Abstract

We theoretically analyze and experimentally demonstrate broadband Brillouin slow light using multiple equal-amplitude spectral lines generated by multifrequency phase modulation. The theoretical analysis shows that 4n1 equal-amplitude spectral lines can be obtained if the modulation signal comprises the fundamental frequency and the odd harmonic waves, where n denotes the number of frequency components in the modulation signal. In experiment, 7 and 11 equal-amplitude spectral lines are obtained and Brillouin bandwidths of 340 and 570MHz are gained, respectively. The experimental results also indicate that the slope of the broadening factor for the delayed signal decreases in the case of broad and flattened Brillouin gain spectrum.

© 2008 Optical Society of America

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  1. R. W. Boyd and D. J. Gauthier, “'Slow' and 'fast' light,” Prog. Opt. 43, 497-530 (2002).
    [CrossRef]
  2. D. J. Gauthier, “Slow light brings faster communication,” Phys. World 18, 30-32 (2005).
  3. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200-202 (2003).
    [CrossRef] [PubMed]
  4. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meterspersecond in an ultracold atomic gas,” Nature 397, 594-598 (1999).
    [CrossRef]
  5. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
    [CrossRef] [PubMed]
  6. Z. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “Broadband SBS slow light in an optical fiber,” J. Lightwave Technol. 25, 201-206 (2007).
    [CrossRef]
  7. M. D. Stenner, M. A. Neifeld, Z. M. Zhu, A. M. C. Dawes, and D. J. Gauthier, “Distortion management in slow-light pulse delay,” Opt. Express 13, 9995-10002 (2005).
    [CrossRef] [PubMed]
  8. A. Minardo, R. Bernini, and L. Zeni, “Low distortion Brillouin slow light in optical fibers using AM modulation,” Opt. Express 14, 5866-5876 (2006).
    [CrossRef] [PubMed]
  9. T. Sakamoto, T. Yamamoto, K. Shiraki, and T. Kurashima, “Low distortion slow light in flat Brillouin gain spectrum by using optical frequency comb,” Opt. Express 16, 8026-8032 (2008).
    [CrossRef] [PubMed]
  10. Z. Lu, Y. Dong, and Q. Li, “Slow light in multi-line Brillouin gain spectrum,” Opt. Express 15, 1871-1877 (2007).
    [CrossRef] [PubMed]
  11. Z. Shi, R. Pant, Z. Zhu, M. D. Stenner, M. A. Neifeld, D. J. Gauthier, and R. W. Boyd, “Design of a tunable time-delay element using multiple gain lines for increased fractional delay with high data fidelity,” Opt. Lett. 32, 1986-1988 (2007).
    [CrossRef] [PubMed]
  12. T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, “Distortion reduction in cascaded slow light delays,” Electron. Lett. 42, 1110-1111 (2006).
    [CrossRef]
  13. R. Pant, M. D. Stenner, M. A. Neifeld, and D. J. Gauthier, “Optimal pump profile designs for broadband SBS slow-light systems,” Opt. Express 16, 2764-2777 (2008).
    [CrossRef] [PubMed]
  14. Y. Dong, Z. Lu, Q. Li, and W. Gao, “Long optical delay lines enhanced by ring configuration in optical fibers,” Chin. Phys. Lett. 24, 1568-1570 (2007).
  15. Y. Dong, Z. Lu, Q. Li, and W. Gao, “Controllable optical delay line using a Brillouin optical fiber ring laser,” Chin. Opt. Lett. 4, 628-630 (2006).

2008 (2)

2007 (4)

2006 (3)

2005 (3)

M. D. Stenner, M. A. Neifeld, Z. M. Zhu, A. M. C. Dawes, and D. J. Gauthier, “Distortion management in slow-light pulse delay,” Opt. Express 13, 9995-10002 (2005).
[CrossRef] [PubMed]

D. J. Gauthier, “Slow light brings faster communication,” Phys. World 18, 30-32 (2005).

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

2003 (1)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200-202 (2003).
[CrossRef] [PubMed]

2002 (1)

R. W. Boyd and D. J. Gauthier, “'Slow' and 'fast' light,” Prog. Opt. 43, 497-530 (2002).
[CrossRef]

1999 (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meterspersecond in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meterspersecond in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

Bernini, R.

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200-202 (2003).
[CrossRef] [PubMed]

Boyd, R. W.

Z. Shi, R. Pant, Z. Zhu, M. D. Stenner, M. A. Neifeld, D. J. Gauthier, and R. W. Boyd, “Design of a tunable time-delay element using multiple gain lines for increased fractional delay with high data fidelity,” Opt. Lett. 32, 1986-1988 (2007).
[CrossRef] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200-202 (2003).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, “'Slow' and 'fast' light,” Prog. Opt. 43, 497-530 (2002).
[CrossRef]

Dawes, A. M. C.

Dong, Y.

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meterspersecond in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

Gaeta, A. L.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Gao, W.

Y. Dong, Z. Lu, Q. Li, and W. Gao, “Long optical delay lines enhanced by ring configuration in optical fibers,” Chin. Phys. Lett. 24, 1568-1570 (2007).

Y. Dong, Z. Lu, Q. Li, and W. Gao, “Controllable optical delay line using a Brillouin optical fiber ring laser,” Chin. Opt. Lett. 4, 628-630 (2006).

Gauthier, D. J.

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meterspersecond in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meterspersecond in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

Henker, R.

T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, “Distortion reduction in cascaded slow light delays,” Electron. Lett. 42, 1110-1111 (2006).
[CrossRef]

Junker, M.

T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, “Distortion reduction in cascaded slow light delays,” Electron. Lett. 42, 1110-1111 (2006).
[CrossRef]

Kurashima, T.

Lauterbach, K. U.

T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, “Distortion reduction in cascaded slow light delays,” Electron. Lett. 42, 1110-1111 (2006).
[CrossRef]

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200-202 (2003).
[CrossRef] [PubMed]

Li, Q.

Lu, Z.

Minardo, A.

Neifeld, M. A.

Okawachi, Y.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Pant, R.

Sakamoto, T.

Schneider, T.

T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, “Distortion reduction in cascaded slow light delays,” Electron. Lett. 42, 1110-1111 (2006).
[CrossRef]

Schweinsberg, A.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Sharping, J. E.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Shi, Z.

Shiraki, K.

Stenner, M. D.

Willner, A. E.

Yamamoto, T.

Zeni, L.

Zhang, L.

Zhu, Z.

Zhu, Z. M.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

M. D. Stenner, M. A. Neifeld, Z. M. Zhu, A. M. C. Dawes, and D. J. Gauthier, “Distortion management in slow-light pulse delay,” Opt. Express 13, 9995-10002 (2005).
[CrossRef] [PubMed]

Chin. Opt. Lett. (1)

Chin. Phys. Lett. (1)

Y. Dong, Z. Lu, Q. Li, and W. Gao, “Long optical delay lines enhanced by ring configuration in optical fibers,” Chin. Phys. Lett. 24, 1568-1570 (2007).

Electron. Lett. (1)

T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, “Distortion reduction in cascaded slow light delays,” Electron. Lett. 42, 1110-1111 (2006).
[CrossRef]

J. Lightwave Technol. (1)

Nature (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meterspersecond in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Phys. World (1)

D. J. Gauthier, “Slow light brings faster communication,” Phys. World 18, 30-32 (2005).

Prog. Opt. (1)

R. W. Boyd and D. J. Gauthier, “'Slow' and 'fast' light,” Prog. Opt. 43, 497-530 (2002).
[CrossRef]

Science (1)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200-202 (2003).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Spectrum of seven equal-amplitude spectral lines: (a) simulation; (b) experiment. F denotes the flatness.

Fig. 2
Fig. 2

Spectrum of 11 equal-amplitude spectral lines: (a) simulation; (b) experiment. F denotes the flatness.

Fig. 3
Fig. 3

Experimental setup: P, polarizer; IM, intensity modulator; PM, phase modulator; PC, polarization controller; EDFA, erbium-doped fiber amplifier; OC, optical circulator; OI, optical isolator; AFG, arbitrary function generator; VOA, variable optical attenuator; D, detector. In the dotted frame is a Brillouin optical fiber ring laser.

Fig. 4
Fig. 4

Measured delays and fractional delays versus Brillouin gain with 7 (square) and 11 (round) equal-amplitude spectral lines.

Fig. 5
Fig. 5

Broadening factors versus fractional delay with 7 (square) and 11 (round) equal-amplitude spectral lines.

Fig. 6
Fig. 6

Different curves represent temporal evolution of 2 ns input Stokes pulse (solid curve) and output Stokes pulses with seven (dotted curve) and eleven (dashed curve) equal-amplitude spectral line with a gain of 20 dB .

Tables (1)

Tables Icon

Table 1 Parameters to Obtain 7 and 11 Equal-Amplitude Spectral Lines

Equations (39)

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m ( t ) = k = 0 + γ k sin ( 2 π k f m t + ϕ k ) .
E m ( t ) = cos [ 2 π f c t + k = 1 + γ k sin ( 2 π k f m t + ϕ k ) ] ,
E m ( t ) = Re [ exp ( j 2 π f c t + k = 1 + j γ k sin ( 2 π k f m t + ϕ k ) ) ] = Re [ exp ( j 2 π f c t ) k = 1 + exp ( j γ k sin ( 2 π k f m t + ϕ k ) ) ] .
E m ( t ) = Re [ exp ( j 2 π f c t ) k = 1 + ( n k = + J n k ( γ k , ϕ k ) exp ( j 2 π n k k f m t ) ) ] = n 1 = + n 2 = + n k = + [ k = 1 + J n k ( γ k , ϕ k ) cos ( 2 π ( f c + k = 1 + n k k f m ) t ) ] ,
J n ( γ , ϕ ) = 1 2 π π π exp ( j ( γ sin ( x + ϕ ) n x ) ) d x
n = 0 , ± 1 , ± 2 ,
A 0 = k = 1 + k n k = 0 k = 1 + J n k ( γ k , ϕ k ) ,
A i = k = 1 + k n k = i k = 1 + J n k ( γ k , ϕ k ) ,
A i = k = 1 + k n k = i k = 1 + J n k ( γ k , ϕ k ) , i = 1 , 2 , 3 , ,
J 2 k ( γ , φ ) = J 2 k * ( γ , φ ) ,
π π exp [ j γ sin ( x + φ ) j 2 k x ] d x = π π exp [ j γ sin ( x + φ ) j 2 k x ] d x ,
π π { exp [ j γ sin ( x + φ ) j 2 k x ] exp [ j γ sin ( x + φ ) j 2 k x ] } d x = 0 ,
π π exp ( j 2 k x ) { exp [ j γ sin ( x + φ ) ] exp [ j γ sin ( x + φ ) ] } d x = 0 .
π π 2 j cos 2 k x sin [ γ sin ( x + φ ) ] d x + π π 2 j sin 2 k x sin [ γ sin ( x + φ ) ] d x = 0 .
F 1 = π π 2 j cos 2 k x sin [ γ sin ( x + φ ) ] d x ,
F 2 = π π 2 j sin 2 k x sin [ γ sin ( x + φ ) ] d x .
F 1 = π π 2 j cos 2 k x sin [ γ sin x cos φ + γ cos x sin φ ] d x = π π 2 j cos 2 k x sin ( γ sin x cos φ ) cos ( γ cos x sin φ ) d x + π π 2 j cos 2 k x cos ( γ sin x cos φ ) sin ( γ cos x sin φ ) d x .
F 1 = π π 2 j cos 2 k x cos ( γ sin x cos φ ) sin ( γ cos x sin φ ) d x .
F 1 = 2 j π 2 π 2 cos 2 k ( θ + π 2 ) cos [ γ sin ( θ + π 2 ) cos φ ] sin [ γ cos ( θ + π 2 ) sin φ ] d θ = ( 1 ) k + 1 2 j π 2 π 2 cos 2 k θ cos ( γ cos θ cos φ ) sin ( γ sin θ sin φ ) d θ .
F 1 = 0 .
J 2 k + 1 ( γ , φ ) = J ( 2 k + 1 ) * ( γ , φ ) ,
π π exp ( j ( 2 k + 1 ) x ) { exp [ j γ sin ( x + φ ) ] + exp [ j γ sin ( x + φ ) ] } d x = 0 .
π π 2 cos ( 2 k + 1 ) x cos [ γ sin ( x + φ ) ] d x + π π 2 j sin ( 2 k + 1 ) x cos [ γ sin ( x + φ ) ] d x = 0 .
F 3 = π π 2 cos ( 2 k + 1 ) x cos [ γ sin ( x + φ ) ] d x ,
F 4 = π π 2 j sin ( 2 k + 1 ) x cos [ γ sin ( x + φ ) ] d x .
A i = J m J n ,
A i = J m J n ,
a i = J m J n .
a i * = J m * J n * = J m J n = a i .
a i = J m J n .
a i * = J m * J n * = J m ( J n ) = J m J n = a i .
b i = J m J n .
b i * = J m * J n * = J m J n = b i .
A i = J m J n J k ,
A i = J m J n J k ,
a i = J m J n J k = J m J n J k = a i .
b i = J m J n J k = J m J n ( J k ) = b i .
a i = J m J n J k = J m J n ( J k ) = a i .
b i = J m J n J k = J m J n J k = b i .

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