Abstract

Fourier synthesis pulse shaping methods allowing generation of programmable, user defined femtosecond optical waveforms have been widely applied in ultrafast optical science and technology. In the electrical domain, arbitrary waveform generation is well established at frequencies below approximately 1 GHz, but is difficult at higher frequencies due to limitations in digital-to-analog converter technology. In this paper we demonstrate a method for electrical waveform synthesis at substantially higher frequencies (approximately 20 GHz electrical bandwidth) by combining Fourier optical pulse shaping (extended to hyperfine frequency resolution) and heterodyne optical to electrical conversion. Our scheme relies on coherent manipulation of fields and phases at all stages, both for processing in the optical domain and for conversion from the optical to the electrical domain. We illustrate this technique through a number of examples, including programmable retardation or advancement of short electrical pulses in time over a range exceeding ten pulse durations. Such optically implemented, coherent Fourier transform electrical pulse shaping should open new prospects in ultrawideband electromagnetics.

© 2006 Optical Society of America

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References

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  1. A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
    [CrossRef]
  2. J. D. McKinney, D. E. Leaird, A. M. Weiner, "Millimeter-wave arbitrary waveform generation with a direct space-to-time pulse shaper," Opt. Lett. 27, 1345-1347 (2002).
    [CrossRef]
  3. I. S. Lin, J. D. McKinney, and A. M. Weiner, "Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication," IEEE Microwave Wireless Component Lett. 15, 226-228 (2005).
    [CrossRef]
  4. J. Chou, Y. Han, and B. Jalai, "Adaptive rf-photonic arbitrary waveform generator," IEEE Photon. Technol. Lett.,  15, 581-583 (2003).
    [CrossRef]
  5. Y. Liu, S. Park, and A. M. Weiner, "Enhancement of narrow-band terahertz radiation from photoconducting antennas by optical pulse shaping," Opt. Lett. 21, 1762 (1996).
    [CrossRef] [PubMed]
  6. J. H. Reed, Ed., An Introduction to Ultra Wideband Communication Systems (Prentice Hall, 2005).
  7. R. J. Fontana, "Recent system applications of short-pulse ultra-wideband (UWB) technology," invited, IEEE Trans. Microwave Theory Technol. 52, 2087-2104 (2004).
    [CrossRef]
  8. H. L. Bertoni, L. Carin, L. B. Felsen, Ultra-wideband, short-pulse electromagnetics (New York : Plenum Press, 1993).
    [CrossRef]
  9. A. Vilcot, B. Cabon, and J. Chazelas, Microwave Photonics: from components to applications and systems (Boston: Kluwer Academic, 2003).
  10. J. Capmany, B. Ortega, D. Pastor and S. Sales, "Discrete-time optical processing of microwave signals," J. Lightwave Technol. 23, 702-723 (2005).
    [CrossRef]
  11. S. Xiao and A. M. Weiner, "Coherent photonic processing of microwave signals using spatial light modulator: programmable amplitude filters," J. Lightwave Technol.Special Issue of Optical Signal Processing (to be published).
  12. M. Shirasaki, "Large angular dispersion by a virtually imaged phased array and its application to a wavelength demultiplexer,"Opt. Lett. 21, 366-368 (1996).
    [CrossRef] [PubMed]
  13. S. Xiao and A. M. Weiner, "An eight-channel hyperfine wavelength demultiplexer using a virtually-imaged phased-array (VIPA)," IEEE Photon. Technol. Lett. 17, 372-374 (2005).
    [CrossRef]
  14. J. P. Heritage, A. M. Weiner and R. N. Thurston, "Picosecond pulse shaping by spectral phase and amplitude manipulation," Opt. Lett. 10, 609-611 (1985)
    [CrossRef] [PubMed]
  15. W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernsterin, "The first demonstration of an optically steered microwave phased array antenna using true-time-delay" J. Lightwave Technol.,  9, 1124-1131 (1991).
    [CrossRef]
  16. B. Ortega, J. L. Cruz, J. Capmany, M. V. Andres, and D. Pastor, "Variable delay line for phased-antenna based on a chirped fiber grating," IEEE Trans. Microwave Theory Technol.,  48, 1352-1360 (2000).
    [CrossRef]
  17. J. Yang, S. Tjin and N. Ngao, "All chirped fiber gratings based true-time delay for phased-array antenna beam forming," Appl. Phys. B 80, 703-706 (2005).
    [CrossRef]
  18. S. Xiao, A. M. Weiner and C. Lin, "A dispersion law for virtually-imaged phased array based on paraxial wave theory," IEEE J. Quantum Electron. 40, 420 (2004)
    [CrossRef]
  19. Y. Vlasov, M. O’Boyle, H. Hamann and S. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65 (2005)
    [CrossRef] [PubMed]
  20. M. Bigelow, N. Lepeshkin and R. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200 (2003)
    [CrossRef] [PubMed]
  21. L. J. Wang, A. Kuzmich and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277 (2000)
    [CrossRef] [PubMed]

2005 (5)

I. S. Lin, J. D. McKinney, and A. M. Weiner, "Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication," IEEE Microwave Wireless Component Lett. 15, 226-228 (2005).
[CrossRef]

S. Xiao and A. M. Weiner, "An eight-channel hyperfine wavelength demultiplexer using a virtually-imaged phased-array (VIPA)," IEEE Photon. Technol. Lett. 17, 372-374 (2005).
[CrossRef]

J. Yang, S. Tjin and N. Ngao, "All chirped fiber gratings based true-time delay for phased-array antenna beam forming," Appl. Phys. B 80, 703-706 (2005).
[CrossRef]

Y. Vlasov, M. O’Boyle, H. Hamann and S. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65 (2005)
[CrossRef] [PubMed]

J. Capmany, B. Ortega, D. Pastor and S. Sales, "Discrete-time optical processing of microwave signals," J. Lightwave Technol. 23, 702-723 (2005).
[CrossRef]

2004 (2)

S. Xiao, A. M. Weiner and C. Lin, "A dispersion law for virtually-imaged phased array based on paraxial wave theory," IEEE J. Quantum Electron. 40, 420 (2004)
[CrossRef]

R. J. Fontana, "Recent system applications of short-pulse ultra-wideband (UWB) technology," invited, IEEE Trans. Microwave Theory Technol. 52, 2087-2104 (2004).
[CrossRef]

2003 (2)

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

M. Bigelow, N. Lepeshkin and R. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200 (2003)
[CrossRef] [PubMed]

2002 (1)

2000 (3)

B. Ortega, J. L. Cruz, J. Capmany, M. V. Andres, and D. Pastor, "Variable delay line for phased-antenna based on a chirped fiber grating," IEEE Trans. Microwave Theory Technol.,  48, 1352-1360 (2000).
[CrossRef]

L. J. Wang, A. Kuzmich and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277 (2000)
[CrossRef] [PubMed]

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

1996 (2)

1991 (1)

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernsterin, "The first demonstration of an optically steered microwave phased array antenna using true-time-delay" J. Lightwave Technol.,  9, 1124-1131 (1991).
[CrossRef]

1985 (1)

Andres, M. V.

B. Ortega, J. L. Cruz, J. Capmany, M. V. Andres, and D. Pastor, "Variable delay line for phased-antenna based on a chirped fiber grating," IEEE Trans. Microwave Theory Technol.,  48, 1352-1360 (2000).
[CrossRef]

Bernsterin, N.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernsterin, "The first demonstration of an optically steered microwave phased array antenna using true-time-delay" J. Lightwave Technol.,  9, 1124-1131 (1991).
[CrossRef]

Bigelow, M.

M. Bigelow, N. Lepeshkin and R. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200 (2003)
[CrossRef] [PubMed]

Boyd, R.

M. Bigelow, N. Lepeshkin and R. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200 (2003)
[CrossRef] [PubMed]

Capmany, J.

J. Capmany, B. Ortega, D. Pastor and S. Sales, "Discrete-time optical processing of microwave signals," J. Lightwave Technol. 23, 702-723 (2005).
[CrossRef]

B. Ortega, J. L. Cruz, J. Capmany, M. V. Andres, and D. Pastor, "Variable delay line for phased-antenna based on a chirped fiber grating," IEEE Trans. Microwave Theory Technol.,  48, 1352-1360 (2000).
[CrossRef]

Chou, J.

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

Cruz, J. L.

B. Ortega, J. L. Cruz, J. Capmany, M. V. Andres, and D. Pastor, "Variable delay line for phased-antenna based on a chirped fiber grating," IEEE Trans. Microwave Theory Technol.,  48, 1352-1360 (2000).
[CrossRef]

Dogariu, A.

L. J. Wang, A. Kuzmich and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277 (2000)
[CrossRef] [PubMed]

Fontana, R. J.

R. J. Fontana, "Recent system applications of short-pulse ultra-wideband (UWB) technology," invited, IEEE Trans. Microwave Theory Technol. 52, 2087-2104 (2004).
[CrossRef]

Hamann, H.

Y. Vlasov, M. O’Boyle, H. Hamann and S. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65 (2005)
[CrossRef] [PubMed]

Han, Y.

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

Heritage, J. P.

Jalai, B.

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

Kuzmich, A.

L. J. Wang, A. Kuzmich and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277 (2000)
[CrossRef] [PubMed]

Leaird, D. E.

Lee, J. J.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernsterin, "The first demonstration of an optically steered microwave phased array antenna using true-time-delay" J. Lightwave Technol.,  9, 1124-1131 (1991).
[CrossRef]

Lepeshkin, N.

M. Bigelow, N. Lepeshkin and R. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200 (2003)
[CrossRef] [PubMed]

Lin, C.

S. Xiao, A. M. Weiner and C. Lin, "A dispersion law for virtually-imaged phased array based on paraxial wave theory," IEEE J. Quantum Electron. 40, 420 (2004)
[CrossRef]

Lin, I. S.

I. S. Lin, J. D. McKinney, and A. M. Weiner, "Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication," IEEE Microwave Wireless Component Lett. 15, 226-228 (2005).
[CrossRef]

Liu, Y.

McKinney, J. D.

I. S. Lin, J. D. McKinney, and A. M. Weiner, "Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication," IEEE Microwave Wireless Component Lett. 15, 226-228 (2005).
[CrossRef]

J. D. McKinney, D. E. Leaird, A. M. Weiner, "Millimeter-wave arbitrary waveform generation with a direct space-to-time pulse shaper," Opt. Lett. 27, 1345-1347 (2002).
[CrossRef]

McNab, S.

Y. Vlasov, M. O’Boyle, H. Hamann and S. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65 (2005)
[CrossRef] [PubMed]

Newberg, I. L.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernsterin, "The first demonstration of an optically steered microwave phased array antenna using true-time-delay" J. Lightwave Technol.,  9, 1124-1131 (1991).
[CrossRef]

Ng, W.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernsterin, "The first demonstration of an optically steered microwave phased array antenna using true-time-delay" J. Lightwave Technol.,  9, 1124-1131 (1991).
[CrossRef]

Ngao, N.

J. Yang, S. Tjin and N. Ngao, "All chirped fiber gratings based true-time delay for phased-array antenna beam forming," Appl. Phys. B 80, 703-706 (2005).
[CrossRef]

O’Boyle, M.

Y. Vlasov, M. O’Boyle, H. Hamann and S. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65 (2005)
[CrossRef] [PubMed]

Ortega, B.

J. Capmany, B. Ortega, D. Pastor and S. Sales, "Discrete-time optical processing of microwave signals," J. Lightwave Technol. 23, 702-723 (2005).
[CrossRef]

B. Ortega, J. L. Cruz, J. Capmany, M. V. Andres, and D. Pastor, "Variable delay line for phased-antenna based on a chirped fiber grating," IEEE Trans. Microwave Theory Technol.,  48, 1352-1360 (2000).
[CrossRef]

Park, S.

Pastor, D.

J. Capmany, B. Ortega, D. Pastor and S. Sales, "Discrete-time optical processing of microwave signals," J. Lightwave Technol. 23, 702-723 (2005).
[CrossRef]

B. Ortega, J. L. Cruz, J. Capmany, M. V. Andres, and D. Pastor, "Variable delay line for phased-antenna based on a chirped fiber grating," IEEE Trans. Microwave Theory Technol.,  48, 1352-1360 (2000).
[CrossRef]

Sales, S.

Shirasaki, M.

Tangonan, G. L.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernsterin, "The first demonstration of an optically steered microwave phased array antenna using true-time-delay" J. Lightwave Technol.,  9, 1124-1131 (1991).
[CrossRef]

Thurston, R. N.

Tjin, S.

J. Yang, S. Tjin and N. Ngao, "All chirped fiber gratings based true-time delay for phased-array antenna beam forming," Appl. Phys. B 80, 703-706 (2005).
[CrossRef]

Vlasov, Y.

Y. Vlasov, M. O’Boyle, H. Hamann and S. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65 (2005)
[CrossRef] [PubMed]

Walston, A. A.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernsterin, "The first demonstration of an optically steered microwave phased array antenna using true-time-delay" J. Lightwave Technol.,  9, 1124-1131 (1991).
[CrossRef]

Wang, L. J.

L. J. Wang, A. Kuzmich and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277 (2000)
[CrossRef] [PubMed]

Weiner, A. M.

I. S. Lin, J. D. McKinney, and A. M. Weiner, "Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication," IEEE Microwave Wireless Component Lett. 15, 226-228 (2005).
[CrossRef]

S. Xiao and A. M. Weiner, "An eight-channel hyperfine wavelength demultiplexer using a virtually-imaged phased-array (VIPA)," IEEE Photon. Technol. Lett. 17, 372-374 (2005).
[CrossRef]

S. Xiao, A. M. Weiner and C. Lin, "A dispersion law for virtually-imaged phased array based on paraxial wave theory," IEEE J. Quantum Electron. 40, 420 (2004)
[CrossRef]

J. D. McKinney, D. E. Leaird, A. M. Weiner, "Millimeter-wave arbitrary waveform generation with a direct space-to-time pulse shaper," Opt. Lett. 27, 1345-1347 (2002).
[CrossRef]

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

Y. Liu, S. Park, and A. M. Weiner, "Enhancement of narrow-band terahertz radiation from photoconducting antennas by optical pulse shaping," Opt. Lett. 21, 1762 (1996).
[CrossRef] [PubMed]

J. P. Heritage, A. M. Weiner and R. N. Thurston, "Picosecond pulse shaping by spectral phase and amplitude manipulation," Opt. Lett. 10, 609-611 (1985)
[CrossRef] [PubMed]

S. Xiao and A. M. Weiner, "Coherent photonic processing of microwave signals using spatial light modulator: programmable amplitude filters," J. Lightwave Technol.Special Issue of Optical Signal Processing (to be published).

Xiao, S.

S. Xiao and A. M. Weiner, "An eight-channel hyperfine wavelength demultiplexer using a virtually-imaged phased-array (VIPA)," IEEE Photon. Technol. Lett. 17, 372-374 (2005).
[CrossRef]

S. Xiao, A. M. Weiner and C. Lin, "A dispersion law for virtually-imaged phased array based on paraxial wave theory," IEEE J. Quantum Electron. 40, 420 (2004)
[CrossRef]

S. Xiao and A. M. Weiner, "Coherent photonic processing of microwave signals using spatial light modulator: programmable amplitude filters," J. Lightwave Technol.Special Issue of Optical Signal Processing (to be published).

Yang, J.

J. Yang, S. Tjin and N. Ngao, "All chirped fiber gratings based true-time delay for phased-array antenna beam forming," Appl. Phys. B 80, 703-706 (2005).
[CrossRef]

Appl. Phys. B (1)

J. Yang, S. Tjin and N. Ngao, "All chirped fiber gratings based true-time delay for phased-array antenna beam forming," Appl. Phys. B 80, 703-706 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. Xiao, A. M. Weiner and C. Lin, "A dispersion law for virtually-imaged phased array based on paraxial wave theory," IEEE J. Quantum Electron. 40, 420 (2004)
[CrossRef]

IEEE Microwave Wireless Component Lett. (1)

I. S. Lin, J. D. McKinney, and A. M. Weiner, "Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication," IEEE Microwave Wireless Component Lett. 15, 226-228 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

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

S. Xiao and A. M. Weiner, "An eight-channel hyperfine wavelength demultiplexer using a virtually-imaged phased-array (VIPA)," IEEE Photon. Technol. Lett. 17, 372-374 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Technol. (2)

R. J. Fontana, "Recent system applications of short-pulse ultra-wideband (UWB) technology," invited, IEEE Trans. Microwave Theory Technol. 52, 2087-2104 (2004).
[CrossRef]

B. Ortega, J. L. Cruz, J. Capmany, M. V. Andres, and D. Pastor, "Variable delay line for phased-antenna based on a chirped fiber grating," IEEE Trans. Microwave Theory Technol.,  48, 1352-1360 (2000).
[CrossRef]

J. Lightwave Technol. (2)

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernsterin, "The first demonstration of an optically steered microwave phased array antenna using true-time-delay" J. Lightwave Technol.,  9, 1124-1131 (1991).
[CrossRef]

J. Capmany, B. Ortega, D. Pastor and S. Sales, "Discrete-time optical processing of microwave signals," J. Lightwave Technol. 23, 702-723 (2005).
[CrossRef]

Nature (2)

Y. Vlasov, M. O’Boyle, H. Hamann and S. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65 (2005)
[CrossRef] [PubMed]

L. J. Wang, A. Kuzmich and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277 (2000)
[CrossRef] [PubMed]

Opt. Lett. (4)

Rev. Sci. Instrum. (1)

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

Science (1)

M. Bigelow, N. Lepeshkin and R. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200 (2003)
[CrossRef] [PubMed]

Special Issue of Optical Signal Processing (1)

S. Xiao and A. M. Weiner, "Coherent photonic processing of microwave signals using spatial light modulator: programmable amplitude filters," J. Lightwave Technol.Special Issue of Optical Signal Processing (to be published).

Other (3)

H. L. Bertoni, L. Carin, L. B. Felsen, Ultra-wideband, short-pulse electromagnetics (New York : Plenum Press, 1993).
[CrossRef]

A. Vilcot, B. Cabon, and J. Chazelas, Microwave Photonics: from components to applications and systems (Boston: Kluwer Academic, 2003).

J. H. Reed, Ed., An Introduction to Ultra Wideband Communication Systems (Prentice Hall, 2005).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic layout for photonic spectral phase shaping of ultrawideband microwave pulses. The red color indicates optical fields, and the black color indicates microwave electrical signals. Electrical outputs are sketched under both incoherent and coherent optical-to-electrical conversion. (b,c) Sketches illustrating coherent (b) and incoherent (c) operation. The upper line shows the frequency-dependent optical field corresponding to a specific setting (refer to discussion in connection with Fig. 3) of the hyperfine optical pulse shaper, either with (b) or without (c) a superimposed optical carrier. The lower line sketches the resulting time-dependent voltage amplitudes after conversion into the electrical domain.

Fig. 2.
Fig. 2.

Setup of (optical) hyperfine Fourier transform pulse shaper based on a virtually-imaged phased array (VIPA). CYL: cylindrical lens (300 mm focal length). SLM: spatial light modulator. R: optical power reflectivity. The VIPA consists of a 1.5 mm thick glass etalon with an anti-reflection coated entrance window, front and back reflectivities of approximately 100% and 96%, respectively, and a free spectral range of 50 GHz. The incident angle onto the VIPA is ~ 2.5 deg. The optical insertion loss from the input to output of the circulator is ~ 13 dB in our setup. The two-layered SLM is programmed to control the optical phase for frequencies falling between pixels #40 and #80 (a 28 GHz frequency band) and to block frequencies falling outside this range. The optical carrier is centered at pixel #60. The spectral dispersion amounts to 600–700 MHz per pixel, with lower optical frequencies at higher pixel numbers. A filter programmed for a one-pixel wide passband (not shown) yields a -3dB bandwidth of 500–625 MHz, demonstrating that each pixel controls an independent band of frequencies.

Fig. 3.
Fig. 3.

Electrical doublet pulses generated via insertion of a π phase jump onto the optical spectrum (see sketches in Fig. 1). Electrical reference pulse measured without phase shaping is shown in red; shaped waveforms shown in blue. (a) - (b) are coherent optical-to-electrical conversion in presence of strong carrier wave. The unipolar (~half-cycle) electrical input pulse is converted into a bipolar (~ single-cycle) electrical output. The polarity of the electrical output is switched by interchanging the SLM pixels programmed for 0 and π phase shifts, respectively. Here a wideband electrical DC blocking filter is used to suppress the constant background due to the carrier power. (c) is incoherent optical-to-electrical conversion with suppressed carrier. The input pulse is converted into a unipolar pulse doublet.

Fig. 4.
Fig. 4.

(a)-(b) Ultrafast, ultrawideband electrical pulse shaping via cubic spectral phase and coherent detection. Both (a) and (b) show an asymmetric pulse distortion with a damped ringing tail, as expected. However, the signs of the cubic spectral phase are opposite, leading to a reversal in the sense of the asymmetry with respect to time. (c) Ultrafast, ultrawideband electrical true-time-delay via linear spectral phase shaping. Both retardation or advancement in time is possible, depending on the sign of the linear spectral phase. The case m=0, for which the SLM is essentially deactivated, is taken as the time reference (plotted in red). Data are shown for incoherent detection, although in this case essentially identical results are obtained in the coherent detection case.

Equations (2)

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i ( t ) I ( t ) A 2 + u ( t ) 2 + 2 A Re { u ( t ) }
τ ( ω ) = ψ ( ω ) ω

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