Abstract

A comparison between several 1D periodic structures designed to enhance non-linear effects for high-speed all-optical applications is presented. These structures allow for a small group velocity of the propagating waves, so the light-matter interaction is increased, making the non-linear process to be more efficient. In addition, the propagating wave is compressed, making the field intensity to be higher in the non-linear material. Thus, a significant reduction in both the structure length and the input power needed to induce a particular phase shift is achieved. The selected 1D periodic structures are compared by means of properties such as the modal effective volume, coupling efficiency, mode bandwidth, group velocity dispersion, and easiness of fabrication, in order to determine the optimum configuration in terms of non-linear enhancement.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2006 (1)

J. M. Martinez, J. Herrera, F. Ramos, and J. Marti, "All-optical correlation employing single logic XOR gate with feedback," Electron. Lett. 42, 1170-1171 (2006).
[CrossRef]

2005 (3)

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: role of the fabrication disorder and photon group velocity," Phys.Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

S. Tatsuura, T. Matsubara, H. Mitsu, Y. Sato, I. Iwasa, M. Tian, and M. Furuki, "Cadmium telluride bulk crystal as an ultrafast nonlinear optical switch," Appl. Phys. Lett. 87, 251110 (2005).
[CrossRef]

M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, "Slow-light, band-edge waveguides for tunable time delays," Opt. Express 13, 7145-7159 (2005).
[CrossRef] [PubMed]

2004 (1)

2002 (1)

2001 (3)

N. A. R. Bhat and J. E. Sipe, "Optical pulse propagation in nonlinear photonic crystals," Phys. Rev. E 64, 056604 (2001).
[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

1999 (1)

1995 (1)

Bhat, N. A. R.

N. A. R. Bhat and J. E. Sipe, "Optical pulse propagation in nonlinear photonic crystals," Phys. Rev. E 64, 056604 (2001).
[CrossRef]

Boyd, R. W.

Chen, J. C.

Chigrin, D. N.

Devenyi, A.

Fan, S.

Furuki, M.

S. Tatsuura, T. Matsubara, H. Mitsu, Y. Sato, I. Iwasa, M. Tian, and M. Furuki, "Cadmium telluride bulk crystal as an ultrafast nonlinear optical switch," Appl. Phys. Lett. 87, 251110 (2005).
[CrossRef]

Heebner, J. E.

Herrera, J.

J. M. Martinez, J. Herrera, F. Ramos, and J. Marti, "All-optical correlation employing single logic XOR gate with feedback," Electron. Lett. 42, 1170-1171 (2006).
[CrossRef]

Hughes, S.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: role of the fabrication disorder and photon group velocity," Phys.Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Ibanescu, M.

Ippen, E.

Iwasa, I.

S. Tatsuura, T. Matsubara, H. Mitsu, Y. Sato, I. Iwasa, M. Tian, and M. Furuki, "Cadmium telluride bulk crystal as an ultrafast nonlinear optical switch," Appl. Phys. Lett. 87, 251110 (2005).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Lavrinenko, A. V.

Marti, J.

J. M. Martinez, J. Herrera, F. Ramos, and J. Marti, "All-optical correlation employing single logic XOR gate with feedback," Electron. Lett. 42, 1170-1171 (2006).
[CrossRef]

Martinez, J. M.

J. M. Martinez, J. Herrera, F. Ramos, and J. Marti, "All-optical correlation employing single logic XOR gate with feedback," Electron. Lett. 42, 1170-1171 (2006).
[CrossRef]

Matsubara, T.

S. Tatsuura, T. Matsubara, H. Mitsu, Y. Sato, I. Iwasa, M. Tian, and M. Furuki, "Cadmium telluride bulk crystal as an ultrafast nonlinear optical switch," Appl. Phys. Lett. 87, 251110 (2005).
[CrossRef]

Meade, R. D.

Mitsu, H.

S. Tatsuura, T. Matsubara, H. Mitsu, Y. Sato, I. Iwasa, M. Tian, and M. Furuki, "Cadmium telluride bulk crystal as an ultrafast nonlinear optical switch," Appl. Phys. Lett. 87, 251110 (2005).
[CrossRef]

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Povinelli, M. L.

Ramos, F.

J. M. Martinez, J. Herrera, F. Ramos, and J. Marti, "All-optical correlation employing single logic XOR gate with feedback," Electron. Lett. 42, 1170-1171 (2006).
[CrossRef]

Ramunno, L.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: role of the fabrication disorder and photon group velocity," Phys.Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Sato, Y.

S. Tatsuura, T. Matsubara, H. Mitsu, Y. Sato, I. Iwasa, M. Tian, and M. Furuki, "Cadmium telluride bulk crystal as an ultrafast nonlinear optical switch," Appl. Phys. Lett. 87, 251110 (2005).
[CrossRef]

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Sipe, J. E.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: role of the fabrication disorder and photon group velocity," Phys.Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

N. A. R. Bhat and J. E. Sipe, "Optical pulse propagation in nonlinear photonic crystals," Phys. Rev. E 64, 056604 (2001).
[CrossRef]

Soljacic, M.

Sotomayor Torres, C. M.

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Tatsuura, S.

S. Tatsuura, T. Matsubara, H. Mitsu, Y. Sato, I. Iwasa, M. Tian, and M. Furuki, "Cadmium telluride bulk crystal as an ultrafast nonlinear optical switch," Appl. Phys. Lett. 87, 251110 (2005).
[CrossRef]

Tian, M.

S. Tatsuura, T. Matsubara, H. Mitsu, Y. Sato, I. Iwasa, M. Tian, and M. Furuki, "Cadmium telluride bulk crystal as an ultrafast nonlinear optical switch," Appl. Phys. Lett. 87, 251110 (2005).
[CrossRef]

Winn, J.

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Young, J. F.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: role of the fabrication disorder and photon group velocity," Phys.Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

S. Tatsuura, T. Matsubara, H. Mitsu, Y. Sato, I. Iwasa, M. Tian, and M. Furuki, "Cadmium telluride bulk crystal as an ultrafast nonlinear optical switch," Appl. Phys. Lett. 87, 251110 (2005).
[CrossRef]

Electron. Lett. (1)

J. M. Martinez, J. Herrera, F. Ramos, and J. Marti, "All-optical correlation employing single logic XOR gate with feedback," Electron. Lett. 42, 1170-1171 (2006).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. E (1)

N. A. R. Bhat and J. E. Sipe, "Optical pulse propagation in nonlinear photonic crystals," Phys. Rev. E 64, 056604 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Phys.Rev. Lett. (1)

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: role of the fabrication disorder and photon group velocity," Phys.Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Other (4)

J. García, A. Martínez, and J. Martí, "Influence of Group Velocity on roughness losses for 1D Periodic Structures," in Slow and Fast Light (Optical Society of America, 2007), paper JTuA4.

G. P. Agrawal, Nonlinear Fiber Optics Third Ed., (Academic Press, 2001).

G. P. Agrawal, Fiber-Optic Communication Systems, (Wiley-Interscience, 1997).

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, "Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs," Phys. Rev. B 72, 161318(R) (2005).
[CrossRef]

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Figures (12)

Fig. 1.
Fig. 1.

Coupling efficiency between structures can be increased by adiabatically changing the parameters of the structure. The structure shown in the example is proposed in [5].

Fig. 2.
Fig. 2.

Photonic band diagram of a generic 1D periodic structure [5]. It can be seen that bands 1 and 2 present opposite dispersions near the band edge. The cascaded structure used to compensate the GVD accumulated along the 1D periodic structure is also depicted.

Fig. 3.
Fig. 3.

1D periodic structures analyzed. (a) and (b) show a CdTe rods chain structure with n=1 and n=3 rows of rods, respectively. (c) shows a CdTe waveguide with air holes. (d) and (e) show a CdTe waveguide with n=1 and n=2 rows of adjacent rods, respectively. (f) shows a corrugated CdTe waveguide.

Fig. 4.
Fig. 4.

Mode map for the configuration of the 1D periodic structure with n=3 nanopillars. Configurations giving their band edge at 1550 nm are represented with a solid black line.

Fig. 5.
Fig. 5.

Wavelength maps for the configuration of the 1D periodic structure of air holes in CdTe.

Fig. 6.
Fig. 6.

(a) Transmission spectra of the CdTe strip waveguide with a chain of holes when the 2nd band is placed around 1550 nm. Blue curve depicts the spectra of the waveguide with 61 holes and without any matching technique. Coupling response is enhanced by means of adiabatic transitions implemented at both ends of the waveguide by linearly diminishing the radius of the holes in N steps: N=3 (black curve), N=10 (green curve) and N=20 (red curve). Inset in (a) shows in detail the transmission near the band edge. (b) Scheme of the adiabatic transition implemented.

Fig. 7.
Fig. 7.

(a) Scheme of the adiabatic transition implemented by decreasing the width of the CdTe strip waveguide. (b) Transmission spectra of the CdTe strip waveguide with a chain of holes. Blue and red curves depicts the transmission with direct coupling from access strip waveguide and with an adiabatic transmission of reduced-radius holes (the same as Fig. 6(a)). Black curve depicts the response with a initially widened (800 nm) waveguide (as shown in (a)) and a tapering transition of 5 µm (10 holes).

Fig. 8.
Fig. 8.

(a) Component of the magnetic field perpendicular to the axis of the rods calculated at the horizontal plane for the first TE mode for the configuration with n=1 adjacent row of rods. (b) Band diagram of the configuration with n=2 adjacent row of rods. Red colour indicates TE-polarised modes, while blue colour indicates TM-polarised ones.

Fig. 9.
Fig. 9.

(a) Dispersion relation for a corrugated waveguide with a=363.2 nm and wi =150 nm. Crosses indicate parity in the vertical direction, while circles indicate parity in the transversal direction. Red colour means even parity, while blue colour indicates odd parity. (b) Dispersion relation for the modes with even symmetry in the vertical direction and odd symmetry in the transversal direction.

Fig. 10.
Fig. 10.

Dispersion relations for the configurations with (a) its 1st mode centered at 1550 nm (a=371.7 nm and wi =100 nm) and (b) its 2nd mode centered at 1550 nm (a=390.1 nm and wi =100 nm).

Fig. 11.
Fig. 11.

Transmission spectra for the first two bands of the corrugated waveguide. Dashed line depicts the coupling efficiency when the corrugated is directly connected to the access strip waveguide. Solid blue line depicts the coupling efficiency when the corrugated is connected to the strip waveguide by using a tapered transition of 5 elements (see inset).

Fig. 12.
Fig. 12.

Scheme of an all-optical XOR logic gate based on a Mach-Zehnder interferometer.

Tables (3)

Tables Icon

Table 1. Properties of the selected TE modes for the CdTe strip waveguide with air holes.

Tables Icon

Table 2. Properties of the selected TM modes for the CdTe strip waveguide with air holes.

Tables Icon

Table 3. Properties of the selected TE modes for the CdTe corrugated waveguide.

Equations (5)

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Δ ϕ = Lωσ Δ n n eff ν g ,
Δ n 1 ν g .
Δ ϕ SW = ν g , WG 2 ν g , SW 2 Δ ϕ WG .
V eff = ( basic _ cell E ( x , y , z ) 2 · dx · dy · dz ) 2 non _ linear E ( x , y , z ) 4 · dx · dy · dz ,
V eff , n = V eff a .

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