Abstract

We demonstrate high-resolution amplified pulse shaping using an acousto-optic modulator (AOM) at a center-wavelength of 795nm. The output pulses have energy of 200μJ/pulse and a transform-limited pulsewidth of 150fs. A spectral modulation of over 40 features is achieved in a single pulse. We characterize the pulses using the STRUT (Spectrally and Temporally Resolved Upconversion Technique). Using predistortion techniques, we demonstrate that the pulses can be shaped in amplitude and phase. We create a complex pulse shape with hyperbolic secant amplitude and hyperbolic tangent frequency sweep, which is useful for applications in adiabatic rapid passage experiments.

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  1. J. S. Melinger, S. R. Gandhi, W. S. Warren, "Adiabatic Population Transfer with Frequency Swept Laser Pulses," J. Chem. Phys. 101, 6439 (1994).
    [CrossRef]
  2. L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover Publications, 1987).
  3. D. Goswami, Control of Chemical Dynamics Using Arbitrarily Shaped Optical Pulses and Laser Enhanced NMR Spectroscopy, PhD. Thesis, (Princeton University, 1994).
  4. J. X. Tull, M. A. Dugan, C. W. Hillegas, W. S. Warren, "Robust Pulse Shaping Techniques for Quantum Molecular Control," Ultrafast Phenomena IX, G. A. Mourou and A. H. Zewail, eds.(Springer-Verlag, Berlin, 1995).
  5. J. X. Tull, M. A. Dugan, W. S. Warren, "High Resolution Acousto-Optic Shaping of Unamplified and Amplified Femtosecond Laser Pulses," J. Opt. Soc. B 14, 2348 (1997).
    [CrossRef]
  6. J. X. Tull, The Development of High Resolution Ultrafast Pulse Shaping Techniques, PhD. Thesis, (Princeton University, 1996).
  7. M. M. Wefers, K. A. Nelson, A. M. Weiner, "Multi-Dimensional Femtosecond Pulse Shaping," Ultrafast Phenomena X, P. F. Barbara, J. G. Fujimoto, W. H. Knox and W. Zinth, eds. (Springer-Verlag, Berlin, 1996).
    [CrossRef]
  8. A. M. Weiner, D. E. Learid, J. S. Patel, J. R. Wullert, "A Programmable Shaping Shaping of Femtosecond Optical Pulses by use of 128-element liquid-crystal phase modulator," J. Quantum Electron. 28, 908-920 (1992).
    [CrossRef]
  9. D. Strickland, G. Mourou, "Compression of Amplified Chirped Optical Pulses," Opt. Commun, 58, 219 (1985).
    [CrossRef]
  10. J-K. Rhee T. S. Sosnowski, A.-C. Tien, and T. B. Norris, "Real- Time Dispersion Analyzer of Femtosecond Laser Pulses with Use of a Spectrally and Temporally Resolved Upconversion Technique," J. Opt. Soc. Am. B 13, 1780-1785.
  11. J-K. Rhee, T. S. Sosnowski, T. B. Norris, J. A. Arns, W. S. Colburn, "Chirped-Pulse Amplification of 85-fs Pulses at 250 KHz with 3rd-Order Dispersion Compensation by use of Holographic Transmission Gratings," Opt. Lett. 19, 1550-1552 (1994).
    [CrossRef] [PubMed]
  12. J. P. Foing, J. P. Likforman, M. Joffre, A. Migus, "Femtosecond Pulse Phase Measurement by Spectrally Resolved Up-Conversion- Application to Continuum Compression," J. Quantum Electron. 28, 2285-2290 (1992).
    [CrossRef]
  13. Coherent Lasers, http://www.cohr.com, Santa Clara, Ca.
  14. Clark-MXR Inc., http://www.clark-mxr.com, Dexter, MI.
  15. Brimrose Corporation of America, http://www.brimrose.com, Baltimore, MD.
  16. LeCroy Corporation, http://www.lecroy.com, Chestnut Ridge, NY.
  17. M. R. Fetterman, Demonstration of an Amplified Pulse Shaping System, and its Applications to Adiabatic Rapid Passage, PhD. Thesis, (Princeton University, 1999).
  18. W. Yang, F. Huang, M. R. Fetterman, D. Goswami, W. S. Warren, "Demonstration of Amplitude Feedback in an Ultrafast Pulse Shaping System at 1.55mm," Opt. Lett. (1999) (to be published).
  19. W. Yang, J. Davis, D. Goswami, M. R. Fetterman, W. S. Warren, "Optical wavelength domain code-division multiplexing using AOM-base ultrafast optical pulse shaping," All-Optical Networking: Architecture, Control, and Management Issues, SPIE Vol. 353 (1998).
  20. M. R. Fetterman, D. Goswami, D. Keusters, J.-K Rhee, W. S. Warren, "Generation of Amplified Shaped Pulses for Highly Adiabatic Excitation," Ultrafast Phenomena IX, G. A. Mourou and A. H. Zewail, eds.(Springer-Verlag, Berlin, 1995).

Other (20)

J. S. Melinger, S. R. Gandhi, W. S. Warren, "Adiabatic Population Transfer with Frequency Swept Laser Pulses," J. Chem. Phys. 101, 6439 (1994).
[CrossRef]

L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover Publications, 1987).

D. Goswami, Control of Chemical Dynamics Using Arbitrarily Shaped Optical Pulses and Laser Enhanced NMR Spectroscopy, PhD. Thesis, (Princeton University, 1994).

J. X. Tull, M. A. Dugan, C. W. Hillegas, W. S. Warren, "Robust Pulse Shaping Techniques for Quantum Molecular Control," Ultrafast Phenomena IX, G. A. Mourou and A. H. Zewail, eds.(Springer-Verlag, Berlin, 1995).

J. X. Tull, M. A. Dugan, W. S. Warren, "High Resolution Acousto-Optic Shaping of Unamplified and Amplified Femtosecond Laser Pulses," J. Opt. Soc. B 14, 2348 (1997).
[CrossRef]

J. X. Tull, The Development of High Resolution Ultrafast Pulse Shaping Techniques, PhD. Thesis, (Princeton University, 1996).

M. M. Wefers, K. A. Nelson, A. M. Weiner, "Multi-Dimensional Femtosecond Pulse Shaping," Ultrafast Phenomena X, P. F. Barbara, J. G. Fujimoto, W. H. Knox and W. Zinth, eds. (Springer-Verlag, Berlin, 1996).
[CrossRef]

A. M. Weiner, D. E. Learid, J. S. Patel, J. R. Wullert, "A Programmable Shaping Shaping of Femtosecond Optical Pulses by use of 128-element liquid-crystal phase modulator," J. Quantum Electron. 28, 908-920 (1992).
[CrossRef]

D. Strickland, G. Mourou, "Compression of Amplified Chirped Optical Pulses," Opt. Commun, 58, 219 (1985).
[CrossRef]

J-K. Rhee T. S. Sosnowski, A.-C. Tien, and T. B. Norris, "Real- Time Dispersion Analyzer of Femtosecond Laser Pulses with Use of a Spectrally and Temporally Resolved Upconversion Technique," J. Opt. Soc. Am. B 13, 1780-1785.

J-K. Rhee, T. S. Sosnowski, T. B. Norris, J. A. Arns, W. S. Colburn, "Chirped-Pulse Amplification of 85-fs Pulses at 250 KHz with 3rd-Order Dispersion Compensation by use of Holographic Transmission Gratings," Opt. Lett. 19, 1550-1552 (1994).
[CrossRef] [PubMed]

J. P. Foing, J. P. Likforman, M. Joffre, A. Migus, "Femtosecond Pulse Phase Measurement by Spectrally Resolved Up-Conversion- Application to Continuum Compression," J. Quantum Electron. 28, 2285-2290 (1992).
[CrossRef]

Coherent Lasers, http://www.cohr.com, Santa Clara, Ca.

Clark-MXR Inc., http://www.clark-mxr.com, Dexter, MI.

Brimrose Corporation of America, http://www.brimrose.com, Baltimore, MD.

LeCroy Corporation, http://www.lecroy.com, Chestnut Ridge, NY.

M. R. Fetterman, Demonstration of an Amplified Pulse Shaping System, and its Applications to Adiabatic Rapid Passage, PhD. Thesis, (Princeton University, 1999).

W. Yang, F. Huang, M. R. Fetterman, D. Goswami, W. S. Warren, "Demonstration of Amplitude Feedback in an Ultrafast Pulse Shaping System at 1.55mm," Opt. Lett. (1999) (to be published).

W. Yang, J. Davis, D. Goswami, M. R. Fetterman, W. S. Warren, "Optical wavelength domain code-division multiplexing using AOM-base ultrafast optical pulse shaping," All-Optical Networking: Architecture, Control, and Management Issues, SPIE Vol. 353 (1998).

M. R. Fetterman, D. Goswami, D. Keusters, J.-K Rhee, W. S. Warren, "Generation of Amplified Shaped Pulses for Highly Adiabatic Excitation," Ultrafast Phenomena IX, G. A. Mourou and A. H. Zewail, eds.(Springer-Verlag, Berlin, 1995).

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the AOM pulse shaping system. The femtosecond Gaussian pulse (plotted as a function of time in the box below A) is the input pulse on the left side of the figure. The grating B spectrally spreads the pulse. The acousto-optic modulator C is in the center of the system. The RF-wave D propagates through the AOM, creates a spatial mask inside the crystal and shapes the optical pulse. In this schematic, we have modeled the input optical pulse as consisting of four different wavelengths, blue, yellow, orange, and red, which would represent a 4-bit system. In principle, the AOM is capable of shaping 1000 bits. The undiffracted beam E passes out of the system. The white parts of the diffracted spectrum are left undiffracted by the AOM. The spectrum recombines in grating F. The output (G and the box below the G) shows the shaped output pulse as a function of wavelength. As the rf wave propagates, different shapes are created. The pulse picker G picks the pulse at the correct time out of the pulse train. Here the pulse picker is shown separately selecting a particular pulse H, but in the experiment, the pulse picker is located inside the regenerative amplifier I. [Media 1]

Fig. 2.
Fig. 2.

Calibration curves for AOM pulse shaper. A. Each line in this figure represents a different optical spectrum. Application of a short RF pulse with a different delay time into the AOM created each spectrum. The different delay time corresponds to a different spatial position on the AOM and therefore a different spectral position. By using this figure, we can calibrate the pulse-shaper response-function with respect to amplitude and time. B. The data from A is viewed as a contour plot. The solid red line fits the data so that we can calibrate the RF time with respect to optical wavelength.

Fig. 3.
Fig. 3.

High Resolution Pulse Shaping. A. The RF signal used to modulate the spectrum. (top) The bit stream, which is given as Eq.(4) in the text. The numbers show the imposed bit pattern, a 43 bit sequence. The lower figure shows that the actual RF signal was the product of this bit stream with a sinusoidal wave. B. The spectrum resulting from the modulated RF signal of A. C. This shows the data of B (blue), with a theoretical fit (magenta). The fit shows that we have recovered the 43 bits imposed upon the spectrum. The numbers at the top of this figure correspond to those in A.

Fig.4
Fig.4

A. The RF pulses that are used to create an optical pulse with cubic phase, g(tRF)=exp[i(βt)3)]. The blue curve is the real part and the red curve is the imaginary part. B. STRUT image of a pulse with cubic phase. The x-axis shows wavelength and the y-axis shows time. C. The red curve shows the recovered phase derivative dϕ/dω from the STRUT image. The blue curve is the theoretically predicted result, using the data from Fig.2 and the RF signals of Fig.4A as input parameters.

Fig.5.
Fig.5.

Predistortion. A. This figure has two x-axis: the lower wavelength x-axis is for the green curve and the upper RF time axis is for the blue and magenta curves. The original gaussian pulse (green color, optical spectrum) which has a somewhat distorted shape is shown. The blue square pulse in Fig.5A is a RF pulse. The magenta curve is a RF wave, calculated from Eq. (2), that will create an optical square pulse. B. These are all optical spectra. Blue curve: the clipped wave, generated by sending in the blue rf pulse of Fig.5A Magenta curve: square pulse that is actually wider than the natural response of the system. C. Blue curve: another square wave, which is square to within 90%. Red curve shows modulation of this square wave.

Fig.6
Fig.6

Results for hyperbolic secant amplitude with hyperbolic tangent frequency sweep pulse A. RF signal used to create sec+ pulse. B. STRUT trace (experimental). C. STRUT trace (theoretical).

Fig.7
Fig.7

Analysis of STRUT data of Fig.6B. A. Derivative of the phase, both theoretical and experiemental. The theoretical intensity is also shown. B. Intensity and phase, both theoretical and experimental.

Equations (7)

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E out ( ω ) = M ( ω ) E in ( ω )
M 1 ( ω ) = D ( ω ) E in ( ω ) 1
M 2 ( ω ) = D ( ω ) E in ( ω ) 1
M ( ω ) = f ( t RF = αω )
Ψ = [ 0110 0111 1101 1100 1110 1011 1000 1111 0011 1100 111 ]
E out ( ω ) = exp ( i [ αβ ( ω ω 0 ) ] 3 ) E in ( ω )
E ( t ) = sech ( ρ t ) ( 1 + μi )

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