Abstract

The efficiency and uniformity of photon echoes are investigated in optical coherent transient sequences using temporally overlapped linear frequency-chirped programming pulses. Distortions in the power spectrum of the programming pulses due to edge effects are found to cause fluctuations in echo efficiency as a function of echo time delay. Smoothing the edges of the programming pulse envelopes is found to significantly reduce distortion in the power spectrum of the pulses, which leads to echoes that are both more efficient and more uniform than those generated by pulses without smoothed edges. The effect of programming pulse strength on echo efficiency and uniformity is shown and discussed through simulations for an optically thin medium and through experiment in Tm3+:YAG at 4K.

© 2006 Optical Society of America

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    [CrossRef]
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2004 (2)

T. Chang, M. Tian, and W. R. Babbitt, "Numerical modeling of optical coherent transient processes with complex configurations—>I. Angled beam geometry," J. Lumin. 107, 129-137 (2004).
[CrossRef]

T. Chang, M. Tian, Z. W. Barber, and W. R. Babbitt, "Numerical modeling of optical coherent transient processes with complex configurations—>II. Angled beams with arbitrary phase modulations," J. Lumin. 107, 138-145 (2004).
[CrossRef]

2002 (2)

2001 (1)

2000 (1)

1999 (1)

1998 (2)

M. Azadeh, C. S. Cornish, W. R. Babbitt, and L. Tsang, "Efficient photon echoes in optically thick media," Phys. Rev. A 57, 4662-4668 (1998).
[CrossRef]

K. D. Merkel and W. R. Babbitt, "Chirped-pulse programming of optical coherent transient true-time delays," Opt. Lett. 23, 528-530 (1998).
[CrossRef]

1982 (1)

1960 (1)

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, "The theory and design of chirp radars," Bell Syst. Tech. J. 34, 745-808 (1960).

1899 (1)

J. W. Gibbs, "Fourier series," Nature 59, 200 and 606 (1899).
[CrossRef]

Afzelius, M.

Albersheim, W. J.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, "The theory and design of chirp radars," Bell Syst. Tech. J. 34, 745-808 (1960).

Azadeh, M.

M. Azadeh, C. S. Cornish, W. R. Babbitt, and L. Tsang, "Efficient photon echoes in optically thick media," Phys. Rev. A 57, 4662-4668 (1998).
[CrossRef]

C. S. Cornish, M. Azadeh, W. R. Babbitt, and L. Tsang, "Efficient waveform recall in absorbing media," in The International Society for Optical Engineering, P.A.Mitkas and Z.Hasan, eds., Proc. SPIE 3468, 174-181 (1998).

Babbitt, W. R.

T. Chang, M. Tian, Z. W. Barber, and W. R. Babbitt, "Numerical modeling of optical coherent transient processes with complex configurations—>II. Angled beams with arbitrary phase modulations," J. Lumin. 107, 138-145 (2004).
[CrossRef]

T. Chang, M. Tian, and W. R. Babbitt, "Numerical modeling of optical coherent transient processes with complex configurations—>I. Angled beam geometry," J. Lumin. 107, 129-137 (2004).
[CrossRef]

R. R. Reibel, Z. Barber, M. Tian, and W. R. Babbitt, "Temporally overlapped linear frequency-chirped pulse programming for true-time-delay applications," Opt. Lett. 27, 494-496 (2002).
[CrossRef]

Z. Barber, M. Tian, R. R. Reibel, and W. R. Babbitt, "Optical pulse shaping using optical coherent transients," Opt. Express 10, 1145-1150 (2002).
[PubMed]

M. Tian, R. R. Reibel, and W. R. Babbitt, "Demonstration of optical coherent transient true-time delay at 4 Gbits/s," Opt. Lett. 26, 1143-1145 (2001).
[CrossRef]

K. D. Merkel and W. R. Babbitt, "Chirped-pulse programming of optical coherent transient true-time delays," Opt. Lett. 23, 528-530 (1998).
[CrossRef]

M. Azadeh, C. S. Cornish, W. R. Babbitt, and L. Tsang, "Efficient photon echoes in optically thick media," Phys. Rev. A 57, 4662-4668 (1998).
[CrossRef]

C. S. Cornish, M. Azadeh, W. R. Babbitt, and L. Tsang, "Efficient waveform recall in absorbing media," in The International Society for Optical Engineering, P.A.Mitkas and Z.Hasan, eds., Proc. SPIE 3468, 174-181 (1998).

R. R. Reibel, T. Chang, M. Tian, and W. R. Babbitt, "Optical linear sideband chirp compression for microwave arbitrary waveform generation," in Proceedings of IEEE International Topical Meeting on Microwave Photonics (Institute of Electrical and Electronics Engineers, 2004), pp. 197-200.

Barber, Z.

Barber, Z. W.

T. Chang, M. Tian, Z. W. Barber, and W. R. Babbitt, "Numerical modeling of optical coherent transient processes with complex configurations—>II. Angled beams with arbitrary phase modulations," J. Lumin. 107, 138-145 (2004).
[CrossRef]

Carlsten, J. L.

Chang, T.

T. Chang, M. Tian, Z. W. Barber, and W. R. Babbitt, "Numerical modeling of optical coherent transient processes with complex configurations—>II. Angled beams with arbitrary phase modulations," J. Lumin. 107, 138-145 (2004).
[CrossRef]

T. Chang, M. Tian, and W. R. Babbitt, "Numerical modeling of optical coherent transient processes with complex configurations—>I. Angled beam geometry," J. Lumin. 107, 129-137 (2004).
[CrossRef]

R. R. Reibel, T. Chang, M. Tian, and W. R. Babbitt, "Optical linear sideband chirp compression for microwave arbitrary waveform generation," in Proceedings of IEEE International Topical Meeting on Microwave Photonics (Institute of Electrical and Electronics Engineers, 2004), pp. 197-200.

Cone, R. L.

Cornish, C. S.

M. Azadeh, C. S. Cornish, W. R. Babbitt, and L. Tsang, "Efficient photon echoes in optically thick media," Phys. Rev. A 57, 4662-4668 (1998).
[CrossRef]

C. S. Cornish, M. Azadeh, W. R. Babbitt, and L. Tsang, "Efficient waveform recall in absorbing media," in The International Society for Optical Engineering, P.A.Mitkas and Z.Hasan, eds., Proc. SPIE 3468, 174-181 (1998).

Darlington, S.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, "The theory and design of chirp radars," Bell Syst. Tech. J. 34, 745-808 (1960).

Gibbs, J. W.

J. W. Gibbs, "Fourier series," Nature 59, 200 and 606 (1899).
[CrossRef]

Gustafsson, U.

Klauder, J. R.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, "The theory and design of chirp radars," Bell Syst. Tech. J. 34, 745-808 (1960).

Kröll, S.

Merkel, K. D.

Mossberg, T. W.

Ohlsson, N.

Price, A. C.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, "The theory and design of chirp radars," Bell Syst. Tech. J. 34, 745-808 (1960).

Reibel, R. R.

Sellin, P. B.

Strickland, N. M.

Tian, M.

T. Chang, M. Tian, and W. R. Babbitt, "Numerical modeling of optical coherent transient processes with complex configurations—>I. Angled beam geometry," J. Lumin. 107, 129-137 (2004).
[CrossRef]

T. Chang, M. Tian, Z. W. Barber, and W. R. Babbitt, "Numerical modeling of optical coherent transient processes with complex configurations—>II. Angled beams with arbitrary phase modulations," J. Lumin. 107, 138-145 (2004).
[CrossRef]

R. R. Reibel, Z. Barber, M. Tian, and W. R. Babbitt, "Temporally overlapped linear frequency-chirped pulse programming for true-time-delay applications," Opt. Lett. 27, 494-496 (2002).
[CrossRef]

Z. Barber, M. Tian, R. R. Reibel, and W. R. Babbitt, "Optical pulse shaping using optical coherent transients," Opt. Express 10, 1145-1150 (2002).
[PubMed]

M. Tian, R. R. Reibel, and W. R. Babbitt, "Demonstration of optical coherent transient true-time delay at 4 Gbits/s," Opt. Lett. 26, 1143-1145 (2001).
[CrossRef]

R. R. Reibel, T. Chang, M. Tian, and W. R. Babbitt, "Optical linear sideband chirp compression for microwave arbitrary waveform generation," in Proceedings of IEEE International Topical Meeting on Microwave Photonics (Institute of Electrical and Electronics Engineers, 2004), pp. 197-200.

Tsang, L.

M. Azadeh, C. S. Cornish, W. R. Babbitt, and L. Tsang, "Efficient photon echoes in optically thick media," Phys. Rev. A 57, 4662-4668 (1998).
[CrossRef]

C. S. Cornish, M. Azadeh, W. R. Babbitt, and L. Tsang, "Efficient waveform recall in absorbing media," in The International Society for Optical Engineering, P.A.Mitkas and Z.Hasan, eds., Proc. SPIE 3468, 174-181 (1998).

Wang, X.

Bell Syst. Tech. J. (1)

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, "The theory and design of chirp radars," Bell Syst. Tech. J. 34, 745-808 (1960).

J. Lumin. (2)

T. Chang, M. Tian, and W. R. Babbitt, "Numerical modeling of optical coherent transient processes with complex configurations—>I. Angled beam geometry," J. Lumin. 107, 129-137 (2004).
[CrossRef]

T. Chang, M. Tian, Z. W. Barber, and W. R. Babbitt, "Numerical modeling of optical coherent transient processes with complex configurations—>II. Angled beams with arbitrary phase modulations," J. Lumin. 107, 138-145 (2004).
[CrossRef]

Nature (1)

J. W. Gibbs, "Fourier series," Nature 59, 200 and 606 (1899).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. A (1)

M. Azadeh, C. S. Cornish, W. R. Babbitt, and L. Tsang, "Efficient photon echoes in optically thick media," Phys. Rev. A 57, 4662-4668 (1998).
[CrossRef]

Other (2)

C. S. Cornish, M. Azadeh, W. R. Babbitt, and L. Tsang, "Efficient waveform recall in absorbing media," in The International Society for Optical Engineering, P.A.Mitkas and Z.Hasan, eds., Proc. SPIE 3468, 174-181 (1998).

R. R. Reibel, T. Chang, M. Tian, and W. R. Babbitt, "Optical linear sideband chirp compression for microwave arbitrary waveform generation," in Proceedings of IEEE International Topical Meeting on Microwave Photonics (Institute of Electrical and Electronics Engineers, 2004), pp. 197-200.

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Figures (5)

Fig. 1
Fig. 1

(a) Envelope and power spectrum of a single sharp chirped rf programming pulse envelope centered at 125 MHz . Half-periods of cosine waves ( 50 ns each) are used to round the edges. (b) The envelope and power spectrum of a single smooth chirped rf programming pulse envelope of the same total bandwidth and duration, but with 400 ns cosine edges. Both chirps have a total bandwidth of B C = 15 MHz and duration (including edges) of τ C = 4 μ s .

Fig. 2
Fig. 2

Echo intensities simulated by the Fourier-transform approximation are shown for various time delays for both sharp envelope and smooth envelope programming pulse sequences. For sharp programming pulses, the highest level of fluctuation occurs at τ C 3 = 1.3 μ s . In both cases, τ C = 4 μ s , B C = 15 MHz , and B probe = 5 MHz .

Fig. 3
Fig. 3

Simulated values of echo fluctuation with spline interpolations for an optically thin medium. Fluctuation is smaller in sequences with smooth chirped programming pulse envelopes because of the smoother power spectrum of these pulses. The increase in fluctuation for large values of Ω C indicates that this fluctuation is related to saturation in the material. Here B C = 15 MHz , τ C = 4 μ s , B probe = 5 MHz , Ω probe = 0.55 MHz .

Fig. 4
Fig. 4

(a) Experimental values of echo efficiencies for various programmed time delays with sharp programming pulse envelopes. The peak efficiencies occur for Ω C = 0.60 MHz , although this comes at the cost of large fluctuations. (b) Experimental values of echo efficiencies programmed with smooth programming pulse envelopes. These echoes display greater efficiency and uniformity than those shown in (a). In both plots, B C = 15 MHz , τ C = 4 μ s , B probe = 5 MHz , and Ω probe = 0.55 MHz .

Fig. 5
Fig. 5

Experimental echo fluctuations, calculated from the data shown in Fig. 4. As expected from the simulations, smooth programming pulse envelopes generate echoes with slightly less fluctuation. Experimental noise explains the high values compared with simulation for small values of Ω C , where the echo intensity is low and close to the noise floor. Here B C = 15 MHz , τ C = 4 μ s , B probe = 5 MHz , and Ω probe = 0.55 MHz .

Equations (3)

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E echo ( ω ) E 1 * ( ω ) E 2 ( ω ) E 3 ( ω ) .
B prog B C Δ τ edge 2 κ .
fluctuation η rms η avg = i = 1 N ( η i η i line ) 2 η avg N ,

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