Abstract

We show that long-period fiber grating (LPG) incorporating N1 π-phase shifts can serve as an Nth order temporal differentiator that operates in transmission. Due to the inherent large bandwidth provided by LPGs, subpicosecond (terahertz-bandwidth) optical signals may be processed with centimeters-length devices. Design parameters for up to fifth-order differentiators are given.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. J. Xu, X. Zhang, J. Dong, D. Liu, and D. Huang, Opt. Lett. 32, 1872 (2007).
    [CrossRef] [PubMed]
  2. M. A. Preciado, V. García-Muñoz, and M. A. Muriel, Opt. Express 15, 7196 (2007).
    [CrossRef] [PubMed]
  3. N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
    [CrossRef]
  4. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, Opt. Express 14, 10699 (2006).
    [CrossRef] [PubMed]
  5. N. K. Berger, B. Levit, B. Fischer, M. Kulishov, D. V. Plant, and J. Azaña, Opt. Express 15, 371 (2007).
    [CrossRef] [PubMed]
  6. Y. Park, J. Azaña, and R. Slavík, Opt. Lett. 32, 710 (2007).
    [CrossRef] [PubMed]
  7. M. Kulishov and J. Azaña, Opt. Express 15, 6152 (2007).
    [CrossRef] [PubMed]
  8. M. Kulishov and J. Azaña, Opt. Lett. 30, 2700 (2005).
    [CrossRef] [PubMed]
  9. T. Erdogan, JOSA A 14, 1760 (1997).
    [CrossRef]

2007

2006

2005

2004

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
[CrossRef]

1997

T. Erdogan, JOSA A 14, 1760 (1997).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Transfer functions of the designed Nth-order temporal differentiators with N= (a) 2, (b) 3, (c) 4, and (d) 5 (black, long-dashed line) and corresponding ideal differentiator characteristics [with ( ω o p t ω 0 ) N dependence] (red, solid curve). Phase dependencies are shown as green, dashed–dotted curves (designed differentiators) and as blue, short-dashed lines [ideal differentiators with linear term (that corresponds to a nondispersive propagation time delay) adjusted to allow for direct comparison with the designed differentiators].

Fig. 2
Fig. 2

Temporal envelopes of an input Gaussian pulse [dotted (blue) curve] and of the waveform at the LPG output [for the (a) second-, (b) third-, (c) fourth- and (d) fifth-order differentiator] [solid (black) curve], and ideal waveforms of differentiated pulses [dashed (red) curve].

Equations (9)

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

f ( ω ω 0 ) = f ( ω 0 ) + ( f ( ω ω 0 ) ) ( ω ω 0 ) + 0.5 ( f ( ω ω 0 ) ) ( ω ω 0 ) 2 + ,
F i = [ cos ( γ L i ) + j σ γ sin ( γ L i ) j κ γ sin ( γ L i ) j κ γ sin ( γ L i ) cos ( γ L i ) j σ γ sin ( γ L i ) ] .
Φ = [ e ( j π 2 ) 0 0 e ( + j π 2 ) ] = [ j 0 0 j ] ,
F = F n × Φ × F n 1 × Φ × × Φ × F 2 × Φ × F 1 .
cos [ κ ( L 1 L 2 ) ] = 0 , sin [ κ ( L 1 + L 2 ) ] = 0 .
cos [ κ ( L 1 L 2 + L 3 ) ] = 0 ,
sin [ κ ( L 1 L 2 L 3 ) ] sin [ κ ( L 1 + L 2 L 3 ) ] sin [ κ ( L 1 L 2 + L 3 ) ] = 0 ,
2 cos [ κ ( L 1 L 2 + L 3 ) ] 2 cos [ κ ( L 1 + L 2 + L 3 ) ] + κ ( L 1 L 2 + L 3 ) sin [ κ ( L 1 L 2 + L 3 ) ] = 0 .
2 sin { k π + κ [ ± arcos ( cos ( k π 2 κ L 3 ) ( 1 ) k ) + ( 2 m k ) π + 2 L 3 ] } + ( π 2 + k π ) ( 1 ) k = 0 ,

Metrics