Abstract

We discuss an approach for the practical implementation of photonic arbitrary waveform generation of microwave signals. We describe and demonstrate an approach using spatial-spectral (S2) holography in rare earth ion doped crystals that has the potential to achieve extremely wide bandwidths (>40GHz) using conventional electro-optic phase modulators and low bandwidth (<100MHz) control electronics. We provide analysis of this approach, show simulations, and perform experimental demonstrations of the technique. We show a pulse compression factor of 15,000 and demonstrate the largest effective bandwidth of 3.8GHz to date for pulse compression using S2 holography. We also show control and manipulation of up to 30 independent compressed pulses for the creation of arbitrary waveforms.

© 2007 Optical Society of America

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References

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  1. Agilent, "N6030A Arbitrary Waveform Generator," http://cp.literature.agilent.com/litweb/pdf/5989-1457EN.pdf.
  2. Tektronix, "Arbitrary Waveform Generator 7102," http://www.tek.com/products/signallowbarsources/awg7000/index.html.
  3. W. Cheng, R. Stevens, F. Rupp, C. Engels, W. Ali, M. Choi, D. Devendorf, S. Ding, L. Linder, K. Liu, and T. Tat, "A 3b 40GS/s ADC-DAC in 0.12 mu m SiGe," in Proceedings of IEEE International Solid State Circuits Conference (IEEE, 2004), pp. 262-263.
  4. J. Chou, Y. Han, and B. Jalali, "Adaptive RF-photonic arbitrary waveform generator," IEEE Photon. Technol. Lett. 15, 581-583 (2003).
    [CrossRef]
  5. J. D. McKinney, I. S. Lin, and A. M. Weiner, "Ultrabroadband arbitrary electromagnetic waveform synthesis," Opt. Photonics News 17, 24-29 (2006).
    [CrossRef]
  6. G. H. Lee and A. M. Weiner, "Programmable optical pulse burst manipulation using a virtually imaged phased array (VIPA) based Fourier transform pulse shaper," J. Lightwave Technol. 23, 3916-3923 (2005).
    [CrossRef]
  7. T. Yilmaz, C. M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, "Toward a photonic arbitrary waveform generator using a modelocked external cavity semiconductor laser," IEEE Photon. Technol. Lett. 14, 1608-1610 (2002).
    [CrossRef]
  8. H. Kim, A. B. Kozyrev, S. J. Ho, and D. W. van der Weide, "Fourier synthesizer using left-handed transmission lines," in Proceedings of IEEE International Microwave Symposium (IEEE, 2005) pp. 4-8.
  9. Y. Han, O. Boyraz, and B. Jalali, "Tera-sample per second real-time waveform digitizer," Appl. Phys. Lett. 87, 241116 (2005).
    [CrossRef]
  10. X. Ribeyre, C. Rouyer, F. Raoult, D. Husson, C. Sauteret, and A. Migus, "All-optical programmable shaping of narrow-band nanosecond pulses with picosecond accuracy by use of adapted chirps and quadratic nonlinearities," Opt. Lett. 26, 1173-1175 (2001).
    [CrossRef]
  11. Z. Barber, M. Tian, R. Reibel, and W. R. Babbitt, "Optical pulse shaping using optical coherent transients," Opt. Express 10, 1145-1147 (2002).
    [PubMed]
  12. R. Reibel, T. Chang, M. Tian, and W. R. Babbitt, "Optical linear sideband chirp compression for microwave arbitrary waveform generation," in IEEE Microwave Photonics Conference Proceedings (IEEE, 2004) pp. 197-200.
  13. R. Reibel, Z. Barber, M. Tian, and W. R. Babbitt, "High bandwidth spectral gratings programmed with linear frequency chirps," J. Lumin. 98, 355-365 (2002).
    [CrossRef]
  14. Z. W. Barber, J. Law, M. Tian, and W. R. Babbitt, "Optical coherent transient high bandwidth arbitrary waveform generation and pulse shaping," presented at the 8th International Meeting on Hole Burning, Single Molecule, and Related Spectroscopies: Science and Applications (HBSM'03)MT, USA, 27-31July 2003.
  15. V. Crozatier, G. Gorju, J.-L. Le Gouët, F. Bretenaker, and I. Lorgeré, "Wideband and high-resolution coherent optical transients with a frequency-agile laser oscillator," Opt. Lett. 31, 3264-3266 (2006).
    [CrossRef] [PubMed]
  16. See, e.g., EOSPACE product line (www.eospace.com).
  17. R. Reibel, Z. Barber, M. Tian, and W. R. Babbitt, "Temporally overlapped linear frequency chirped programming for true-time delay applications," Opt. Lett. 27, 494-496 (2002).
    [CrossRef]
  18. E. C. Farnett and G. H. Stevens, "Pulse compression radar," in Radar Handbook, 2nd ed., M.Skolnik, ed. (McGraw-Hill, 1990) pp. 10.11-10.13.
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  20. Y. S. Bai and T. W. Mossberg, "Experimental studies of photon-echo pulse compression," Opt. Lett. 11, 30-32 (1986).
    [CrossRef] [PubMed]
  21. L. Menager, J. L. Le Gouet, and I. Lorgere, "Time-to-frequency Fourier transformation with photon echoes," Opt. Lett. 26, 1397-1399 (2001).
    [CrossRef]
  22. L. Ménager, I. Lorgeré, J.-L. Le Gouët, R. Mohan Krishna, and S. Kröll, "Time-domain Fresnel-to-Fraunhofer diffraction with photon echoes," Opt. Lett. 24, 927-929 (1999).
    [CrossRef]
  23. V. Crozatier, V. Lavielle, F. Bretenaker, J.-L. Le Gouët, and I. Lorgeré, "High resolution radio frequency spectral analysis with photon echo chirp transfor in an Er:YSO crystal," IEEE J. Quantum Electron. 40, 1450-1457 (2004).
    [CrossRef]
  24. K. D. Merkel and W. R. Babbitt, "Optical coherent transient continuously programmed continuous processor," Opt. Lett. 24, 172-174 (1999).
    [CrossRef]
  25. T. W. Mossberg, "Time-domain frequency-selective optical storage," Opt. Lett. 7, 77-79 (1982).
    [CrossRef] [PubMed]
  26. X. Wang, M. Afzelius, N. Ohlsson, U. Gustafsson, and S. Kroll, "Coherent transient data-rate conversion and data transformation," Opt. Lett. 25, 945-947 (2000).
    [CrossRef]
  27. L. Levin, "Mode-hop-free electro-optically tuned diode laser," Opt. Lett. 27, 237-239 (2002).
    [CrossRef]
  28. K. S. Repasky, J. D. Williams, J. L. Carlsten, E. J. Noonan, and G. W. Switzer, "Tunable external-cavity diode laser based on integrated waveguide structures," Opt. Eng. (Bellingham) 42, 2229-2234 (2003).
    [CrossRef]
  29. V. Lavielle, I. Lorgere, J.-L. Gouet, S. Tonda, and D. Dolfi, "Wideband versatile radio-frequency spectrum analyzer," Opt. Lett. 28, 384-386 (2003).
    [CrossRef] [PubMed]
  30. C. Greiner, B. Boggs, T. Wang, and T. W. Mossberg, "Laser frequency stabilization by means of optical self-heterodyne beat-frequency control," Opt. Lett. 23, 1280-1282 (1998).
    [CrossRef]
  31. V. Crozatier, G. Gorju, F. Bretenaker, J.-L. Le Gouët, I. Lorgeré, C. Gagnol, and E. Ducloux, "Phase locking of a frequency agile laser," Appl. Phys. Lett. 89, 261115 (2006).
    [CrossRef]
  32. G. Gorju, A. Jucha, A. Jain, V. Crozatier, I. Lorgeré, J.-L. Le Gouët, F. Bretenaker, and M. Colice, "Active stabilization of a rapidly chirped laser by an optoelectronic digital servo-loop control," Opt. Lett. 32, 484-486 (2007).
    [CrossRef] [PubMed]
  33. P. B. Sellin, N. M. Strickland, T. Böttger, J. L. Carlsten, and R. L. Cone, "Laser stabilization at 1536nm using regenerative spectral hole burning," Phys. Rev. B 63, 155111 (2001).
    [CrossRef]
  34. R. Willyard, Airborne Radar for Measuring Snow Thickness over Sea Ice (U. of Kansas, 2004).
  35. R. Reibel, Z. Barber, M. Tian, W. R. Babbitt, Z. Cole, and K. D. Merkel, "Amplification of high bandwidth phase modulated signals at 793nm," J. Opt. Soc. Am. B 19, 2315-2322 (2002).
    [CrossRef]
  36. 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]
  37. T. K. Noguchi, O. Mitomi, and H. Miyazawa, "Millimeter-wave Ti:LiNbO optical modulators," J. Lightwave Technol. 16, 615-619 (1998).
    [CrossRef]
  38. O. V. Kolokoltsev, C. S. Pérez, and R. A. Correa, "Phase-reversal broad-band traveling-wave LiNbO3 electro-optic modulator optimized for time-domain applications by a genetic algorithm," IEEE J. Quantum Electron. 8, 1258-1264 (2002).
    [CrossRef]

2007

2006

V. Crozatier, G. Gorju, F. Bretenaker, J.-L. Le Gouët, I. Lorgeré, C. Gagnol, and E. Ducloux, "Phase locking of a frequency agile laser," Appl. Phys. Lett. 89, 261115 (2006).
[CrossRef]

J. D. McKinney, I. S. Lin, and A. M. Weiner, "Ultrabroadband arbitrary electromagnetic waveform synthesis," Opt. Photonics News 17, 24-29 (2006).
[CrossRef]

V. Crozatier, G. Gorju, J.-L. Le Gouët, F. Bretenaker, and I. Lorgeré, "Wideband and high-resolution coherent optical transients with a frequency-agile laser oscillator," Opt. Lett. 31, 3264-3266 (2006).
[CrossRef] [PubMed]

2005

2004

V. Crozatier, V. Lavielle, F. Bretenaker, J.-L. Le Gouët, and I. Lorgeré, "High resolution radio frequency spectral analysis with photon echo chirp transfor in an Er:YSO crystal," IEEE J. Quantum Electron. 40, 1450-1457 (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]

2003

K. S. Repasky, J. D. Williams, J. L. Carlsten, E. J. Noonan, and G. W. Switzer, "Tunable external-cavity diode laser based on integrated waveguide structures," Opt. Eng. (Bellingham) 42, 2229-2234 (2003).
[CrossRef]

V. Lavielle, I. Lorgere, J.-L. Gouet, S. Tonda, and D. Dolfi, "Wideband versatile radio-frequency spectrum analyzer," Opt. Lett. 28, 384-386 (2003).
[CrossRef] [PubMed]

J. Chou, Y. Han, and B. Jalali, "Adaptive RF-photonic arbitrary waveform generator," IEEE Photon. Technol. Lett. 15, 581-583 (2003).
[CrossRef]

2002

Z. Barber, M. Tian, R. Reibel, and W. R. Babbitt, "Optical pulse shaping using optical coherent transients," Opt. Express 10, 1145-1147 (2002).
[PubMed]

R. Reibel, Z. Barber, M. Tian, and W. R. Babbitt, "High bandwidth spectral gratings programmed with linear frequency chirps," J. Lumin. 98, 355-365 (2002).
[CrossRef]

T. Yilmaz, C. M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, "Toward a photonic arbitrary waveform generator using a modelocked external cavity semiconductor laser," IEEE Photon. Technol. Lett. 14, 1608-1610 (2002).
[CrossRef]

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

L. Levin, "Mode-hop-free electro-optically tuned diode laser," Opt. Lett. 27, 237-239 (2002).
[CrossRef]

R. Reibel, Z. Barber, M. Tian, W. R. Babbitt, Z. Cole, and K. D. Merkel, "Amplification of high bandwidth phase modulated signals at 793nm," J. Opt. Soc. Am. B 19, 2315-2322 (2002).
[CrossRef]

O. V. Kolokoltsev, C. S. Pérez, and R. A. Correa, "Phase-reversal broad-band traveling-wave LiNbO3 electro-optic modulator optimized for time-domain applications by a genetic algorithm," IEEE J. Quantum Electron. 8, 1258-1264 (2002).
[CrossRef]

2001

2000

1999

1998

1995

R. L. Cone, R. W. Equall, Y. Sun, R. M. Macfarlane, and R. Hutcheson, "Ultraslow dephasing and dephasing mechanisms in rare earth materials for optical data storage," Laser Phys. 5, 573 (1995).

1986

1982

Appl. Phys. Lett.

Y. Han, O. Boyraz, and B. Jalali, "Tera-sample per second real-time waveform digitizer," Appl. Phys. Lett. 87, 241116 (2005).
[CrossRef]

V. Crozatier, G. Gorju, F. Bretenaker, J.-L. Le Gouët, I. Lorgeré, C. Gagnol, and E. Ducloux, "Phase locking of a frequency agile laser," Appl. Phys. Lett. 89, 261115 (2006).
[CrossRef]

IEEE J. Quantum Electron.

V. Crozatier, V. Lavielle, F. Bretenaker, J.-L. Le Gouët, and I. Lorgeré, "High resolution radio frequency spectral analysis with photon echo chirp transfor in an Er:YSO crystal," IEEE J. Quantum Electron. 40, 1450-1457 (2004).
[CrossRef]

O. V. Kolokoltsev, C. S. Pérez, and R. A. Correa, "Phase-reversal broad-band traveling-wave LiNbO3 electro-optic modulator optimized for time-domain applications by a genetic algorithm," IEEE J. Quantum Electron. 8, 1258-1264 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

T. Yilmaz, C. M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, "Toward a photonic arbitrary waveform generator using a modelocked external cavity semiconductor laser," IEEE Photon. Technol. Lett. 14, 1608-1610 (2002).
[CrossRef]

J. Chou, Y. Han, and B. Jalali, "Adaptive RF-photonic arbitrary waveform generator," IEEE Photon. Technol. Lett. 15, 581-583 (2003).
[CrossRef]

J. Lightwave Technol.

J. Lumin.

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. Reibel, Z. Barber, M. Tian, and W. R. Babbitt, "High bandwidth spectral gratings programmed with linear frequency chirps," J. Lumin. 98, 355-365 (2002).
[CrossRef]

J. Opt. Soc. Am. B

Laser Phys.

R. L. Cone, R. W. Equall, Y. Sun, R. M. Macfarlane, and R. Hutcheson, "Ultraslow dephasing and dephasing mechanisms in rare earth materials for optical data storage," Laser Phys. 5, 573 (1995).

Opt. Eng. (Bellingham)

K. S. Repasky, J. D. Williams, J. L. Carlsten, E. J. Noonan, and G. W. Switzer, "Tunable external-cavity diode laser based on integrated waveguide structures," Opt. Eng. (Bellingham) 42, 2229-2234 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

V. Crozatier, G. Gorju, J.-L. Le Gouët, F. Bretenaker, and I. Lorgeré, "Wideband and high-resolution coherent optical transients with a frequency-agile laser oscillator," Opt. Lett. 31, 3264-3266 (2006).
[CrossRef] [PubMed]

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

X. Ribeyre, C. Rouyer, F. Raoult, D. Husson, C. Sauteret, and A. Migus, "All-optical programmable shaping of narrow-band nanosecond pulses with picosecond accuracy by use of adapted chirps and quadratic nonlinearities," Opt. Lett. 26, 1173-1175 (2001).
[CrossRef]

V. Lavielle, I. Lorgere, J.-L. Gouet, S. Tonda, and D. Dolfi, "Wideband versatile radio-frequency spectrum analyzer," Opt. Lett. 28, 384-386 (2003).
[CrossRef] [PubMed]

C. Greiner, B. Boggs, T. Wang, and T. W. Mossberg, "Laser frequency stabilization by means of optical self-heterodyne beat-frequency control," Opt. Lett. 23, 1280-1282 (1998).
[CrossRef]

G. Gorju, A. Jucha, A. Jain, V. Crozatier, I. Lorgeré, J.-L. Le Gouët, F. Bretenaker, and M. Colice, "Active stabilization of a rapidly chirped laser by an optoelectronic digital servo-loop control," Opt. Lett. 32, 484-486 (2007).
[CrossRef] [PubMed]

Y. S. Bai and T. W. Mossberg, "Experimental studies of photon-echo pulse compression," Opt. Lett. 11, 30-32 (1986).
[CrossRef] [PubMed]

L. Menager, J. L. Le Gouet, and I. Lorgere, "Time-to-frequency Fourier transformation with photon echoes," Opt. Lett. 26, 1397-1399 (2001).
[CrossRef]

L. Ménager, I. Lorgeré, J.-L. Le Gouët, R. Mohan Krishna, and S. Kröll, "Time-domain Fresnel-to-Fraunhofer diffraction with photon echoes," Opt. Lett. 24, 927-929 (1999).
[CrossRef]

K. D. Merkel and W. R. Babbitt, "Optical coherent transient continuously programmed continuous processor," Opt. Lett. 24, 172-174 (1999).
[CrossRef]

T. W. Mossberg, "Time-domain frequency-selective optical storage," Opt. Lett. 7, 77-79 (1982).
[CrossRef] [PubMed]

X. Wang, M. Afzelius, N. Ohlsson, U. Gustafsson, and S. Kroll, "Coherent transient data-rate conversion and data transformation," Opt. Lett. 25, 945-947 (2000).
[CrossRef]

L. Levin, "Mode-hop-free electro-optically tuned diode laser," Opt. Lett. 27, 237-239 (2002).
[CrossRef]

Opt. Photonics News

J. D. McKinney, I. S. Lin, and A. M. Weiner, "Ultrabroadband arbitrary electromagnetic waveform synthesis," Opt. Photonics News 17, 24-29 (2006).
[CrossRef]

Phys. Rev. B

P. B. Sellin, N. M. Strickland, T. Böttger, J. L. Carlsten, and R. L. Cone, "Laser stabilization at 1536nm using regenerative spectral hole burning," Phys. Rev. B 63, 155111 (2001).
[CrossRef]

Other

R. Willyard, Airborne Radar for Measuring Snow Thickness over Sea Ice (U. of Kansas, 2004).

Agilent, "N6030A Arbitrary Waveform Generator," http://cp.literature.agilent.com/litweb/pdf/5989-1457EN.pdf.

Tektronix, "Arbitrary Waveform Generator 7102," http://www.tek.com/products/signallowbarsources/awg7000/index.html.

W. Cheng, R. Stevens, F. Rupp, C. Engels, W. Ali, M. Choi, D. Devendorf, S. Ding, L. Linder, K. Liu, and T. Tat, "A 3b 40GS/s ADC-DAC in 0.12 mu m SiGe," in Proceedings of IEEE International Solid State Circuits Conference (IEEE, 2004), pp. 262-263.

H. Kim, A. B. Kozyrev, S. J. Ho, and D. W. van der Weide, "Fourier synthesizer using left-handed transmission lines," in Proceedings of IEEE International Microwave Symposium (IEEE, 2005) pp. 4-8.

E. C. Farnett and G. H. Stevens, "Pulse compression radar," in Radar Handbook, 2nd ed., M.Skolnik, ed. (McGraw-Hill, 1990) pp. 10.11-10.13.

See, e.g., EOSPACE product line (www.eospace.com).

R. Reibel, T. Chang, M. Tian, and W. R. Babbitt, "Optical linear sideband chirp compression for microwave arbitrary waveform generation," in IEEE Microwave Photonics Conference Proceedings (IEEE, 2004) pp. 197-200.

Z. W. Barber, J. Law, M. Tian, and W. R. Babbitt, "Optical coherent transient high bandwidth arbitrary waveform generation and pulse shaping," presented at the 8th International Meeting on Hole Burning, Single Molecule, and Related Spectroscopies: Science and Applications (HBSM'03)MT, USA, 27-31July 2003.

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Figures (6)

Fig. 1
Fig. 1

Timing diagram for a SSB implementation of S2-PAWG showing two different probing schemes. The programming pulse is two TOLFCs, and the probe pulses are linear frequency chirps (LFCs).

Fig. 2
Fig. 2

Timing diagram for a DSB implementation of S2-PAWG showing two different probing schemes. The programming pulse is two temporally overlapped linear sideband chirps (TOLSCs), and the probe pulses are one or more linear sideband chirps (LSCs). The arbitrary waveform is comprised of the compressed pulses labeled a through f.

Fig. 3
Fig. 3

Schematic of the experiment setup used in the DSB S2-PAWG experiments. Definitions of the acronyms are as follows: beam splitter (B.S.), electro-optic phase modulator (EOPM), pulse-pattern generator (PPG), injection-locked diode amplifier (ILA), low-bandwidth electronic arbitrary waveform generator (E-AWG), acousto-optic modulator (AOM), New Focus 1580 photodiode (NF 1580), and avalanche photodiode (APD).

Fig. 4
Fig. 4

(a) Results from a Maxwell–Bloch simulation for two TOCPs created with the DSB approach (solid curve) and a single compressed pulse created with the SSB approach (dashed curve). The beat modulation due to the TOCP’s offset in frequency is well pronounced. (b) Experimental results showing the TOCPs that were created by the DSB approach. (c) Simulation of DSB S2-PAWG that shows the probe pulses and nine compressed pulses that are approximating a half-period of a sine wave. Note that in this simulation the probe chirp’s frequency offsets were created with an EOPM causing a beat frequency on each compressed pulse.

Fig. 5
Fig. 5

(a) Experimental results that show a typical 4 μ s probe pulse and the corresponding compressed pulse created by the S2 material. (b) Experimental result showing a single compressed pulse with a 260 ps FWHM and an effective bandwidth of 3.8 GHz , which was compressed from a 4 μ s probe pulse, giving a compression factor of 15,000 .

Fig. 6
Fig. 6

Experimental single shot demonstrations of arbitrary waveform generation. (a) Shows a single period of a raised sine wave that was synthesized by 15 separate compressed pulses, each 0.8 ns in duration and spaced by 3.2 ns . (b) Shows a raised sine wave synthesized with thirty 0.8 ns compressed pulses spaced at 1.6 ns . (c) Shows a single period of a square wave that was built from 15 separate compressed pulses, each 0.8 ns in duration and spaced by 3.2 ns . (d) Shows three periods of a square wave that were created with five compressed pulses per period. The duration of these pulses was 0.8 ns and they were spaced by 1.6 ns in the on part of the square wave.

Equations (4)

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

τ d ( f ) = ( f f S 1 ) ( 1 α 2 1 α 1 ) + f 0 α 1 .
α 3 = ( α 1 α 2 ) ( α 2 α 1 ) .
E c p ( t ) 2 π ( f S 1 + f 0 ) 2 π ( f S 1 + f 0 + B ) E 1 * ( ω ) E 2 ( ω ) E 3 ( ω ) exp ( i ω t ) d ω ,
I c p ( t ) sinc 2 ( B t π ) .

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