Abstract

We analyzed optical-signal processing based on time-space conversion in an arrayed-waveguide grating (AWG). General expressions for the electric fields needed to design frequency filters were obtained. We took into account the effects of the waveguides and clearly distinguished the temporal frequency axis from the spatial axis at the focal plane, at which frequency filters were placed. Using the analytical results, we identified the factors limiting the input-pulse width and clarified the windowing effect and the effect ofphase fluctuation in the arrayed waveguide.

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References

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  1. A. M. Weiner, "Femtosecond optical pulse shaping and processing," Prog. Quant. Electron. 19,161-237 (1995).
    [CrossRef]
  2. A. M. Weiner, D. E. Leaird, D. H. Reitze and E. G. Paek, "Femtosecond spectral holography," IEEE J. of Quant. Electron. 28, 2251-2261 (1992).
    [CrossRef]
  3. M. C. Nuss,M.Li, T. H. Chiu, A. M.Weiner, and A.Partovi,"Time-to-space mapping of femtosecond pulses," Opt. Lett. 19, 664-666 (1994).
    [CrossRef] [PubMed]
  4. P. C. Sun, Y. T. Mazurenko, W. S. C. Chang, P.K.L. Yu and Y. Fainman, "All-optical parallel-to-serial conversion by holographic spatial-to-temporal frequency encoding," Opt. Lett. 20, 1728-1730 (1995).
    [CrossRef] [PubMed]
  5. K. Takasago, M. Takekawa, F. Kannari, M. Tani and K. Sakai, "Accurate pulse shaping of femtosecond lasers using programmable phase-only modulator," Jpn. J. Appl. Phys. 35, L1430-L1433 (1996).
    [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. H. Takenouchi, H. Tsuda, K. Naganuma, T. Kurokawa, Y. Inoue and K. Okamoto, "Differential processing of ultrashort optical pulses using arrayed-waveguide grating with phase-only filter," Electron. Lett. 34, 1245-1246 (1998).
    [CrossRef]
  8. H. Tsuda, K. Okamoto, T. Ishii, K. Naganuma, Y. Inoue, H. Takenouchi and T. Kurokawa, "Second- and Third-order Dispersion Compensator Using a High-Resolution Arrayed-Waveguide Grating," IEEE Photon. Technol. Lett. 11, 569-571 (1999).
    [CrossRef]
  9. H. Takenouchi, H. Tsuda, C. Amano, T. Goh, K. Okamoto and T. Kurokawa, "An optical phase-shift keying direct detection receiver using a high-resolution arrayed-waveguide grating," in Technical Digest of Optical Fiber Conference (OFC) '99, paper TuO4.
  10. H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa and C. Amano, "Photonic spectral encoder/decoder using an arrayed-waveguide grating for coherent optical code division multiplexing," in Technical Digest of Optical Fiber Conference (OFC) '99, paper PD32.
  11. 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]
  12. A. M. Weiner, D. E. Leaird,J.S.Patel and J.R.Wullert,"Programmable shaping of femtosecond pulses by use of a 128-element liquid-crystal phase modulator," IEEE J. Quant. Electron. 28, 908-920 (1992).
    [CrossRef]
  13. J. Paye and A. Migus, "Space-time Wigner functions and their application to the analysis of a pulse shaper," J. Opt. Soc. Am. B 12, 1480-1490 (1995).
    [CrossRef]
  14. H. Takenouchi, H. Tsuda, C. Amano, T. Goh, K. Okamoto and T. Kurokawa, "Differential processing using an arrayed-waveguide grating," IEICE Trans. Commun. E82-B, 1252-1258 (1999).
  15. M. Kawachi, "Silica waveguides on silicon and their application to integrated-optic components," Optic. Quant. Electron. 22, 391-416 (1990).
    [CrossRef]
  16. H. Takahashi, K. Oda and H. Toba, "Impact of crosstalk in an arrayed-waveguide multiplexer on N�N optical interconnection," J. Lightwave Technol. 14, 1097-1105 (1996).
    [CrossRef]
  17. K. Takada, H. Yamada and Y. Inoue, "Origin of channel crosstalk in 100-GHz-spaced silica-based arrayed-waveguide grating multiplexer," Electron. Lett. 31, 1176-1177 (1995).
    [CrossRef]
  18. T. Goh, S. Suzuki and A. Sugita, "Estimation of Waveguide Phase Error in Silica-Based Waveguides," J. Lightwave Technol. 15, 2107-2113 (1997).
    [CrossRef]

Other (18)

A. M. Weiner, "Femtosecond optical pulse shaping and processing," Prog. Quant. Electron. 19,161-237 (1995).
[CrossRef]

A. M. Weiner, D. E. Leaird, D. H. Reitze and E. G. Paek, "Femtosecond spectral holography," IEEE J. of Quant. Electron. 28, 2251-2261 (1992).
[CrossRef]

M. C. Nuss,M.Li, T. H. Chiu, A. M.Weiner, and A.Partovi,"Time-to-space mapping of femtosecond pulses," Opt. Lett. 19, 664-666 (1994).
[CrossRef] [PubMed]

P. C. Sun, Y. T. Mazurenko, W. S. C. Chang, P.K.L. Yu and Y. Fainman, "All-optical parallel-to-serial conversion by holographic spatial-to-temporal frequency encoding," Opt. Lett. 20, 1728-1730 (1995).
[CrossRef] [PubMed]

K. Takasago, M. Takekawa, F. Kannari, M. Tani and K. Sakai, "Accurate pulse shaping of femtosecond lasers using programmable phase-only modulator," Jpn. J. Appl. Phys. 35, L1430-L1433 (1996).
[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]

H. Takenouchi, H. Tsuda, K. Naganuma, T. Kurokawa, Y. Inoue and K. Okamoto, "Differential processing of ultrashort optical pulses using arrayed-waveguide grating with phase-only filter," Electron. Lett. 34, 1245-1246 (1998).
[CrossRef]

H. Tsuda, K. Okamoto, T. Ishii, K. Naganuma, Y. Inoue, H. Takenouchi and T. Kurokawa, "Second- and Third-order Dispersion Compensator Using a High-Resolution Arrayed-Waveguide Grating," IEEE Photon. Technol. Lett. 11, 569-571 (1999).
[CrossRef]

H. Takenouchi, H. Tsuda, C. Amano, T. Goh, K. Okamoto and T. Kurokawa, "An optical phase-shift keying direct detection receiver using a high-resolution arrayed-waveguide grating," in Technical Digest of Optical Fiber Conference (OFC) '99, paper TuO4.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa and C. Amano, "Photonic spectral encoder/decoder using an arrayed-waveguide grating for coherent optical code division multiplexing," in Technical Digest of Optical Fiber Conference (OFC) '99, paper PD32.

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]

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

J. Paye and A. Migus, "Space-time Wigner functions and their application to the analysis of a pulse shaper," J. Opt. Soc. Am. B 12, 1480-1490 (1995).
[CrossRef]

H. Takenouchi, H. Tsuda, C. Amano, T. Goh, K. Okamoto and T. Kurokawa, "Differential processing using an arrayed-waveguide grating," IEICE Trans. Commun. E82-B, 1252-1258 (1999).

M. Kawachi, "Silica waveguides on silicon and their application to integrated-optic components," Optic. Quant. Electron. 22, 391-416 (1990).
[CrossRef]

H. Takahashi, K. Oda and H. Toba, "Impact of crosstalk in an arrayed-waveguide multiplexer on N�N optical interconnection," J. Lightwave Technol. 14, 1097-1105 (1996).
[CrossRef]

K. Takada, H. Yamada and Y. Inoue, "Origin of channel crosstalk in 100-GHz-spaced silica-based arrayed-waveguide grating multiplexer," Electron. Lett. 31, 1176-1177 (1995).
[CrossRef]

T. Goh, S. Suzuki and A. Sugita, "Estimation of Waveguide Phase Error in Silica-Based Waveguides," J. Lightwave Technol. 15, 2107-2113 (1997).
[CrossRef]

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Figures (5)

Figure 1.
Figure 1.

Schematic diagrams of time-space-conversion optical-signal processing using (a) DGs and (b) AWGs.

Figure 2.
Figure 2.

Model and axes used for analysis. Spatial frequency axes were used instead of spatial axes at the interface between the I/O waveguide and the first slab waveguide and at the focal plane.

Figure 3.
Figure 3.

Spectral filtering using narrow-stripe mirror: (a) profile of narrow stripe mirror, (b) electric field near ξ=0, (c) temporal frequency spectrum reflected by narrow stripe mirror, (d) temporal output waveform. The shape of the output waveform reflects crosstalk at the focal plane.

Figure 4.
Figure 4.

Figure of merit (flatness of envelope of temporal waveform) and loss versus shape of distribution function (a/Nd). Envelope of temporal waveform became flatter as a/Nd became larger, but the loss became larger. There is thus a trade-off relation between loss and the figure of merit. The a/Nd of the previously reported AWG was 0.57.

Figure 5.
Figure 5.

Number-of-waveguides dependence on coefficient of determination (R 2) calculated from output pulse shape for m=72. A phase error of 0.8×10-2 rad/mm is a typical standard deviation in a silica-based waveguide with a relative refractive index difference of 0.75%.

Tables (1)

Tables Icon

Table 1 Parameters used in AWG simulation

Equations (34)

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f ( t ) = u ( t ) exp ( i 2 π ν 0 t ) ,
F ( ν ) = U ( ν ν 0 ) U ν .
F 0 , ν ( x 0 ) = U ν · e ( x 0 ) = U ν w IO π · exp ( x 0 2 w IO 2 ) .
β ( x 1 ) = w IO π i α exp { ( π w IO ) 2 ( x 1 α ) 2 } ,
α = c L f n s ν 0 ,
f 1 , ν ( x 1 ) = U ν · [ { β ( x 1 ) · rect ( x 1 Nd ) } * δ S ( x 1 ) ] * exp ( π x 1 2 w AW 2 ) ,
δ S ( x ) p = N 2 N 2 1 δ ( x 1 pd ) ,
rect ( x ) = { 1 ( x < 1 2 ) 0 ( otherwize ) ,
θ ( x , ν ) = 2 π m ν ν 0 d x · δ S ( x ) .
f 2 , ν ( x 2 ) = exp { i θ ( x 2 , ν ) } · f 1 , ν ( x 2 )
= U ν · [ { β ( x 2 ) · rect ( x 2 Nd ) · exp ( i 2 π m ν ν 0 d x 2 ) } * δ S ( x 2 ) ]
* exp ( π x 2 2 w AW 2 ) .
F 3 , ν ( ξ ) = π w AW 2 i α U ν { B ( ξ ) * sinc ( Nd ξ ) * δ ( ξ m ν ν 0 d ) } Δ Sum ( ξ ) exp ( π 2 w AW 2 ξ 2 ) ,
ξ ν 0 n s c L f x 3 = x 3 α ,
Δ S ( ξ ) = p = N 2 N 2 1 exp ( i 2 π pd ξ )
B ( ξ ) = α 3 2 i π w IO exp { ( α ξ ) 2 w IO 2 } .
ξ = m ν ν 0 d
γ = ν x 3 = ν 0 2 n s d mc L f = ν 0 d m α .
ν FSR = ν 0 m .
Δ ν = ν 0 Nm .
Δ ν = ν 0 d m Δ ξ ν 0 N eff · m ,
G 3 , ν ( ξ ) = π w AW 2 i α · U ν · H ( ξ ) · { B ( ξ ) * sinc ( Nd ξ ) * δ ( ξ m ν ν 0 d ) }
× Δ S ( ξ ) · exp ( π 2 w AW 2 ξ 2 ) ,
g 2 , ν ( x 2 ) = U ν · { h ( x 2 ) * ( β ( x 2 ) · rect ( x 2 Nd ) · exp ( i 2 π m ν ν 0 d x 2 ) ) * δ S ( x 2 ) }
* exp ( π x 2 2 w 2 )
g 1 , ν ( x 1 ) = U ν · [ { h ( x 1 ) * ( β ( x 1 ) . rect ( x 1 Nd ) · exp ( i 2 π m ν ν 0 d x 1 ) ) * δ S ( x 1 ) }
× exp ( i 2 π m ν ν 0 d x 1 ) ] * exp ( π x 1 2 w 2 ) .
G 0 , ν ( ξ ) = π w AW 2 i α · U ν · { H ( ξ + m ν ν 0 d ) · ( B ( ξ ) * sinc ( Nd ξ ) ) · Δ S ( ξ + m ν ν 0 d ) }
× exp ( π 2 w AW 2 ξ 2 ) .
V ν = e ( α ξ ) · G 0 , ν ( ξ ) d ξ
= π w AW 2 i α · U ν e ( α ξ ) · H ( ξ + m ν ν 0 d ) · ( B ( ξ ) * sinc ( Nd ξ ) ) · Δ S ( ξ + m ν ν 0 d )
× exp ( π 2 w AW 2 ξ 2 ) d ξ .
Δ t = 1 ν FSR = m ν 0 .
T 0 = 1 Δ ν = Nm ν 0 .

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