Abstract

We present investigations of the the relative intensity noise (RIN) of a quantum cascade laser (QC) laser in continuous wave operation. We analyze the intensity noise properties in terms of the relative intensity noise (RIN). In contrast to conventional interband semiconductor diode lasers we obtain a different scaling behavior of RIN with increasing optical output power for QC lasers. From a semiclassical noise model we find that this result is due to the cascaded active regions each incorporating three laser levels, and is therefore a particular feature of QC lasers.

© 2005 Optical Society of America

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References

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    [CrossRef]
  26. T. Gensty, J. von Staden, and W. Els�er, �??Investigations on the generation of light with sub-shot intensity noise with quantum cascade lasers,�?? in Fluctuations and Noise in Photonics and Quantum Optics II, P. Heszler, D. Abbott, J. R. Gea-Banacloche, and Ph. R. Hemmer, eds., Proc. SPIE 5468, 191-197 (2004).
    [CrossRef]
  27. T. Mukai and Y. Yamamoto, �??AM Quantum noise in 1.3 µm InGaAsP lasers,�?? Electron. Lett. 20, 28-29 (1984).
    [CrossRef]
  28. I. Joindot, �??Measurements of relative intensity noise (RIN) in semiconductor-lasers,�?? J. Phys. III 2, 1591-1603 (1992).
  29. D. Kuchta, J. Gamelin, J. D.Walker, J. Lin, K. Y. Lau, and J. S. Smith, �??Relative intensity noise of vertical cavity surface emitting lasers,�?? Appl. Phys. Lett. 62, 1194-1196 (1993).
    [CrossRef]
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    [CrossRef]
  32. F. Koyama, K. Morito, and K. Iga, �??Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers,�?? IEEE J. Quantum Electron. QE-27, 1410-1416 (1991).
    [CrossRef]

Adv. in AMOP

J. Woerdman, M. V. Exter, and N. V. Druten, �??Quantum noise of small lasers,�?? Adv. in Atomic, Molecular, and Optical Physics 47, 205-248 (2001).
[CrossRef]

Adv. in Solid State Phys.

C. Mann, Q. K. Yang, F. Fuchs,W. Bronner, R. Kiefer, K. Khler, H. Schneider, R. Korrmann, H. Fischer, T. Gensty, and W. Els�er, �??Quantum Cascade Lasers for the mid-infrared spectral range: Devices and applications,�?? in B. Kramer, ed., Adv. in Solid State Phys. 43, 351-368 (Springer, Berlin, Heidelberg, 2003).
[CrossRef]

Appl. Phys. Lett.

J. S. Yu, S. Slivken, A. Evans, J. David, and M. Razeghi, �??High-power continuous-wave operation of a 6 µm quantum-cascade laser at room temperature,�?? Appl. Phys. Lett. 82, 3397-3399 (2003).
[CrossRef]

R. Köhler, C. Gmachl, A. Tredicucci, F. Capasso, D. L. Sivco, S.-N. G. Chu, and A. Y. Cho, �??Single-mode tunable, pulsed, and continuous wave quantum-cascade distributed feedback lasers at λ ~= 4.6�??4.7 µm,�?? Appl. Phys. Lett. 76, 1092-1094 (2000).
[CrossRef]

D. Kuchta, J. Gamelin, J. D.Walker, J. Lin, K. Y. Lau, and J. S. Smith, �??Relative intensity noise of vertical cavity surface emitting lasers,�?? Appl. Phys. Lett. 62, 1194-1196 (1993).
[CrossRef]

Electron. Lett.

T. Mukai and Y. Yamamoto, �??AM Quantum noise in 1.3 µm InGaAsP lasers,�?? Electron. Lett. 20, 28-29 (1984).
[CrossRef]

C. Mann, Q. K. Yang, F. Fuchs, W. Bronner, and K. Köhler, �??Continuous-wave operation of 5 µm quantum cascade lasers with high-reflection coated facets,�?? Electron. Lett. 39, 1590-1592 (2003).
[CrossRef]

IEEE J. Quantum Electron.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, and E. A. Whittaker, �??Quantum cascade lasers: Ultra-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,�?? IEEE J. Quantum Electron. QE-38, 511-532 (2002).
[CrossRef]

F. Koyama, K. Morito, and K. Iga, �??Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers,�?? IEEE J. Quantum Electron. QE-27, 1410-1416 (1991).
[CrossRef]

J. Faist, A. Tredicucci, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, �??High-power continuous-wave quantum cascade lasers,�?? IEEE J. Quantum Electron. QE-34, 336-343 (1998).
[CrossRef]

Y. Yamamoto, �??AM and FM quantum noise in semiconductor-lasers. 1. Theoretical-analysis,�?? IEEE J. Quantum Electron. QE-19, 34-46 (1983).
[CrossRef]

Y. Yamamoto, S. Saito, and T. Mukai, �??AM and FM quantum noise in semiconductor-lasers. 2. Comparison of theoretical and experimental results for AlGaAs lasers,�?? IEEE J. Quantum Electron. QE-19, 47-58 (1983).
[CrossRef]

K. Vahala and A. Yariv, �??Semiclassical theory of noise in semiconductor-lasers. 1.,�?? IEEE J. Quantum Electron. QE-19, 1096-1101 (1983)
[CrossRef]

K. Vahala and A. Yariv, �??Semiclassical theory of noise in semiconductor-lasers. 2.,�?? IEEE J. Quantum Electron. QE-19, 1102-1109 (1983).
[CrossRef]

J. Mod. Optics

J. Poizat and P. Grangier, �??Quantum noise of laser diodes,�?? J. Mod. Optics 47, 2841-2856 (2000).

J. Opt. Soc. Am. B

J. Phys. III

I. Joindot, �??Measurements of relative intensity noise (RIN) in semiconductor-lasers,�?? J. Phys. III 2, 1591-1603 (1992).

Opt. Commun.

T. Gantsog, G. M. Meyer, M. O. Scully, and H. Walther, �??Dynamic control of micromaser and laser emission from driven three-level atoms,�?? Opt. Commun. 124, 579-594 (1996).
[CrossRef]

Opt. Express

Phys. Rev.

H. Haug, �??Quantum-mechanical rate equations for semiconductor lasers,�?? Phys. Rev. 184, 338-348 (1969).
[CrossRef]

Phys. Rev. A

B. C. Buchler, E. H. Huntington, C. C. Harb, and T. C. Ralph, �??Feedback control of laser intensity noise,�?? Phys. Rev. A 57, 1286-1294 (1998).
[CrossRef]

M. Orszag, S. Y. Zhu, J. Bergou, and M. O. Scully, �??Noise-reduction, lasing without inversion, and pump statistics in coherently prepared lambda quantum-beat media,�?? Phys. Rev. A 45, 4872-4878 (1992).
[CrossRef] [PubMed]

J.-L. Vey, C. Degen, K. Auen, and W. Els�er, �??Quantum noise and polarization properties of vertical-cavity surface-emitting lasers,�?? Phys. Rev. A 60, 3284-3295 (1999).
[CrossRef]

Phys. Rev. Lett.

K. M. Gheri and D. F. Walls, �??Sub-shot noise lasers without inversion,�?? Phys. Rev. Lett. 68, 3428-3431 (1992).
[CrossRef] [PubMed]

Proc. SPIE

T. Gensty, J. von Staden, and W. Els�er, �??Investigations on the generation of light with sub-shot intensity noise with quantum cascade lasers,�?? in Fluctuations and Noise in Photonics and Quantum Optics II, P. Heszler, D. Abbott, J. R. Gea-Banacloche, and Ph. R. Hemmer, eds., Proc. SPIE 5468, 191-197 (2004).
[CrossRef]

Science

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]

Y. Yamamoto, S. Machida, and R. H. Richardson, �??Photon number squeezed states in semiconductor-lasers,�?? Science 255, 1219-1224 (1992).
[CrossRef] [PubMed]

Other

F. T. Arecchi, Laser Handbook (North-Holland, Amsterdam, 1972).

H. Haken, Laser Theory Vol. XXXV/2C. Encyclopedia of Physics (Springer-Verlag, Berlin, 1970).

H.-A. Bachor, A Guide to Experiments in Quantum Optics (WILEY-VCH, Weinheim, New York, Chichester, Brisbane, Singapore, Toronto , 1998).

The quantum cascade laser structure has been grown by Fraunhofer-Institut für Angewandte Festkörperphysik (IAF), Tullastrasse 72, D-79108 Freiburg, Germany.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic conduction band profile of one gain stage of a 3-level QC laser. Also indicated is the electron transport (arrows) and photon emission (wavy arrow) due to the laser transition between level 3 and 2.

Fig. 2.
Fig. 2.

Scheme of the experimental setup. The emitted light of the quantum cascade laser (QCL) is collected by an elliptical mirror and focused onto the photovoltaic detector (D).The detected signal is is split into the AC current and DC current by a Bias-Tee. The AC part is analyzed by a electrical spectrum analyzer (ESA) after amplification using a low noise amplifier (A). The photocurrent Iph is measured in the DC part of the signal.

Fig. 3.
Fig. 3.

Experimentally determined RIN as a function of the emitted optical power of the investigated QC laser in cw-operation at a heat sink temperature of T=88 K. The RIN is measured at a frequency of 40 MHz. The solid line depicts the least-square fit to the experimental data.

Fig. 4.
Fig. 4.

Calculated relative intensity noise RIN as a function of the optical output power at a frequency of 40 MHz for the QC laser under investigation. The solid line shows the total RIN. Additionally, the individual contributions RPP (dotted) and R 33 (dashed) which give the main contribution to the RIN are indicated. The experimental RIN of Fig. 3 is also shown (squares) for comparison.

Fig. 5.
Fig. 5.

Scaling parameter γ of the calculated RIN as a function of the number of gain stages Z incorporated into the active region of a QC laser at an injection current of 1.2Ithr .

Tables (1)

Tables Icon

Table 1. Parameter values used for RIN calculations. The differential gain parameter is obtained by solving the steady-state rate equations and inserting the experimentally determined threshold current. The spontaneous emission parameter β is determined from a fit to the experimental PI-curve. The photon lifetime is obtained from the measurement of the net modal gain [18] and the phonon scattering times are estimated using Fermi’s Golden rule for the intersubband transition [18].

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

R I N ( ω ) = < δ P 2 > P 0 2 .
R I N ( ω ) = S P ( ω ) B G I ph 2 R ,
d N 3 d t = I in q N 3 τ 32 N 3 τ 31 g ( N 3 N 2 ) P ,
d N 2 d t = N 3 τ 32 N 2 τ 21 + g ( N 3 N 2 ) P ,
d N 1 d t = N 3 τ 31 + N 2 τ 21 I out q ,
d P d t = Z g ( N 3 N 2 ) P + Z β N 3 τ e P τ P .
RIN ( ω ) = R PP ( ω ) + R 33 ( ω )
< F P F P > = 2 Z ( β N 3 τ e + g N 3 P ) 2 D PP
< F 3 F 3 > = 2 ( N 3 τ 31 + N 3 τ 32 + g N 3 P ) 2 D 33 .
R PP ( ω ) = 2 D PP f P ( ω )
R 33 ( ω ) = 2 D 33 f 3 ( ω )

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