Abstract

Wavelength-selective directional couplers with dissimilar waveguides are designed for ultrafast optical differentiation within the femtosecond regime (corresponding to processing bandwidths > 10 THz). The theoretically proposed coupler-based differentiators can be produced by wavelength matching of the propagation constants of two different waveguides in the coupler at the center wavelength. A single directional coupler can be designed to achieve either a 2nd-order differentiator or a 1st-order differentiator by properly fixing the product of coupling coefficient and coupling length of the coupler. We evaluated the differentiation errors (~2%) and energetic efficiency (~11% for 1st order differentiation) of the designed optical differentiators through numerical simulations. The proposed design has a strong potential to provide a feasible solution as an integrated differentiation unit device for ultrafast optical signal processing circuits.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230(1-3), 115–129 (2004).
    [CrossRef]
  2. M. Kulishov and J. Azaña, “Long-period fiber gratings as ultrafast optical differentiators,” Opt. Lett. 30(20), 2700–2702 (2005).
    [CrossRef] [PubMed]
  3. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14(22), 10699–10707 (2006).
    [CrossRef] [PubMed]
  4. M. A. Preciado and M. A. Muriel, “Design of an ultrafast all-optical differentiator based on a fiber Bragg grating in transmission,” Opt. Lett. 33(21), 2458–2460 (2008).
    [CrossRef] [PubMed]
  5. R. Slavík, Y. Park, N. Ayotte, S. Doucet, T.-J. Ahn, S. LaRochelle, and J. Azaña, “Photonic temporal integrator for all-optical computing,” Opt. Express 16(22), 18202–18214 (2008).
    [CrossRef] [PubMed]
  6. Y. Park, J. Azaña, and R. Slavík, “Ultrafast all-optical first- and higher-order differentiators based on interferometers,” Opt. Lett. 32(6), 710–712 (2007).
    [CrossRef] [PubMed]
  7. R. Zengerle and O. Leminger, “Wavelength-selective directional coupler made of nonidentical single-mode fibers,” J. Lightwave Technol. 4(7), 823–827 (1986).
    [CrossRef]
  8. K. Morishita, “Wavelength-selective optical-fiber directional couplers using dispersive materials,” Opt. Lett. 13(2), 158–160 (1988).
    [CrossRef] [PubMed]
  9. A. K. Das and M. A. Mondal, “Precise control of the center wavelength and bandwidth of wavelength-selective single-mode fiber couplers,” Opt. Lett. 19(11), 795–797 (1994).
    [CrossRef] [PubMed]
  10. R. Zengerle and O.G. Leminger, “Investigations of fabrication tolerances of narrow bandwidth directional coupler filters in InP,” Integrated Photonics Research, TuB3–1 (1992).
  11. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press Inc., 1991) Chap. 6 and 7.

2008 (2)

2007 (1)

2006 (1)

2005 (1)

2004 (1)

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230(1-3), 115–129 (2004).
[CrossRef]

1994 (1)

1988 (1)

1986 (1)

R. Zengerle and O. Leminger, “Wavelength-selective directional coupler made of nonidentical single-mode fibers,” J. Lightwave Technol. 4(7), 823–827 (1986).
[CrossRef]

Ahn, T.-J.

Ayotte, N.

Azaña, J.

Das, A. K.

Doucet, S.

Kam, C. H.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230(1-3), 115–129 (2004).
[CrossRef]

Kulishov, M.

LaRochelle, S.

Leminger, O.

R. Zengerle and O. Leminger, “Wavelength-selective directional coupler made of nonidentical single-mode fibers,” J. Lightwave Technol. 4(7), 823–827 (1986).
[CrossRef]

Mondal, M. A.

Morandotti, R.

Morishita, K.

Muriel, M. A.

Ngo, N. Q.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230(1-3), 115–129 (2004).
[CrossRef]

Park, Y.

Preciado, M. A.

Slavík, R.

Tjin, S. C.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230(1-3), 115–129 (2004).
[CrossRef]

Yu, S. F.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230(1-3), 115–129 (2004).
[CrossRef]

Zengerle, R.

R. Zengerle and O. Leminger, “Wavelength-selective directional coupler made of nonidentical single-mode fibers,” J. Lightwave Technol. 4(7), 823–827 (1986).
[CrossRef]

J. Lightwave Technol. (1)

R. Zengerle and O. Leminger, “Wavelength-selective directional coupler made of nonidentical single-mode fibers,” J. Lightwave Technol. 4(7), 823–827 (1986).
[CrossRef]

Opt. Commun. (1)

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230(1-3), 115–129 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Other (2)

R. Zengerle and O.G. Leminger, “Investigations of fabrication tolerances of narrow bandwidth directional coupler filters in InP,” Integrated Photonics Research, TuB3–1 (1992).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press Inc., 1991) Chap. 6 and 7.

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 (4)

Fig. 1
Fig. 1

(a) Schematic concept diagrams of 1st- and 2nd- order optical differentiators with κL = π/2 and κL = π, respectively (an input pulse with a transform-limited Gaussian shape is assumed in the illustration). (b) Amplitude of the spectral transmission function in the bypass waveguide 1 of a 8 mm directional coupler with the coupling slope of 0.02 μm−2 and κL = π/2 (dot curve) and in the crossover waveguide 2 of a 8-mm directional coupler with the coupling slope of 0.02 μm−2 and κL = π (dashed curve). The solid curve represents the energy spectrum of a 3-ps super-Gaussian input pulse with a center wavelength of 1.55 μm (corresponding to 193.55 THz), which was obtained by Fourier transformation of the considered input pulse.

Fig. 2
Fig. 2

Temporal waveform (dashed curves) corresponding to the 3-ps super-Gaussian optical pulse launched at the input of the simulated couplers. Output waveform (a) in the waveguide 1 of the coupler with κL = π/2 [transfer function (dotted curve) in Fig. 1] and (b) in the waveguide 2 of the coupler with κL = π [transfer function (dashed curve) in Fig. 1]. Ideal first (left) and second (right) time derivatives of the input pulse are represented with open circles.

Fig. 3
Fig. 3

(a) 3dB-bandwidth of the transfer functions of 1st-(open circle) and 2nd-(open square) order coupler-based differentiators with respect to coupling length (for η = 0.02 μm−2), together with the estimated bandwidth from Eq. (5) with p = 3.5 for 1st-order differentiation and p = 6.5 for 2nd-order differentiation. (b) 3dB-bandwidth of the transfer functions of 1st-(open circle) and 2nd-(open square) order coupler-based differentiators with respect to the coupling slope (for L = 8 mm), together with the estimated bandwidth from Eq. (5) with p = 3.5 for 1st-order differentiation and p = 6.5 for 2nd-order differentiation.

Fig. 4
Fig. 4

Energetic efficiency with respect to the differentiation bandwidth for (a) 1st-order and (b) 2nd-order differentiator in case of the super-Gaussian input pulse with the temporal width of 1 ps (corresponding to 1 THz).

Equations (5)

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

H 1 = [ cos ( γ L ) j Δ β γ sin ( γ L ) ] exp [ j 2 ( β 1 + β 2 ) L ]
H 2 = j κ γ sin ( γ L ) exp [ j 2 ( β 1 + β 2 ) L ] ,
H 1 [ cos ( κ L ) j Δ β κ sin ( κ L ) ] exp ( j β 1 L )
H 2 j { sin ( κ L ) + Δ β 2 2 κ 2 [ κ L cos ( κ L ) sin ( κ L ) ] } exp ( j β 2 L ) .
Δ ν 3 d B = c p L η λ 0 2     ,

Metrics