrier density N corresponds to the threshold carrier density N th, the gain equals the Figure 6: Out of [7], the refractive index profile and optical mode in a SCH structure is threshold gain g th. A further rise in shown. The optical confinement layer the density leads to greater gain since includes a quantum dot layer. the photons can enter the cavity directly. In the cavity the photons have the chance to multiply resulting in large steady state photon population.[8] Above threshold and for higher photon energy values the semiconductor absorbs again. The gain saturation brought about by a large photon density is needed to stabilize the photon density inside the cavity. Consequently, the threshold carrier density N th and gain g th are never exceeded. The resulting gain spectra shown in figure 7 depicts the broadening caused by the increasing number of charge carriers. Moreover, the peak in the gain spectra g max is shifted to higher photon energies as the bands get gradually filled with charge carriers known as the band filling effect.[9] Clearly, the maximum gain depends linearly on the carrier density. Introducing the differential gain σ with σ = dg/dn, the mathematical relation is described by g max = σ(n N tr ). Experimentally important is the behaviour of the photon density above threshold current as it increases linearly.[8] Consequently, the threshold current can be determined by an extrapolation of the linear output power current characteristic. The corresponding threshold current density, as a function of the threshold carrier density N th, is mathematically formulated by J th = dq ( αi η i τ r σγ + 1 ( ) ) 1 2σLΓ ln + N tr, R 1 R 2 where η i represents the internal quantum efficiency, τ r the carrier lifetime, d the thickness of Figure 7: The gain spectra is depicted. It is taken from [4]. the active layer and q the charge. The first two terms define the losses as derived for the threshold gain, the third expresses the current density at transparency J tr.[10][4] The curve discussion of the threshold current density with respect to the active layer thickness shows a minimum representing an optimal value for the layer thickness at the lowest J th. 6

8 Temperature dependence In addition, the threshold current density depends on the temperature, following J th = J th,0 exp(t J /T 0 ), with the amplitude J th,0, the junction temperature T J and the characteristic temperature T 0. With rising temperature, the threshold current density increases and both the output power and the slope efficiency of the linear power current characteristic decrease as indicated in figure 8. Accompanied by dissipated power and generated heat, the gain is reduced.[6] The indicator in temperature is given by T 0 - the higher its value, the better the temperature stability. Due to the delta-distributed density of states in a quantum dot layer, changes in the Fermi distribution with temperature are irrelevant as long as excited states are energetically well separated.[1] Thus, a quantum dot laser leads to a superior temperature stability. In heterostructures, the values are finite and depend on the overflow of carriers over heterobarriers. Figure 8: The temperature dependence of the power current characterisitc for two semiconductor lasers is illustrated. It is taken from [9]. Chirp Changes in both the temperature and the refractive index are noticeable in the emission wavelengths of measurements. The refractive index is mainly shifted due to the abrupt alteration in the carrier flux density in the active layer resulting in a chirped signal. Consequently, chirping is an effect leading to a rapid change in the center wavelength of the emitted laser light while the laser is modulated. A low chirp means the injection current does not alter the lasing wavelength significantly.[4] Semiconductor Laser Models As semiconductor diode lasers are in general characterized by a wide emission wavelength spectrum, a high efficiency, electrical current laser excitation and modulation, they are versatile applicable.[11] The following section presents an extract of different models ordered by their optimization. Edge-Emitting Lasers In edgeemitters the optical mode propagates parallel to the active layer. Primarily, a gainguided laser as demonstrated in figure 9, with an output beam cross section of typically about one by several microns, is designed. However, the small waveguiding dimensions provide drawbacks like asymme- Figure 9: Ot of [7], an edge-emitter based on a gain-guided cavity is shown. try and strong angular divergence of the output laser beam. Additionally, heat dissipation 7

9 from the active region limit the output beam. Therefore, up to several hundred milliwatts of output power is achievable in a single-transverse mode waveguide configuration.[11] Due to the temperature dependency of both the semiconductor s bandgap and the refraction index the output power can be altered. A tunable diode laser is formed. Considering the temperature dependence of the emission wavelength, the spectrum shows longitudinal mode hopping. It occurs if another longitudinal mode obtains a higher net gain value due to the shifted maximum of the gain curve. Consequently, if a constant oscillation mode over several Nanometers is required, a distributed feedback laser (DFB) needs to be taken into account, as just one mode is provided and amplified.[12] Distributed Feedback Lasers (DFB) The resonator in a distributed feedback laser consists of a periodic diffraction grating which forms a distributed reflector in the wavelength range of laser action. As shown in figure 10 the grating with its integrated gain medium is installed between the doped regions. As optical feedback is provided by the grating, no additional mirrors are required. The examination of the grating structure shows that the active layer should have a length of λ/2. Following this condition, the resulting mode matches with the Bragg wavelength λ B of the grating. In essence, in a semiconductor DFB laser two Bragg gratings with an optical gain of length λ/2 inbetween are connected. Consequencely, a phase shift of π/2 is implemented in the middle of the periodic structure. Distributed feedback Figure 10: Taken from [13], the figure illustrates a distributed feedback laser based on a gain-guided cavity. lasers can be either index-guided or gainguided. While the laser output is marked by a plane front for an additional transversal confinement, it remains curved for gainguided cavities resulting in astigmatism.[12] Besides output powers in the mw range, DFB lasers benefit from their small linewidth of a few hundred khz. Comparing the optical gain spectra of a Fabry-Pérot and DFB laser, the spectral broadening indicates a multimode behaviour for the Fabry-Pérot laser while the latter acts frequency selective. Due to the spectral purity, DFB lasers are predominantly either semiconductor lasers operating on a single resonator mode or fiber lasers. Furthermore, the ability is given to cover a huge distance of several km within a fibre. Unlike edge-emitting lasers, the output laser beam propagates normal to the surface in surface emitting lasers. The laser types optimizing the output beam significantly are vertical-cavity surface-emitting lasers and vertical-external-cavity surface-emitting lasers. Vertical-cavity surface-emitting lasers (VCSELs) In vertical-cavity surface-emitting lasers (VCSELs) the direction of emission is along the standard growth direction of the heterostructure sequence. Consequently, the amplification is confined to a small length of the active layer and a high mirror reflectivity is required to compensate the narrow active region. Therefore, distributed Bragg reflectors, consisting of semiconductor multilayers with alternating high and low refractive index regions, which provide a high reflectivity of 8

10 R > 99,6%, are utilized. The distance between the two mirrors is either λ/2 or a multiple of λ/2 for the same reason as discussed for DFB lasers. Moreover, the short active layer length impacts the mode. Due to very large mode spacing, only a single longitudinal mode is excited in the spectral gain regime.[4] Thus, VCSELs are characterized by an excellent mono-longitudinal mode behaviour and high supression of secondary modes. The multimode operation in transverse direction can be limited by lateral confinement of the active layer through an additional oxide aperture and mesa etching.[12] In figure 11 a simple setup with the marked diameters for the mesa D S and the oxide aperture D A is shown. The guiding mechanism of the optical field with oxide apertures is based on the refractive index step of the oxide aperture and the resulting charge carrier distribution and temperature Figure 11: Out of [14], the figure depicts a VCSEL structure with mesa and oxide aperture. profile. In contrast to edge-emitters, the laser emits solely in the symmetric Gaussian fundamental mode with a low divergence angle for the whole current range, if a certain diameter value in the oxide aperture is guaranteed. However, as for edge-emitting lasers, the heat dissipation limits the output power of several mw.[11] Above, the manufacturing of twodimensional structures on a chip, known as arrays has become a commercialized approach. Arrays are used in applications like parallel processing of information or parallel optical interconnection between computers.[4] Vertical-external-cavity surface-emitting lasers (VECSELs) With vertical-externalcavity surface-emitting lasers (VECSELs) an increase in the output power and beam quality is achieved by transverse mode control through shape and size of external optical cavity elements. As depicted in figure 12 VECSELs combine the design of VCSELs with a curved external mirror. Consequently, the resonator is formed by the distributed Bragg reflector within the semiconductor and the output mirror. Both electrical or optical pumping is feasible. Exemplarily, electrically pumped VECSELs emitting at 980 nm are able to supply 1 W cw multimode and half of the power in a fundamental TEM 00 mode.[4] The only drawback is the injection of carriers across a wide area, as a thick doped semiconductor spreading layer would be required. Therefore, excitations are mostly done by optical pumping. VECSELs are characterized by their output power scalability, as a range of almost four orders of magnitude (10 mw to 60 W) is covered, Figure 12: The schematic drawing of the linear VECSEL setup is shown. It is their maintainance of a good beam quality, as VECSELs operate with a fundamental transverse TEM 00 mode, and their diffraction-limited low beam divergence. Besides, taken from [15]. VECSELs offer a significant wavelength versatility ranging from the UV to the mid-ir.[11] 9

11 Quantum-Dot Lasers (QD) In a quantum dot (QD) laser, the active medium consists of one or several quantum dot layers centered in the active optical confinement region between the doped cladding layers as shown in figure 13. The carriers can be injected from the wide-bandgap regions, the claddings. Due to the quantisation in all three dimensions, the charge carriers are strongly confined in the quantum dots. With decreasing the dimensionality of the active region to 0D the density of states and gain spectrum are described Figure 13: Schematic diagram by a delta function-like distribution. Con- of a QD laser, taken sequently, the number of states to be filled to get from [16]. a transparent active region and to achieve lasing is decreased.[16] A QD laser offers the advantage of a low threshold current density, a high differential gain, a tunability of the gain spectrum and a lower chirp.[4] In addition, superior temperature stability of the threshold current density is given. The temperature dependency can be described by using the characteristic temperature T 0 which follows the theoretical trend expected for realistic QD ensembles. The experimental results, illustrated in figure 14, show a negative T 0 for K, indicating a non-equilibrium charge carrier distribution. In the range of K the carriers are Fermidistributed due to a charge carrier Figure 14: Out of [7], the temperature stability of transfer between the QDs. At higher a QD laser and its characteristic temperatures T 0 are shown. The operainates and the QDs become thermally temperature the leakage current domtion temperature is given by T a. depopulated.[7] Quantum Cascade Laser Quantum cascade lasers are interband diode lasers operating up to around 3 µm. The lasing transition takes place between two quantized states, the subbands, in the conduction band. The transitions occur in many series of coupled quantum wells, connected by injector refgions to supply charge carriers. In conclusion, semiconductor lasers are based on the analogous fundamental properties as atomic lasers do. If charge carrier population inversion is guaranteed and a threshold current, accompanied by a certain threshold gain and threshold carrier density, is supplied, lasing operation is feasible. The optimization by gain-guided or index-guided cavities will lead to lower threshold values and increasing beam qualities. The variety in semiconductor laser models reachs from edge- and surface-emitting lasers to distributed feedback lasers, quantum dot lasers and quantum cascade lasers. As already a wide range of requirements has been covered, semiconductor lasers are seen as a suitable device for modern technology. 10

12 References [1] M. GRUNDMANN The Physics of Semiconductors, Springer Berlin 2006 [2] GEORG A. REIDER Photonik, 3rd edition, Springer 2012 [3] J.SINGH Semiconductor Optoelectronics, Physics and Technology,Mc Graw-Hill 1995 [4] P.W. EPPERLEIN Semiconductor Laser, Engineering, Reliability and Diagnostics, John Wiley & Sons Ltd, 2013 [5] P. L. DERRY, L. FIGUEROA, C. HONG Semiconductor Lasers, Chapter 13, Boeing Defense & Space Group, Seattle [6] E. KAPON Semiconductor Lasers II, Materials and Structure, Academic Press 1999 [7] W. M. SCHULZ InP/AlGaInP Quantenpunkte, Universität Stuttgart, 2011 [8] INTERNET pdf called 19th May 2016, 17:20 [9] T. NUMAI Fundamentals of Semiconductor Lasers, 2nd edition, Springer 2015 [10] W.W. CHOW, S.W. KOCH Semiconductor - Laser Fundamentals, Springer, 1999 [11] O. G. OKHOTNIKOV Semiconductor Disk Lasers, WILEY-VCH 2010 [12] H. FOUCKHARDT Halbleiterlaser, 1st edition, Vieweg+Teubner 2011 [13] J. WEIS Lecture Semiconductor Physics II, Summer Term 2016 [14] IEEE JOURNAL IEEE Journal of selected topics in quantum electronics, vol. 17, No. 3, May/June 2011 [15] H. KAHLE, R. BEK, M. HELDMAIER, T. SCHWARZBÄCK, M. JETTER, P. MICHLER High optical output power in the UVA range of a frequency-doubled, strain-compensated AlGaInP-VECSEL, Applied Physics Express 7, (2014) [16] L. V. ASRYAN, R. A. SURIS Theory of Threshold Characteristics of Semiconductor Quantum Dot Lasers, published 30th April