Abstract

We characterize both the group delay and the transmission of a layered semiconductor structure in a single easily interpreted plot. The data spans a 50 nm wide spectral range with 1.7 nanometer wavelength resolution, and a 1.3 picosecond wide temporal range with temporal resolution of tens of femtoseconds. Specific data for a 28 period GaAs/AlAs layered photonic band-gap structure that characterizes both group delay and transmission of multiple photonic resonances in a single display are presented and compared to theory.

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References

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  1. M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, R. P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: Large tunable group delay with minimal distortion and loss," Phys. Rev. E 54, R1078-R1081 (1996)
    [CrossRef]
  2. T. R. Nelson, J. P. Loehr, Q. Xie, J. E. Ehret, J. E. VanNostrand, L. J. Gamble, D. K. Jones, S. T. Cole, R. A. Trimm, W. M. Diffey, R. L. Fork, A. S. Keys, "Electrically tunable group delays using quantum wells in a distributed bragg reflector," in Enabling Photonic Technologies for Aerospace Applications, Proc. SPIE 3714, 12-23 (1999).
  3. J. M. Bendickson, J. P. Dowling, M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53,4101-4121 (1996).
    [CrossRef]
  4. Y. A. Vlasov, S. Petit, G. Klein, B. Honerlange, C. Hirlimann, "Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal," Phys. Rev. E 60, 1030-1035 (1999).
    [CrossRef]
  5. S. Wang, H. Erlig, H. R. Fetterman, E. Yablonovitch, V. Grubsky, D. S. Starodubov, J. Feinberg, "Measurement of the temporal delay of a light pulse through a one-dimensional photonic crystal," Micro. Opt. Technol. Let. 20, 17-21 (1999).
    [CrossRef]
  6. R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
    [CrossRef]
  7. J. P. Foing, J. P. Likforman, M. Joffre, A. Migus, "Femtosecond pulse phase measurement by spectrally resolved up-conversion: Application to continuum compression," IEEE J. Quantum Electron 28, 2285-2290 (1992).
    [CrossRef]
  8. R. L. Fork "Optical frequency filter for ultrashort pulses," Opt. Let. 11, 629-631 (1986).
    [CrossRef]
  9. K. L. Schehrer, R. L. Fork, H. Avramopoulos, E. S. Fry "Derivation and measurement of the reversible temporal lengthening of femtosecond pulses for the case of a four-prism sequence," Opt. Let. 15, 550-552 (1990).
    [CrossRef]

Other (9)

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, R. P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: Large tunable group delay with minimal distortion and loss," Phys. Rev. E 54, R1078-R1081 (1996)
[CrossRef]

T. R. Nelson, J. P. Loehr, Q. Xie, J. E. Ehret, J. E. VanNostrand, L. J. Gamble, D. K. Jones, S. T. Cole, R. A. Trimm, W. M. Diffey, R. L. Fork, A. S. Keys, "Electrically tunable group delays using quantum wells in a distributed bragg reflector," in Enabling Photonic Technologies for Aerospace Applications, Proc. SPIE 3714, 12-23 (1999).

J. M. Bendickson, J. P. Dowling, M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53,4101-4121 (1996).
[CrossRef]

Y. A. Vlasov, S. Petit, G. Klein, B. Honerlange, C. Hirlimann, "Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal," Phys. Rev. E 60, 1030-1035 (1999).
[CrossRef]

S. Wang, H. Erlig, H. R. Fetterman, E. Yablonovitch, V. Grubsky, D. S. Starodubov, J. Feinberg, "Measurement of the temporal delay of a light pulse through a one-dimensional photonic crystal," Micro. Opt. Technol. Let. 20, 17-21 (1999).
[CrossRef]

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

J. P. Foing, J. P. Likforman, M. Joffre, A. Migus, "Femtosecond pulse phase measurement by spectrally resolved up-conversion: Application to continuum compression," IEEE J. Quantum Electron 28, 2285-2290 (1992).
[CrossRef]

R. L. Fork "Optical frequency filter for ultrashort pulses," Opt. Let. 11, 629-631 (1986).
[CrossRef]

K. L. Schehrer, R. L. Fork, H. Avramopoulos, E. S. Fry "Derivation and measurement of the reversible temporal lengthening of femtosecond pulses for the case of a four-prism sequence," Opt. Let. 15, 550-552 (1990).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Spectral variation of the theoretical transmission and delay of a 28 period GaAs/AlAs PBG structure.

Fig. 2.
Fig. 2.

Experimental setup.

Fig. 3.
Fig. 3.

The raw data sets. The leftmost data set represents the upconverted spectral region of the continuum, and the data set on the right is that of the continuum through the sample. For display purposes, here, zero delay has been arbitrarily set to coincide with the center of the continuum data set. The choice of where “zero” is located is not important as we are interested only in the difference between the delay of the two data sets.

Fig. 4.
Fig. 4.

The data sets after they have been fit to a Gaussian.

Fig. 5.
Fig. 5.

Transmission recovered from the raw data sets (red), predicted by theory (blue), and measured at WPAFB (green). The spectral width of the reference pulse (black), actually centered at 809 nm, is shown here for comparison with the size of the features.

Fig. 6.
Fig. 6.

The delay obtained from measurement (red) and from theory (red). The delay imparted by the substrate is shown here in black.

Equations (6)

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Delay = d sample V g d sample c = d ϕ d ω d sample c .
E signal ( ω , τ ) = f Xtal ( ω ) E p ( ω 1 ) e i ω 1 τ E ref ( ω ω 1 ) d ω 1 ,
E p ( ω 1 ) E p ( ω p ) e i [ ϕ p ( ω p ) + ( ω 1 ω p ) ϕ p ( ω p ) ]
I signal ( ω p , τ ) = E signal ( ω p , τ ) 2 e [ τ ϕ p ( ω p ) ] 2 2 Δ ω r 2
Delay ( ω ) = τ Sample max ( ω ) τ NoSamp max ( ω ) = ϕ Sample ( ω ) d Sample c
T ( ω ) = I Sample [ ω , τ Sample max ( ω ) ] I NoSamp [ ω , τ NoSamp max ( ω ) ]

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