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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 2 — Jan. 27, 2014
  • pp: 2111–2118
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Distributed-feedback quantum cascade laser emitting at 3.2 μm

Johanna M. Wolf, Alfredo Bismuto, Mattias Beck, and Jérôme Faist  »View Author Affiliations


Optics Express, Vol. 22, Issue 2, pp. 2111-2118 (2014)
http://dx.doi.org/10.1364/OE.22.002111


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Abstract

In this work, we present GaInAs/AlAs/AlInAs quantum cascade lasers emitting from 3.2 to 3.4 μm. Single-mode emission is obtained using buried distributed-feedback gratings fabricated using standard deep-UV contact lithography. This technique can easily be transferred to industrial production. Devices with single-mode emission down to 3.19 μm were achieved with peak power of up to 250 mW at −20 °C. A tuning range of 11 cm−1 was obtained by changing the device temperature between −30 °C and 20 °C.

© 2014 Optical Society of America

1. Introduction

The mid-infrared wavelength region is very important for gas sensing as many molecules have their vibrational-rotational modes there. For example, gases containing the methyl group, nitrous oxide, nitrogen dioxide, carbon dioxide, carbon monoxide and formaldehyde are all in the 3–5 μm spectral region [1

1. NIST, “Nist chemistry webbook,”.

]. Hydrocarbons like methane, ethane or formaldehyde could be measured with a high sensitivity (ppt) at this frequency range. This would enhance the possibilities for leak detection in industry, environmental monitoring and sensing for medical purposes. For many of these applications, a tunable single-mode emission at a previously determined wavelength is required.

The mid-infrared spectral region can be covered with different types of lasers. Interband cascade lasers (ICL) have been presented with distributed feedback (DFB) emitters [2

2. C. S. Kim, M. Kim, J. Abell, W. W. Bewley, C. D. Merritt, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Mid-infrared distributed-feedback interband cascade lasers with continuous-wave single-mode emission to 80 °C,” Appl. Phys. Lett. 101, 061104 (2012). [CrossRef]

]. The grating, placed on top of the waveguide, was fabricated using e-beam lithography. Interband diode lasers achieved continuous-wave operation at 3.2 μm wavelength [3

3. G. Belenky, L. Shterengas, G. Kipshidze, and T. Hosoda, “Type-I Diode Lasers for Spectral Region Above 3 μ m,” IEEE J. Sel. Topics Quantum Electron. 17, 1426–1434 (2011). [CrossRef]

].

The devices mentioned above exploit interband emission, but the spectral range around 3 μm can be covered using intersubband transitions with a quantum cascade laser (QCL) [4

4. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Laser,” Science 264, 553–556 (1994). [CrossRef] [PubMed]

] as well. Laser operation at 3.05 μm was shown at 80 K using different well materials for the upper and lower lasing state [5

5. M. P. Semtsiv, M. Wienold, S. Dressler, and W. T. Masselink, “Short-wavelength (λ≈3.05μ m) InP-based strain-compensated quantum-cascade laser,” Appl. Phys. Lett. 90, 051111 (2007). [CrossRef]

]. Emission down to 3.15 μm was reported [6

6. A. Bismuto, S. Riedi, B. Hinkov, M. Beck, and J. Faist, “Sb-free quantum cascade lasers in the 3 μ m spectral range,” Semicond. Sci. Technol. 27, 045013 (2012). [CrossRef]

, 7

7. A. Bismuto, M. Beck, and J. Faist, “High power Sb-free quantum cascade laser emitting at 3.3 μ m above 350 K,” Appl. Phys. Lett. 98, 191104 (2011). [CrossRef]

]. Lasers on a Sb-free material system showed watt-level emission at room-temperature. More recently, room-temperature continuous-wave operation was reported at 3 and 3.2 μm [8

8. N. Bandyopadhyay, Y. Bai, S. Tsao, S. Nida, S. Slivken, and M. Razeghi, “Room temperature continuous wave operation of lambda 3–3.2μm quantum cascade lasers,” Appl. Phys. Lett. 101, 241110 (2012). [CrossRef]

].

Additionally, mode selection has been shown at 3.36 μm [9

9. J. P. Commin, K. Kennedy, D. G. Revin, S. Y. Zhang, A. B. Krysa, and J. W. Cockburn, “λ≈ 3.36 μ m room temperature InGaAs/AlAs(Sb) quantum cascade lasers with third order distributed feedback grating,” Appl. Phys. Lett. 97, 111113 (2010). [CrossRef]

], where a third-order buried DFB grating was corrugated on top of a InGaAs/AlAs (Sb) QCL active region. Single-mode ring-CSELs based on quantum cascade structures were presented with a radial second-order grating at 8 μm [10

10. E. Mujagić, C. Schwarzer, W. Schrenk, J. Chen, C. Gmachl, and G. Strasser, “Ring-cavity surface-emitting lasers as a building block for tunable and coherent quantum cascade laser arrays,” Semicond. Sci. Technol. 26, 014019 (2011). [CrossRef]

]. Fabrication was done using e-beam lithography. The devices showed a low beam divergence (8°).

QCLs show good thermal qualities, output stabilities and tuning abilities. The GaInAs/AlAs/AlInAs material system on InP substrate is well-developed in terms of fabrication technologies. This is partially due to their widespread use in the telecommunication industry. Because of the extensive research, high quality growth of quantum wells is achieved today. A broad spectral coverage can be achieved with heterogeneous active regions, e.g. covering the spectral range from 3 to 4 μm [11

11. S. Riedi, A. Hugi, A. Bismuto, M. Beck, and J. Faist, “Broadband external cavity tuning in the 3–4 μ m window,” Appl. Phys. Lett. 103, 031108 (2013). [CrossRef]

]. Furthermore, applications for detecting propane and butane were demonstrated by EMPA using devices around 3.3 μm [12

12. J. Jágerská, B. Tuzson, H. Looser, A. Bismuto, J. Faist, H. Prinz, and L. Emmenegger, “Highly sensitive and fast detection of propane-butane using a 3 μ m quantum cascade laser,” Appl. Opt. 52, 4613–4619 (2013). [CrossRef]

].

We present in this work QCL devices fabricated for output wavelength close to 3.3 μm. To achieve a better single-mode yield, a distributed feedback configuration with a first-order grating was chosen and realized by means of standard optical lithography.

2. Methods

The QCL active region is a copy of the strain compensated structure published in 2011 [7

7. A. Bismuto, M. Beck, and J. Faist, “High power Sb-free quantum cascade laser emitting at 3.3 μ m above 350 K,” Appl. Phys. Lett. 98, 191104 (2011). [CrossRef]

] on a GaInAs/AlAs/AlInAs material system. The thickness of the InGaAs layer on top of the active region, used for the DFB grating, was changed to 200 nm. The devices were fabricated as buried heterostructures [13

13. A. Bismuto, R. Terazzi, M. Beck, and J. Faist, “Electrically tunable, high performance quantum cascade laser,” Appl. Phys. Lett. 96, 141105 (2010). [CrossRef]

] to improve thermal transport.

The ridges were etched with width from 3 to 7 μm. The grating was done by partly etching the InGaAs layer. On the top of the etched grating, a n-doped cladding was deposited by MOVPE constituted by 3 μm of n-doped InP:Si (2 × 1017cm−3) followed by an 80 nm thick InGaAs:Si contact layer (6 × 1018cm−3). The lasers were processed using standard buried heterostructure technique. The cleaved devices were mounted epilayer-up on copper blocks. Measurements were performed on a Peltier cooler.

The gratings were obtained by a single optical lithography (deep-UV light at 220 nm wavelength) and wet etching. They were designed for emission wavelengths between 3.2 and 3.45 μm and contain a quarter-wave shift placed in the center of each laser structure. Because of a mask fabrication resolution of about 10 nm, we used only three different grating pitches, namely 500, 520 and 540 nm. In order to obtain a specific effective grating period, a combination of two grating pitches is used. For example, a 505 nm effective grating period could be obtained with 30 periods of a 500 nm grating followed by 10 periods of a 520 nm grating. This combination is repeated on the photolithography mask. In the following we will refer to these composed gratings as dual-gratings and to the non-composed gratings as single-gratings.

The left part of Fig. 1 is a SEM picture of the facet of a laser. It shows that the ridge cross section has a quasi-rectangular shape. On the right a SEM picture of a device cleaved along the waveguide is presented and displays the grating on top of the active region. The grating depth is 160 nm and the duty cycle is 25%. Compared to a 50% duty cycle, this leads to a reduced coupling constant of the optical mode towards the grating [14

14. W. Streifer, D. R. Scifres, and R. Burnham, “Coupling Coefficients for Distributed Feedback Single- and Double-Heterostructure Diode Lasers,” IEEE J. Quantum Electron. 11, 867–873 (1975). [CrossRef]

].

Fig. 1 SEM pictures. Left: A laser facet with a ridge width of 4.2 μm. Right: A cross section of the waveguide along the ridge direction. It shows the grating on top of the active region with an etching depth of 160 nm.

3. Results

The measured spontaneous emission of the active region is shown in Fig. 2 along with the measured laser spectra from several devices. Spontaneous emission data was taken at room-temperature from a 1.6 mm long device. The device was measured perpendicular to the ridge with an applied voltage of 15.8 V. Laser spectra were measured under different driving conditions at 0 °C in pulsed operation. The spontaneous emission displays a full width half maximum of 621 cm−1, with a broad maxima from 3.15 to 3.34 μm. Laser emission ranged from 3.19 to 3.42 μm. In the bottom plot of Fig. 3 we show the stopband of one device. The device was measured below threshold with an applied voltage of 14.8 V at 10 °C. It exhibits a spectral width of Δk =6.1 cm−1 at 3070 cm−1 with a quarter-wave shift mode in its center, as predicted by theory [15

15. H. Haus and C. Shank, “Antisymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. 12, 532–539 (1976). [CrossRef]

]. The device was lasing at 3070 cm−1, on the edge of the stopband and at a higher-order mode at 3000 cm−1. The dimensions of this device are 2.6 mm × 4 μm. The stopband width corresponds to a coupling constant of κ = π * neff * Δk * sin(π* dc) = 43 cm−1 [14

14. W. Streifer, D. R. Scifres, and R. Burnham, “Coupling Coefficients for Distributed Feedback Single- and Double-Heterostructure Diode Lasers,” IEEE J. Quantum Electron. 11, 867–873 (1975). [CrossRef]

], where the effective refractive index neff is 3.2 and dc is the duty cycle of the grating. The coupling constant was not optimized for a value of κ*L around 1 for the presented device lengths L, but adapted for losses of around 1 cm−1 obtained by transfer-matrix simulations.

Fig. 2 Room-temperature spontaneous emission of the active region(blue) showing a FWHM of 621 cm−1 at 15.8 V. Additionally lasing spectra of some devices in pulsed operation under different driving conditions at 0 °C are presented.
Fig. 3 Top: Transfer-matrix simulation of the transmission and threshold of a 2 mm long dual-grating DFB with an effective periodicity of 515 nm and effective refractive index of 3.165. Bottom: Measured amplified spontaneous emission of a 2.6 mm × 4 μm lasing device with the same dual-grating as the simulation.

The supplementary stopbands aside from the one at 3070 cm−1 are due to higher-order lateral modes and due to the design of the grating. The presented example includes the periodicities 500 nm and 520 nm with a ratio of 10:30. This leads to a superperiod of Lsuperperiod=20.6 μm. Therefore additional dual-grating modes of order n appear at wavenumbers of ±n*12*neff*Lsuperperiod=±n*75.8cm1 around the fundamental mode [16

16. A. Yariv and P. Yeh, Optical Waves in Crystals (John Wiley and Sons, 1984).

]. Transfer-matrix simulations reproduced the stopbands including their quarter-wave shift modes. Not predicted are the higher order lateral modes which cannot be retrieved by the 1-D simulation (top plot of Fig. 3). A 2 mm long device was used in the simulations having the same grating design as the device presented. The separation to the higher-order dual-grating modes can be adjusted by changing Lsuperperiod.

In order to help distinguish the various mode types (dual-grating modes and higher-order lateral modes) the amplified spontaneous emission data of several devices was analysed. Fig. 4 illustrates the quarter-wave shift mode wavelengths versus grating periods. The 2nd order dual-grating mode has a lower coupling constant, and therefore, a narrower stopband. This is used for differentiating the 1st and 2nd order dual-grating mode. For the retrieval of the 2nd order lateral mode wavelengths, devices with only one grating period were analysed. In these cases the luminescence shows 1 or 2 stopbands, which correspond to 1st and 2nd order lateral modes. With this analysis we group the data and approximate with linear fits using the formula for the Bragg wavelength:
λB=2neffi*(1Λ+j*1Lsuperperiod)1=2neffi*Λ(1+j*1NΛ)1
  • (j-th dual-grating mode; i-th lateral mode)
where Λ stands for the effective periodicity in the structure, NΛ for the length of the superperiod divided by Λ, i = 1, 2 for the first and second-order lateral mode respectively, j = 0, ±1 for the first and second-order dual-grating mode respectively.

Fig. 4 Plot of the quarter-wave shift mode wavelengths versus grating period showing the fundamental mode (black), 2nd order dual-grating modes (light blue and dark blue) and 2nd order lateral modes (red, green). The purple crosses mark the lasing wavelengths.

The black line in Fig. 4 is a linear fit for the fundamental dual-grating and the fundamental lateral modes. The 2nd order dual-grating modes are fitted by the light blue and dark blue lines while the 2nd order lateral modes are fitted by the red and green lines. The effective refractive index deduced from Fig. 4 is 3.165 for the fundamental lateral modes (fundamental and 1st order dual-grating modes) and 3.12 for the second-order lateral modes. Plotting the lasing frequencies versus the grating period (purple cross, Fig. 4), we deduce that almost all devices are lasing on the fundamental mode. Few devices are lasing on the 2nd order dual-grating mode or on a combination of the first and second-order lateral mode. For all measured devices we found a single mode yield of about 80%. We have not observed higher order lateral modes for ridge width narrower than 5 μm.

Calculations of the optical mode intensity profile along the ridge, given by the transfer-matrix method, show periodic modulations of the mode. Fig. 5 shows the mode intensity profile of the fundamental and the two 2nd order dual-grating modes. The periodicity along the ridge amounts to 2πΔβ2κ2 [16

16. A. Yariv and P. Yeh, Optical Waves in Crystals (John Wiley and Sons, 1984).

], where the imaginary part of the coupling constant κ and gain within the structure is neglected and Δβ=2*β2*πΛ is the detuning of the propagation constant β from the Bragg frequency. In the case presented, the transfer-matrix simulation gave a periodicity of 20.6 μm, equal to the result for the formula above. Spacially modulated injection, with the same periodicity as the optical mode, could be used for generating tunable single mode emission.

Fig. 5 Simulation of the optical mode intensity along the ridge for a 412 μm long device made of periodicities of 500 nm and 520 nm with a superperiod of 20.6 μm and an effective periodicity of 515 nm. Red: Data evaluated at λ = 3.2594 μm which corresponds to the fundamental quarter-wave shift mode. Blue and Green: Evaluation at λ = 3.1803 μm and λ = 3.3436 μm which correspond to the 2nd order dual-grating mode.

Fig. 6 and 7 show a device emitting around 3.29 μm with a side-mode suppression ratio of over 20 dB. The ridge length is 2.64 mm and the width is 7 μm. The temperature tuning reached 10.5 cm−1 from −20 to 30 °C, giving a temperature tuning coefficient of 0.21cm1K. The threshold current density is 4.7kAcm2. A slope efficiency of 284mWA was measured at −20 °C. The output power for the uncoated device per facet is 160 mW at −20 °C whereas the highest output power we achieved was 250 mW on a multimode device. Based on the transfer-matrix computations of the losses, the lowest cavity loss should be achieved on the defect mode in the center of the stopband, whereas we observed our lasers to operate mostly on the band edge mode. We attributed this to fabrication defects that affected most the modes that are highly confined in the center of the cavity.

Fig. 6 Spectra of an device emitting at 3.3 μm for various submount temperatures.
Fig. 7 Power-current-voltage characteristics of the device shown in Fig. 6. The slope efficiency is 284mWA and the threshold current density is 4.7kAcm2 at −20°C.

4. Conclusion

We demonstrated single-mode lasing from 3.19 to 3.41 μm and the quarter-wave shift mode in the spontaneous amplified emission. Temperature tuning of the single-mode emission is 0.21cm1K, and the output power is sufficient for most spectroscopic applications. Because of the relatively large thermal dissipation at threshold, continuous-wave operation has not yet been achieved. The results agree well with the coupled-mode theory and are reproduced by transfer-matrix simulations. Additionally the predicted optical mode intensity profile along the ridge was presented. The incorporated DFB grating was accomplished with standard deep-UV optical lithography using only three grating periodicities. The spectral spacing towards the higher-order dual grating modes is proportional to 1Lsuperperiod. Therefore lasing on the second-order grating modes could be avoided by using a shorter superperiod. We believe a reduction of defects will lead towards continuous-wave operation and lasing on the quarter-wave mode.

Acknowledgments

The authors would like to thank Martin Ebnöther and Emilio Gini for the MOVPE regrowth. Processing was done in FIRST Center for Micro- and Nanoscience. The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007–2013) under grant agreement n° 317884, the collaborative Integrated Project MIRIFISENS.

References and links

1.

NIST, “Nist chemistry webbook,”.

2.

C. S. Kim, M. Kim, J. Abell, W. W. Bewley, C. D. Merritt, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Mid-infrared distributed-feedback interband cascade lasers with continuous-wave single-mode emission to 80 °C,” Appl. Phys. Lett. 101, 061104 (2012). [CrossRef]

3.

G. Belenky, L. Shterengas, G. Kipshidze, and T. Hosoda, “Type-I Diode Lasers for Spectral Region Above 3 μ m,” IEEE J. Sel. Topics Quantum Electron. 17, 1426–1434 (2011). [CrossRef]

4.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Laser,” Science 264, 553–556 (1994). [CrossRef] [PubMed]

5.

M. P. Semtsiv, M. Wienold, S. Dressler, and W. T. Masselink, “Short-wavelength (λ≈3.05μ m) InP-based strain-compensated quantum-cascade laser,” Appl. Phys. Lett. 90, 051111 (2007). [CrossRef]

6.

A. Bismuto, S. Riedi, B. Hinkov, M. Beck, and J. Faist, “Sb-free quantum cascade lasers in the 3 μ m spectral range,” Semicond. Sci. Technol. 27, 045013 (2012). [CrossRef]

7.

A. Bismuto, M. Beck, and J. Faist, “High power Sb-free quantum cascade laser emitting at 3.3 μ m above 350 K,” Appl. Phys. Lett. 98, 191104 (2011). [CrossRef]

8.

N. Bandyopadhyay, Y. Bai, S. Tsao, S. Nida, S. Slivken, and M. Razeghi, “Room temperature continuous wave operation of lambda 3–3.2μm quantum cascade lasers,” Appl. Phys. Lett. 101, 241110 (2012). [CrossRef]

9.

J. P. Commin, K. Kennedy, D. G. Revin, S. Y. Zhang, A. B. Krysa, and J. W. Cockburn, “λ≈ 3.36 μ m room temperature InGaAs/AlAs(Sb) quantum cascade lasers with third order distributed feedback grating,” Appl. Phys. Lett. 97, 111113 (2010). [CrossRef]

10.

E. Mujagić, C. Schwarzer, W. Schrenk, J. Chen, C. Gmachl, and G. Strasser, “Ring-cavity surface-emitting lasers as a building block for tunable and coherent quantum cascade laser arrays,” Semicond. Sci. Technol. 26, 014019 (2011). [CrossRef]

11.

S. Riedi, A. Hugi, A. Bismuto, M. Beck, and J. Faist, “Broadband external cavity tuning in the 3–4 μ m window,” Appl. Phys. Lett. 103, 031108 (2013). [CrossRef]

12.

J. Jágerská, B. Tuzson, H. Looser, A. Bismuto, J. Faist, H. Prinz, and L. Emmenegger, “Highly sensitive and fast detection of propane-butane using a 3 μ m quantum cascade laser,” Appl. Opt. 52, 4613–4619 (2013). [CrossRef]

13.

A. Bismuto, R. Terazzi, M. Beck, and J. Faist, “Electrically tunable, high performance quantum cascade laser,” Appl. Phys. Lett. 96, 141105 (2010). [CrossRef]

14.

W. Streifer, D. R. Scifres, and R. Burnham, “Coupling Coefficients for Distributed Feedback Single- and Double-Heterostructure Diode Lasers,” IEEE J. Quantum Electron. 11, 867–873 (1975). [CrossRef]

15.

H. Haus and C. Shank, “Antisymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. 12, 532–539 (1976). [CrossRef]

16.

A. Yariv and P. Yeh, Optical Waves in Crystals (John Wiley and Sons, 1984).

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(140.3070) Lasers and laser optics : Infrared and far-infrared lasers
(140.5960) Lasers and laser optics : Semiconductor lasers
(230.5590) Optical devices : Quantum-well, -wire and -dot devices
(300.6360) Spectroscopy : Spectroscopy, laser
(140.5965) Lasers and laser optics : Semiconductor lasers, quantum cascade

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: November 1, 2013
Revised Manuscript: December 23, 2013
Manuscript Accepted: January 9, 2014
Published: January 24, 2014

Citation
Johanna M. Wolf, Alfredo Bismuto, Mattias Beck, and Jérôme Faist, "Distributed-feedback quantum cascade laser emitting at 3.2 μm," Opt. Express 22, 2111-2118 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-2-2111


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References

  1. NIST, “Nist chemistry webbook,”.
  2. C. S. Kim, M. Kim, J. Abell, W. W. Bewley, C. D. Merritt, C. L. Canedy, I. Vurgaftman, J. R. Meyer, “Mid-infrared distributed-feedback interband cascade lasers with continuous-wave single-mode emission to 80 °C,” Appl. Phys. Lett. 101, 061104 (2012). [CrossRef]
  3. G. Belenky, L. Shterengas, G. Kipshidze, T. Hosoda, “Type-I Diode Lasers for Spectral Region Above 3 μ m,” IEEE J. Sel. Topics Quantum Electron. 17, 1426–1434 (2011). [CrossRef]
  4. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, A. Y. Cho, “Quantum Cascade Laser,” Science 264, 553–556 (1994). [CrossRef] [PubMed]
  5. M. P. Semtsiv, M. Wienold, S. Dressler, W. T. Masselink, “Short-wavelength (λ≈3.05μ m) InP-based strain-compensated quantum-cascade laser,” Appl. Phys. Lett. 90, 051111 (2007). [CrossRef]
  6. A. Bismuto, S. Riedi, B. Hinkov, M. Beck, J. Faist, “Sb-free quantum cascade lasers in the 3 μ m spectral range,” Semicond. Sci. Technol. 27, 045013 (2012). [CrossRef]
  7. A. Bismuto, M. Beck, J. Faist, “High power Sb-free quantum cascade laser emitting at 3.3 μ m above 350 K,” Appl. Phys. Lett. 98, 191104 (2011). [CrossRef]
  8. N. Bandyopadhyay, Y. Bai, S. Tsao, S. Nida, S. Slivken, M. Razeghi, “Room temperature continuous wave operation of lambda 3–3.2μm quantum cascade lasers,” Appl. Phys. Lett. 101, 241110 (2012). [CrossRef]
  9. J. P. Commin, K. Kennedy, D. G. Revin, S. Y. Zhang, A. B. Krysa, J. W. Cockburn, “λ≈ 3.36 μ m room temperature InGaAs/AlAs(Sb) quantum cascade lasers with third order distributed feedback grating,” Appl. Phys. Lett. 97, 111113 (2010). [CrossRef]
  10. E. Mujagić, C. Schwarzer, W. Schrenk, J. Chen, C. Gmachl, G. Strasser, “Ring-cavity surface-emitting lasers as a building block for tunable and coherent quantum cascade laser arrays,” Semicond. Sci. Technol. 26, 014019 (2011). [CrossRef]
  11. S. Riedi, A. Hugi, A. Bismuto, M. Beck, J. Faist, “Broadband external cavity tuning in the 3–4 μ m window,” Appl. Phys. Lett. 103, 031108 (2013). [CrossRef]
  12. J. Jágerská, B. Tuzson, H. Looser, A. Bismuto, J. Faist, H. Prinz, L. Emmenegger, “Highly sensitive and fast detection of propane-butane using a 3 μ m quantum cascade laser,” Appl. Opt. 52, 4613–4619 (2013). [CrossRef]
  13. A. Bismuto, R. Terazzi, M. Beck, J. Faist, “Electrically tunable, high performance quantum cascade laser,” Appl. Phys. Lett. 96, 141105 (2010). [CrossRef]
  14. W. Streifer, D. R. Scifres, R. Burnham, “Coupling Coefficients for Distributed Feedback Single- and Double-Heterostructure Diode Lasers,” IEEE J. Quantum Electron. 11, 867–873 (1975). [CrossRef]
  15. H. Haus, C. Shank, “Antisymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. 12, 532–539 (1976). [CrossRef]
  16. A. Yariv, P. Yeh, Optical Waves in Crystals (John Wiley and Sons, 1984).

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