Abstract

We describe a novel method for subpicosecond pulse shaping based on longitudinal spectral decomposition in dispersive media. The entire system is created with standard telecommunications equipment allowing for integration with optical communication networks. The technique has the potential for time–bandwidth products 104 due to exclusive reliance on time-domain processing. We introduce the principle of operation and subsequently support it with results from our experimental system. Both theory and experiments suggest third-order dispersion as the principle limitation to realizing a large number of resolvable spots. Chirped fiber Bragg gratings offer a route to increase the time–bandwidth product for high-speed signal processing applications.

© 2005 Optical Society of America

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  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]
  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]
  3. 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,” IEEE J. Quantum Electron.  28, 908–920 (1992).
    [CrossRef]
  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]
  5. 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]
  6. 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]
  7. M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron.  32, 161–172 (1996).
    [CrossRef]
  8. 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]
  12. 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).
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  13. 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).
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  15. S. Shen, C. C. Chang, H. P. Sardesai, V. Binjrajka, and A. M. Weiner, “Effects of self-phase modulation on sub-500 fs pulse transmission over dispersion compensated fiber links,” J. Lightwave Technol.  17, 452–461 (1999).
    [CrossRef]
  16. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  17. M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, “1 m long continuously-written fiber Bragg grating for combined second- and third-order dispersion compensation,” Electron. Lett.  33, 1891–1893 (1997).
    [CrossRef]
  18. L. F. Mollenauer, P. V. Mamyshev, J. Gripp, M. J. Neubelt, N. Mamysheva, L. Grüner-Nielsen, and T. Veng, “Demonstration of massive wavelength-division multiplexing over transoceanic distances by use of dispersion-managed solitons,” Opt. Lett.  25, 704–706 (2000).
    [CrossRef]

2004

2002

2000

1999

1997

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, “1 m long continuously-written fiber Bragg grating for combined second- and third-order dispersion compensation,” Electron. Lett.  33, 1891–1893 (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]

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]

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]

1996

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

1994

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron.  30, 1951–1963 (1994).
[CrossRef]

1993

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

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,” IEEE J. Quantum Electron.  28, 908–920 (1992).
[CrossRef]

1990

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

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

Azaña, J.

Belmonte, M.

Binjrajka, V.

Brennan, J. F.

Chan, L. Y.

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]

Chang, C. C.

Chen, L. R.

Chou, P. C.

Cole, M. J.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, “1 m long continuously-written fiber Bragg grating for combined second- and third-order dispersion compensation,” Electron. Lett.  33, 1891–1893 (1997).
[CrossRef]

Dahleh, M.

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

Dugan, M. A.

Durkin, M.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, “1 m long continuously-written fiber Bragg grating for combined second- and third-order dispersion compensation,” Electron. Lett.  33, 1891–1893 (1997).
[CrossRef]

Fainman, Y.

Gripp, J.

Grüner-Nielsen, L.

Haus, H. A.

Heritage, J. P.

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]

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]

Ibsen, M.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, “1 m long continuously-written fiber Bragg grating for combined second- and third-order dispersion compensation,” Electron. Lett.  33, 1891–1893 (1997).
[CrossRef]

Inoue, Y.

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]

Ishii, M.

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]

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]

Kamei, S.

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]

Kirschner, E. M.

Kolner, B. H.

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron.  30, 1951–1963 (1994).
[CrossRef]

Kurokawa, T.

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]

Laming, R. I.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, “1 m long continuously-written fiber Bragg grating for combined second- and third-order dispersion compensation,” Electron. Lett.  33, 1891–1893 (1997).
[CrossRef]

Laporta, P.

Leaird, D. E.

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]

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,” IEEE J. Quantum Electron.  28, 908–920 (1992).
[CrossRef]

Longhi, S.

Mamyshev, P. V.

Mamysheva, N.

Marano, M.

Mollenauer, L. F.

Naganuma, K.

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]

Nelson, K. A.

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

Neubelt, M. J.

Okamoto, K.

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]

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]

Panasenko, D.

Patel, J. S.

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,” IEEE J. Quantum Electron.  28, 908–920 (1992).
[CrossRef]

Rabitz, H.

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

Salehi, J. A.

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]

Saperstein, R. E.

Sardesai, H. P.

Shen, S.

Sugita, A.

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]

Svelto, O.

Takenouchi, H.

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]

Tong, Y. C.

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]

Tsang, H. K.

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]

Tsuda, H.

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]

Tull, J. X.

Veng, T.

Warren, W. S.

Wefers, M. M.

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

Weiner, A. M.

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]

S. Shen, C. C. Chang, H. P. Sardesai, V. Binjrajka, and A. M. Weiner, “Effects of self-phase modulation on sub-500 fs pulse transmission over dispersion compensated fiber links,” J. Lightwave Technol.  17, 452–461 (1999).
[CrossRef]

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,” IEEE J. Quantum Electron.  28, 908–920 (1992).
[CrossRef]

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]

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]

Wullert, J. R.

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,” IEEE J. Quantum Electron.  28, 908–920 (1992).
[CrossRef]

Electron. Lett.

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]

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]

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, “1 m long continuously-written fiber Bragg grating for combined second- and third-order dispersion compensation,” Electron. Lett.  33, 1891–1893 (1997).
[CrossRef]

IEEE J. Quantum Electron.

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

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,” IEEE J. Quantum Electron.  28, 908–920 (1992).
[CrossRef]

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron.  30, 1951–1963 (1994).
[CrossRef]

IEEE Photon. Technol. Lett.

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. Lightwave Technol.

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]

S. Shen, C. C. Chang, H. P. Sardesai, V. Binjrajka, and A. M. Weiner, “Effects of self-phase modulation on sub-500 fs pulse transmission over dispersion compensated fiber links,” J. Lightwave Technol.  17, 452–461 (1999).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Science

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

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

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Figures (6)

Fig. 1
Fig. 1

Block diagram description of the pulse-shaping technique based on standard electrical system schematics. U in and U out are the input and output pulse envelopes, respectively. U ( z , t ) is the launched pulse envelope, ν ( t ) is the modulating signal, and V ( 2 B t ) is the microwave signal spectrum scaled to time. The boxes contain impulse responses associated with passage through the respective element. In the boxes associated with second-order dispersion, B = 1 ( 2 β 2 z ) , while in the others D ( t ) and D * ( t ) represent the impulse responses originating from all higher-order dispersion terms.

Fig. 2
Fig. 2

(a) Intensity of a temporal waveform output from the system modeled by Eq. (4). Time is measured relative to the central pulse corresponding to the constant (dc) component of the modulating signal ν ( t ) . The satellite pulses relate to the microwave sidebands, ± 7 GHz . Here the microwave signal is weaker than the dc. (b) 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 spike and satellite pulses in (a) form the pulses at ± 2.3 ps in (b).

Fig. 3
Fig. 3

Experimental setup for realization of subpicosecond pulse shaping. OPO, optical parametric oscillator.

Fig. 4
Fig. 4

Experimental intensity ACTs of signals with 7 GHz modulation. RF power is maintained at 15 dBm while the bias voltage is varied. (a) ACT in the presence of a strong dc component in the modulating signal ν ( t ) . Experimental result shows agreement with the trace obtained from our linear model in Fig. 2b. (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. 5
Fig. 5

Overlaid experimental intensity autocorrelations showing the effect of increased modulation frequency on a pulse-shaped waveform. The temporal broadening of the 6 GHz upshifted and downshifted pulses is apparent when comparing its FWHM with that of the 3 GHz side pulses.

Fig. 6
Fig. 6

Modeling results of pulse shaping in the combined presence of β 3 and residual second-order chromatic dispersion. (a) Intensity traces showing the asymmetric pulse pairs created for four modulation frequencies. For a system with 60 cm extra SMF (out of 2.6 km ), the trailing pulses in the pairs are broadened significantly as compared with the lead pulses. (b) Intensity ACTs of the waveforms in part (a). The results in (b) show agreement with the experimental data displayed in Fig. 5.

Equations (8)

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U ( z , ω ) = U ( 0 , ω ) exp ( j 1 2 β 2 z ω 2 ) exp ( j 1 6 β 3 z ω 3 ) .
U out ( z , ω ) = { V ( ω ω ) U ( 0 , ω ) exp [ j 1 2 β 2 z ( ω ) 2 j 1 6 β 3 z ( ω ) 3 ] d ω } × exp ( j 1 2 β 2 z ω 2 j 1 6 β 3 z ω 3 ) .
U out ( z , ω ) = A U ( z , ω ) + { B U ( z , ω ω 0 ) exp [ j 1 6 ( 3 β 2 z + β 3 z ω 0 ) ω 0 2 ] × exp [ j ( β 2 z + 1 2 β 3 z ω 0 ) ω 0 ω ] exp ( j 1 2 β 3 z ω 0 ω 2 ) } + { B U ( z , ω + ω 0 ) exp [ j 1 6 ( 3 β 2 z β 3 z ω 0 ) ω 0 2 ] × exp [ j ( β 2 z 1 2 β 3 z ω 0 ) ω 0 ω ] exp ( j 1 2 β 3 z ω 0 ω 2 ) } .
U out ( z , t ) = A U ( z , t ) exp ( j ω c t ) + { B exp [ j ( 1 2 β 2 z + 1 3 β 3 z ω 0 ) ω 0 2 ] exp [ j ( ω c + ω 0 ) t ] × U ( z , t β 2 z ω 0 1 2 β 3 z ω 0 2 ) exp ( j t 2 2 β 3 z ω 0 ) } + { B exp [ j ( 1 2 β 2 z 1 3 β 3 z ω 0 ) ω 0 2 ] exp [ j ( ω c ω 0 ) t ] × U ( z , t + β 2 z ω 0 1 2 β 3 z ω 0 2 ) exp ( j t 2 2 β 3 z ω 0 ) } .
U out ( z , t ) = A U ( 0 , t ) exp ( j ω c t ) + β 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 ] .
t field ( ν ) = cos [ ϕ 0 2 + π ν ( t ) 2 V π ] .
t field ( V b , V m , f m , t ) = cos ( ϕ 0 2 + π V b 2 V π ) cos [ π V m 2 V π sin ( 2 π f m t ) ] sin ( ϕ 0 2 + π V b 2 V π ) sin [ π V m 2 V π sin ( 2 π f m t ) ] .
t field ( V b , V m , f m , t ) = cos ( ϕ 0 2 + π V b 2 V π ) [ J 0 ( π V m 2 V π ) + n = 2 n , even 2 J n ( π V m 2 V π ) sin ( 2 π n f m t ) ] sin ( ϕ 0 2 + π V b 2 V π ) [ n = 1 n , odd 2 J n ( π V m 2 V π ) sin ( 2 π n f m t ) ] .

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