Abstract

A scheme is proposed to transform an optical pulse into a millimeter-wave frequency modulation pulse by using a weak fiber Bragg grating (FBG) in a fiber-optics system. The Fourier transformation method is used to obtain the required spectrum response function of the FBG for the Gaussian pulse, soliton pulse, and Lorenz shape pulse. On the condition of the first-order Born approximation of the weak fiber grating, the relation of the refractive index distribution and the spectrum response function of the FBG satisfies the Fourier transformation, and the corresponding refractive index distribution forms are obtained for single-frequency modulation and linear-frequency modulation millimeter-wave pulse generation. The performances of the designed fiber gratings are also studied by a numerical simulation method for a supershort pulse transmission.

© 2007 Optical Society of America

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References

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  1. H. Harada, K. Sato, and M. Fujise, "A radio-on-fiber based millimeter-wave road-vehicle communication system by a code division multiplexing radio transmission scheme," IEEE Trans. Intell. Transp. Syst. 2, 165-179 (2001).
    [CrossRef]
  2. H. Al-Raweshidy and S. Komaki, eds., Radio over Fiber Technologies for Mobile Communications Networks (Norwood, 2002).
  3. U. Gliese, S. Ngrskov, and T. N. Nielsen, "Chromatic dispersion in fiber-optic microwave and millimeter-wave links," IEEE Trans. Microwave Theory Tech. 44, 1716-1724 (1996).
    [CrossRef]
  4. R. Hofstetter, H. Schmuck, and R. Heidemann, "Dispersion effects in optical mm-wave systems using self heterodyne method for transport and generation," IEEE Trans. Microwave Theory Tech. 43, 2263-2269 (1995).
    [CrossRef]
  5. O. Levinson and M. Horowitz, "Generation of complex microwave and millimeter-wave pulses using dispersion and Kerr effect in optical fiber systems," J. Lightwave Technol. 21, 1179-1187 (2003).
    [CrossRef]
  6. A. Zeitouny, S. Stepanov, O. Levinson, and M. Horowitz, "Optical generation of linearly chirped microwave pulses using fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 660-662 (2005).
    [CrossRef]
  7. 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]
  8. 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 shape," IEEE Photon. Technol. Lett. 16, 1936-1938 (2004).
    [CrossRef]
  9. 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]
  10. 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]
  11. K. A. Winick and J. E. Roman, "Design of corrugated waveguide filters by Fourier transform techniques," IEEE J. Quantum Electron. 26, 1918-1929 (1990).
    [CrossRef]
  12. Q. Ye, F. Liu, R. Qu, and Z. Fang, "Generation of millimeter-wave in optical pulse carrier by using an apodized Moiré fiber grating," Opt. Commun. 266, 532-535 (2006).
    [CrossRef]

2006 (1)

Q. Ye, F. Liu, R. Qu, and Z. Fang, "Generation of millimeter-wave in optical pulse carrier by using an apodized Moiré fiber grating," Opt. Commun. 266, 532-535 (2006).
[CrossRef]

2005 (1)

A. Zeitouny, S. Stepanov, O. Levinson, and M. Horowitz, "Optical generation of linearly chirped microwave pulses using fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 660-662 (2005).
[CrossRef]

2004 (1)

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 shape," IEEE Photon. Technol. Lett. 16, 1936-1938 (2004).
[CrossRef]

2003 (1)

2002 (2)

2001 (2)

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]

H. Harada, K. Sato, and M. Fujise, "A radio-on-fiber based millimeter-wave road-vehicle communication system by a code division multiplexing radio transmission scheme," IEEE Trans. Intell. Transp. Syst. 2, 165-179 (2001).
[CrossRef]

1996 (1)

U. Gliese, S. Ngrskov, and T. N. Nielsen, "Chromatic dispersion in fiber-optic microwave and millimeter-wave links," IEEE Trans. Microwave Theory Tech. 44, 1716-1724 (1996).
[CrossRef]

1995 (1)

R. Hofstetter, H. Schmuck, and R. Heidemann, "Dispersion effects in optical mm-wave systems using self heterodyne method for transport and generation," IEEE Trans. Microwave Theory Tech. 43, 2263-2269 (1995).
[CrossRef]

1990 (1)

K. A. Winick and J. E. Roman, "Design of corrugated waveguide filters by Fourier transform techniques," IEEE J. Quantum Electron. 26, 1918-1929 (1990).
[CrossRef]

Al-Raweshidy, H.

H. Al-Raweshidy and S. Komaki, eds., Radio over Fiber Technologies for Mobile Communications Networks (Norwood, 2002).

Azaña, J.

Chen, L. R.

Ellis, A. D.

Fang, Z.

Q. Ye, F. Liu, R. Qu, and Z. Fang, "Generation of millimeter-wave in optical pulse carrier by using an apodized Moiré fiber grating," Opt. Commun. 266, 532-535 (2006).
[CrossRef]

Fujise, M.

H. Harada, K. Sato, and M. Fujise, "A radio-on-fiber based millimeter-wave road-vehicle communication system by a code division multiplexing radio transmission scheme," IEEE Trans. Intell. Transp. Syst. 2, 165-179 (2001).
[CrossRef]

Gliese, U.

U. Gliese, S. Ngrskov, and T. N. Nielsen, "Chromatic dispersion in fiber-optic microwave and millimeter-wave links," IEEE Trans. Microwave Theory Tech. 44, 1716-1724 (1996).
[CrossRef]

Harada, H.

H. Harada, K. Sato, and M. Fujise, "A radio-on-fiber based millimeter-wave road-vehicle communication system by a code division multiplexing radio transmission scheme," IEEE Trans. Intell. Transp. Syst. 2, 165-179 (2001).
[CrossRef]

Heidemann, R.

R. Hofstetter, H. Schmuck, and R. Heidemann, "Dispersion effects in optical mm-wave systems using self heterodyne method for transport and generation," IEEE Trans. Microwave Theory Tech. 43, 2263-2269 (1995).
[CrossRef]

Hofstetter, R.

R. Hofstetter, H. Schmuck, and R. Heidemann, "Dispersion effects in optical mm-wave systems using self heterodyne method for transport and generation," IEEE Trans. Microwave Theory Tech. 43, 2263-2269 (1995).
[CrossRef]

Horowitz, M.

A. Zeitouny, S. Stepanov, O. Levinson, and M. Horowitz, "Optical generation of linearly chirped microwave pulses using fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 660-662 (2005).
[CrossRef]

O. Levinson and M. Horowitz, "Generation of complex microwave and millimeter-wave pulses using dispersion and Kerr effect in optical fiber systems," J. Lightwave Technol. 21, 1179-1187 (2003).
[CrossRef]

Ibsen, M.

Komaki, S.

H. Al-Raweshidy and S. Komaki, eds., Radio over Fiber Technologies for Mobile Communications Networks (Norwood, 2002).

Leaird, D. E.

Levinson, O.

A. Zeitouny, S. Stepanov, O. Levinson, and M. Horowitz, "Optical generation of linearly chirped microwave pulses using fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 660-662 (2005).
[CrossRef]

O. Levinson and M. Horowitz, "Generation of complex microwave and millimeter-wave pulses using dispersion and Kerr effect in optical fiber systems," J. Lightwave Technol. 21, 1179-1187 (2003).
[CrossRef]

Liu, F.

Q. Ye, F. Liu, R. Qu, and Z. Fang, "Generation of millimeter-wave in optical pulse carrier by using an apodized Moiré fiber grating," Opt. Commun. 266, 532-535 (2006).
[CrossRef]

McKinney, J. D.

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 shape," IEEE Photon. Technol. Lett. 16, 1936-1938 (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]

Ngrskov, S.

U. Gliese, S. Ngrskov, and T. N. Nielsen, "Chromatic dispersion in fiber-optic microwave and millimeter-wave links," IEEE Trans. Microwave Theory Tech. 44, 1716-1724 (1996).
[CrossRef]

Nielsen, T. N.

U. Gliese, S. Ngrskov, and T. N. Nielsen, "Chromatic dispersion in fiber-optic microwave and millimeter-wave links," IEEE Trans. Microwave Theory Tech. 44, 1716-1724 (1996).
[CrossRef]

Petropoulos, P.

Qu, R.

Q. Ye, F. Liu, R. Qu, and Z. Fang, "Generation of millimeter-wave in optical pulse carrier by using an apodized Moiré fiber grating," Opt. Commun. 266, 532-535 (2006).
[CrossRef]

Richardson, D. J.

Roman, J. E.

K. A. Winick and J. E. Roman, "Design of corrugated waveguide filters by Fourier transform techniques," IEEE J. Quantum Electron. 26, 1918-1929 (1990).
[CrossRef]

Sato, K.

H. Harada, K. Sato, and M. Fujise, "A radio-on-fiber based millimeter-wave road-vehicle communication system by a code division multiplexing radio transmission scheme," IEEE Trans. Intell. Transp. Syst. 2, 165-179 (2001).
[CrossRef]

Schmuck, H.

R. Hofstetter, H. Schmuck, and R. Heidemann, "Dispersion effects in optical mm-wave systems using self heterodyne method for transport and generation," IEEE Trans. Microwave Theory Tech. 43, 2263-2269 (1995).
[CrossRef]

Stepanov, S.

A. Zeitouny, S. Stepanov, O. Levinson, and M. Horowitz, "Optical generation of linearly chirped microwave pulses using fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 660-662 (2005).
[CrossRef]

Weiner, A. M.

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 shape," IEEE Photon. Technol. Lett. 16, 1936-1938 (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]

Winick, K. A.

K. A. Winick and J. E. Roman, "Design of corrugated waveguide filters by Fourier transform techniques," IEEE J. Quantum Electron. 26, 1918-1929 (1990).
[CrossRef]

Xiao, S.

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 shape," IEEE Photon. Technol. Lett. 16, 1936-1938 (2004).
[CrossRef]

Ye, Q.

Q. Ye, F. Liu, R. Qu, and Z. Fang, "Generation of millimeter-wave in optical pulse carrier by using an apodized Moiré fiber grating," Opt. Commun. 266, 532-535 (2006).
[CrossRef]

Zeitouny, A.

A. Zeitouny, S. Stepanov, O. Levinson, and M. Horowitz, "Optical generation of linearly chirped microwave pulses using fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 660-662 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. A. Winick and J. E. Roman, "Design of corrugated waveguide filters by Fourier transform techniques," IEEE J. Quantum Electron. 26, 1918-1929 (1990).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

A. Zeitouny, S. Stepanov, O. Levinson, and M. Horowitz, "Optical generation of linearly chirped microwave pulses using fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 660-662 (2005).
[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 shape," IEEE Photon. Technol. Lett. 16, 1936-1938 (2004).
[CrossRef]

IEEE Trans. Intell. Transp. Syst. (1)

H. Harada, K. Sato, and M. Fujise, "A radio-on-fiber based millimeter-wave road-vehicle communication system by a code division multiplexing radio transmission scheme," IEEE Trans. Intell. Transp. Syst. 2, 165-179 (2001).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

U. Gliese, S. Ngrskov, and T. N. Nielsen, "Chromatic dispersion in fiber-optic microwave and millimeter-wave links," IEEE Trans. Microwave Theory Tech. 44, 1716-1724 (1996).
[CrossRef]

R. Hofstetter, H. Schmuck, and R. Heidemann, "Dispersion effects in optical mm-wave systems using self heterodyne method for transport and generation," IEEE Trans. Microwave Theory Tech. 43, 2263-2269 (1995).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

Q. Ye, F. Liu, R. Qu, and Z. Fang, "Generation of millimeter-wave in optical pulse carrier by using an apodized Moiré fiber grating," Opt. Commun. 266, 532-535 (2006).
[CrossRef]

Opt. Lett. (1)

Other (1)

H. Al-Raweshidy and S. Komaki, eds., Radio over Fiber Technologies for Mobile Communications Networks (Norwood, 2002).

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Figures (8)

Fig. 1
Fig. 1

(a) Spectra of the different input pulse shapes and (b) corresponding transfer functions of FBGs under the conditions that τ 0 = 1   ps , τ 1 = 100   ps , and f = 120   GHz . (The solid curve is a Gaussian pulse, the dashed curve is a soliton pulse, and the dotted curve is a Lorenz shape pulse.)

Fig. 2
Fig. 2

(a) Refractive index distribution and (b) corresponding reflection spectrum of a FBG for single-frequency MMW pulse generation.

Fig. 3
Fig. 3

Comparison of the output pulse from the fiber grating and the target pulse for the 1   ps initial input pulse. (The solid curve is the output pulse from the FBG, and the dashed curve is the target pulse.)

Fig. 4
Fig. 4

Output pulse for asymmetric reflection spectra (the inset figure is the related reflective spectra of the fiber grating).

Fig. 5
Fig. 5

(a) Refractive index distribution and (b) corresponding reflection spectrum of a FBG for linear-frequency MMW pulse generation.

Fig. 6
Fig. 6

Comparison of the output pulse from the fiber grating and the target pulse for the 1   ps initial input pulse. (The solid curve is the output pulse from the FBG, and the dashed curve is the target pulse.)

Fig. 7
Fig. 7

(a) Refractive index distribution and (b) corresponding reflection spectrum of a FBG for linear-frequency MMW pulse generation.

Fig. 8
Fig. 8

Comparison of the output pulse from the fiber grating and the target pulse for the 1   ps initial input pulse. (The solid curve is the output pulse from the FBG, and the dashed curve is the target pulse.)

Equations (21)

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E ˜ i n ( ω ) = 1 2 E 0 τ 0   exp [ ( ω ω 0 ) 2 τ 0 2 8 ] ,
E o u t = E 1   exp [ 2 t 2 / τ 1 2 ] exp ( i ω 0 t ) cos ( π f t ) ,
E ˜ o u t ( ω ) = 1 2 E 1 τ 1   exp ( π 2 f 2 τ 1 2 8 ) exp [ ( ω ω 0 ) 2 τ 1 2 8 ] × cosh [ π f ( ω ω 0 ) τ 1 2 4 ] .
H FBG ( ω ) = E ˜ o u t ( ω ) / E ˜ i n ( ω ) = E 1 τ 1 E 0 τ 0   exp ( π 2 f 2 τ 1 2 8 ) exp [ ( ω ω 0 ) 2 ( τ 1 2 τ 0 2 ) 8 ] × cosh [ π f ( ω ω 0 ) τ 1 2 4 ] .
E i n ( t ) = E 0   sec h ( t τ 0 ) exp ( i ω 0 t ) ,
E ˜ i n ( ω ) = E 0   sec h ( t τ 0 ) exp ( i ω 0 t ) exp ( i ω t ) d t = π E 0 τ 0  sec h [ 2 ( ω ω 0 ) τ 0 ] .
E o u t ( t ) = E 1   sec h ( t τ 1 ) exp ( i ω 0 t ) cos ( π f t ) ,
E ˜ o u t ( ω ) = 1 2 π E 1 τ 1 { sec h [ 2 ( π f τ 1 + ω τ 1 ω 0 τ 1 ) ] + sec h [ 2 ( π f τ 1 + ω τ 1 ω 0 τ 1 ) ] } .
H FBG ( ω ) = E ˜ o u t ( ω ) / E ˜ i n ( ω ) .
E i n ( t ) = E 0   exp ( | t | τ 0 ) exp ( i ω 0 t ) ,
E ˜ i n ( ω ) = E 0   exp ( | t | τ 0 ) exp ( i ω 0 t ) exp ( i ω t ) d t = 2 E 0 τ 0 1 + τ 0 2 ( ω ω 0 ) 2 .
E o u t ( t ) = E 1   exp ( | t | τ 1 ) exp ( i ω 0 t ) cos ( π f t ) ,
E ˜ o u t ( ω ) = 2 E 1 τ 1 ( A 2 τ 1 2 ω ω 0 ) [ A + 2 π f τ 1 2 ( ω ω 0 ) ] [ A 2 π f τ 1 2 ( ω ω 0 ) ] .
f ( z ) H FBG ( ω ) e i ω t d ω ,
ε = 10 × log   I j + I j + 1 2 I m i d ,
E 1 / E 0 = 2 m τ 0 τ 1   exp ( π 2 f 2 τ 0 2 8 ) ,
I 1 / I 0 = 2 m 2 τ 0 τ 1   exp [ π 2 f 2 τ 0 2 4 ] ,
E o u t ( t ) = E 1   exp [ 2 t 2 / τ 1 2 ] exp ( i ω 0 t ) cos ( π f max t 2 / t 0 ) ,
H FBG ( ω ) = exp ( t 0 2 τ 1 2 ( ω ω 0 ) 2 4 ( t 0 2 + π 2 f max 2 τ 1 4 ) + 1 8 τ 0 2 ( ω ω 0 ) 2 ) 2 τ 0 π 2 f max 2 t 0 2 + 1 τ 1 4 × | exp ( t 0 τ 1 2 ( ω ω 0 ) 2 8 ( t 0 i π f max τ 1 2 ) ) i π f max t 0 + 1 τ 1 2 + exp ( t 0 τ 1 2 ( ω ω 0 ) 2 8 ( t 0 + i π f max τ 1 2 ) ) i π f max t 0 + 1 τ 1 2 | .
E o u t ( t ) = E 1   exp [ 2 t 2 / τ 1 2 ] exp ( i ω 0 t ) × cos ( π f max t ( t + t 0 ) / t 0 ) ,
H FBG ( ω ) = 1 2 τ 0 π 2 f max 2 t 0 2 + 1 τ 1 4   exp ( 1 8 τ 0 2 ( ω ω 0 ) 2 t 0 2 τ 1 2 8 × | ( 2 π f + ω ω 0 ) 2 t 0 + i π f τ 1 2 + ( 2 π f ω + ω 0 ) 2 t 0 i π f τ 1 2 | ) × | exp ( t 0 τ 1 2 ( 2 π f ω + ω 0 ) 2 8 ( t 0 i π f max τ 1 2 ) ) i π f max t 0 + 1 τ 1 2 + exp ( t 0 τ 1 2 ( 2 π f + ω ω 0 ) 2 8 ( t 0 + i π f max τ 1 2 ) ) i π f max t 0 + 1 τ 1 2 | .

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