Abstract

The last two decades have seen a wealth of optical instrumentation based upon the concepts of space-time duality. A historical overview of how this beautiful framework has been exploited to develop instruments for optical signal processing is presented. The power of this framework is then demonstrated by reviewing four devices in detail based upon space-time dualities that have been experimentally demonstrated: 1) a time-lens timing-jitter compensator for ultralong-haul dense-wavelength-division-multiplexed dispersion-managed soliton transmission, 2) a multiwavelength pulse generator using time-lens compression, 3) a programmable ultrafast optical delay line by use of a time-prism pair, and 4) an enhanced ultrafast optical delay line by use of soliton propagation between a time-prism pair.

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Other (80)

A. Papoulis, Systems and Transforms With Applications in Optics, New York: McGraw-Hill, 1968, pp. 200-204.

S. A. Akhmanov, A. P. Sukhorukov and A. S. Chirkin, "Nonstationary phenomena and space-time analogy in nonlinear optics", Sov. Phys.-JETP, vol. 28, no. 4, pp. 748-757, 1969.

E. B. Treacy, "Optical pulse compression with diffraction gratings", IEEE J. Quantum Electron., vol. QE-5, no. 9, pp. 454-458, Sep. 1969.

T. Jannson and J. Jannson, "Temporal self-imaging effect in single-mode fibers", J. Opt. Soc. Amer., vol. 71, no. 11, pp. 1373-1376, Nov. 1981.

I. P. Christov, "Design of a compound ‘time lens’", J. Mod. Opt., vol. 36, no. 8, pp. 1027-1030, Aug. 1989.

S. P. Dijaili, A. Dienes and J. S. Smith, "ABCD matrices for dispersive pulse propagation", IEEE J. Quantum Electron., vol. 29, no. 6, pp. 1158-1164, Jun. 1990.

A. G. Kostenbauder, "Ray-pulse matrices: A rational treatment for dispersive optical systems", IEEE J. Quantum Electron., vol. 26, no. 6, pp. 1148-1157, Jun. 1990.

A. W. Lohmann and D. Mendlovic, "Temporal filtering with time lenses", Appl. Opt., vol. 31, no. 29, pp. 6212-6219, Oct. 1992.

M. T. Kaufman, A. A. Godil, B. A. Auld, W. C. Banyai and D. M. Bloom, "Applications of time lens optical systems", Electron. Lett., vol. 39, no. 3, pp. 268-269, Feb. 1993.

A. A. Godil, B. A. Auld and D. M. Bloom, "Picosecond time-lenses", IEEE J. Quantum Electron., vol. 30, no. 3, pp. 827-837, Mar. 1994.

B. H. Kolner, "Space-time duality and the theory of temporal imaging", IEEE J. Quantum Electron., vol. 30, no. 8, pp. 1951-1963, Aug. 1994.

A. Papoulis, "Pulse compression, fiber communications and diffraction: A unified approach", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 11, no. 1, pp. 3-13, Jan. 1994.

P. Naulleau and E. Leith, "Stretch, time lenses and incoherent time imaging", Appl. Opt., vol. 34, no. 20, pp. 4119-4128, Jul. 1995.

X. Yang, "Implementation of time lenses and optical temporal processors", Opt. Commun., vol. 116, no. 1-3, pp. 193-207, Feb. 1995.

V. B. Yurchenko, "Improving the accuracy of a time lens", J. Opt. Soc. Amer. B, Opt. Phys., vol. 14, no. 11, pp. 2921-2924, Nov. 1997.

C. V. Bennett and B. H. Kolner, "Upconversion time microscope demonstrating 103x magnification of femtosecond waveforms", Opt. Lett., vol. 24, no. 11, pp. 783-785, Jun. 1999.

J. Azana and M. A. Muriel, "Technique for multiplying the repetition rates of periodic trains of pulses by means of a temporal self-imaging effect in chirped fiber gratings", Opt. Lett., vol. 24, no. 23, pp. 1672-1674, Dec. 1999.

N. K. Berger, B. Levit, S. Atkins and B. Fischer, "Time-lens-based spectral analysis of optical pulses by electrooptic phase modulation", Electron. Lett., vol. 36, no. 19, pp. 1644-1646, Sep. 2000.

S. Longhi, M. Marano, P. Laporta, O. Svelto, M. Belmonte, B. Agogliati, L. Arcangeli, V. Pruneri, M. N. Zervas and M. Ibsen, "40-GHz pulse-train generation at 1.5 mm with a chirped pulse fiber grating as a frequency multiplier", Opt. Lett., vol. 25, no. 19, pp. 1481-1483, Oct. 2000.

L. K. Mouradian, F. Louradour, V. Messager, A. Barthelemy and C. Froehly, "Spectro-temporal imaging of femtosecond events", IEEE J. Quantum Electron., vol. 36, no. 7, pp. 795-801, Jul. 2000.

M. Nakazawa and T. Hirooka, "Distortion-free optical transmission using time-domain optical Fourier transformation and transform-limited optical pulses", J. Opt. Soc. Amer. B, Opt. Phys., vol. 22, no. 9, pp. 1842-1855, Sep. 2005.

J. van Howe and C. Xu, "Ultrafast optical delay line by use of a time-prism pair", Opt. Lett., vol. 30, no. 1, pp. 99-101, Jan. 2005.

H. Hakimi, F. Hakimi, K. L. Hall and K. A. Rauschenbach, "A new wide-band pulse-restoration technique for digital fiber-optic communication systems using temporal gratings", IEEE Photon. Technol. Lett., vol. 11, no. 8, pp. 1048-1050, Aug. 1999.

J. Azana and M. A. Muriel, "Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings", IEEE J. Quantum Electron., vol. 36, no. 5, pp. 517-526, May 2000.

L. E. Hargrove, R. L. Fork and M. A. Pollack, "Locking of He-Ne laser modes induced by synchronous intracavity modulation", App. Phys. Lett., vol. 5, no. 1, pp. 4-5, Jul. 1964.

J. A. Giordmaine, M. A. Duguay and J. W. Hansen, "Compression of optical pulses", IEEE J. Quantum Electron., vol. QE-4, no. 5, pp. 252-255, May 1968.

J. W. Goodman, Introduction to Fourier Optics, New York: McGraw-Hill, 1968, pp. 1-3.

W. J. Caputi, "Stretch: A time-transformation technique", IEEE Trans. Aerospace Electron. Syst., vol. AES-7, no. 2, pp. 269-278, Mar. 1971.

T. Jannson, "Real-time Fourier transformation in dispersive optical fibers", Opt. Lett., vol. 8, no. 4, pp. 232-234, Apr. 1983.

B. H. Kolner and M. Nazarathy, "Temporal imaging with a time lens", Opt. Lett., vol. 14, no. 12, pp. 630-632, Jun. 1989.

J. Azana, N. K. Berger, B. Levit and B. Fischer, "Reconfigurable generation of high-repetition-rate optical pulse sequences by time-domain phase-only filtering", Opt. Lett., vol. 30, no. 23, pp. 3228-3230, Dec. 2005.

D. Dragoman and M. Dragoman, "Temporal implementation of Fourier-related transforms", Opt. Commun., vol. 145, no. 1-6, pp. 33-37, Jan. 1998.

J. van Howe, J. Hansryd and C. Xu, "Multiwavelength pulse generator using time-lens compression", Opt. Lett., vol. 29, no. 13, pp. 1470-1472, Jul. 2004.

M. Hanna, P. Lacourt, S. Poinsot and J. M. Dudley, "Optical pulse generation using soliton-assisted time-lens compression", Opt. Express, vol. 13, no. 5, pp. 1743-1748, Mar. 2005.

L. F. Mollenauer and C. Xu, "Time-lens timing-jitter compensator in ultra-long haul DWDM dispersion managed soliton transmissions", presented at the Conf. Lasers and Electro-Optics, Paper CPDB1-1, 2002.

T. Sakano, K. Uchiyama, I. Shake, T. Morioka and K. Hagimoto, "Large-dispersion-tolerance optical signal transmission system based on temporal imaging", Opt. Lett., vol. 27, no. 8, pp. 583-585, Apr. 2002.

J. Azana, N. K. Berger, B. Levit and B. Fischer, "Spectro-temporal imaging of optical pulses with a single time lens", IEEE Photon. Technol. Lett., vol. 16, no. 3, pp. 882-883, Mar. 2004.

M. Beck, M. G. Raymer, I. A. Walmsley and V. Wong, "Chronocyclic tomography for measuring the amplitude and phase-structure of optical pulses", Opt. Lett., vol. 18, no. 23, pp. 2041-2043, Dec. 1993.

K. L. Hall, D. T. Moriarty, H. Hakimi, F. Hakimi, B. S. Robinson and K. A. Rauschenbach, "An ultrafast variable optical delay technique", IEEE Photon. Technol. Lett., vol. 12, no. 2, pp. 208-210, Feb. 2000.

J. van Howe and C. Xu, "Ultrafast optical delay line using soliton propagation between a time-prism pair", Opt. Express, vol. 13, no. 4, pp. 1138-1143, Feb. 2005.

J. R. Klauder, A. C. Price, S. Darlington and W. J. Albersheim, "The theory and design of chirp radars", Bell Syst. Tech. J., vol. 39, no. 4, pp. 745-808, Jul. 1960.

M. A. Duguay and J. W. Hansen, "Compression of pulses from a mode-locked He-Ne laser", Appl. Phys. Lett., vol. 14, no. 1, pp. 14-16, Jan. 1969.

J. E. Bjorkholm, E. H. Turner and D. B. Pearson, "Conversion of CW light into a train of subnanosecond pulses using frequency modulation and the dispersion of a near-resonant atomic vapor", App. Phys. Lett., vol. 26, no. 10, pp. 564-566, May 1975.

J. K. Wigmore and D. R. Grischkowsky, "Temporal compression of light", IEEE J. Quantum Electron., vol. QE-14, no. 4, pp. 310-315, Apr. 1978.

C. V. Shank, R. L. Fork, R. Yen and R. H. Stolen, "Compression of femtosecond optical pulses", App. Phys. Lett., vol. 40, no. 9, pp. 761-763, May 1982.

H. G. Winful, "Pulse compression in optical fiber filters", Appl. Phys. Lett., vol. 46, no. 6, pp. 527-529, Mar. 1985.

R. L. Fork, C. H. B. Cruz, P. C. Becker and C. V. Shank, "Compression of optical pulses to six femtoseconds by using cubic phase compensation", Opt. Lett., vol. 12, no. 7, pp. 483-485, Jul. 1987.

T. Kobayashi, A. Morimoto, T. Fujita, K. Amano, T. Uemura and T. Sueta, "Direct generation of picosecond pulses using electrooptic modulation methods", in Proc. Ultrafast Phenom. V, Snowmass, CO, 1986, pp. 134-136.

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