Abstract

A new concept of electro-optically reconfigurable waveguide superimposed gratings with their widely controllable transmission characteristics are present. It is based on two types of superimposed refractive index gratings, electronically induced in an electro-optically active core. These gratings can be independently switched ON and OFF or both simultaneously activated with the controllable weighting factor. In this case its transmission characteristics represent double-dip rejection band spectrum with independent control of the dip positions and bandwidth. This simple concept opens opportunities for developing a number of tunable devices for integrated optics by use of the proposed design as a building block.

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References

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  1. M. Kulishov, P. Cheben, X. Daxhelet, S. Delprat, "Electro-optically induced tilted phase gratings in waveguide," J. Opt. Soc. Am. B 18, 457-464 (2001).
    [CrossRef]
  2. M. Kulishov, "Interdigitated electrode-induced phase grating with an electrically switchable and tunable period," Appl. Opt. 38, 7356-7363 (1998).
    [CrossRef]
  3. T. Erdogan, "Fiber grating spectra," J. Lightwave Techn. 15, 1277-1294 (1997).
    [CrossRef]
  4. P. Cheben, F. del Monte, D. J. Worsfold, D. Carrisson, C. P. Grover, J. D. Mackenzie, "A photorefractive organically modified silica glasses with high optical gain," Nature 2000, 408, 64-66 (2000).
    [CrossRef] [PubMed]
  5. J. Zhao, X. Shen, Y. Xia, "Beam splitting, combining and cross coupling through multiple superimposed volume index gratings," Opt. & Laser Technol. 33, 23-28 (2001)
    [CrossRef]

Other (5)

M. Kulishov, P. Cheben, X. Daxhelet, S. Delprat, "Electro-optically induced tilted phase gratings in waveguide," J. Opt. Soc. Am. B 18, 457-464 (2001).
[CrossRef]

M. Kulishov, "Interdigitated electrode-induced phase grating with an electrically switchable and tunable period," Appl. Opt. 38, 7356-7363 (1998).
[CrossRef]

T. Erdogan, "Fiber grating spectra," J. Lightwave Techn. 15, 1277-1294 (1997).
[CrossRef]

P. Cheben, F. del Monte, D. J. Worsfold, D. Carrisson, C. P. Grover, J. D. Mackenzie, "A photorefractive organically modified silica glasses with high optical gain," Nature 2000, 408, 64-66 (2000).
[CrossRef] [PubMed]

J. Zhao, X. Shen, Y. Xia, "Beam splitting, combining and cross coupling through multiple superimposed volume index gratings," Opt. & Laser Technol. 33, 23-28 (2001)
[CrossRef]

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Figures (5)

Fig.1.
Fig.1.

Cross-sectional view (a) of the waveguide EO grating with two particular electric potential configurations when ΔV=-2V0 (b) and ΔV=0 (c) that induce correspondent refractive index distributions.

Fig.2.
Fig.2.

Two transmission spectra of the waveguide gratings with the both structures b and c activated. The shift between peaks of the solid and dashed curves has been achieved by EO tuning through the bias voltage V0 . The device parameters: l=15.5 µm; L=15.7 mm; (β1 -β2 +σ11 -σ22)λ/2π=0.09973; (β1 -β3 +σ11 -σ33 )λ/=0.05; κ12 =κ13=10-4 µm-1; κ23 =10-5 µm-1 (red); κ12 =0.7×10-4 µm-1; κ13 =0.5×10-4 µm-1; κ23 =0.12×10-4 µm-1 (blue); κ13 =0.5×10-4 µm-1; κ13 =0.7×10-4 µm-1; κ23 =0.9×10-5 µm-1 (magenta).

Fig.3.
Fig.3.

Momentum diagram showing the mode interaction in the waveguide.

Fig.4.
Fig.4.

The electric potential application scheme (a) for EO indiced waveguide superimposed gratings that prevents from coupling between the cladding modes TE2 andTE3with the corresponding potential distributions for each partial gratings at ΔV=0 (b) and ΔV=-2V0 (c), with the mode distributions involved in the interaction (d) and the momentum diagram, where β2 -β3 coupling is forbidden.

Fig.5.
Fig.5.

Transmission spectrum of the superimposed gratings with the same width of the dips: The device parameters: l=15.5 µm; (β1 -β2 +σ11 -σ22 )λ/2π=0.09973; (β1 -β3 +σ11 -σ33 )λ/2π=0.05; red: κ12 =10-4 µm-1; κ13 =0.5×10-4 µm-1 κ23 =0.1×10-4 µm-1; over the length L1 =16 mm and κ13 =0; κ12 =0.5×10-4 µm-1 κ23 =0.1×10-4 µm-1; over the length L2 =16 mm, and blue: κ12 =0.5×10-4 µm-1; κ13 =0.5×10-4 µm-1 κ23 =0.1×10-4 µm-1; over the length L1 =32 mm.m

Equations (11)

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φ a ( x , z ) = Δ V 2 V 0 φ b ( x , z ) + ( 1 + Δ V 2 V 0 ) φ c ( x , z )
d a 0 dz = j κ 12 a i exp ( j Δ β 12 z ) j κ 13 a 3 exp ( j Δ β 13 z )
d a 2 dz = j κ 12 a 1 exp ( j Δ β 12 z ) j κ 23 a 3 exp ( j Δ β 23 z )
d a 3 dz = j κ 13 a 1 exp ( j Δ β 13 z ) j κ 23 a 2 exp ( j Δ β 23 z )
dR dz = j Δ β 12 + Δ β 13 2 R j κ 12 S j κ 13 P
dS dz = j Δ β 12 + Δ β 13 2 S j κ 12 R j κ 13 P
dP dz = + j Δ β 12 + Δ β 13 2 P j κ 13 S j κ 23 S
κ 12 = β 1 β 2 2 μ 0 k 0 c Δ V 2 r n o 4 h + h e 1 t ( x ) e 2 t ( x ) E x ( b ) ( x ) d x ;
κ 13 = β 1 β 3 2 μ 0 k 0 c ( 1 + Δ V 2 V 0 ) r n o 4 h + h e 1 t ( x ) e 3 t ( x ) E x ( c ) ( x ) d x ;
κ 23 = β 2 β 3 2 μ 0 k 0 c Δ V 2 r n o 4 h + h e 2 t ( x ) e 3 t ( x ) E x ( b ) ( x ) d x ;
σ jj = β j 2 μ 0 k 0 c E x 0 ( 1 + Δ V 2 V 0 ) r n o 4 h + h e jt ( x ) 2 d x ;

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