Abstract

A time-resolved mid-infrared upconversion technique based on sum-frequency generation was applied to measure pulse propagation in λ~5.0 µm quantum cascade lasers operated in continuous wave at 30 K. The wavelength-dependent propagation delay of femtosecond mid-infrared pulses was measured to determine the total group-velocity dispersion. The material and waveguide dispersion were calculated and their contributions to the total group-velocity dispersion were found to be relatively small and constant. The small-signal gain dispersion was estimated from a measurement of the electroluminescence spectrum without a laser cavity, and was found to be the largest component of the total GVD. A negative group-velocity dispersion of β 2 (=d 2 β/ 2) approximately -4.6×10-6 ps2/µm was observed at the peak emission wavelength, and good agreement was found for the measured and calculated pulse-broadening.

© 2007 Optical Society of America

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References

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  1. G. P. Agrawal, "Effect of gain dispersion on ultrashort pulse amplification," IEEE J. Quantum Electron. 27, 1843-1849 (1991).
    [CrossRef]
  2. H. A. Haus and Y. Silberberg, "Laser Mode Locking with Addition of Nonlinear Index," IEEE J. Quantum Electron. QE-22, 1048-1060 (1986).
  3. W. Lu, L. Yan, and C. R. Menyuk, "Dispersion effects in an actively mode-locked inhomogeneously broadened laser," IEEE J. Quantum Electron. QE-22, 1317-1324 (2002).
    [CrossRef]
  4. R. Paiella, F. Capasso, C. Gmachl, and H. Y. Hwang, D. L. Svico, A. L. Hutchinson, A. Y. Cho and H. C. Liu, "Monolithic active mode locking of quantum cascade lasers," Appl. Phys. Lett. 77, 169-171 (2000).
    [CrossRef]
  5. A. Soibel and F. Capasso and C. Gmachl and M. L. Peabody and A. M. Sergent and R. Paiella and H. Y. Hwang and D. L. Sivco and A. Y. Cho and H. C. Liu and C. Jirauschek and F. X. Kärtner, "Active mode locking of broadband quantum cascade lasers," IEEE J. Quantum Electron. 40, 844-851 (2004).
    [CrossRef]
  6. R. Paiella and F. Capasso and C. Gmachl and D. L. Svico and J. N. Bailargeon and A. L. Hutchinson and A. Y. Cho, "Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearities," Science 290, 1739-1742 (2000).
    [CrossRef] [PubMed]
  7. C. Y. Wang and L. Diehl and A. Gordon and C. Jirauschek and F. X. K¨artner and A. Belyanin and D. Bour and S. Corzine and G. Hofler and M. Troccoli and J. Faist and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802-1-031802-4 (2007).
    [CrossRef]
  8. D. Hofstetter and J. Faist, "Measurement of semiconductor laser gain and dispersion curves utilizing Fourier transforms of the Emission Spectra," IEEE Photon. Technol. Lett. 11, 1372-1374 (1999).
    [CrossRef]
  9. C. Gmachl and A. Straub and R. Colombelli and D. L. Sivco and F. Capasso and A. Y. Cho, "Minimal group refractive index dispersion and gain evolution in ultra-broad-band quantum cascade lasers," IEEE Photon. Technol. Lett. 14, 1671-1673 (2002).
    [CrossRef]
  10. J. Shah, "Ultrafast Luminescence Spectroscopy Using Sum Frequency Generation," IEEE J. Quantum Electron. 24, 276-288 (1988).
    [CrossRef]
  11. M. P. Kesler and E. P. Ippen, "Femtosecond time-domain measurements of group velocity dispersion in Al-GaAs diode lasers," Electron. Lett. 25, 640-642 (1989).
    [CrossRef]
  12. M. P. Kesler and E. P. Ippen, "Femtosecond time-domain measurements of group velocity dispersion in diode lasers at 1.5 μm," J. Lightwave Technol. 10, 616-619 (1992).
    [CrossRef]
  13. R. Gordon and A. P. Heberle and J. R. A. Cleaver, "Measuring the above-threshold group-velocity dispersion and gain curvature of a semiconductor laser by pulse-propagation techniques," J. Opt. Soc. Am. B 21, 29-35 (1994).
    [CrossRef]
  14. L. Diehl and D. Bour and S. Corzine and J. Zhu and G. Höfler and B. G. Lee and C. Y. Wang and M. Troccoli and F. Capasso, "Pulsed- and continuous-mode operation at high temperature of strained quantum-cascade lasers grown by metalorganic vapor phase epitaxy," Appl. Phys. Lett. 88, 2011151-2011515 (2006).
    [CrossRef]
  15. L. Diehl and D. Bour and S. Corzine and J. Zhu and G. Höfler and M. Lončar and M. Troccoli and F. Capasso, "High-power quantum cascade lasers grown by low-pressure metal organic vapor-phase epitaxy operating continuous wave above 400 K," Appl. Phys. Lett. 88, 0411021-0411023 (2006).
  16. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).
  17. R. Maulini and M. Beck and J. Faist and E. Gini, "Broadband tuning of external cavity bound-to-continuum quantum-cascade lasers," Appl. Phys. Lett. 84, 1659-1661 (2004).
    [CrossRef]
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  19. A. Siegman, Lasers (University Science Books, Sausalito, California, 1986).

2006 (1)

L. Diehl and D. Bour and S. Corzine and J. Zhu and G. Höfler and M. Lončar and M. Troccoli and F. Capasso, "High-power quantum cascade lasers grown by low-pressure metal organic vapor-phase epitaxy operating continuous wave above 400 K," Appl. Phys. Lett. 88, 0411021-0411023 (2006).

2004 (1)

R. Maulini and M. Beck and J. Faist and E. Gini, "Broadband tuning of external cavity bound-to-continuum quantum-cascade lasers," Appl. Phys. Lett. 84, 1659-1661 (2004).
[CrossRef]

2002 (2)

W. Lu, L. Yan, and C. R. Menyuk, "Dispersion effects in an actively mode-locked inhomogeneously broadened laser," IEEE J. Quantum Electron. QE-22, 1317-1324 (2002).
[CrossRef]

C. Gmachl and A. Straub and R. Colombelli and D. L. Sivco and F. Capasso and A. Y. Cho, "Minimal group refractive index dispersion and gain evolution in ultra-broad-band quantum cascade lasers," IEEE Photon. Technol. Lett. 14, 1671-1673 (2002).
[CrossRef]

2000 (2)

R. Paiella, F. Capasso, C. Gmachl, and H. Y. Hwang, D. L. Svico, A. L. Hutchinson, A. Y. Cho and H. C. Liu, "Monolithic active mode locking of quantum cascade lasers," Appl. Phys. Lett. 77, 169-171 (2000).
[CrossRef]

R. Paiella and F. Capasso and C. Gmachl and D. L. Svico and J. N. Bailargeon and A. L. Hutchinson and A. Y. Cho, "Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearities," Science 290, 1739-1742 (2000).
[CrossRef] [PubMed]

1999 (1)

D. Hofstetter and J. Faist, "Measurement of semiconductor laser gain and dispersion curves utilizing Fourier transforms of the Emission Spectra," IEEE Photon. Technol. Lett. 11, 1372-1374 (1999).
[CrossRef]

1994 (1)

1992 (1)

M. P. Kesler and E. P. Ippen, "Femtosecond time-domain measurements of group velocity dispersion in diode lasers at 1.5 μm," J. Lightwave Technol. 10, 616-619 (1992).
[CrossRef]

1991 (1)

G. P. Agrawal, "Effect of gain dispersion on ultrashort pulse amplification," IEEE J. Quantum Electron. 27, 1843-1849 (1991).
[CrossRef]

1989 (1)

M. P. Kesler and E. P. Ippen, "Femtosecond time-domain measurements of group velocity dispersion in Al-GaAs diode lasers," Electron. Lett. 25, 640-642 (1989).
[CrossRef]

1988 (1)

J. Shah, "Ultrafast Luminescence Spectroscopy Using Sum Frequency Generation," IEEE J. Quantum Electron. 24, 276-288 (1988).
[CrossRef]

1986 (1)

H. A. Haus and Y. Silberberg, "Laser Mode Locking with Addition of Nonlinear Index," IEEE J. Quantum Electron. QE-22, 1048-1060 (1986).

Appl. Phys. Lett. (3)

R. Paiella, F. Capasso, C. Gmachl, and H. Y. Hwang, D. L. Svico, A. L. Hutchinson, A. Y. Cho and H. C. Liu, "Monolithic active mode locking of quantum cascade lasers," Appl. Phys. Lett. 77, 169-171 (2000).
[CrossRef]

L. Diehl and D. Bour and S. Corzine and J. Zhu and G. Höfler and M. Lončar and M. Troccoli and F. Capasso, "High-power quantum cascade lasers grown by low-pressure metal organic vapor-phase epitaxy operating continuous wave above 400 K," Appl. Phys. Lett. 88, 0411021-0411023 (2006).

R. Maulini and M. Beck and J. Faist and E. Gini, "Broadband tuning of external cavity bound-to-continuum quantum-cascade lasers," Appl. Phys. Lett. 84, 1659-1661 (2004).
[CrossRef]

Electron. Lett. (1)

M. P. Kesler and E. P. Ippen, "Femtosecond time-domain measurements of group velocity dispersion in Al-GaAs diode lasers," Electron. Lett. 25, 640-642 (1989).
[CrossRef]

IEEE J. Quantum Electron. (4)

J. Shah, "Ultrafast Luminescence Spectroscopy Using Sum Frequency Generation," IEEE J. Quantum Electron. 24, 276-288 (1988).
[CrossRef]

G. P. Agrawal, "Effect of gain dispersion on ultrashort pulse amplification," IEEE J. Quantum Electron. 27, 1843-1849 (1991).
[CrossRef]

H. A. Haus and Y. Silberberg, "Laser Mode Locking with Addition of Nonlinear Index," IEEE J. Quantum Electron. QE-22, 1048-1060 (1986).

W. Lu, L. Yan, and C. R. Menyuk, "Dispersion effects in an actively mode-locked inhomogeneously broadened laser," IEEE J. Quantum Electron. QE-22, 1317-1324 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

D. Hofstetter and J. Faist, "Measurement of semiconductor laser gain and dispersion curves utilizing Fourier transforms of the Emission Spectra," IEEE Photon. Technol. Lett. 11, 1372-1374 (1999).
[CrossRef]

C. Gmachl and A. Straub and R. Colombelli and D. L. Sivco and F. Capasso and A. Y. Cho, "Minimal group refractive index dispersion and gain evolution in ultra-broad-band quantum cascade lasers," IEEE Photon. Technol. Lett. 14, 1671-1673 (2002).
[CrossRef]

J. Lightwave Technol. (1)

M. P. Kesler and E. P. Ippen, "Femtosecond time-domain measurements of group velocity dispersion in diode lasers at 1.5 μm," J. Lightwave Technol. 10, 616-619 (1992).
[CrossRef]

J. Opt. Soc. Am. B (1)

Science (1)

R. Paiella and F. Capasso and C. Gmachl and D. L. Svico and J. N. Bailargeon and A. L. Hutchinson and A. Y. Cho, "Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearities," Science 290, 1739-1742 (2000).
[CrossRef] [PubMed]

Other (6)

C. Y. Wang and L. Diehl and A. Gordon and C. Jirauschek and F. X. K¨artner and A. Belyanin and D. Bour and S. Corzine and G. Hofler and M. Troccoli and J. Faist and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802-1-031802-4 (2007).
[CrossRef]

A. Soibel and F. Capasso and C. Gmachl and M. L. Peabody and A. M. Sergent and R. Paiella and H. Y. Hwang and D. L. Sivco and A. Y. Cho and H. C. Liu and C. Jirauschek and F. X. Kärtner, "Active mode locking of broadband quantum cascade lasers," IEEE J. Quantum Electron. 40, 844-851 (2004).
[CrossRef]

A. Yariv, Quantum Electronics (WILEY, New York, 1989).

A. Siegman, Lasers (University Science Books, Sausalito, California, 1986).

L. Diehl and D. Bour and S. Corzine and J. Zhu and G. Höfler and B. G. Lee and C. Y. Wang and M. Troccoli and F. Capasso, "Pulsed- and continuous-mode operation at high temperature of strained quantum-cascade lasers grown by metalorganic vapor phase epitaxy," Appl. Phys. Lett. 88, 2011151-2011515 (2006).
[CrossRef]

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).

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Figures (10)

Fig. 1.
Fig. 1.

CW L-I-V characteristics of the D3281 QCL at 30 K. Inset: lasing spectrum (~5 µm) at the bias current of 0.14 A. Note that all the upconversion experiments for the GVD have been done below threshold (0.12 A at 30K) to prevent the device’s self-heating and also to minimize the optical feedback effect.

Fig. 2.
Fig. 2.

Experimental setup for the GVD measurements in a QCL. Transmitted mid-IR pulse is upconverted with 800-nm pulse to detect the sum frequency photon.

Fig. 3.
Fig. 3.

(a) Typical cross-correlation trace of mid-IR pulse at 5 µm, showing the intensity FWHM of ~220 fs. (b) Spectrally tunable mid-IR pulses are used to measure the mid-IR peak wavelength dependent pulse transit time.

Fig. 4.
Fig. 4.

(a) An example of a time-resolved upconversion trace is displayed for a QCL bias current of 0.12 A. (b) The upconversion signal at the reference time delay, i.e. time-zero delay, is shown for center wavelengths 4.92 µm (dashed) and 5.12 µm (solid). (c) Upconversion signals for two different center wavelengths are shown, illustrating the shift in pulse group delay with wavelength.

Fig. 5.
Fig. 5.

(a) The measured propagation delays (filled squares) are displayed as a function of the peak wavelength of the injected mid-IR pulse. A third-order polynomial fit (dashed line) to the measured delays is used to calculate GVD parameter β2 via Eqs. 2–3. (b) Assuming the mid-IR pulse as a Gaussian, the intensity FWHM of reference pulses (filled circles) and that of transmitted mid-IR pulses (filled upper triangles) are shown as a function of wavelength. The error bars from the chi-squared determined errors (~± 5 fs) are due to the long-term intensity fluctuation of our femtosecond laser sources.

Fig. 6.
Fig. 6.

(a) Effective refractive index vs. wavelength curve. The dashed line is a polynomial fit of the calculated discrete points. (b) The corresponding refractive index dispersion dn/ is shown as a function of wavelength.

Fig. 7.
Fig. 7.

Electroluminescence spectrum (D3281, solid line) without the laser cavity was measured at 30 K in order to determine the gain spectrum and thus the dispersion via the Kramers-Kronig relations. For simplicity, the spectrum was approximated by a Lorentzian line shape; the fit to the gain spectrum and the resulting dispersion are shown.

Fig. 8.
Fig. 8.

Calculated refractive index based on the Eq. 8 is displayed for three different values of the population inversion ΔN.

Fig. 9.
Fig. 9.

Calculated index dispersion dn/ and β 2 (using Eq. 45) only due to the small-signal gain are displayed in (a) and (b), respectively.

Fig. 10.
Fig. 10.

(a) Contributions to the total GVD are separately displayed. Filled squares are the total β2 (=d 2 β/d ω 2) from the upconversion measurements of Fig. 5(a). The material and waveguide dispersion (see Fig. 6) are shown as the dashed line, the gain dispersion (see Fig. 9) is as the dotted line, and total dispersion (sum of material, waveguide, and gain dispersion) is displayed as the solid line. (b) Corresponding pulse broadening, FWHM ratio τp /τp 0, is displayed. Filled squares are from the upconversion measurements and dashed line is from the total GVD calculations.

Equations (8)

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τ delay = L v g = L c n g
d n g d λ = c L d τ delay d λ
β 2 = d 2 β d ω 2 = d λ d ω d d λ ( 1 v g ) = λ 2 2 π c L d τ delay d λ
v g = c ( n λ d n d λ ) 1
β 2 = d 2 β d ω 2 = d λ d ω d d λ ( 1 v g ) = λ 3 2 π c 2 d 2 n d λ 2
χ " ( v ) = e 2 z if 2 Δ N 2 ε 0 h ̅ Δ v 2 π ( v v 0 ) 2 + ( Δ v 2 ) 2
χ ' ( v ) = e 2 z if 2 ( ω 0 ω ) T 2 Δ N 2 ε 0 h ̅ Δ v 2 π ( v v 0 ) 2 + ( Δ v 2 ) 2
n = Re ( ε b + ε 0 χ )

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