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Quantum-cascade laser

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1700: 2648:. Here, the QC material is also etched to produce an isolated ridge. Now, however, new semiconductor material is grown over the ridge. The change in index of refraction between the QC material and the overgrown material is sufficient to create a waveguide. Dielectric material is also deposited on the overgrown material around QC ridge to guide the injected current into the QC gain medium. Buried heterostructure waveguides are efficient at removing heat from the QC active area when light is being produced. 101: 2708: 2750: 2544: 170: 2446: 2487: 213: 4427: 1747:, the overlap of the upper and lower laser levels is reduced. This is often achieved through designing the layer thicknesses such that the upper laser level is mostly localised in the left-hand well of the 3QW active region, while the lower laser level wave function is made to mostly reside in the central and right-hand wells. This is known as a 1164: 893: 554: 713: 2715:
In an external cavity (EC) quantum cascade laser, the quantum cascade device serves as the laser gain medium. One, or both, of the waveguide facets has an anti-reflection coating that defeats the optical cavity action of the cleaved facets. Mirrors are then arranged in a configuration external to the
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values. For interband optical transitions, carriers change momentum through a slow, intermediate scattering process, dramatically reducing the optical emission intensity. Intersubband optical transitions, however, are independent of the relative momentum of conduction band and valence band minima and
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built on top of the waveguide to prevent it from emitting at other than the desired wavelength. This forces single mode operation of the laser, even at higher operating currents. DFB lasers can be tuned chiefly by changing the temperature, although an interesting variant on tuning can be obtained by
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material is typically deposited in the trenches to guide injected current into the ridge, then the entire ridge is typically coated with gold to provide electrical contact and to help remove heat from the ridge when it is producing light. Light is emitted from the cleaved ends of the waveguide, with
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The short wavelength limit of QCLs is determined by the depth of the quantum well and recently QCLs have been developed in material systems with very deep quantum wells in order to achieve short wavelength emission. The InGaAs/AlAsSb material system has quantum wells 1.6 eV deep and has been used to
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proving that the QC concept is not restricted to one material system. This material system has a varying quantum well depth depending on the aluminium fraction in the barriers. Although GaAs-based QCLs have not matched the performance levels of InP-based QCLs in the mid-infrared, they have proven to
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between two subbands in the system which is required in order to achieve laser emission. Because the position of the energy levels in the system is primarily determined by the layer thicknesses and not the material, it is possible to tune the emission wavelength of QCLs over a wide range in the same
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Fabry-Perot (FP) quantum cascade lasers were first commercialized in 1998, distributed feedback (DFB) devices were first commercialized in 2004, and broadly-tunable external cavity quantum cascade lasers first commercialized in 2006. The high optical power output, tuning range and room temperature
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The couple InAs/AlSb is the most recent QCL material family compared to alloys grown on InP and GaAs substrates. The main advantage of the InAs/AlSb material system is the small effective electron mass in quantum wells, which favors a high intersubband gain. This benefit can be better exploited in
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This is the simplest of the quantum cascade lasers. An optical waveguide is first fabricated out of the quantum cascade material to form the gain medium. The ends of the crystalline semiconductor device are then cleaved to form two parallel mirrors on either end of the waveguide, thus forming a
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There exists several methods to extend the tuning range of quantum cascade lasers using only monolithically integrated elements. Integrated heaters can extend the tuning range at fixed operation temperature to 0.7% of the central wavelength and superstructure gratings operating through the
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Bidaux, Yves; Bismuto, Alfredo; Tardy, Camille; Terazzi, Romain; Gresch, Tobias; Blaser, Stéphane; Muller, Antoine; Faist, Jerome (4 November 2015). "Extended and quasi-continuous tuning of quantum cascade lasers using superstructure gratings and integrated heaters".
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of the subbands. The scattering rate between two subbands is heavily dependent upon the overlap of the wave functions and energy spacing between the subbands. The figure shows the wave functions in a three quantum well (3QW) QCL active region and injector.
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long-wavelength QCLs where the lasing transition levels are close to the bottom of the conduction band, and the effect of nonparabolicity is weak. InAs-based QCLs have demonstrated room temperature (RT) continuous wave (CW) operation at wavelengths up to
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Hannemann, M.; Antufjew, A.; Borgmann, K.; Hempel, F.; Ittermann, T.; Welzel, S.; Weltmann, K.D.; Völzke, H.; Röpcke, J. (2011). "Influence of age and sex in exhaled breath samples investigated by means of infrared laser absorption spectroscopy".
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Two types of optical waveguides are in common use. A ridge waveguide is created by etching parallel trenches in the quantum cascade gain material to create an isolated stripe of QC material, typically ~10 um wide, and several mm long. A
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When used in multiple-laser systems, intrapulse QCL spectroscopy offers broadband spectral coverage that can potentially be used to identify and quantify complex heavy molecules such as those in toxic chemicals, explosives, and drugs.
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If a frequency-selective element is included in the external cavity, it is possible to reduce the laser emission to a single wavelength, and even tune the radiation. For example, diffraction gratings have been used to create a
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resonator. The residual reflectivity on the cleaved facets from the semiconductor-to-air interface is sufficient to create a resonator. Fabry–Pérot quantum cascade lasers are capable of producing high powers, but are typically
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quantum cascade emitters have been made. Intersubband electroluminescence from non-polar SiGe heterostructures has been observed for mid-infrared and far-infrared wavelengths, both in the valence and conduction band.
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into the next period of the structure where another photon can be emitted. This process of a single electron causing the emission of multiple photons as it traverses through the QCL structure gives rise to the name
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Revin, D. G.; Cockburn, J. W.; Steer, M. J.; Airey, R. J.; Hopkinson, M.; Krysa, A. B.; Wilson, L. R.; Menzel, S. (2007-01-08). "InGaAs/AlAsSb/InP quantum cascade lasers operating at wavelengths close to 3μm".
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Additionally, in semiconductor laser diodes, electrons and holes are annihilated after recombining across the band gap and can play no further part in photon generation. However, in a unipolar QCL, once an
1650: 120:, which is sparsely populated with high energy electrons. The two energy bands are separated by an energy band gap in which there are no permitted states available for electrons to occupy. Conventional 3739:
Stark, David; Mirza, Muhammad; Persichetti, Luca; Montanari, Michele; Markmann, Sergej; Beck, Mattias; Grange, Thomas; Birner, Stefan; Virgilio, Michele; Ciano, Chiara; Ortolani, Michele (2021-03-08).
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Zibik, E. A.; W. H. Ng; D. G. Revin; L. R. Wilson; J. W. Cockburn; K. M. Groom; M. Hopkinson (March 2006). "Broadband 6 μm < λ < 8 μm superluminescent quantum cascade light-emitting diodes".
959: 4152: 1159:{\displaystyle {\frac {\mathrm {d} n_{i}}{\mathrm {d} t}}=\sum \limits _{j=1}^{N}{\frac {n_{j}}{\tau _{ji}}}-n_{i}\sum \limits _{j=1}^{N}{\frac {1}{\tau _{ij}}}+I(\delta _{iN}-\delta _{i1})} 888:{\displaystyle {\frac {\mathrm {d} n_{1}}{\mathrm {d} t}}={\frac {n_{2}}{\tau _{21}}}+{\frac {n_{3}}{\tau _{31}}}-{\frac {n_{1}}{\tau _{13}}}-{\frac {n_{1}}{\tau _{12}}}-I_{\mathrm {out} }} 549:{\displaystyle {\frac {\mathrm {d} n_{3}}{\mathrm {d} t}}=I_{\mathrm {in} }+{\frac {n_{1}}{\tau _{13}}}+{\frac {n_{2}}{\tau _{23}}}-{\frac {n_{3}}{\tau _{31}}}-{\frac {n_{3}}{\tau _{32}}}} 1356: 4340: 4231: 3979: 161:
and leads to the splitting of the band of permitted energies into a number of discrete electronic subbands. By suitable design of the layer thicknesses it is possible to engineer a
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In quantum cascade structures, electrons undergo intersubband transitions and photons are emitted. The electrons tunnel to the next period of the structure and the process repeats.
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Faist, Jérome; Claire Gmachl; Frederico Capasso; Carlo Sirtori; Deborah L. Silvco; James N. Baillargeon; Alfred Y. Cho (May 1997). "Distributed feedback quantum cascade lasers".
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in the valence band. The energy of the photon and hence the emission wavelength of laser diodes is therefore determined by the band gap of the material system used.
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Lang, N.; Röpcke, J.; Wege, S.; Steinach, A. (2009). "In situ diagnostic of etch plasmas for process control using quantum cascade laser absorption spectroscopy".
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Lynch, S. A.; Bates, R.; Paul, D. J.; Norris, D. J.; Cullis, A. G.; Ikonic, Z.; Kelsall, R. W.; Harrison, P.; Arnone, D. D.; Pidgeon, C. R. (2002-08-26).
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Bismuto, Alfredo; Bidaux, Yves; Tardy, Camille; Terazzi, Romain; Gresch, Tobias; Wolf, Johanna; Blaser, Stéphane; Muller, Antoine; Faist, Jerome (2015).
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Maulini, Richard; Mattias Beck; Jérome Faist; Emilio Gini (March 2004). "Broadband tuning of external cavity bound-to-continuum quantum-cascade lasers".
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End view of QC facet with buried heterostructure waveguide. Darker gray: InP, lighter gray: QC layers, black: dielectric. Heterostructure ~ 10 um wide
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are the initial and final subband indices. Assuming that no other subbands are populated, the rate equations for the three level lasers are given by:
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Barate, D.; Teissier, R.; Wang, Y.; Baranov, A. N. (2005). "Short wavelength intersubband emission from InAs/AlSb quantum cascade structures".
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transition is one in which the upper laser level is localised in mainly the central and right-hand wells. This increases the overlap and hence
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Loghmari, Z.; Rodriguez, J.-B.; Baranov, A. N.; Rio-Calvo, M.; Cerutti, L.; Meguekam, A.; Bahriz, M.; Teissier, R.; Tournié, E. (2020-04-01).
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End view of QC facet with ridge waveguide. Darker gray: InP, lighter gray: QC layers, black: dielectric, gold: Au coating. Ridge ~ 10 um wide.
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Kazarinov, R. F.; Suris, R. A. (April 1971). "Possibility of amplification of electromagnetic waves in a semiconductor with a superlattice".
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Faist, Jerome; Federico Capasso; Deborah L. Sivco; Carlo Sirtori; Albert L. Hutchinson; Alfred Y. Cho (April 1994). "Quantum Cascade Laser".
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Schematic of QC device in external cavity with frequency selective optical feedback provided by diffraction grating in Littrow configuration.
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Walther, C.; Fischer, M.; Scalari, G.; Terazzi, R.; Hoyler, N.; Faist, J. (2007). "Quantum cascade lasers operating from 1.2 to 1.6 THz".
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Slivken, S.; A. Evans; J. David; M. Razeghi (December 2002). "High-average-power, high-duty-cycle (λ ~ 6 μm) quantum cascade lasers".
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Electron wave functions are repeated in each period of a three quantum well QCL active region. The upper laser level is shown in bold.
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QCLs currently cover the wavelength range from 2.63 μm to 250 μm (and extends to 355 μm with the application of a magnetic field.)
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The scattering rates are tailored by suitable design of the layer thicknesses in the superlattice which determine the electron
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Cathabard, O.; Teissier, R.; Devenson, J.; Moreno, J.C.; Baranov, A.N. (2010). "Quantum cascade lasers emitting near 2.6 μm".
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Kinjalk, Kumar; Díaz-Thomas, Daniel Andres; Loghmari, Zeineb; Bahriz, Michael; Teissier, Roland; Baranov, Alexei N. (2022).
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light in a superluminescent configuration, it is most commonly used in combination with an optical cavity to form a laser.
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energy (~36 meV in GaAs) so that resonant LO phonon-electron scattering can quickly depopulate the lower laser level.
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Nguyen Van, Hoang; Loghmari, Zeineb; Philip, Hadrien; Bahriz, Michael; Baranov, Alexei N.; Teissier, Roland (2019).
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The first step in processing quantum cascade gain material to make a useful light-emitting device is to confine the
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which reduces the population inversion, but it increases the strength of the radiative transition and therefore the
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Dehlinger, G.; Diehl, L.; Gennser, U.; Sigg, H.; Faist, J.; Ensslin, K.; Grützmacher, D.; Müller, E. (2000-12-22).
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at higher operating currents. The wavelength can be changed chiefly by changing the temperature of the QC device.
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A QCL however does not use bulk semiconductor materials in its optically active region. Instead, it consists of a
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may be applied and the system can be modelled using rate equations. Each subband contains a number of electrons
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Loghmari, Z.; Bahriz, M.; Thomas, D. Díaz; Meguekam, A.; Van, H. Nguyen; Teissier, R.; Baranov, A.N. (2018).
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Subband populations are determined by the intersubband scattering rates and the injection/extraction current.
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QCLs may also allow laser operation in materials traditionally considered to have poor optical properties.
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steady-state rate equations are summed, the right hand side becomes zero, meaning that the system is
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substrate. This particular material system has a conduction band offset (quantum well depth) of 520
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of greater than unity possible which leads to higher output powers than semiconductor laser diodes.
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operation make QCLs useful for spectroscopic applications such as remote sensing of environmental
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of electrons occupying different positions over the length of the device. This is referred to as
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can extend it to 4% of the central wavelength, compared to <0.1% for a standard DFB device.
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As an approximation, it can be assumed that all the carriers in the system are supplied by
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further, the energy spacing between the subbands is designed such that it is equal to the
152: 117: 85: 3639:"Intersubband electroluminescence from Si/SiGe cascade emitters at terahertz frequencies" 3333: 4317: 4266: 4106: 4060: 4021: 3957: 3922: 3887: 3852: 3817: 3766: 3701: 3654: 3562: 3510: 3461: 3406: 3349: 3300: 3245: 3190: 3147: 3085: 3043: 2992: 2870: 4274: 2818: 2781: 1844: 362: 342: 258: 3570: 2749: 2543: 1903:
fabricate QCLs emitting at 3.05 μm. InAs/AlSb QCLs have quantum wells 2.1 eV deep and
1871:. These InP-based devices have reached very high levels of performance across the mid- 17: 4616: 4045:"Extended tuning of mid-ir quantum cascade lasers using integrated resistive heaters" 3790: 3741:"THz intersubband electroluminescence from n-type Ge/SiGe quantum cascade structures" 3725: 3578: 3543: 3479: 3430: 2979:
Razeghi, Manijeh (2009). "High-Performance InP-Based Mid-IR Quantum Cascade Lasers".
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at room temperature have been demonstrated. The threshold obtained is lower than the
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being emitted when a high energy electron in the conduction band recombines with a
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Interband transitions in conventional semiconductor lasers emit a single photon.
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materials such as silicon have minimum electron and hole energies at different
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have also been achieved in InAs-based QCLs emitting in other spectral regions:
2947: 2822: 2637: 2625: 276: 51: 4356: 4227: 3782: 3717: 3686:"The progress towards terahertz quantum cascade lasers on silicon substrates" 3670: 3544:"Si/SiGe heterostructures: from material and physics to devices and circuits" 3528: 3519: 3494: 3422: 3367: 3318: 3309: 3284: 3261: 3206: 3163: 3111: 3093: 4394: 4325: 3446:"InAs-based quantum cascade lasers grown on on-axis (001) silicon substrate" 2830: 2814: 2690:(DFB) quantum cascade laser is similar to a Fabry–Pérot laser, except for a 4282: 4078: 3709: 3623: 3375: 2886: 2695:
pulsing a DFB laser. In this mode, the wavelength of the laser is rapidly "
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in the atmosphere and security. They may eventually be used for vehicular
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and a population inversion will exist. The population ratio is defined as
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such as breath analyzers. QCLs are also used to study plasma chemistry.
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an active area that is typically only a few micrometers in dimension.
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to be built such that light can be coupled back into the gain medium.
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of the best reported InP-based QCLs to date without facet treatment.
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Under the assumption that absorption processes can be ignored, (i.e.
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Howieson, Iain; Normand, Erwan; McCulloch, Michael T. (2005-03-01).
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Normand, Erwan; Howieson, Iain; McCulloch, Michael T. (April 2007).
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Baranov, Alexei N.; Bahriz, Michael; Teissier, Roland (2016-08-08).
3757: 2275:(QCL grown on InAs). Most recently, InAs-based QCLs operating near 2826: 2788:
may be grown on to a substrate using a variety of methods such as
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across the length of the device, meaning that there is a varying
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Although the quantum cascade gain medium can be used to produce
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population of carriers in each subband may be determined using:
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series of thin layers of varying material composition forming a
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spectral range, achieving high power, above room-temperature,
1645:{\displaystyle \sum \limits _{i=1}^{N}n_{i}=N_{\mathrm {2D} }} 4389: 2624:. This makes it possible to direct the emitted light into a 1244:, valid at low temperatures) the middle rate equation gives 3230:"Quantum Cascade Lasers in the InAs/AlSb Material System" 309:(reciprocal of the average intersubband scattering rate 92:" by R. F. Kazarinov and R. A. Suris in 1971. 4182:"Tunable QC laser opens up mid-IR sensing applications" 2761: 2555: 182:
has undergone an intersubband transition and emitted a
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IEEE Journal of Selected Topics in Quantum Electronics
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IEEE Journal of Selected Topics in Quantum Electronics
954:{\displaystyle I_{\mathrm {in} }=I_{\mathrm {out} }=I} 2507:. Please help to ensure that disputed statements are 2387: 2340: 2310: 2281: 2252: 2205: 2176: 2129: 2100: 2053: 2023: 1976: 1946: 1917: 1907:
at wavelengths as short as 2.5 μm has been observed.
1822: 1795: 1761: 1726: 1670: 1592: 1553: 1447: 1404: 1364: 1324: 1253: 1176: 978: 961:. The general rate equation for electrons in subband 908: 724: 565: 388: 365: 345: 315: 285: 261: 234: 4582: 4561: 4517: 4500: 4437: 4188:. PennWell Publications. 2006-07-01. Archived from 4159:. PennWell Publications. 2004-04-19. Archived from 4153:"Alpes offers CW and pulsed quantum cascade lasers" 3986:. PennWell Publications. 2005-03-01. Archived from 2403: 2373: 2326: 2296: 2267: 2238: 2191: 2162: 2115: 2086: 2039: 2009: 1962: 1932: 1835: 1808: 1774: 1739: 1688: 1644: 1571: 1528: 1430: 1390: 1350: 1307: 1236: 1158: 953: 887: 707: 548: 371: 351: 331: 301: 267: 247: 2724:that can tune over 15% of its center wavelength. 4531:Vertical-external-cavity surface-emitting-laser 1696:is approximately equal to the doping density. 81:in a repeated stack of semiconductor multiple 4410: 4306:The European Physical Journal Applied Physics 3228:Baranov, Alexei N.; Teissier, Roland (2015). 902:, the time derivatives are equal to zero and 8: 2780:The alternating layers of the two different 2474:Learn how and when to remove these messages 4457:Separate confinement heterostructure laser 4417: 4403: 4395: 2829:, industrial process control, and medical 186:in one period of the superlattice, it can 4068: 3756: 3518: 3469: 3357: 3308: 3101: 2580:Learn how and when to remove this message 2527:Learn how and when to remove this message 2392: 2386: 2365: 2353: 2339: 2315: 2309: 2280: 2251: 2230: 2218: 2204: 2175: 2154: 2142: 2128: 2099: 2078: 2066: 2052: 2028: 2022: 2001: 1989: 1975: 1951: 1945: 1916: 1827: 1821: 1800: 1794: 1766: 1760: 1731: 1725: 1676: 1675: 1669: 1660:. If the dopant species has a negligible 1632: 1631: 1618: 1608: 1597: 1591: 1559: 1558: 1552: 1518: 1508: 1502: 1491: 1481: 1475: 1464: 1454: 1448: 1446: 1422: 1409: 1403: 1382: 1369: 1363: 1342: 1329: 1323: 1297: 1287: 1281: 1270: 1260: 1254: 1252: 1220: 1210: 1204: 1193: 1183: 1177: 1175: 1144: 1128: 1104: 1095: 1089: 1078: 1068: 1050: 1040: 1034: 1028: 1017: 999: 991: 982: 979: 977: 932: 931: 914: 913: 907: 872: 871: 856: 846: 840: 829: 819: 813: 802: 792: 786: 775: 765: 759: 745: 737: 728: 725: 723: 697: 687: 681: 670: 660: 654: 643: 633: 627: 616: 606: 600: 586: 578: 569: 566: 564: 538: 528: 522: 511: 501: 495: 484: 474: 468: 457: 447: 441: 428: 427: 409: 401: 392: 389: 387: 364: 344: 320: 314: 290: 284: 260: 239: 233: 2716:QC device to create the optical cavity. 2503:Relevant discussion may be found on the 1940:with a pulsed threshold current density 1351:{\displaystyle \tau _{32}>\tau _{21}} 143:. The superlattice introduces a varying 2942:. Graduate Texts in Physics. Springer. 2846: 4525:Vertical-cavity surface-emitting laser 4341:"Quantum-cascade lasers smell success" 3980:"Quantum-cascade lasers smell success" 2852: 2850: 2798:metalorganic chemical vapor deposition 2644:The second waveguide type is a buried 1863:material system lattice-matched to an 1579:in the system is also known, then the 96:Intersubband vs. interband transitions 3022:Sirtori; et al. (1998). "GaAs/Al 7: 1855:The first QCL was fabricated in the 4312:(13110) (published 2009-12-11): 3. 4261:(27101) (published 2011-04-01): 9. 1594: 1075: 1014: 3067:"Terahertz quantum-cascade lasers" 1890:QCLs were demonstrated by Sirtori 1680: 1636: 1563: 1000: 983: 939: 936: 933: 918: 915: 879: 876: 873: 746: 729: 587: 570: 432: 429: 410: 393: 25: 4463:Distributed Bragg reflector laser 4129:"Extrait du registre du commerce" 2911:Fizika I Tekhnika Poluprovodnikov 2794:metalorganic vapour phase epitaxy 2692:distributed Bragg reflector (DBR) 2455:This section has multiple issues. 1689:{\displaystyle N_{\mathrm {2D} }} 1572:{\displaystyle N_{\mathrm {2D} }} 4425: 4390:Optipedia: Quantum Cascade Laser 2748: 2542: 2485: 2444: 1845:longitudinal optical (LO) phonon 1391:{\displaystyle W_{21}>W_{32}} 220:QCLs are typically based upon a 4602:List of semiconductor materials 2463:or discuss these issues on the 2087:{\displaystyle 0.715~kA/cm^{2}} 279:between levels with a lifetime 42:and were first demonstrated by 3065:Williams, Benjamin S. (2007). 2939:Quantum Photonics, 2nd edition 2239:{\displaystyle 0.75~kA/cm^{2}} 2163:{\displaystyle 0.99~kA/cm^{2}} 1431:{\displaystyle n_{3}>n_{2}} 1153: 1121: 1: 3690:Laser & Photonics Reviews 3616:10.1126/science.290.5500.2277 2374:{\displaystyle 0.6~kA/cm^{2}} 69:through the recombination of 34:that emit in the mid- to far- 4451:Double heterostructure laser 4275:10.1088/1752-7155/5/2/027101 3030:As quantum cascade lasers". 2879:10.1126/science.264.5158.553 275:is the subband index) which 108:Within a bulk semiconductor 3571:10.1088/0268-1242/19/10/R02 2682:Distributed feedback lasers 2010:{\displaystyle 1~kA/cm^{2}} 969:level system is therefore: 124:generate light by a single 4649: 4574:Laser diode rate equations 4569:Semiconductor laser theory 4469:Distributed-feedback laser 4255:Journal of Breath Research 3254:10.1109/JSTQE.2015.2426412 3001:10.1109/JSTQE.2008.2006764 2423:theoretical proposals for 1933:{\displaystyle 17.7~\mu m} 1895:be very successful in the 302:{\displaystyle \tau _{if}} 122:semiconductor laser diodes 2948:10.1007/978-3-030-47325-9 2936:Pearsall, Thomas (2020). 2268:{\displaystyle 7.7~\mu m} 67:electromagnetic radiation 61:Unlike typical interband 4548:Semiconductor ring laser 3542:Paul, Douglas J (2004). 3520:10.3390/photonics9100747 3310:10.3390/photonics6010031 3094:10.1038/nphoton.2007.166 2297:{\displaystyle 14~\mu m} 2192:{\displaystyle 11~\mu m} 2116:{\displaystyle 15~\mu m} 1899:region of the spectrum. 79:intersubband transitions 40:electromagnetic spectrum 4542:Interband cascade laser 4095:Applied Physics Letters 4010:Applied Physics Letters 3946:Applied Physics Letters 3911:Applied Physics Letters 3841:Applied Physics Letters 3806:Applied Physics Letters 3745:Applied Physics Letters 3643:Applied Physics Letters 3179:Applied Physics Letters 3136:Applied Physics Letters 2796:(MOVPE), also known as 2786:quantum heterostructure 2728:Extended tuning devices 3710:10.1002/lpor.200910038 3551:Semicond. Sci. Technol 2825:, collision avoidance 2821:in conditions of poor 2790:molecular beam epitaxy 2712: 2703:External cavity lasers 2613: 2605: 2405: 2404:{\displaystyle J_{th}} 2375: 2328: 2327:{\displaystyle J_{th}} 2298: 2269: 2240: 2193: 2164: 2117: 2088: 2041: 2040:{\displaystyle J_{th}} 2011: 1964: 1963:{\displaystyle J_{th}} 1934: 1837: 1836:{\displaystyle W_{21}} 1810: 1809:{\displaystyle W_{21}} 1776: 1775:{\displaystyle W_{32}} 1741: 1740:{\displaystyle W_{32}} 1704: 1690: 1646: 1613: 1573: 1530: 1432: 1392: 1352: 1309: 1238: 1160: 1094: 1033: 955: 889: 709: 550: 373: 353: 333: 332:{\displaystyle W_{if}} 303: 269: 249: 217: 174: 105: 28:Quantum-cascade lasers 18:Quantum cascade lasers 4491:External-cavity laser 4485:Quantum-cascade laser 4326:10.1051/epjap/2009198 2710: 2611: 2603: 2406: 2376: 2329: 2299: 2270: 2241: 2194: 2165: 2118: 2089: 2042: 2012: 1965: 1935: 1838: 1811: 1789:In order to increase 1777: 1742: 1720:In order to decrease 1708:Active region designs 1702: 1691: 1647: 1593: 1574: 1531: 1433: 1393: 1353: 1310: 1239: 1161: 1074: 1013: 956: 890: 710: 551: 374: 354: 334: 304: 270: 250: 248:{\displaystyle n_{i}} 215: 172: 156:multiple quantum well 103: 4633:Terahertz technology 4628:Semiconductor lasers 4537:Hybrid silicon laser 4508:Volume Bragg grating 4431:Semiconductor lasers 4133:Registre du commerce 4070:10.1364/OE.23.029715 3684:Paul, D. J. (2010). 3415:10.1049/el.2018.5258 3359:10.1364/OE.24.018799 2688:distributed feedback 2496:factual accuracy is 2436:Emission wavelengths 2385: 2338: 2308: 2279: 2250: 2203: 2174: 2127: 2098: 2051: 2021: 1974: 1944: 1915: 1820: 1793: 1759: 1724: 1668: 1590: 1551: 1445: 1402: 1362: 1322: 1251: 1174: 976: 906: 722: 563: 386: 363: 343: 313: 283: 259: 232: 226:Schrödinger equation 203:Operating principles 163:population inversion 73:across the material 63:semiconductor lasers 32:semiconductor lasers 4623:American inventions 4318:2010EPJAP..49a3110L 4267:2011JBR.....5b7101H 4107:2015ApPhL.107v1108B 4061:2015OExpr..2329715B 4055:(23): 29715–29722. 4022:2004ApPhL..84.1659M 3958:1997ApPhL..70.2670F 3923:2002ApPhL..81.4321S 3888:2006ApPhL..88l1109Z 3853:2007ApPhL..91m1122W 3818:2010ApPhL..96n1110C 3767:2021ApPhL.118j1101S 3702:2010LPRv....4..610P 3655:2002ApPhL..81.1543L 3610:(5500): 2277–2280. 3563:2004SeScT..19R..75P 3511:2022Photo...9..747K 3462:2020APLP....5d1302L 3407:2018ElL....54.1045L 3395:Electronics Letters 3350:2016OExpr..2418799B 3344:(16): 18799–19506. 3301:2019Photo...6...31N 3246:2015IJSTQ..21...85B 3191:2005ApPhL..87e1103B 3148:2007ApPhL..90b1108R 3086:2007NaPho...1..517W 3044:1998ApPhL..73.3486S 2993:2009IJSTQ..15..941R 2871:1994Sci...264..553F 2628:beam, and allows a 1905:electroluminescence 71:electron–hole pairs 4475:Quantum well laser 2760:. You can help by 2713: 2664:Fabry–Perot lasers 2614: 2606: 2596:Optical waveguides 2554:. You can help by 2401: 2371: 2324: 2294: 2265: 2236: 2189: 2160: 2113: 2084: 2037: 2007: 1960: 1930: 1833: 1806: 1772: 1737: 1705: 1686: 1642: 1569: 1526: 1428: 1388: 1348: 1305: 1234: 1156: 951: 885: 705: 546: 369: 349: 329: 299: 265: 245: 222:three-level system 218: 197:quantum efficiency 175: 145:electric potential 106: 4610: 4609: 4480:Quantum dot laser 4385:Bell Labs summary 4345:Laser Focus World 4216:Laser Focus World 4186:Laser Focus World 4157:Laser Focus World 4115:10.1063/1.4936931 4030:10.1063/1.1667609 3984:Laser Focus World 3931:10.1063/1.1526462 3917:(23): 4321–4323. 3896:10.1063/1.2188371 3861:10.1063/1.2793177 3826:10.1063/1.3385778 3775:10.1063/5.0041327 3663:10.1063/1.1501759 3471:10.1063/5.0002376 3401:(17): 1045–1047. 3199:10.1063/1.2007854 3156:10.1063/1.2431035 2957:978-3-030-47324-2 2865:(5158): 553–556. 2778: 2777: 2590: 2589: 2582: 2572: 2571: 2537: 2536: 2529: 2478: 2346: 2287: 2258: 2211: 2182: 2135: 2106: 2059: 1982: 1923: 1662:ionisation energy 1524: 1497: 1470: 1303: 1276: 1226: 1199: 1113: 1059: 1008: 862: 835: 808: 781: 754: 703: 676: 649: 622: 595: 544: 517: 490: 463: 418: 372:{\displaystyle f} 352:{\displaystyle i} 268:{\displaystyle i} 166:material system. 56:Bell Laboratories 16:(Redirected from 4640: 4596:Gallium arsenide 4429: 4419: 4412: 4405: 4396: 4372: 4371: 4369: 4368: 4359:. Archived from 4336: 4330: 4329: 4301: 4295: 4294: 4249: 4243: 4242: 4240: 4239: 4230:. Archived from 4207: 4201: 4200: 4198: 4197: 4178: 4172: 4171: 4169: 4168: 4149: 4143: 4142: 4140: 4139: 4125: 4119: 4118: 4089: 4083: 4082: 4072: 4040: 4034: 4033: 4005: 3999: 3998: 3996: 3995: 3976: 3970: 3969: 3966:10.1063/1.119208 3941: 3935: 3934: 3906: 3900: 3899: 3876:Appl. Phys. Lett 3871: 3865: 3864: 3836: 3830: 3829: 3801: 3795: 3794: 3760: 3736: 3730: 3729: 3681: 3675: 3674: 3649:(9): 1543–1545. 3634: 3628: 3627: 3595: 3589: 3588: 3586: 3585: 3557:(10): R75–R108. 3548: 3539: 3533: 3532: 3522: 3490: 3484: 3483: 3473: 3441: 3435: 3434: 3386: 3380: 3379: 3361: 3329: 3323: 3322: 3312: 3280: 3274: 3273: 3225: 3219: 3218: 3174: 3168: 3167: 3130: 3124: 3123: 3105: 3074:Nature Photonics 3071: 3062: 3056: 3055: 3052:10.1063/1.122812 3032:Appl. Phys. Lett 3019: 3013: 3012: 2976: 2970: 2969: 2933: 2927: 2926: 2919: 2905: 2899: 2898: 2854: 2773: 2770: 2752: 2745: 2585: 2578: 2567: 2564: 2546: 2539: 2532: 2525: 2521: 2518: 2512: 2509:reliably sourced 2489: 2488: 2481: 2470: 2448: 2447: 2440: 2416:Indirect bandgap 2410: 2408: 2407: 2402: 2400: 2399: 2380: 2378: 2377: 2372: 2370: 2369: 2357: 2344: 2333: 2331: 2330: 2325: 2323: 2322: 2303: 2301: 2300: 2295: 2285: 2274: 2272: 2271: 2266: 2256: 2245: 2243: 2242: 2237: 2235: 2234: 2222: 2209: 2198: 2196: 2195: 2190: 2180: 2169: 2167: 2166: 2161: 2159: 2158: 2146: 2133: 2122: 2120: 2119: 2114: 2104: 2093: 2091: 2090: 2085: 2083: 2082: 2070: 2057: 2046: 2044: 2043: 2038: 2036: 2035: 2017:. Low values of 2016: 2014: 2013: 2008: 2006: 2005: 1993: 1980: 1969: 1967: 1966: 1961: 1959: 1958: 1939: 1937: 1936: 1931: 1921: 1851:Material systems 1842: 1840: 1839: 1834: 1832: 1831: 1815: 1813: 1812: 1807: 1805: 1804: 1781: 1779: 1778: 1773: 1771: 1770: 1746: 1744: 1743: 1738: 1736: 1735: 1695: 1693: 1692: 1687: 1685: 1684: 1683: 1651: 1649: 1648: 1643: 1641: 1640: 1639: 1623: 1622: 1612: 1607: 1578: 1576: 1575: 1570: 1568: 1567: 1566: 1535: 1533: 1532: 1527: 1525: 1523: 1522: 1513: 1512: 1503: 1498: 1496: 1495: 1486: 1485: 1476: 1471: 1469: 1468: 1459: 1458: 1449: 1437: 1435: 1434: 1429: 1427: 1426: 1414: 1413: 1397: 1395: 1394: 1389: 1387: 1386: 1374: 1373: 1357: 1355: 1354: 1349: 1347: 1346: 1334: 1333: 1314: 1312: 1311: 1306: 1304: 1302: 1301: 1292: 1291: 1282: 1277: 1275: 1274: 1265: 1264: 1255: 1243: 1241: 1240: 1235: 1227: 1225: 1224: 1215: 1214: 1205: 1200: 1198: 1197: 1188: 1187: 1178: 1165: 1163: 1162: 1157: 1152: 1151: 1136: 1135: 1114: 1112: 1111: 1096: 1093: 1088: 1073: 1072: 1060: 1058: 1057: 1045: 1044: 1035: 1032: 1027: 1009: 1007: 1003: 997: 996: 995: 986: 980: 960: 958: 957: 952: 944: 943: 942: 923: 922: 921: 894: 892: 891: 886: 884: 883: 882: 863: 861: 860: 851: 850: 841: 836: 834: 833: 824: 823: 814: 809: 807: 806: 797: 796: 787: 782: 780: 779: 770: 769: 760: 755: 753: 749: 743: 742: 741: 732: 726: 714: 712: 711: 706: 704: 702: 701: 692: 691: 682: 677: 675: 674: 665: 664: 655: 650: 648: 647: 638: 637: 628: 623: 621: 620: 611: 610: 601: 596: 594: 590: 584: 583: 582: 573: 567: 555: 553: 552: 547: 545: 543: 542: 533: 532: 523: 518: 516: 515: 506: 505: 496: 491: 489: 488: 479: 478: 469: 464: 462: 461: 452: 451: 442: 437: 436: 435: 419: 417: 413: 407: 406: 405: 396: 390: 378: 376: 375: 370: 358: 356: 355: 350: 338: 336: 335: 330: 328: 327: 308: 306: 305: 300: 298: 297: 274: 272: 271: 266: 254: 252: 251: 246: 244: 243: 86:heterostructures 48:Federico Capasso 21: 4648: 4647: 4643: 4642: 4641: 4639: 4638: 4637: 4613: 4612: 4611: 4606: 4590:Indium arsenide 4578: 4557: 4553:Polariton laser 4513: 4496: 4433: 4423: 4381: 4376: 4375: 4366: 4364: 4338: 4337: 4333: 4303: 4302: 4298: 4251: 4250: 4246: 4237: 4235: 4209: 4208: 4204: 4195: 4193: 4180: 4179: 4175: 4166: 4164: 4151: 4150: 4146: 4137: 4135: 4127: 4126: 4122: 4091: 4090: 4086: 4042: 4041: 4037: 4007: 4006: 4002: 3993: 3991: 3978: 3977: 3973: 3943: 3942: 3938: 3908: 3907: 3903: 3873: 3872: 3868: 3838: 3837: 3833: 3803: 3802: 3798: 3738: 3737: 3733: 3683: 3682: 3678: 3636: 3635: 3631: 3597: 3596: 3592: 3583: 3581: 3546: 3541: 3540: 3536: 3492: 3491: 3487: 3443: 3442: 3438: 3388: 3387: 3383: 3331: 3330: 3326: 3282: 3281: 3277: 3227: 3226: 3222: 3176: 3175: 3171: 3132: 3131: 3127: 3069: 3064: 3063: 3059: 3029: 3025: 3021: 3020: 3016: 2978: 2977: 2973: 2958: 2935: 2934: 2930: 2913: 2907: 2906: 2902: 2856: 2855: 2848: 2843: 2806: 2784:which form the 2774: 2768: 2765: 2758:needs expansion 2743: 2730: 2705: 2684: 2666: 2654: 2646:heterostructure 2630:laser resonator 2598: 2586: 2575: 2574: 2573: 2568: 2562: 2559: 2552:needs expansion 2533: 2522: 2516: 2513: 2502: 2494:This section's 2490: 2486: 2449: 2445: 2438: 2388: 2383: 2382: 2361: 2336: 2335: 2311: 2306: 2305: 2277: 2276: 2248: 2247: 2226: 2201: 2200: 2172: 2171: 2150: 2125: 2124: 2096: 2095: 2074: 2049: 2048: 2024: 2019: 2018: 1997: 1972: 1971: 1947: 1942: 1941: 1913: 1912: 1877:continuous wave 1853: 1823: 1818: 1817: 1796: 1791: 1790: 1762: 1757: 1756: 1727: 1722: 1721: 1710: 1671: 1666: 1665: 1627: 1614: 1588: 1587: 1554: 1549: 1548: 1545:underdetermined 1514: 1504: 1487: 1477: 1460: 1450: 1443: 1442: 1418: 1405: 1400: 1399: 1378: 1365: 1360: 1359: 1338: 1325: 1320: 1319: 1293: 1283: 1266: 1256: 1249: 1248: 1216: 1206: 1189: 1179: 1172: 1171: 1140: 1124: 1100: 1064: 1046: 1036: 998: 987: 981: 974: 973: 927: 909: 904: 903: 867: 852: 842: 825: 815: 798: 788: 771: 761: 744: 733: 727: 720: 719: 693: 683: 666: 656: 639: 629: 612: 602: 585: 574: 568: 561: 560: 534: 524: 507: 497: 480: 470: 453: 443: 423: 408: 397: 391: 384: 383: 361: 360: 341: 340: 316: 311: 310: 286: 281: 280: 257: 256: 235: 230: 229: 210: 205: 153:one-dimensional 118:conduction band 98: 38:portion of the 23: 22: 15: 12: 11: 5: 4646: 4644: 4636: 4635: 4630: 4625: 4615: 4614: 4608: 4607: 4605: 4604: 4599: 4593: 4586: 4584: 4580: 4579: 4577: 4576: 4571: 4565: 4563: 4559: 4558: 4556: 4555: 4550: 4545: 4539: 4534: 4528: 4521: 4519: 4515: 4514: 4512: 4511: 4504: 4502: 4498: 4497: 4495: 4494: 4488: 4482: 4477: 4472: 4466: 4460: 4454: 4448: 4441: 4439: 4435: 4434: 4424: 4422: 4421: 4414: 4407: 4399: 4393: 4392: 4387: 4380: 4379:External links 4377: 4374: 4373: 4331: 4296: 4244: 4202: 4173: 4144: 4120: 4101:(22): 221108. 4084: 4049:Optics Express 4035: 4000: 3971: 3936: 3901: 3882:(12): 121109. 3866: 3847:(13): 131122. 3831: 3812:(14): 141110. 3796: 3751:(10): 101101. 3731: 3696:(5): 610–632. 3676: 3629: 3590: 3534: 3485: 3436: 3381: 3338:Optics Express 3324: 3275: 3220: 3169: 3125: 3080:(9): 517–525. 3057: 3027: 3023: 3014: 2987:(3): 941–951. 2971: 2956: 2928: 2900: 2845: 2844: 2842: 2839: 2819:cruise control 2805: 2802: 2782:semiconductors 2776: 2775: 2755: 2753: 2742: 2739: 2735:Vernier effect 2729: 2726: 2704: 2701: 2683: 2680: 2665: 2662: 2653: 2650: 2620:in an optical 2597: 2594: 2588: 2587: 2570: 2569: 2549: 2547: 2535: 2534: 2493: 2491: 2484: 2479: 2453: 2452: 2450: 2443: 2437: 2434: 2398: 2395: 2391: 2368: 2364: 2360: 2356: 2352: 2349: 2343: 2321: 2318: 2314: 2293: 2290: 2284: 2264: 2261: 2255: 2233: 2229: 2225: 2221: 2217: 2214: 2208: 2188: 2185: 2179: 2157: 2153: 2149: 2145: 2141: 2138: 2132: 2112: 2109: 2103: 2081: 2077: 2073: 2069: 2065: 2062: 2056: 2034: 2031: 2027: 2004: 2000: 1996: 1992: 1988: 1985: 1979: 1957: 1954: 1950: 1929: 1926: 1920: 1852: 1849: 1830: 1826: 1803: 1799: 1769: 1765: 1751:transition. A 1734: 1730: 1714:wave functions 1709: 1706: 1682: 1679: 1674: 1654: 1653: 1638: 1635: 1630: 1626: 1621: 1617: 1611: 1606: 1603: 1600: 1596: 1565: 1562: 1557: 1537: 1536: 1521: 1517: 1511: 1507: 1501: 1494: 1490: 1484: 1480: 1474: 1467: 1463: 1457: 1453: 1425: 1421: 1417: 1412: 1408: 1385: 1381: 1377: 1372: 1368: 1345: 1341: 1337: 1332: 1328: 1318:Therefore, if 1316: 1315: 1300: 1296: 1290: 1286: 1280: 1273: 1269: 1263: 1259: 1233: 1230: 1223: 1219: 1213: 1209: 1203: 1196: 1192: 1186: 1182: 1168: 1167: 1155: 1150: 1147: 1143: 1139: 1134: 1131: 1127: 1123: 1120: 1117: 1110: 1107: 1103: 1099: 1092: 1087: 1084: 1081: 1077: 1071: 1067: 1063: 1056: 1053: 1049: 1043: 1039: 1031: 1026: 1023: 1020: 1016: 1012: 1006: 1002: 994: 990: 985: 950: 947: 941: 938: 935: 930: 926: 920: 917: 912: 896: 895: 881: 878: 875: 870: 866: 859: 855: 849: 845: 839: 832: 828: 822: 818: 812: 805: 801: 795: 791: 785: 778: 774: 768: 764: 758: 752: 748: 740: 736: 731: 716: 715: 700: 696: 690: 686: 680: 673: 669: 663: 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159:confinement 149:probability 30:(QCLs) are 4617:Categories 4367:2008-01-25 4238:2008-01-25 4196:2008-03-26 4167:2007-12-01 4138:2016-04-28 3994:2008-03-26 3758:2101.05518 3584:2007-02-18 3547:(abstract) 2841:References 2823:visibility 2815:pollutants 2658:incoherent 2638:dielectric 2626:collimated 2460:improve it 2334:as low as 1970:as low as 1879:emission. 65:that emit 52:Alfred Cho 4583:Materials 4357:0740-2511 4228:1043-8092 3791:231602947 3783:0003-6951 3726:120927848 3718:1863-8899 3671:0003-6951 3579:250846255 3529:2304-6732 3499:Photonics 3480:218844666 3431:126174361 3423:0013-5194 3368:1094-4087 3319:2304-6732 3295:(1): 31. 3289:Photonics 3262:1077-260X 3207:0003-6951 3164:0003-6951 3112:1749-4885 2966:240934073 2895:220111282 2800:(MOCVD). 2792:(MBE) or 2769:June 2008 2622:waveguide 2563:June 2008 2505:talk page 2466:talk page 2289:μ 2260:μ 2184:μ 2108:μ 1925:μ 1897:terahertz 1595:∑ 1489:τ 1479:τ 1340:τ 1327:τ 1295:τ 1268:τ 1218:τ 1191:τ 1142:δ 1138:− 1126:δ 1102:τ 1076:∑ 1062:− 1048:τ 1015:∑ 865:− 854:τ 838:− 827:τ 811:− 800:τ 773:τ 695:τ 679:− 668:τ 652:− 641:τ 614:τ 536:τ 520:− 509:τ 493:− 482:τ 455:τ 339:), where 288:τ 58:in 1994. 4533:(VECSEL) 4291:23963086 4283:21460420 4079:26698453 3624:11125134 3376:27505843 3270:46218942 3215:40872029 3120:29073195 3009:37864645 2887:17732739 2498:disputed 2420:momentum 1882:In 1998 1873:infrared 1753:vertical 1749:diagonal 1581:absolute 180:electron 137:periodic 75:band gap 36:infrared 4527:(VCSEL) 4314:Bibcode 4263:Bibcode 4103:Bibcode 4057:Bibcode 4018:Bibcode 3954:Bibcode 3919:Bibcode 3884:Bibcode 3849:Bibcode 3814:Bibcode 3763:Bibcode 3698:Bibcode 3651:Bibcode 3604:Science 3559:Bibcode 3507:Bibcode 3458:Bibcode 3403:Bibcode 3346:Bibcode 3297:Bibcode 3242:Bibcode 3187:Bibcode 3144:Bibcode 3082:Bibcode 3040:Bibcode 2989:Bibcode 2867:Bibcode 2859:Science 2697:chirped 1539:If all 1398:) then 898:In the 277:scatter 255:(where 193:cascade 110:crystal 4598:(GaAs) 4592:(InAs) 4562:Theory 4355:  4289:  4281:  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1420:n 1411:3 1407:n 1380:W 1367:W 1289:2 1285:n 1279:= 1262:3 1258:n 1232:0 1229:= 1212:2 1208:n 1202:= 1185:1 1181:n 1166:, 1154:) 1149:1 1146:i 1133:N 1130:i 1122:( 1119:I 1116:+ 1109:j 1106:i 1098:1 1091:N 1086:1 1083:= 1080:j 1070:i 1066:n 1055:i 1052:j 1042:j 1038:n 1030:N 1025:1 1022:= 1019:j 1011:= 1005:t 1001:d 993:i 989:n 984:d 967:N 963:i 949:I 946:= 940:t 937:u 934:o 929:I 925:= 919:n 916:i 911:I 880:t 877:u 874:o 869:I 848:1 844:n 821:1 817:n 794:3 790:n 784:+ 767:2 763:n 757:= 751:t 747:d 739:1 735:n 730:d 689:2 685:n 662:2 658:n 635:1 631:n 625:+ 608:3 604:n 598:= 592:t 588:d 580:2 576:n 571:d 530:3 526:n 503:3 499:n 476:2 472:n 466:+ 449:1 445:n 439:+ 433:n 430:i 425:I 421:= 415:t 411:d 403:3 399:n 394:d 367:f 347:i 325:f 322:i 318:W 295:f 292:i 263:i 241:i 237:n 20:)

Index

Quantum cascade lasers
semiconductor lasers
infrared
electromagnetic spectrum
Jérôme Faist
Federico Capasso
Alfred Cho
Bell Laboratories
semiconductor lasers
electromagnetic radiation
electron–hole pairs
band gap
intersubband transitions
quantum well
heterostructures
superlattice

crystal
valence band
conduction band
semiconductor laser diodes
photon
hole
periodic
superlattice
electric potential
probability
one-dimensional
multiple quantum well
confinement

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