Abstract

We describe what we believe to be novel methods for waveform synthesis and detection relying on longitudinal spectral decomposition of subpicosecond optical pulses. Optical processing is performed in both all-fiber and mixed fiber–free-space systems. Demonstrated applications include ultrafast optical waveform synthesis, microwave spectrum analysis, and high-speed electrical arbitrary waveform generation. The techniques have the potential for time–bandwidth products of 104 due to exclusive reliance on time-domain processing. We introduce the principles of operation and subsequently support these with results from our experimental systems. Both theory and experiments suggest third-order dispersion as the principle limitation to large time–bandwidth products. Chirped-fiber Bragg gratings offer a route to increasing the number of resolvable spots for use in high-speed signal processing applications.

© 2008 Optical Society of America

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References

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    [CrossRef]
  2. A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, "Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator," J. Quantum Electron. 28, 908-920 (1992).
    [CrossRef]
  3. M. A. Dugan, J. X. Tull, and W. S. Warren, "High-resolution acousto-optic shaping of unamplified and amplified femtosecond laser pulses," J. Opt. Soc. Am. B 14, 2348-2358 (1997).
    [CrossRef]
  4. T. Kurokawa, H. Tsuda, K. Okamoto, K. Naganuma, H. Takenouchi, Y. Inoue, and M. Ishii, "Time-space-conversion optical signal processing using arrayed-waveguide grating," Electron. Lett. 33, 1890-1891 (1997).
    [CrossRef]
  5. P.-C. Sun, Y. Mazurenko, and Y. Fainman, "Femtosecond pulse imaging: ultrafast optical oscilloscope," J. Opt. Soc. Am. A 14, 1159-1170 (1997).
    [CrossRef]
  6. D. M. Marom, D. Panasenko, P.-C. Sun, and Y. Fainman, "Spatial-temporal wave mixing for space-to-time conversion," Opt. Lett. 24, 563-565 (1999).
    [CrossRef]
  7. D. M. Marom, D. Panasenko, R. Rokitski, P.-C. Sun, and Y. Fainman, "Time reversal of ultrafast waveforms by wave mixing of spectrally decomposed waves," Opt. Lett. 25, 132-134 (2000).
    [CrossRef]
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    [CrossRef]
  9. D. E. Leaird, A. M. Weiner, S. Kamei, M. Ishii, A. Sugita, and K. Okamoto, "Generation of flat-topped 500-GHz pulse bursts using loss engineered arrayed waveguide gratings," IEEE Photon. Technol. Lett. 14, 816-818 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  25. M. Ghavami, L. B. Michael, and R. Kohno, Ultra-wideband Signals and Systems in Communication Engineering (Wiley, 2004).
  26. J. U. Kang, M. Y. Frankel, and R. D. Esman, "Demonstration of microwave frequency shifting by use of a highly chirped mode-locked fiber laser," Opt. Lett. 23, 1188-1190 (1998).
    [CrossRef]
  27. J. Chou, Y. Han, and B. Jalali, "Adaptive RF-photonic arbitrary waveform generator," IEEE Photon. Technol. Lett. 15, 581-583 (2003).
    [CrossRef]
  28. J. Azaña, N. K. Berger, B. Levit, V. Smulakovsky, and B. Fischer, "Frequency shifting of microwave signals by use of a general temporal self-imaging (Talbot) effect in optical fibers," Opt. Lett. 29, 2849-2851 (2004).
    [CrossRef]
  29. J. D. McKinney, D. E. Leaird, and A. M. Weiner, "Millimeter-wave arbitrary waveform generation with a direct space-to-time pulse shaper," Opt. Lett. 27, 1345-1347 (2002).
    [CrossRef]
  30. S. Xiao, J. D. McKinney, and A. M. Weiner, "Photonic microwave arbitrary waveform generation using a virtually imaged phased-array (VIPA) direct space-to-time pulse shaper," IEEE Photon. Technol. Lett. 16, 1936-1938 (2004).
    [CrossRef]
  31. J. D. McKinney, I.-S. Lin, and A. M. Weiner, "Shaping the power spectrum of ultra-wideband radio-frequency signals," IEEE Trans. Microwave Theory Tech. 54, 4247-4255 (2006).
    [CrossRef]
  32. 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]
  33. R. E. Saperstein, N. Alic, R. Rokitski, and Y. Fainman, "High-speed, electronic arbitrary waveform generation using time-domain processing of ultrashort optical pulses," in Summer Topical Meetings 2005 (IEEE, 2005), paper WC2.4.
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    [CrossRef] [PubMed]
  35. J. Sharping, Y. Okawachi, J. van Howe, C. Xu, Y. Wang, A. Willner, and A. Gaeta, "All-optical, wavelength and bandwidth preserving, pulse delay based on parametric wavelength conversion and dispersion," Opt. Express 13, 7872-7877 (2005).
    [CrossRef] [PubMed]
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  37. N. Alic and S. Radic, Electrical and Computer Engineering Department, University of California, San Diego, 9500 Gilman Drive, Mail Stop 0407, La Jolla, Calif. 92093, USA, are preparing a manuscript to be called "Optical delay elements based on wavelength conversion."
  38. Advanced Optical Solutions, www.aos-fiber.com.
  39. Proximion Fiber Systems AB, http://www.proximion.com/.
  40. P. Petropoulos, M. Ibsen, A. D. Ellis, and D. J. Richardson, "Rectangular pulse generation based on pulse reshaping using a superstructured fiber Bragg grating," J. Lightwave Technol. 19, 746-752 (2001).
    [CrossRef]
  41. S. Longhi, M. Marano, P. Laporta, O. Svelto, and M. Belmonte, "Propagation, manipulation, and control of picosecond optical pulses at 1.5 m in fiber Bragg gratings," J. Opt. Soc. Am. B 19, 2742-2757 (2002).
    [CrossRef]
  42. J. Azaña and L. R. Chen, "Synthesis of temporal optical waveforms by fiber Bragg gratings: a new approach based on space-to-frequency-to-time mapping," J. Opt. Soc. Am. B 19, 2758-2769 (2002).
    [CrossRef]
  43. X. Wang, K. Matsushima, K. Kitayama, A. Nishiki, N. Wada, and F. Kubota, "High-performance optical code generation and recognition by use of a 511-chip, 640-Gchip/s phase-shifted superstructured fiber Bragg grating," Opt. Lett. 30, 355-357 (2005).
    [CrossRef] [PubMed]
  44. P. C. Chou, and H. A. Haus, and J. F. Brennan III, "Reconfigurable time-domain spectral shaping of an optical pulse stretched by a fiber Bragg grating," Opt. Lett. 25, 524-526 (2000).
    [CrossRef]

2006 (1)

J. D. McKinney, I.-S. Lin, and A. M. Weiner, "Shaping the power spectrum of ultra-wideband radio-frequency signals," IEEE Trans. Microwave Theory Tech. 54, 4247-4255 (2006).
[CrossRef]

2005 (4)

2004 (3)

2003 (2)

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

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

2002 (6)

2001 (1)

2000 (2)

1999 (1)

1998 (1)

1997 (4)

M. A. Dugan, J. X. Tull, and W. S. Warren, "High-resolution acousto-optic shaping of unamplified and amplified femtosecond laser pulses," J. Opt. Soc. Am. B 14, 2348-2358 (1997).
[CrossRef]

T. Kurokawa, H. Tsuda, K. Okamoto, K. Naganuma, H. Takenouchi, Y. Inoue, and M. Ishii, "Time-space-conversion optical signal processing using arrayed-waveguide grating," Electron. Lett. 33, 1890-1891 (1997).
[CrossRef]

P.-C. Sun, Y. Mazurenko, and Y. Fainman, "Femtosecond pulse imaging: ultrafast optical oscilloscope," J. Opt. Soc. Am. A 14, 1159-1170 (1997).
[CrossRef]

Y. C. Tong, L. Y. Chan, and H. K. Tsang, "Fiber dispersion or pulse spectrum measurement using a sampling oscilloscope," Electron. Lett. 33, 983-985 (1997).
[CrossRef]

1996 (1)

M. M. Wefers and K. A. Nelson, "Space-time profiles of shaped ultrafast optical waveforms," IEEE J. Quantum Electron. 32, 161-172 (1996).
[CrossRef]

1995 (1)

1994 (2)

A. Papoulis, "Pulse compression, fiber communications, and diffraction: a unified approach," J. Opt. Soc. Am. A 11, 3-13 (1994).
[CrossRef]

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, "Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas," Appl. Phys. Lett. 64, 137-139 (1994).
[CrossRef]

1993 (1)

W. S. Warren, H. Rabitz, and M. Dahleh, "Coherent control of quantum dynamics: the dream is alive," Science 259, 1581-1589 (1993).
[CrossRef] [PubMed]

1992 (2)

Y. Takagi, T. Kobayashi, K. Yoshihara, and S. Imamura, "Multiple- and single-shot autocorrelator based on two-photon conductivity in semiconductors," Opt. Lett. 17, 658-660 (1992).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, "Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator," J. Quantum Electron. 28, 908-920 (1992).
[CrossRef]

1990 (1)

J. A. Salehi, A. M. Weiner, and J. P. Heritage, "Coherent ultrashort light pulse code-division multiple-access communication systems," J. Lightwave Technol. 8, 478-491 (1990).
[CrossRef]

1988 (2)

M. Haner and W. S. Warren, "Synthesis of crafted optical pulses by time domain modulation in a fiber-grating compressor," Appl. Phys. Lett. 52, 1548-1550 (1988).
[CrossRef]

A. M. Weiner, J. P. Heritage, and E. M. Kirschner, "High-resolution femtosecond pulse shaping," J. Opt. Soc. Am. B 5, 1563-1572 (1988).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, "Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas," Appl. Phys. Lett. 64, 137-139 (1994).
[CrossRef]

M. Haner and W. S. Warren, "Synthesis of crafted optical pulses by time domain modulation in a fiber-grating compressor," Appl. Phys. Lett. 52, 1548-1550 (1988).
[CrossRef]

Electron. Lett. (2)

Y. C. Tong, L. Y. Chan, and H. K. Tsang, "Fiber dispersion or pulse spectrum measurement using a sampling oscilloscope," Electron. Lett. 33, 983-985 (1997).
[CrossRef]

T. Kurokawa, H. Tsuda, K. Okamoto, K. Naganuma, H. Takenouchi, Y. Inoue, and M. Ishii, "Time-space-conversion optical signal processing using arrayed-waveguide grating," Electron. Lett. 33, 1890-1891 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Wefers and K. A. Nelson, "Space-time profiles of shaped ultrafast optical waveforms," IEEE J. Quantum Electron. 32, 161-172 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

D. E. Leaird, A. M. Weiner, S. Kamei, M. Ishii, A. Sugita, and K. Okamoto, "Generation of flat-topped 500-GHz pulse bursts using loss engineered arrayed waveguide gratings," IEEE Photon. Technol. Lett. 14, 816-818 (2002).
[CrossRef]

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

S. Xiao, J. D. McKinney, and A. M. Weiner, "Photonic microwave arbitrary waveform generation using a virtually imaged phased-array (VIPA) direct space-to-time pulse shaper," IEEE Photon. Technol. Lett. 16, 1936-1938 (2004).
[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]

IEEE Trans. Microwave Theory Tech. (1)

J. D. McKinney, I.-S. Lin, and A. M. Weiner, "Shaping the power spectrum of ultra-wideband radio-frequency signals," IEEE Trans. Microwave Theory Tech. 54, 4247-4255 (2006).
[CrossRef]

J. Lightwave Technol. (2)

J. A. Salehi, A. M. Weiner, and J. P. Heritage, "Coherent ultrashort light pulse code-division multiple-access communication systems," J. Lightwave Technol. 8, 478-491 (1990).
[CrossRef]

P. Petropoulos, M. Ibsen, A. D. Ellis, and D. J. Richardson, "Rectangular pulse generation based on pulse reshaping using a superstructured fiber Bragg grating," J. Lightwave Technol. 19, 746-752 (2001).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (5)

J. Quantum Electron. (1)

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, "Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator," J. Quantum Electron. 28, 908-920 (1992).
[CrossRef]

Opt. Express (1)

Opt. Lett. (12)

J. U. Kang, M. Y. Frankel, and R. D. Esman, "Demonstration of microwave frequency shifting by use of a highly chirped mode-locked fiber laser," Opt. Lett. 23, 1188-1190 (1998).
[CrossRef]

J. Azaña, N. K. Berger, B. Levit, V. Smulakovsky, and B. Fischer, "Frequency shifting of microwave signals by use of a general temporal self-imaging (Talbot) effect in optical fibers," Opt. Lett. 29, 2849-2851 (2004).
[CrossRef]

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

B. B. Hu and M. C. Nuss, "Imaging with terahertz waves," Opt. Lett. 20, 1716-1718 (1995).
[CrossRef] [PubMed]

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

D. M. Marom, D. Panasenko, P.-C. Sun, and Y. Fainman, "Spatial-temporal wave mixing for space-to-time conversion," Opt. Lett. 24, 563-565 (1999).
[CrossRef]

D. M. Marom, D. Panasenko, R. Rokitski, P.-C. Sun, and Y. Fainman, "Time reversal of ultrafast waveforms by wave mixing of spectrally decomposed waves," Opt. Lett. 25, 132-134 (2000).
[CrossRef]

Y. Takagi, T. Kobayashi, K. Yoshihara, and S. Imamura, "Multiple- and single-shot autocorrelator based on two-photon conductivity in semiconductors," Opt. Lett. 17, 658-660 (1992).
[CrossRef] [PubMed]

R. E. Saperstein, D. Panasenko, and Y. Fainman, "Demonstration of a microwave spectrum analyzer using time-domain optical processing in fiber," Opt. Lett. 29, 501-503 (2004).
[CrossRef] [PubMed]

X. Wang, K. Matsushima, K. Kitayama, A. Nishiki, N. Wada, and F. Kubota, "High-performance optical code generation and recognition by use of a 511-chip, 640-Gchip/s phase-shifted superstructured fiber Bragg grating," Opt. Lett. 30, 355-357 (2005).
[CrossRef] [PubMed]

P. C. Chou, and H. A. Haus, and J. F. Brennan III, "Reconfigurable time-domain spectral shaping of an optical pulse stretched by a fiber Bragg grating," Opt. Lett. 25, 524-526 (2000).
[CrossRef]

J. van Howe and C. Xu, "Ultrafast optical delay line by use of a time-prism pair," Opt. Lett. 30, 99-101 (2005).
[CrossRef] [PubMed]

Science (1)

W. S. Warren, H. Rabitz, and M. Dahleh, "Coherent control of quantum dynamics: the dream is alive," Science 259, 1581-1589 (1993).
[CrossRef] [PubMed]

Other (9)

A. M. Weiner and J. P. Heritage, "Optical systems and methods based upon temporal stretching, modulation, and recompression of ultrashort pulses," U.S. patent 4,928,316 (22 May 1990).

H. Zmuda and E. N. Toughlian, Photonic Aspects of Modern Radar (Artech House, 1994).

R. E. Saperstein, X. B. Xie, P. K. L. Yu, and Y. Fainman, "Demonstration of a microwave spectrum analyzer based on time domain processing of ultrafast pulses," in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics Series, (Optical Society of America, 2005), paper CTuAA4.

M. Ghavami, L. B. Michael, and R. Kohno, Ultra-wideband Signals and Systems in Communication Engineering (Wiley, 2004).

J. Ren, N. Alic, E. Myslivets, R. E. Saperstein, C. J. McKinstrie, R. M. Jopson, A. H. Gnauck, P. A. Andrekson, and S. Radic, "12.47 ns continuously-tunable two-pump parametric delay," in Proceedings of the European Conference on Optical Communication (SEE, 2006), postdeadline paper Th4.4.3.

N. Alic and S. Radic, Electrical and Computer Engineering Department, University of California, San Diego, 9500 Gilman Drive, Mail Stop 0407, La Jolla, Calif. 92093, USA, are preparing a manuscript to be called "Optical delay elements based on wavelength conversion."

Advanced Optical Solutions, www.aos-fiber.com.

Proximion Fiber Systems AB, http://www.proximion.com/.

R. E. Saperstein, N. Alic, R. Rokitski, and Y. Fainman, "High-speed, electronic arbitrary waveform generation using time-domain processing of ultrashort optical pulses," in Summer Topical Meetings 2005 (IEEE, 2005), paper WC2.4.

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Figures (11)

Fig. 1
Fig. 1

(Color online) General pulse-shaping approach using dispersive fiber and an electro-optic modulator for signal processing.

Fig. 2
Fig. 2

(a) Modeled intensity of a temporal waveform output from the system as described by Eq. (2). Time is designated relative to the central pulse corresponding to the constant (dc) component of the modulating signal v(t). The satellite pulses relate to the microwave sidebands, ± 7 GHz . Here the microwave signal is weaker than the dc. (b) Modeled intensity autocorrelation trace (with background) of the optical waveform in (a). The small pulses occurring at ± 4.7 ps are cross correlations of the pulses at ± 2.3 ps in (a). The cross correlation of the dc and satellite pulses in (a) form the pulses at ± 2.3 ps in (b).

Fig. 3
Fig. 3

Experimental intensity autocorrelation traces of signals with 7 GHz modulation. The rf power is maintained at 15 dBm while bias voltage is varied. (a) ACT in the presence of a strong dc component in the modulating signal v(t). Experimental result shows agreement with the trace obtained from our linear model in Fig. 2(b). (b) ACT when the modulator was null biased. The autocorrelation process leads to the formation of three pulses as the inner two satellite pulses drop out.

Fig. 4
Fig. 4

(Color online) Schematic diagram of the microwave spectrum analyzer shown. The signal voltage is a single rf tone with a bias. The correlation output shows the two sidebands and the central dc spike.

Fig. 5
Fig. 5

Correlation trace from experimental proof of concept. The rf signal consists of dc and 760 MHz components. Results are filtered in postprocessing to remove background fluctuations. The upper axis gives temporal correlation delays as recorded. The lower axis shows a scaling of the delay axis to frequency ( f = τ / 2 π β 2 z ) .

Fig. 6
Fig. 6

(Color online) Schematic of our proposed method for electrical arbitrary waveform generation. Longitudinal SDWs are delayed and modulated before mixing in a fast square-law detector. A bandpass filter separates the dc terms to create a bipolar signal. The superposition of channels leads to a linear synthesis of modulated microwave carriers at the output.

Fig. 7
Fig. 7

(a) Oscilloscope recorded waveform from single-channel realization of an electrical arbitrary waveform generation technique. A 3 GHz high-pass filter removes the slow dc signal producing a bipolar waveform. (b) FFT of recorded waveform shows the 4.5 GHz carrier and 760 MHz envelope feature.

Fig. 8
Fig. 8

(Color online) Overlaid intensity autocorrelations showing the effect of increased modulation frequency on a pulse-shaped waveform. The temporal broadening of the 6 GHz up- and down-shifted pulses is apparent when comparing their FWHM to those pulses originating from 3 GHz modulation.

Fig. 9
Fig. 9

(Color online) Time–frequency plot visualizations of longitudinal SDWs with β 3 distortion. The interference of two delayed copies (upper portion) produces the beat tone under the SDW envelope (lower portion). For larger delays the detected photocurrent has a large microwave chirp. This chirp broadens the linewidth of the microwave signals used in the techniques of Sections 3 and 4.

Fig. 10
Fig. 10

(Color online) Overlaid FFTs collected from time-domain interference of delayed longitudinal SDW copies. Solid curves correspond to SMF-produced SDWs and dashed curves are CFBG-originated SDWs. An 40 ps delay results in ∼13 GHz beat frequency between SDW copies, and the ∼10 ps delay produces an ∼3 GHz beat. (a) Modeling results created with 25.2 km of SMF, β 2 = 20 ps 2 / km , and β 3 = .1 ps 3 / km . CFBG has a β 2 z value of 430 ps 2 / km . (b) Experimental results agree well with modeling.

Fig. 11
Fig. 11

(Color online) Polarization states displayed on a Poincaré sphere for cw signals between 1535 and 1565 nm with 1 nm step. Propagation is through (a) SMF patch cables and an optical circulator and (b) SMF patch cables, the circulator, and the 3M CFBG.

Equations (7)

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

U ( z , ω ) = U ( 0 , ω ) exp ( j 1 2 β 2 z ω 2 ) .
U out ( z , t ) = A U ( 0 , t ) exp ( j ω c t ) + B exp [ j 1 2 β 2 z ω 0 2 ] × U ( 0 , t β 2 z ω 0 ) exp [ j ( ω c + ω 0 ) t ] + B exp [ j 1 2 β 2 z ω 0 2 ] U ( 0 , t + β 2 z ω 0 ) × exp [ j ( ω c ω 0 ) t ] .
U ( z , t ) = e j t 2 2 β 2 z U ( 0 , t ) e j t β 2 z t d t = e j t 2 2 β 2 z F { U ( 0 , t ) } t 2 π β 2 z .
U r ( z , t ) = e j ( t τ ) 2 2 β 2 z F { U ( z , t ) } t τ 2 π β 2 z + e j t 2 2 β 2 z s ( t ) F { U ( z , t ) } t 2 π β 2 z .
1 T 0 T | F { U ( 0 , t ) } t 2 π β 2 z | 2 s ( t ) cos [ 2 π ( τ 2 π β 2 z ) t τ 2 2 β 2 z ] d t .
U ( z , ω ) = U ( 0 , ω ) exp ( j 1 2 β 2 z ω 2 ) exp ( j 1 6 β 3 z ω 3 ) .
T s = 3 T o 2 | β 2 / β 3 | .

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