## Monte Carlo study of terahertz difference frequency generation in quantum cascade lasers |

Optics Express, Vol. 21, Issue 5, pp. 6180-6185 (2013)

http://dx.doi.org/10.1364/OE.21.006180

Acrobat PDF (768 KB)

### Abstract

We present an extended ensemble Monte Carlo approach, allowing for the self-consistent modeling of terahertz difference frequency generation in quantum cascade lasers. Our simulations are validated against available experimental data for a current room temperature design. Tera-hertz output powers in the mW range are predicted for ideal light extraction.

© 2013 OSA

## 1. Introduction

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

2. M. 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**, 201101 (2008) [CrossRef] .

5. K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett. **100**, 251104 (2012) [CrossRef] .

2. M. 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**, 201101 (2008) [CrossRef] .

4. Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett. **99**, 131106 (2011) [CrossRef] .

5. K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett. **100**, 251104 (2012) [CrossRef] .

6. S. Fathololoumi, E. Dupont, C. Chan, Z. Wasilewski, S. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, and H. Liu, “Terahertz quantum cascade lasers operating up to ∼200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express **20**, 3866–3876 (2012) [CrossRef] [PubMed] .

7. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. **42**, 89–90 (2006) [CrossRef] .

*μ*W range [2

2. M. 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**, 201101 (2008) [CrossRef] .

4. Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett. **99**, 131106 (2011) [CrossRef] .

5. K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett. **100**, 251104 (2012) [CrossRef] .

8. R. C. Iotti and F. Rossi, “Carrier thermalization versus phonon-assisted relaxation in quantum-cascade lasers: A Monte Carlo approach,” Appl. Phys. Lett. **78**, 2902–2904 (2001) [CrossRef] .

10. A. Mátyás, P. Lugli, and C. Jirauschek, “Photon-induced carrier transport in high efficiency midinfrared quantum cascade lasers,” J. Appl. Phys. **110**, 013108 (2011) [CrossRef] .

11. R. Köhler, R. C. Iotti, A. Tredicucci, and F. Rossi, “Design and simulation of terahertz quantum cascade lasers,” Appl. Phys. Lett. **79**, 3920–3922 (2001) [CrossRef] .

10. A. Mátyás, P. Lugli, and C. Jirauschek, “Photon-induced carrier transport in high efficiency midinfrared quantum cascade lasers,” J. Appl. Phys. **110**, 013108 (2011) [CrossRef] .

17. C. Jirauschek, “Monte Carlo study of carrier-light coupling in terahertz quantum cascade lasers,” Appl. Phys. Lett. **96**, 011103 (2010) [CrossRef] .

18. C. Jirauschek, “Monte Carlo study of intrinsic linewidths in terahertz quantum cascade lasers,” Opt. Express **18**, 25922–25927 (2010) [CrossRef] [PubMed] .

4. Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett. **99**, 131106 (2011) [CrossRef] .

## 2. Modeling of difference frequency generation

*ω*

_{1}and

*ω*

_{2}are used to pump a medium with giant optical nonlinearity, generating THz radiation at a frequency

*ω*=

*ω*

_{1}−

*ω*

_{2}. The effective second order susceptibility in the nonlinear medium is given by [19]

*m*

^{*},

*ε*

_{0}and

*ħ*denote the effective mass, vacuum permittivity and reduced Planck constant, respectively. Furthermore,

*ω*= (

_{mn}*E*−

_{m}*E*) /

_{n}*ħ*and

*d*are the resonance frequency and the dipole matrix element of the optical transition between the subbands

_{mn}*i*=

*m*,

*n*with corresponding eigenenergies

*E*. The optical linewidth

_{i}*γ*(

_{mn}*ε*) and the occupation probability

*f*(

_{i}*ε*) depend on the kinetic electron energy

*ε*.

20. C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys. **105**, 123102 (2009) [CrossRef] .

*γ*(

_{mn}*ε*) = [

*γ*(

_{m}*ε*) +

*γ*(

_{n}*ε*)]/2 with the intersubband outscattering rates

*γ*(

_{i}*ε*) [20

20. C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys. **105**, 123102 (2009) [CrossRef] .

*ℓ*of a single central period, along with all available states

*m*,

*n*(including those in neighboring periods);

*L*

_{P}is then the length of a QCL period. Nonparabolicity effects are included in our Schrödinger-Poisson solver [21

21. C. Jirauschek, “Accuracy of transfer matrix approaches for solving the effective mass Schrödinger equation,” IEEE J. Quantum Electron. **45**, 1059–1067 (2009) [CrossRef] .

*ℓ*[10

10. A. Mátyás, P. Lugli, and C. Jirauschek, “Photon-induced carrier transport in high efficiency midinfrared quantum cascade lasers,” J. Appl. Phys. **110**, 013108 (2011) [CrossRef] .

*ω*(

_{mn}*ε*) = (

*E*+

_{m}*ε*−

_{m}*E*−

_{n}*ε*) /

_{n}*ħ*,

*γ*(

_{mn}*ε*) = [

*γ*(

_{m}*ε*) +

_{m}*γ*(

_{n}*ε*)] / 2 with

_{n}*z*direction, we write the electric field as

*E*(

_{i}*x*,

*y*,

*z*) =

*A*(

_{i}*z*)

*F*(

_{i}*x*,

*y*)exp(i

*k*− i

_{i}z*ω*) + c.c. [22], with (∬|

_{i}t*F*|

_{i}^{2}d

*x*d

*y*)

^{1/2}= 1.

*A*and

_{i}*F*denote the complex amplitude and transverse mode distribution of the field component with frequency

_{i}*ω*and wavenumber

_{i}*k*, and c.c. refers to the complex conjugate. The optical power at frequency

_{i}*ω*is then given by

_{i}*P*= 2

_{i}*cε*

_{0}

*n*|

_{i}*A*|

_{i}^{2}, with the effective refractive index of the corresponding mode

*n*and the vacuum speed of light

_{i}*c*. The propagation of the THz field component generated by the DFG process is in the slowly varying amplitude approximation described by [23] where Δ

*=*

_{k}*k*

_{3}−

*k*

_{1}+

*k*

_{2}is the phase mismatch,

*a*denotes the THz resonator loss coefficient at frequency

*ω*, and

*χ*

^{(2)}is the peak value of the nonlinear susceptibility

*χ*

^{(2)}(

*x*,

*y*) in the QCL waveguide. Furthermore, the asterisk denotes the complex conjugate. The overlap integral

*f*

_{321}is defined as

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

*P*

_{1}and

*P*

_{2}are commonly taken to be constant over the resonator length

*L*, which holds for moderate MIR outcoupling at the facets. Furthermore, the depletion of the MIR pump beams due to the DFG process is negligible. The calculation is greatly simplified for

*L*≫

*a*

^{−1}. With

*a*∼ 100cm

^{−1}and

*L*in the mm range [1

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

**92**, 201101 (2008) [CrossRef] .

**99**, 131106 (2011) [CrossRef] .

*S*

_{eff}= |

*f*

_{321}|

^{−2}and the coherence length

*P*

_{f}=

*P*

_{3}(

*L*) is then obtained as [1

**1**, 288–292 (2007) [CrossRef] .

*∂*

_{z}P_{3}|

_{a}= −

*aP*

_{3}in the resulting equation corresponds to the THz power lost in the waveguide. Integration over the propagation length yields the total absorbed power

*P*

_{a}. For

*L*≫

*a*

^{−1}, we can approximate

*P*

_{3}=

*P*

_{f}and thus obtain

*P*

_{a}= −2

*LaP*

_{f}, where 2

*L*is the cavity roundtrip length and

*P*

_{f}is given by Eq. (3). The total generated power is then

3. C. Pflügl, M. Belkin, Q. 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**, 161110 (2008) [CrossRef] .

**100**, 251104 (2012) [CrossRef] .

*κ*, the theoretical description can easily be adapted by replacing

*a*with

*a*+

*κ*in Eq. (2). In analogy to Eq. (4), we obtain for

*L*≫ (

*a*+

*κ*)

^{−1}the generated power Here

*P*

_{f}is given by Eq. (3) with a modified coherence length

*LaP*

_{f}corresponds to the power absorbed in the waveguide, and the second contribution is the power outcoupled at the surface

## 3. Analysis of a terahertz source based on difference frequency generation

*μ*W in single mode operation [4

**99**, 131106 (2011) [CrossRef] .

**99**, 131106 (2011) [CrossRef] .

### 3.1. Device simulation

**110**, 013108 (2011) [CrossRef] .

**110**, 013108 (2011) [CrossRef] .

20. C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys. **105**, 123102 (2009) [CrossRef] .

24. C. Jirauschek, A. Matyas, and P. Lugli, “Modeling bound-to-continuum terahertz quantum cascade lasers: The role of Coulomb interactions,” J. Appl. Phys. **107**, 013104 (2010) [CrossRef] .

**110**, 013108 (2011) [CrossRef] .

17. C. Jirauschek, “Monte Carlo study of carrier-light coupling in terahertz quantum cascade lasers,” Appl. Phys. Lett. **96**, 011103 (2010) [CrossRef] .

18. C. Jirauschek, “Monte Carlo study of intrinsic linewidths in terahertz quantum cascade lasers,” Opt. Express **18**, 25922–25927 (2010) [CrossRef] [PubMed] .

21. C. Jirauschek, “Accuracy of transfer matrix approaches for solving the effective mass Schrödinger equation,” IEEE J. Quantum Electron. **45**, 1059–1067 (2009) [CrossRef] .

**92**, 201101 (2008) [CrossRef] .

**99**, 131106 (2011) [CrossRef] .

*L*= 3mm and the width is

*w*

_{0}= 16

*μ*m, tapered to

*w*

_{f}= 60

*μ*m toward the front facet with a small taper angle of 1° [4

**99**, 131106 (2011) [CrossRef] .

*A*= 0.076mm

^{2}and an average waveguide width of

*w*̄ =

*A/L*= 25

*μ*m, used to calculate the current and MIR powers from the current density and optical intensities delivered by EMC. Furthermore, we assume a confinement factor of 0.4 in both gain sections [2

**92**, 201101 (2008) [CrossRef] .

**99**, 131106 (2011) [CrossRef] .

^{−1}+ 2.1cm

^{−1}for both MIR modes. Here the common assumption is made that the optical power in each mode is equally distributed over the resonator length [17

17. C. Jirauschek, “Monte Carlo study of carrier-light coupling in terahertz quantum cascade lasers,” Appl. Phys. Lett. **96**, 011103 (2010) [CrossRef] .

25. K. Chiang, “Performance of the effective-index method for the analysis of dielectric waveguides,” Opt. Lett. **16**, 714–716 (1991) [CrossRef] [PubMed] .

*S*

_{eff},

*a*, and the facet transmittance

*T*

_{f}[26

26. J. Butler and J. Zoroofchi, “Radiation fields of GaAs-(AlGa)As injection lasers,” IEEE J. Quantum Electron. **10**, 809–815 (1974) [CrossRef] .

27. S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. **97**, 053106 (2005) [CrossRef] .

18. C. Jirauschek, “Monte Carlo study of intrinsic linewidths in terahertz quantum cascade lasers,” Opt. Express **18**, 25922–25927 (2010) [CrossRef] [PubMed] .

*a*≈ 150cm

^{−1}[4

**99**, 131106 (2011) [CrossRef] .

*S*

_{eff},

*a*and

*T*

_{f}are calculated for the waveguide width at the facet

*w*

_{f}= 60

*μ*m. Furthermore, a phase mismatch of Δ

*= 7cm*

_{k}^{−1}≪

*a*is assumed [4

**99**, 131106 (2011) [CrossRef] .

*P*

_{out}=

*T*

_{f}

*P*

_{f}, with

*P*

_{f}given by Eq. (3).

### 3.2. Results

**99**, 131106 (2011) [CrossRef] .

*P*

_{out}reaches its maximum value, the EMC simulation yields a current of 11.7A, which agrees very well with the measured value of 12A [4

**99**, 131106 (2011) [CrossRef] .

*P*

_{1}= 1.55W (32THz) and

*P*

_{2}= 0.60W (28THz) agree reasonably well with the measured values of 1.2 and 0.8W [4

**99**, 131106 (2011) [CrossRef] .

*P*

_{out}and the conversion efficiency

*η*=

*P*

_{out}/ (

*P*

_{1}

*P*

_{2}) [4

**99**, 131106 (2011) [CrossRef] .

*S*

_{eff}= 5300

*μ*m

^{2},

*T*

_{f}= 0.23, |

*χ*

^{(2)}| = 44nm/V and

*a*= 150cm

^{−1}, we obtain

*P*

_{out}= 12

*μ*W and

*η*= 13

*μ*W/W

^{2}, as compared to 8.5

*μ*W and 10

*μ*W/W

^{2}found in experiment [4

**99**, 131106 (2011) [CrossRef] .

*χ*

^{(2)}|≈ 40nm/V) and the waveguide loss (

*a*≈ 150cm

^{−1}) [4

**99**, 131106 (2011) [CrossRef] .

**110**, 013108 (2011) [CrossRef] .

**92**, 201101 (2008) [CrossRef] .

**99**, 131106 (2011) [CrossRef] .

*P*

_{1}and

*P*

_{2}are displayed for optimum bias where

*P*

_{out}is maximum. The corresponding outcoupled THz power

*P*

_{out}and conversion efficiency

*η*are shown in Fig. 2(b). In agreement with experiment [2

**92**, 201101 (2008) [CrossRef] .

*P*

_{1},

*P*

_{2}and

*P*

_{out}strongly degrade with increasing temperature, while

*η*is insensitive over a wide temperature range.

3. C. Pflügl, M. Belkin, Q. 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**, 161110 (2008) [CrossRef] .

*P*

_{s}in Eq. (6) is maximized for near-perfect phase matching Δ

*≪*

_{k}*a*and a coupling coefficient

*κ*=

*a*. In the following, we assume ideal surface emission from our investigated structure in order to estimate the maximum extractable THz power. The corresponding surface grating is here considered to have a negligible effect on the MIR laser modes [3

3. C. Pflügl, M. Belkin, Q. 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**, 161110 (2008) [CrossRef] .

*A*rather than at the facet, the average waveguide width

*w*̄ =

*A/L*instead of

*w*

_{f}is used for the waveguide simulations, yielding a reduced

*S*

_{eff}= 2200

*μ*m

^{2}while

*a*does not change significantly. In Fig. 2(c), the emitted THz power

*P*

_{s}and conversion efficiency

*η*

_{s}=

*P*

_{s}/ (

*P*

_{1}

*P*

_{2}) are shown. The outcoupled power at 300K is now

*P*

_{s}= 3.1mW, suggesting that room temperature output powers in the mW range should be feasible with an improved outcoupling scheme. From Eqs. (5) and (6) it follows that for

*κ*=

*a*, 50% of the generated THz power is emitted. By contrast, for the case of facet emission shown in Fig. 2(b), the outcoupling ratio is only

*P*

_{out}/

*P*

_{g}≈ 0.1%. On a practical note, experimental structures with grating-based outcoupling have up to now only yielded moderate improvement [3

**93**, 161110 (2008) [CrossRef] .

*κ*≈

*a*[5

**100**, 251104 (2012) [CrossRef] .

**100**, 251104 (2012) [CrossRef] .

## 4. Conclusion

## Acknowledgments

## References and links

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

2. | M. 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. |

3. | C. Pflügl, M. Belkin, Q. 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. |

4. | Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett. |

5. | K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett. |

6. | S. Fathololoumi, E. Dupont, C. Chan, Z. Wasilewski, S. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, and H. Liu, “Terahertz quantum cascade lasers operating up to ∼200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express |

7. | B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. |

8. | R. C. Iotti and F. Rossi, “Carrier thermalization versus phonon-assisted relaxation in quantum-cascade lasers: A Monte Carlo approach,” Appl. Phys. Lett. |

9. | X. Gao, D. Botez, and I. Knezevic, “X-valley leakage in GaAs-based midinfrared quantum cascade lasers: A Monte Carlo study,” J. Appl. Phys. |

10. | A. Mátyás, P. Lugli, and C. Jirauschek, “Photon-induced carrier transport in high efficiency midinfrared quantum cascade lasers,” J. Appl. Phys. |

11. | R. Köhler, R. C. Iotti, A. Tredicucci, and F. Rossi, “Design and simulation of terahertz quantum cascade lasers,” Appl. Phys. Lett. |

12. | H. Callebaut, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Analysis of transport properties of terahertz quantum cascade lasers,” Appl. Phys. Lett. |

13. | O. Bonno, J.-L. Thobel, and F. Dessenne, “Modeling of electron-electron scattering in Monte Carlo simulation of quantum cascade lasers,” J. Appl. Phys. |

14. | J. T. Lü and J. C. Cao, “Coulomb scattering in the Monte Carlo simulation of terahertz quantum-cascade lasers,” Appl. Phys. Lett. |

15. | C. Jirauschek, G. Scarpa, P. Lugli, M. S. Vitiello, and G. Scamarcio, “Comparative analysis of resonant phonon THz quantum cascade lasers,” J. Appl. Phys. |

16. | A. Mátyás, M. Belkin, P. Lugli, and C. Jirauschek, “Temperature performance analysis of terahertz quantum cascade lasers: Vertical versus diagonal designs,” Appl. Phys. Lett. |

17. | C. Jirauschek, “Monte Carlo study of carrier-light coupling in terahertz quantum cascade lasers,” Appl. Phys. Lett. |

18. | C. Jirauschek, “Monte Carlo study of intrinsic linewidths in terahertz quantum cascade lasers,” Opt. Express |

19. | Y. Shen, |

20. | C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys. |

21. | C. Jirauschek, “Accuracy of transfer matrix approaches for solving the effective mass Schrödinger equation,” IEEE J. Quantum Electron. |

22. | G. Agrawal, |

23. | N. Bloembergen, |

24. | C. Jirauschek, A. Matyas, and P. Lugli, “Modeling bound-to-continuum terahertz quantum cascade lasers: The role of Coulomb interactions,” J. Appl. Phys. |

25. | K. Chiang, “Performance of the effective-index method for the analysis of dielectric waveguides,” Opt. Lett. |

26. | J. Butler and J. Zoroofchi, “Radiation fields of GaAs-(AlGa)As injection lasers,” IEEE J. Quantum Electron. |

27. | S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. |

**OCIS Codes**

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

(140.3430) Lasers and laser optics : Laser theory

(190.2620) Nonlinear optics : Harmonic generation and mixing

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

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: January 17, 2013

Revised Manuscript: February 20, 2013

Manuscript Accepted: February 23, 2013

Published: March 4, 2013

**Citation**

Christian Jirauschek, Alpar Matyas, Paolo Lugli, and Markus-Christian Amann, "Monte Carlo study of terahertz difference frequency generation in quantum cascade lasers," Opt. Express **21**, 6180-6185 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-6180

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### References

- M. Belkin, F. Capasso, A. Belyanin, D. Sivco, A. Cho, D. Oakley, C. Vineis, and G. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics1, 288–292 (2007). [CrossRef]
- M. 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, 201101 (2008). [CrossRef]
- C. Pflügl, M. Belkin, Q. 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, 161110 (2008). [CrossRef]
- Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011). [CrossRef]
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