Abstract

In standing-wave lasers, spatial hole burning induces a static grating of the population inversion, enabling multimode operation with several independent lasing modes. In the presence of a mode-locking mechanism, these modes may become correlated, giving origin to a frequency comb. Quantum cascade lasers, owing to their ultrafast gain dynamics, are ideally suited to achieve comb operation. Here we experimentally demonstrate that the modes of a quantum cascade laser frequency comb coherently beat to produce time-dependent population inversion gratings, which spatially modulate the current in the device at frequencies equal to the mode separation and its higher harmonics. This phenomenon allows the laser to serve as a phased collection of microwave local oscillators and is utilized to demonstrate quadrature amplitude modulation, a staple of modern communications. These findings may provide for a new class of integrated transmitters, potentially extending from the microwave to the low terahertz band.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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  6. A. E. Siegman, Appl. Phys. Lett. 30, 21 (1977).
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2017 (1)

D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. En Zah, K. Lascola, A. Belyanin, and F. Capasso, Nat. Photonics 11, 789 (2017).
[Crossref]

2016 (3)

M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, Appl. Phys. Lett. 108, 171104 (2016).
[Crossref]

T. Nagatsuma, G. Ducournau, and C. C. Renaud, Nat. Photonics 10, 371 (2016).
[Crossref]

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

2015 (1)

2012 (1)

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, Nature 492, 229 (2012).
[Crossref]

2008 (1)

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, Phys. Rev. Lett. 100, 167401 (2008).
[Crossref]

1997 (1)

F. Girardin and G.-H. Duan, IEEE J. Sel. Top. Quantum Electron. 3, 461 (1997).
[Crossref]

1995 (1)

W. C. W. Fang, C. G. Bethea, Y. K. Chen, and S. L. Chuang, IEEE J. Sel. Top. Quantum Electron. 1, 117 (1995).
[Crossref]

1992 (1)

M. R. Phillips, T. E. Darcie, and E. J. Flynn, IEEE Photon. Technol. Lett. 4, 1201 (1992).
[Crossref]

1991 (1)

L. J. P. Ketelsen, I. Hoshino, and D. A. Ackerman, IEEE J. Quantum Electron. 27, 957 (1991).
[Crossref]

1977 (1)

A. E. Siegman, Appl. Phys. Lett. 30, 21 (1977).
[Crossref]

1963 (1)

C. L. Tang, H. Statz, and G. Demars, J. Appl. Phys. 34, 2289 (1963).
[Crossref]

Ackerman, D. A.

L. J. P. Ketelsen, I. Hoshino, and D. A. Ackerman, IEEE J. Quantum Electron. 27, 957 (1991).
[Crossref]

Aoust, G.

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Beck, M.

M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, Appl. Phys. Lett. 108, 171104 (2016).
[Crossref]

Belyanin, A.

D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. En Zah, K. Lascola, A. Belyanin, and F. Capasso, Nat. Photonics 11, 789 (2017).
[Crossref]

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Y. Wang and A. Belyanin, Opt. Express 23, 4173 (2015).
[Crossref]

Bethea, C. G.

W. C. W. Fang, C. G. Bethea, Y. K. Chen, and S. L. Chuang, IEEE J. Sel. Top. Quantum Electron. 1, 117 (1995).
[Crossref]

Blaser, S.

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, Nature 492, 229 (2012).
[Crossref]

Bosco, L.

M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, Appl. Phys. Lett. 108, 171104 (2016).
[Crossref]

Caffey, D. P.

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Caneau, C.

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Capasso, F.

D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. En Zah, K. Lascola, A. Belyanin, and F. Capasso, Nat. Photonics 11, 789 (2017).
[Crossref]

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, Phys. Rev. Lett. 100, 167401 (2008).
[Crossref]

Chen, Y. K.

W. C. W. Fang, C. G. Bethea, Y. K. Chen, and S. L. Chuang, IEEE J. Sel. Top. Quantum Electron. 1, 117 (1995).
[Crossref]

Chevalier, P.

D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. En Zah, K. Lascola, A. Belyanin, and F. Capasso, Nat. Photonics 11, 789 (2017).
[Crossref]

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Choi, H.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, Phys. Rev. Lett. 100, 167401 (2008).
[Crossref]

Chuang, S. L.

W. C. W. Fang, C. G. Bethea, Y. K. Chen, and S. L. Chuang, IEEE J. Sel. Top. Quantum Electron. 1, 117 (1995).
[Crossref]

Connors, M. K.

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Darcie, T. E.

M. R. Phillips, T. E. Darcie, and E. J. Flynn, IEEE Photon. Technol. Lett. 4, 1201 (1992).
[Crossref]

Day, T.

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Demars, G.

C. L. Tang, H. Statz, and G. Demars, J. Appl. Phys. 34, 2289 (1963).
[Crossref]

Diehl, L.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, Phys. Rev. Lett. 100, 167401 (2008).
[Crossref]

Duan, G.-H.

F. Girardin and G.-H. Duan, IEEE J. Sel. Top. Quantum Electron. 3, 461 (1997).
[Crossref]

Ducournau, G.

T. Nagatsuma, G. Ducournau, and C. C. Renaud, Nat. Photonics 10, 371 (2016).
[Crossref]

Eichler, H. J.

H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer, 1986).

En Zah, C.

D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. En Zah, K. Lascola, A. Belyanin, and F. Capasso, Nat. Photonics 11, 789 (2017).
[Crossref]

Faist, J.

M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, Appl. Phys. Lett. 108, 171104 (2016).
[Crossref]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, Nature 492, 229 (2012).
[Crossref]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, Phys. Rev. Lett. 100, 167401 (2008).
[Crossref]

J. Faist, A. Hugi, and G. Villares, “Method and device for frequency control and stabilization of a semiconductor laser,” U.S. patentWO2015059082A1 (April 30, 2015).

Fang, W. C. W.

W. C. W. Fang, C. G. Bethea, Y. K. Chen, and S. L. Chuang, IEEE J. Sel. Top. Quantum Electron. 1, 117 (1995).
[Crossref]

Flynn, E. J.

M. R. Phillips, T. E. Darcie, and E. J. Flynn, IEEE Photon. Technol. Lett. 4, 1201 (1992).
[Crossref]

Giovannini, M.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, Phys. Rev. Lett. 100, 167401 (2008).
[Crossref]

Girardin, F.

F. Girardin and G.-H. Duan, IEEE J. Sel. Top. Quantum Electron. 3, 461 (1997).
[Crossref]

Gunter, P.

H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer, 1986).

Hoshino, I.

L. J. P. Ketelsen, I. Hoshino, and D. A. Ackerman, IEEE J. Quantum Electron. 27, 957 (1991).
[Crossref]

Hugi, A.

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, Nature 492, 229 (2012).
[Crossref]

J. Faist, A. Hugi, and G. Villares, “Method and device for frequency control and stabilization of a semiconductor laser,” U.S. patentWO2015059082A1 (April 30, 2015).

Kazakov, D.

D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. En Zah, K. Lascola, A. Belyanin, and F. Capasso, Nat. Photonics 11, 789 (2017).
[Crossref]

Ketelsen, L. J. P.

L. J. P. Ketelsen, I. Hoshino, and D. A. Ackerman, IEEE J. Quantum Electron. 27, 957 (1991).
[Crossref]

Lapidoth, A.

A. Lapidoth, A Foundation in Digital Communication (Cambridge University, 2009).

Lascola, K.

D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. En Zah, K. Lascola, A. Belyanin, and F. Capasso, Nat. Photonics 11, 789 (2017).
[Crossref]

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Liu, H. C.

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, Nature 492, 229 (2012).
[Crossref]

Mansuripur, T. S.

D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. En Zah, K. Lascola, A. Belyanin, and F. Capasso, Nat. Photonics 11, 789 (2017).
[Crossref]

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Missaggia, L. J.

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Nagatsuma, T.

T. Nagatsuma, G. Ducournau, and C. C. Renaud, Nat. Photonics 10, 371 (2016).
[Crossref]

Norris, T. B.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, Phys. Rev. Lett. 100, 167401 (2008).
[Crossref]

Phillips, M. R.

M. R. Phillips, T. E. Darcie, and E. J. Flynn, IEEE Photon. Technol. Lett. 4, 1201 (1992).
[Crossref]

Piccardo, M.

D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. En Zah, K. Lascola, A. Belyanin, and F. Capasso, Nat. Photonics 11, 789 (2017).
[Crossref]

Pohl, D. W.

H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer, 1986).

Renaud, C. C.

T. Nagatsuma, G. Ducournau, and C. C. Renaud, Nat. Photonics 10, 371 (2016).
[Crossref]

Rösch, M.

M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, Appl. Phys. Lett. 108, 171104 (2016).
[Crossref]

Scalari, G.

M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, Appl. Phys. Lett. 108, 171104 (2016).
[Crossref]

Schwarz, B.

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Siegman, A. E.

A. E. Siegman, Appl. Phys. Lett. 30, 21 (1977).
[Crossref]

A. E. Siegman, Lasers (University Science Books, 1986).

Statz, H.

C. L. Tang, H. Statz, and G. Demars, J. Appl. Phys. 34, 2289 (1963).
[Crossref]

Tang, C. L.

C. L. Tang, H. Statz, and G. Demars, J. Appl. Phys. 34, 2289 (1963).
[Crossref]

Vernet, C.

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Villares, G.

M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, Appl. Phys. Lett. 108, 171104 (2016).
[Crossref]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, Nature 492, 229 (2012).
[Crossref]

J. Faist, A. Hugi, and G. Villares, “Method and device for frequency control and stabilization of a semiconductor laser,” U.S. patentWO2015059082A1 (April 30, 2015).

Wang, C. A.

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Wang, Y.

D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. En Zah, K. Lascola, A. Belyanin, and F. Capasso, Nat. Photonics 11, 789 (2017).
[Crossref]

Y. Wang and A. Belyanin, Opt. Express 23, 4173 (2015).
[Crossref]

Wu, Z.-K.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, Phys. Rev. Lett. 100, 167401 (2008).
[Crossref]

Xie, F.

D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. En Zah, K. Lascola, A. Belyanin, and F. Capasso, Nat. Photonics 11, 789 (2017).
[Crossref]

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Zah, C.-E.

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Appl. Phys. Lett. (2)

A. E. Siegman, Appl. Phys. Lett. 30, 21 (1977).
[Crossref]

M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, Appl. Phys. Lett. 108, 171104 (2016).
[Crossref]

IEEE J. Quantum Electron. (1)

L. J. P. Ketelsen, I. Hoshino, and D. A. Ackerman, IEEE J. Quantum Electron. 27, 957 (1991).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

W. C. W. Fang, C. G. Bethea, Y. K. Chen, and S. L. Chuang, IEEE J. Sel. Top. Quantum Electron. 1, 117 (1995).
[Crossref]

F. Girardin and G.-H. Duan, IEEE J. Sel. Top. Quantum Electron. 3, 461 (1997).
[Crossref]

IEEE Photon. Technol. Lett. (1)

M. R. Phillips, T. E. Darcie, and E. J. Flynn, IEEE Photon. Technol. Lett. 4, 1201 (1992).
[Crossref]

J. Appl. Phys. (1)

C. L. Tang, H. Statz, and G. Demars, J. Appl. Phys. 34, 2289 (1963).
[Crossref]

Nat. Photonics (2)

T. Nagatsuma, G. Ducournau, and C. C. Renaud, Nat. Photonics 10, 371 (2016).
[Crossref]

D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. En Zah, K. Lascola, A. Belyanin, and F. Capasso, Nat. Photonics 11, 789 (2017).
[Crossref]

Nature (1)

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, Nature 492, 229 (2012).
[Crossref]

Opt. Express (1)

Phys. Rev. A (1)

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, Phys. Rev. A 94, 063807 (2016).
[Crossref]

Phys. Rev. Lett. (1)

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, Phys. Rev. Lett. 100, 167401 (2008).
[Crossref]

Other (4)

H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer, 1986).

A. E. Siegman, Lasers (University Science Books, 1986).

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Supplementary Material (1)

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Figures (2)

Fig. 1.
Fig. 1. Mapping time-dependent population inversion gratings in QCL combs. (a)–(c) Emergence of inversion grating effects, known as SHB, in a standing-wave laser: an optical mode m starts lasing inside the cavity (a), inducing a static grating ΔNS (b). This in turn allows another mode m+1 to oscillate and beat with the first mode, inducing a dynamic grating ΔNB that oscillates periodically (c) in the direction indicated by the arrows (two snapshots of such oscillatory grating taken at times differing by half of the oscillation cycle are shown in two shades of green). (d) Measured optical spectrum of QCL1 operating in a comb regime. (e) Schematic of the setup used for the measurement of intracavity beat profiles in a QCL. Two microwave probes are positioned on the top electrode of the laser with cavity length L. As one probe is scanned across the longitudinal axis of the cavity, the detected signals can be recorded with a digital sampling oscilloscope (OSC) or a microwave spectrum analyzer (SA). (f) Spectra measured on the SA (resolution bandwidth: 1 kHz) of the fundamental (f0=5.6  GHz) and second order (f0=11.2  GHz) beat notes of QCL1. (g) Power and phase of the intracavity beat profiles measured on QCL1 (circles) at fB (top) and 2fB (bottom). Also shown are the predictions of the analytical model presented in the text (continuous lines, parameters: L=8  mm, R=0.28) and of numerical simulations (crosses). (h) Intracavity beat profiles measured at fB (top) and 2fB (bottom) on four different devices with emission wavelength and cavity length specified in the table.
Fig. 2.
Fig. 2. QCL as a microwave quadrature mixer. (a) Block diagram of a generic quadrature mixer. I(t) and Q(t) are two input baseband signals, fc is the carrier frequency, sQAM is the QAM waveform. (b) Schematic of the setup used to demonstrate microwave QAM with a QCL comb generator. The rectangular bar is the top view of the laser contact. Two sinusoidal signals are injected and electrically mixed inside the laser with intermodal beat notes fB,0° and fB,90° offset by 90°, producing in-phase (I) and quadrature (Q) signals. The modulation products are extracted by two additional microwave probes, recombined using a power splitter and recorded on the OSC or SA. (c) Microwave spectrum of the signal extracted from QCL1 and acquired with the SA. The inset shows the current-voltage curve of the device and the operating point for QAM (square). (d) Demodulated microwave spectra of the I and Q channels retrieved after digital processing of the time-domain QAM waveform.

Equations (2)

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IB,n=m=1NnAmAm+n[cos(nkBx+nωBt+Δϕm+n,m)egx+cos(nkBxnωBtΔϕm+n,m)eg(Lx)],
IB,n=m=1Nn2AmAm+ncos(nkBx)cos(nωBt+Δϕm+n,m),

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