Abstract

The strong dispersion and large third-order nonlinearity in Si photonic wires are intimately linked in the optical physics needed for the optical modification of phase. By carefully choosing the waveguide dimensions, both linear and nonlinear optical properties of Si wires can be engineered. In this paper we provide a review of the modification of phase using nonlinear-optical effects such as self-phase and cross-phase modulation in dispersion-engineered Si wires. The low threshold powers for phase-changing effects in Si-wires make them potential candidates for functional nonlinear optical devices of just a few millimeters in length.

© 2008 Optical Society of America

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2007

R Dekker, N Usechak, M Först, A Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D: Appl. Phys. 40, R249–R271 (2007).
[CrossRef]

F. Xia, L. Sekaric, Y. A. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nature Photonics 1, 65–71 (2007).
[CrossRef]

A. D. Bristow, N. Rotenberg, H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91, 21111 (2007).
[CrossRef]

L. Yin, Q. Lin, G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32, 391–393 (2007).
[CrossRef] [PubMed]

I. -W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, Jr., S. J. McNab, Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 1135–1146 (2007).
[CrossRef] [PubMed]

C. Koos, L. Jacome, C. Poulton, J. Leuthold, W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15, 5976–5990 (2007).
[CrossRef] [PubMed]

E. -K. Tien, N. S. Yuksek, F. Qian, Ö. Boyraz, “Pulse compression and modelocking by using TPA in silicon waveguides,” Opt. Express 15, 6500–6506 (2007).
[CrossRef] [PubMed]

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, P. M. Fauchet, “Optical solitons in a silicon waveguide,” Opt. Express 15, 7682–7688 (2007).
[CrossRef] [PubMed]

I. -W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C. -Y. Chou, F. Xia, W. M. Green, Y. A. Vlasov, R. M. Osgood, “Supercontinuum generation in silicon photonic wires,” Opt. Express 15, 15242–15249 (2007).
[CrossRef] [PubMed]

2006

B. Jalali, S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24, 4600–4615 (2006).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Plots of computed effective index of refraction, and first- through third-order dispersion as a function of wavelength for four different Si-wire dimensions. Blue: 350×220 nm2, green, 360×220 nm2, red 450×220 nm2, light blue 450×330 nm2. Inset: waveguide geometry.

Fig. 2.
Fig. 2.

Contours of the zero-GVD map of a silicon photonic-wire channel waveguide. The zero GVD wavelengths are expressed in units of micrometers.

Fig. 3.
Fig. 3.

Dependence of output power on coupled input power for (a) 1.8 ps (from Ref. 61) and (b) 200 fs pulses (from Ref. 62). Experiment: squares. Simulations: curves.

Fig. 4.
Fig. 4.

Experimental observation of SPM with (a) 1.8 ps pulses (figure from Ref. 61) (b) 200 fs pulses (data from Ref. 62).

Fig 5.
Fig 5.

Measured and experimental transmission through a Si photonic wire waveguide with γP 0=56.3 cm-1. Left panel: measured spectra (brown). Right panel: simulation using hyperbolic secant input pulse (red). Blue curves on both panels correspond to γP 0=1.1 cm-1 (with sech input pulse for simulation). Dashed line: OSA noise floor. The numbers are shown to illustrate the correspondence between experiment and simulation. From Ref. 62.

Fig 6.
Fig 6.

Evolution of spectra at different excitation conditions γP 0=1.1, 11.3, 33.8, 45.0 cm-1 (bottom to top) spectra. Note also the evolution of soliton radiation (dashed line) at 1590 nm.

Fig 7.
Fig 7.

Demonstration of cross-phase modulation in silicon photonic wires. Dependence of probe spectrum on pump power and pump-probe delay for (a) τd =δ and (b) τd =5δ. Red and blue curves denote spectra in the absence and presence of pump, respectively.

Fig. 8.
Fig. 8.

Experimental (red) and numerical simulation (blue) results showing the dependence of cross-phase modulation on the normalized time delay. The center wavelength of the probe is ~1590 nm.

Fig. 9.
Fig. 9.

Calculated modulation instability gain spectra for (a) case A and (b) case B as described in the text.

Fig. 10.
Fig. 10.

Simulation of pulse compression via cross-phase modulation. Signal (left panel) and pump (right panel) field envelopes vs. time and propagation distance. The temporal width is 200 fs for both the pump and signal pulses. Here γpsPp ≈100 cm-1 for the pump, with a center frequency of 1625 nm. For the signal Ps Pp and the center frequency of it is 1451 nm. Insets: initial and final pulse envelopes. The waveguide dimensions are w×h=360×220 nm2.

Tables (1)

Tables Icon

Table 1. Comparison of characteristic lengths for ultrashort (200 fs) and long (10 ps) pulses, and the γ parameter in a Si photonic wire (dimensions: 220×450 nm2) and a single-mode optical fiber for γ=1.55µm.

Equations (18)

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i ( u p z + 1 ν g , p u p t ) β 2 , p 2 2 u p t 2 i β 3 , p 6 3 u p t 3 = i c κ p 2 n ν g , p ( α in + α FC p ) u p ω p κ p n ν g , p δ n FC p u p
3 ω p 4 ε 0 A 0 ν g , p ( P p Γ p ν g , p u p 2 + 2 P s Γ sp ν g , s u s 2 ) u p ,
i ( u s z + 1 ν g , s u s t ) β 2 , s 2 2 u s t 2 i β 3 , s 6 3 u s t 3 = i c κ s 2 n ν g , s ( α in + α FC s ) u s ω s κ s n ν g , s δ n FC s u s
3 ω s 4 ε 0 A 0 ν g , s ( P s Γ s ν g , s u s 2 + 2 P p Γ ps ν g , p u p 2 ) u s ,
N t = N t c + 3 4 ε 0 ħ A 0 2 [ P p 2 Γ p ν g , p 2 u p 4 + P s 2 Γ s ν g , s 2 u s 4 + 4 ( ω p Γ sp + ω s Γ sp ) P p P s ( ω p + ω s ) ν g , p ν g , s u p u s 2 ] ,
Γ j = A 0 A 0 e j * · χ ( 3 ) e j e j * e j dA J j 2
Γ jl = A 0 A 0 e l * · χ ( 3 ) e j e j * e l dA ( J j J l )
ϕ s ( z , T ) = z γ s P s u s ( 0 , T ) 2 + 2 γ ps P p 0 z u p ( 0 , T + z Δ ) 2 d z
γ i = 3 ω i Γ i 4 ε 0 A 0 v g , i 2
γ ji = 3 ω i Γ ji 4 ε 0 A 0 v g , j v g , i
ϕ s ( z , τ ) = γ ps P p z π δ [ erf ( τ τ d + δ ) erf ( τ τ d ) ] ,
δ ω s ( z , τ ) = 1 T p ϕ s ( z , τ ) τ = 2 γ ps P p z T p δ { exp [ ( τ τ d + δ ) 2 ] exp [ ( τ τ d ) 2 ] } .
i ( u z + 1 v g u t ) β 2 2 2 u t 2 i β 3 6 3 u t 3
= i c κ 2 n v g ( α in + α FC ) u ω κ n v g δ n FC u 3 ω P 0 Γ 4 ε 0 A 0 v g 2 u 2 u ,
N t = N t c + 3 P 0 2 Γ 4 ε 0 ћ A 0 2 v g 2 u 4
n 2 = 3 Γ 4 ε 0 c n 2
β = 3 ω Γ 2 n 2 c 2 ε 0 .
[ ( Λ Ω v g , p ) 2 ρ p ] [ ( Λ Ω v g , s ) 2 ρ s ] = η Ω 4

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