## Gain competition in dual wavelength quantum cascade lasers

Optics Express, Vol. 18, Issue 10, pp. 9900-9908 (2010)

http://dx.doi.org/10.1364/OE.18.009900

Acrobat PDF (3515 KB)

### Abstract

We investigated dual wavelength mid-infrared quantum cascade lasers based on heterogeneous cascades. We found that due to gain competition laser action tends to start in higher order lateral modes. The mid-infrared mode with the lower threshold current reduces population inversion for the second laser with the higher threshold current due to stimulated emission. We developed a rate equation model to quantitatively describe mode interactions due to mutual gain depletion.

© 2010 OSA

## 1. Introduction

1. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science **264**(5158), 553–556 (1994). [CrossRef] [PubMed]

2. S. Y. Zhang, D. G. Revin, J. W. Cockburn, K. Kennedy, A. B. Krysa, and M. Hopkinson, “λ–3.1µm room temperature InGaAs/AlAsSb/InP quantum cascade lasers,” Appl. Phys. Lett. **94**(3), 031106 (2009). [CrossRef]

3. M. Rochat, D. Hofstetter, M. Beck, and J. Faist, “Long-wavelength (λ~16 µm), room-temperature, single-frequency quantum-cascade lasers based on a bound-to-continuum transition,” Appl. Phys. Lett. **79**(26), 4271 (2001). [CrossRef]

4. A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. Kumar N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 µm,” Appl. Phys. Lett. **92**, 111110 (2008). [CrossRef]

7. Y. Bai, S. Slivken, S. R. Darvish, and M. Razeghi, “Room temperature continuous wave operation of quantum cascade lasers with 12.5% wall plug efficiency,” Appl. Phys. Lett. **93**(2), 021103 (2008). [CrossRef]

8. C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, F. Capasso, and A. Y. Cho, “Quantum cascade lasers with a heterogeneous cascade: two-wavelength operation,” Appl. Phys. Lett. **79**(5), 572 (2001). [CrossRef]

9. R. Maulini, A. Mohan, M. Giovannini, J. Faist, and E. Gini, “External cavity quantum-cascade laser tunable from 8.2 to 10.4 µm using a gain element with a heterogeneous cascade,” Appl. Phys. Lett. **88**(20), 201113 (2006). [CrossRef]

10. A. Hugi, R. Terazzi, Y. Bonetti, A. Wittmann, M. Fischer, M. Beck, J. Faist, and E. Gini, “External cavity quantum cascade laser tunable from 7.6 to 11.4 µm,” Appl. Phys. Lett. **95**(6), 061103 (2009). [CrossRef]

11. E. Rosencher, A. Fiore, B. Vinter, V. Berger, Ph. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science **271**(5246), 168–173 (1996). [CrossRef]

12. C. Sirtori, F. Capasso, J. Faist, L. N. Pfeiffer, and K. W. West, “Far-infrared generation by doubly resonant difference frequency mixing in a coupled quantum well two-dimensional electron gas system,” Appl. Phys. Lett. **65**(4), 445 (1994). [CrossRef]

13. N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. **90**(4), 043902 (2003). [CrossRef] [PubMed]

14. M. Austerer, C. Pflügl, S. Golka, W. Schrenk, A. M. Andrews, T. Roch, and G. Strasser, “Coherent 5.35 µm surface emission from a GaAs-based distributed feedback quantum-cascade laser,” Appl. Phys. Lett. **88**(12), 121104 (2006). [CrossRef]

13. N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. **90**(4), 043902 (2003). [CrossRef] [PubMed]

15. M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics **1**(5), 288–292 (2007). [CrossRef]

16. M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. **92**(20), 201101 (2008). [CrossRef]

17. C. Pflügl, M. A. Belkin, Q. J. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. **93**(16), 161110 (2008). [CrossRef]

## 2. Active region and waveguide design

18. J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and two-phonon resonance quantum-cascade lasers for high duty cycle, high-temperature operation,” IEEE J. Quantum Electron. **38**(6), 533–546 (2002). [CrossRef]

18. J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and two-phonon resonance quantum-cascade lasers for high duty cycle, high-temperature operation,” IEEE J. Quantum Electron. **38**(6), 533–546 (2002). [CrossRef]

16. M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. **92**(20), 201101 (2008). [CrossRef]

^{(2)}for efficient generation of the difference-frequency of the two mid-IR lasers. To obtain a large value for χ

^{(2)}, the lasing transition of the DPR laser is close to resonance (difference is ~5 meV) with the transition 4 → 3 (see Fig. 1 (b) and (d) transition green-red) in the BTC design.

^{17}cm

^{−3}) InP wafer consecutively, followed by a 3.5µm thick cladding layer (~5*10

^{16}cm

^{−3}) and a 200nm thick highly doped plasmon layer (~5*10

^{18}cm

^{−3}). This dielectric waveguide confines both mid-IR modes in the vertical direction [16

16. M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. **92**(20), 201101 (2008). [CrossRef]

## 3. Device processing and measurement techniques

17. C. Pflügl, M. A. Belkin, Q. J. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. **93**(16), 161110 (2008). [CrossRef]

## 4. Device performance and far field behavior

_{00}mode for the DPR laser and higher order lateral mode operation (typically TM

_{02}or TM

_{03}) for the BTC laser, except for one device, which showed TM

_{00}operation for both wavelengths. Only for very narrow devices (~12µm wide), both pump beams lased consistently in TM

_{00}. Observed differences in performance (e. g. appearance of different higher order modes) between nominally identical devices can be explained by losses due to sidewall roughness scattering which can vary from device to device. In narrower ridges, where only TM00 modes are present, higher order modes overlap significantly with the lossy SiN insulation layer at the sidewall of the ridges, which suppresses the appearance of these modes.

*120K*, resulting in the BTC laser having a lower J

_{th}above this temperature.

_{00}mode for the DPR laser and TM

_{02}for the BTC laser (see Fig. 5a ). Above 120K, however, when the BTC laser has a lower threshold current density than the DPR laser, both lasers operate in TM

_{00}mode (Fig. 5b).

_{00}mode has its intensity maximum. This leads to a stronger reduction of the gain in the center of the ridge compared to the edges of the ridge, favoring lasing in higher order modes of the BTC laser.

## 5. Rate equation model

_{inject}is the injection current density,

*τ*are the transition lifetimes from state

_{ij}*i*to state

*j*,

*τ*is the total nonradiative lifetime of state

_{i nonrad}*i*and

*n*is the local sheet carrier density in state

_{i}*i*. x and y describe the spatial position within the device cross-section as explained below. S(x, y) is the photon flux density with a spatial distribution which is determined by the TM

_{00}mode profile of the cold cavity at 10.5μm wavelength. σ

_{1}and σ

_{2}are the cross sections for stimulated transitions from the upper state 4 to the states 3 and 2 respectively. They are defined in Eq. (5):

_{ij}is the dipole matrix element for the transition i → j, n is the effective refractive index of the 10.5µm mode, λ is the vacuum wavelength, L

_{p}is the thickness of one stage in the active region (60nm), γ

_{ij}is the half width at half maximum (HWHM) of the respective transition i → j (in our model we assumed γ

_{ij}= 7.5meV for the mid-IR transitions 4-3 and 4-2), E is the energy of the 10.5µm photons and E

_{ij}is the energy difference between states i and j.

*τ*ps,

_{4 nonrad}= 1*τ*ps,

_{43}= 12.5*τ*ps,

_{42}= 2.3*τ*ps,

_{41}= 2.1*τ*ps,

_{3 nonrad.}= 0.13*τ*ps,

_{32}= 3.0*τ*ps and

_{31}= 0.15*τ*ps. These calculated lifetimes are based on LO-phonon scattering at an applied field of 33kV/cm (corresponds to the threshold voltage of the BTC laser). Matrix elements are:

_{21}= 0.18*z*nm and

_{43}= 1.57*z*nm. The photon flux density of the 10.5µm mode is deduced from the measured edge emission power of a typical device slightly below the threshold current density of the BTC laser.

_{42}= 1.80*3000*pixels. The injection current density of 6kA/cm

^{2}used in the model is higher than the 10.5µm DPR laser threshold current density at RT and lower than the threshold current density for the 8.9µm BTC laser. Figure 6 shows the calculated spatially dependent population inversion in the BTC active region in the presence of the 10.5µm TM

_{00}mode of intracavity power corresponding to 30mW facet emission in a 24µm wide ridge.

_{0a}, a = 0, 1, 2,… of the

*8.9*µm laser is given by the sum of the contributions of each pixel g

_{TM0a}(x,y), x = 1…100, y = 1…30. The gain for one pixel is shown in Eq. (6):

*ω*is the angular frequency of the

_{8.9µm}*8.9µm*mode,

*e*is the elementary charge,

*z*is the dipole transition matrix element from 4 to 2,

_{42}*c*is the speed of light in vacuum,

*n*is the effective refractive index,

*L*is the thickness of one stage in the active region (60nm) and Γ

_{p}_{TM0a}(x,y) is the overlap of the transversal mode TM

_{0a}with the current pixel. Furthermore, Eq. (7) defines the complex detunings, with

*γ*being the HWHM of the transition between states i and j (7.5meV for the mid-IR transitions 4→2 and 4→3 and 0.75meV for the 3→2 transition),

_{ij}*ΔE*is the energy difference between levels i and j.

_{ij}*Ω(x,y) = ez*is the Rabi frequency, where

_{34}E_{ω1}(x,y)/ħ*E*

_{ω1}(x,y) is the electric field in the 10.5µm laser mode.

^{−1}for different lateral modes for a 24µm wide ridge as shown in Fig. 6. The total modal gain for the 8.9µm mode was calculated in the presence and without a 10.5µm mode.

_{00}and TM

_{03}mode for example was calculated to be ~1.25cm

^{−1}with the TM

_{00}mode having lower losses. The difference in waveguide losses is larger than the difference in gain, leading to a larger net gain (modal gain minus waveguide losses) for the TM

_{00}mode compared to higher order modes.

_{00}mode and is smaller for higher order modes than for the TM

_{00}mode. This effect increases the difference in modal gain for different modes. Table 1 shows that already for small photon intensities –corresponding to an output power of 30mW at 10.5µm - the difference between the TM

_{00}and TM

_{03}mode is about ~2cm-1. This difference overcompensates for the larger waveguide losses for the higher order mode, leading to a higher net gain for the TM

_{03}mode compared to the TM

_{00}mode. This is in accordance with our experimental results which show higher order mode operation for the 8.9µm mode in broad ridges (>20µm).in the presence of 10.5µm radiation.

## 6. Summary and conclusions

_{00}, has its intensity maximum. This leads to a stronger reduction of the gain in the center of the ridge compared to the outer parts of the ridge, favoring lasing in higher lateral modes of the second wavelength. The predictions of this model match the experimental findings. The model developed in this work can also be expanded to any type of multi-wavelength and broadband QCL based on heterogeneous cascades which are interesting for many applications such as sensing.

## References and links

1. | J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science |

2. | S. Y. Zhang, D. G. Revin, J. W. Cockburn, K. Kennedy, A. B. Krysa, and M. Hopkinson, “λ–3.1µm room temperature InGaAs/AlAsSb/InP quantum cascade lasers,” Appl. Phys. Lett. |

3. | M. Rochat, D. Hofstetter, M. Beck, and J. Faist, “Long-wavelength (λ~16 µm), room-temperature, single-frequency quantum-cascade lasers based on a bound-to-continuum transition,” Appl. Phys. Lett. |

4. | A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. Kumar N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 µm,” Appl. Phys. Lett. |

5. | A. Lyakh, R. Maulini, A. Tsekoun, R. Go, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, and C. K. N. Patel, “3 Watt continuous-wave room temperature single-facet emission from quantum cascade lasers based on non-resonant extraction design approach,” Appl. Phys. Lett. |

6. | R. Maulini, A. Lyakh, A. Tsekoun, R. Go, C. Pflügl, L. Diehl, F. Capasso, and C. K. N. Patel, “High power thermoelectrically-cooled and uncooled quantum cascade lasers with optimized reflectivity facet coatings,” Appl. Phys. Lett. |

7. | Y. Bai, S. Slivken, S. R. Darvish, and M. Razeghi, “Room temperature continuous wave operation of quantum cascade lasers with 12.5% wall plug efficiency,” Appl. Phys. Lett. |

8. | C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, F. Capasso, and A. Y. Cho, “Quantum cascade lasers with a heterogeneous cascade: two-wavelength operation,” Appl. Phys. Lett. |

9. | R. Maulini, A. Mohan, M. Giovannini, J. Faist, and E. Gini, “External cavity quantum-cascade laser tunable from 8.2 to 10.4 µm using a gain element with a heterogeneous cascade,” Appl. Phys. Lett. |

10. | A. Hugi, R. Terazzi, Y. Bonetti, A. Wittmann, M. Fischer, M. Beck, J. Faist, and E. Gini, “External cavity quantum cascade laser tunable from 7.6 to 11.4 µm,” Appl. Phys. Lett. |

11. | E. Rosencher, A. Fiore, B. Vinter, V. Berger, Ph. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science |

12. | C. Sirtori, F. Capasso, J. Faist, L. N. Pfeiffer, and K. W. West, “Far-infrared generation by doubly resonant difference frequency mixing in a coupled quantum well two-dimensional electron gas system,” Appl. Phys. Lett. |

13. | N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. |

14. | M. Austerer, C. Pflügl, S. Golka, W. Schrenk, A. M. Andrews, T. Roch, and G. Strasser, “Coherent 5.35 µm surface emission from a GaAs-based distributed feedback quantum-cascade laser,” Appl. Phys. Lett. |

15. | M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics |

16. | M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. |

17. | C. Pflügl, M. A. Belkin, Q. J. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. |

18. | J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and two-phonon resonance quantum-cascade lasers for high duty cycle, high-temperature operation,” IEEE J. Quantum Electron. |

19. | A. Belyanin, M. Troccoli, and F. Capasso, “Raman Injection and Inversionless Intersubband Lasers” in |

**OCIS Codes**

(140.3070) Lasers and laser optics : Infrared and far-infrared lasers

(230.5590) Optical devices : Quantum-well, -wire and -dot devices

(140.5965) Lasers and laser optics : Semiconductor lasers, quantum cascade

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: January 19, 2010

Revised Manuscript: March 25, 2010

Manuscript Accepted: April 1, 2010

Published: April 27, 2010

**Citation**

Markus Geiser, Christian Pflügl, Alexey Belyanin, Qi Jie Wang, Nanfang Yu, Tadanaka Edamura, Masamichi Yamanishi, Hirofumi Kan, Milan Fischer, Andreas Wittmann, Jérôme Faist, and Federico Capasso, "Gain competition in dual wavelength quantum cascade lasers," Opt. Express **18**, 9900-9908 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-10-9900

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### References

- J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994). [CrossRef] [PubMed]
- S. Y. Zhang, D. G. Revin, J. W. Cockburn, K. Kennedy, A. B. Krysa, and M. Hopkinson, “λ–3.1µm room temperature InGaAs/AlAsSb/InP quantum cascade lasers,” Appl. Phys. Lett. 94(3), 031106 (2009). [CrossRef]
- M. Rochat, D. Hofstetter, M. Beck, and J. Faist, “Long-wavelength (λ~16 µm), room-temperature, single-frequency quantum-cascade lasers based on a bound-to-continuum transition,” Appl. Phys. Lett. 79(26), 4271 (2001). [CrossRef]
- A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. Kumar N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 µm,” Appl. Phys. Lett. 92, 111110 (2008). [CrossRef]
- A. Lyakh, R. Maulini, A. Tsekoun, R. Go, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, and C. K. N. Patel, “3 Watt continuous-wave room temperature single-facet emission from quantum cascade lasers based on non-resonant extraction design approach,” Appl. Phys. Lett. 95(14), 141113 (2009). [CrossRef]
- R. Maulini, A. Lyakh, A. Tsekoun, R. Go, C. Pflügl, L. Diehl, F. Capasso, and C. K. N. Patel, “High power thermoelectrically-cooled and uncooled quantum cascade lasers with optimized reflectivity facet coatings,” Appl. Phys. Lett. 95(15), 151112 (2009). [CrossRef]
- Y. Bai, S. Slivken, S. R. Darvish, and M. Razeghi, “Room temperature continuous wave operation of quantum cascade lasers with 12.5% wall plug efficiency,” Appl. Phys. Lett. 93(2), 021103 (2008). [CrossRef]
- C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, F. Capasso, and A. Y. Cho, “Quantum cascade lasers with a heterogeneous cascade: two-wavelength operation,” Appl. Phys. Lett. 79(5), 572 (2001). [CrossRef]
- R. Maulini, A. Mohan, M. Giovannini, J. Faist, and E. Gini, “External cavity quantum-cascade laser tunable from 8.2 to 10.4 µm using a gain element with a heterogeneous cascade,” Appl. Phys. Lett. 88(20), 201113 (2006). [CrossRef]
- A. Hugi, R. Terazzi, Y. Bonetti, A. Wittmann, M. Fischer, M. Beck, J. Faist, and E. Gini, “External cavity quantum cascade laser tunable from 7.6 to 11.4 µm,” Appl. Phys. Lett. 95(6), 061103 (2009). [CrossRef]
- E. Rosencher, A. Fiore, B. Vinter, V. Berger, Ph. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271(5246), 168–173 (1996). [CrossRef]
- C. Sirtori, F. Capasso, J. Faist, L. N. Pfeiffer, and K. W. West, “Far-infrared generation by doubly resonant difference frequency mixing in a coupled quantum well two-dimensional electron gas system,” Appl. Phys. Lett. 65(4), 445 (1994). [CrossRef]
- N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90(4), 043902 (2003). [CrossRef] [PubMed]
- M. Austerer, C. Pflügl, S. Golka, W. Schrenk, A. M. Andrews, T. Roch, and G. Strasser, “Coherent 5.35 µm surface emission from a GaAs-based distributed feedback quantum-cascade laser,” Appl. Phys. Lett. 88(12), 121104 (2006). [CrossRef]
- M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics 1(5), 288–292 (2007). [CrossRef]
- M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. 92(20), 201101 (2008). [CrossRef]
- C. Pflügl, M. A. Belkin, Q. J. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. 93(16), 161110 (2008). [CrossRef]
- J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and two-phonon resonance quantum-cascade lasers for high duty cycle, high-temperature operation,” IEEE J. Quantum Electron. 38(6), 533–546 (2002). [CrossRef]
- A. Belyanin, M. Troccoli, and F. Capasso, “Raman Injection and Inversionless Intersubband Lasers” in Intersubband Transitions in Quantum Structures, R. Paiella (McGraw-Hill Companies, 2006), chapter 6.3.5.

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