Abstract

A new design for an adjustable electro-optic phase grating inside a waveguide is proposed. The electric field and the refractive-index distribution induced inside a waveguide by voltage applied to double-sided periodic interdigitated electrode arrays are calculated rigorously on the basis of an original analytical technique. The modeling was carried out with the Mathcad software. It is shown that the fundamental periodicity of the induced grating inside the waveguide can be switched between l and 2l by application of the appropriate voltage, where l is the spatial periodicity of the interdigitated electrodes. One can also fine tune the peak grating reflectivity by changing the constant component of the induced refractive index with the help of the constant component of the electric field inside the waveguide. The suggested design can be used as a basic idea for a variety of optical communication networking applications, including switching, modulation, deflection, and data processing.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Elachi, C. Yeh, “Periodic structures in integrated optics,” J. Appl. Phys. 44, 3146–3152 (1973).
    [CrossRef]
  2. T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
    [CrossRef]
  3. J.-P. Weber, B. Stoltz, H. Sano, M. Dasler, O. Oberg, J. Wolz, “An integratable polarization-independent tunable filter for WDM systems: the multigrating filter,” J. Lightwave Technol. 14, 2719–2735 (1996).
    [CrossRef]
  4. D. Sun, C. Zhao, R. T. Chen, “Intraplane to interplane optical interconnects with a high diffraction efficiency electro-optic grating,” Appl. Opt. 36, 629–634 (1997).
    [CrossRef] [PubMed]
  5. Z. Yu, S. J. Schablitsky, S. Y. Chou, “Nanoscale GaAs metal–semiconductor–metal photodetectors fabricated using nanoimprint lithography,” Appl. Phys. Lett. 74, 2381–2383 (1999).
    [CrossRef]
  6. M. Kulishov, “Modeling of a converging gradient-index lens with variable focal length in a lanthanum-modified lead zirconate titanate ceramic cylinder with a lateral multielectrode structure,” Appl. Opt. 37, 3506–3514 (1998).
    [CrossRef]
  7. M. A. Hussain, S. L. Pu, “Dynamic stress intensity factor for an unbounded plate having collinear cracks,” Eng. Fract. Mech. 4, 865–876 (1972).
    [CrossRef]
  8. I. S. Gradshtein, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), Secs. 1.441.1 and 1.441.4.
  9. E. N. Glytsis, T. K. Gaylord, M. G. Moharam, “Electric field, permittivity, and strain distributions induced by interdigitated electrodes of electrooptic waveguides,” J. Lightwave Technol. LT-5, 668–681 (1987).
    [CrossRef]
  10. L. B. Aronson, “Electro-optic tuning and sidelobe control in acousto-optic tunable filters,” Opt. Lett. 20, 46–48 (1995).
    [CrossRef] [PubMed]
  11. M. J. Weber, ed., CRC Handbook of Laser Science and Technology (CRC Press, Boca, Raton, Fla., 1986), Vol. IV, Part 2.

1999

Z. Yu, S. J. Schablitsky, S. Y. Chou, “Nanoscale GaAs metal–semiconductor–metal photodetectors fabricated using nanoimprint lithography,” Appl. Phys. Lett. 74, 2381–2383 (1999).
[CrossRef]

1998

1997

1996

J.-P. Weber, B. Stoltz, H. Sano, M. Dasler, O. Oberg, J. Wolz, “An integratable polarization-independent tunable filter for WDM systems: the multigrating filter,” J. Lightwave Technol. 14, 2719–2735 (1996).
[CrossRef]

1995

1987

E. N. Glytsis, T. K. Gaylord, M. G. Moharam, “Electric field, permittivity, and strain distributions induced by interdigitated electrodes of electrooptic waveguides,” J. Lightwave Technol. LT-5, 668–681 (1987).
[CrossRef]

1986

T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[CrossRef]

1973

C. Elachi, C. Yeh, “Periodic structures in integrated optics,” J. Appl. Phys. 44, 3146–3152 (1973).
[CrossRef]

1972

M. A. Hussain, S. L. Pu, “Dynamic stress intensity factor for an unbounded plate having collinear cracks,” Eng. Fract. Mech. 4, 865–876 (1972).
[CrossRef]

Aronson, L. B.

Chen, R. T.

Chou, S. Y.

Z. Yu, S. J. Schablitsky, S. Y. Chou, “Nanoscale GaAs metal–semiconductor–metal photodetectors fabricated using nanoimprint lithography,” Appl. Phys. Lett. 74, 2381–2383 (1999).
[CrossRef]

Dasler, M.

J.-P. Weber, B. Stoltz, H. Sano, M. Dasler, O. Oberg, J. Wolz, “An integratable polarization-independent tunable filter for WDM systems: the multigrating filter,” J. Lightwave Technol. 14, 2719–2735 (1996).
[CrossRef]

Elachi, C.

C. Elachi, C. Yeh, “Periodic structures in integrated optics,” J. Appl. Phys. 44, 3146–3152 (1973).
[CrossRef]

Gaylord, T. K.

E. N. Glytsis, T. K. Gaylord, M. G. Moharam, “Electric field, permittivity, and strain distributions induced by interdigitated electrodes of electrooptic waveguides,” J. Lightwave Technol. LT-5, 668–681 (1987).
[CrossRef]

Glytsis, E. N.

E. N. Glytsis, T. K. Gaylord, M. G. Moharam, “Electric field, permittivity, and strain distributions induced by interdigitated electrodes of electrooptic waveguides,” J. Lightwave Technol. LT-5, 668–681 (1987).
[CrossRef]

Gradshtein, I. S.

I. S. Gradshtein, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), Secs. 1.441.1 and 1.441.4.

Hussain, M. A.

M. A. Hussain, S. L. Pu, “Dynamic stress intensity factor for an unbounded plate having collinear cracks,” Eng. Fract. Mech. 4, 865–876 (1972).
[CrossRef]

Kulishov, M.

Moharam, M. G.

E. N. Glytsis, T. K. Gaylord, M. G. Moharam, “Electric field, permittivity, and strain distributions induced by interdigitated electrodes of electrooptic waveguides,” J. Lightwave Technol. LT-5, 668–681 (1987).
[CrossRef]

Nishihara, H.

T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[CrossRef]

Oberg, O.

J.-P. Weber, B. Stoltz, H. Sano, M. Dasler, O. Oberg, J. Wolz, “An integratable polarization-independent tunable filter for WDM systems: the multigrating filter,” J. Lightwave Technol. 14, 2719–2735 (1996).
[CrossRef]

Pu, S. L.

M. A. Hussain, S. L. Pu, “Dynamic stress intensity factor for an unbounded plate having collinear cracks,” Eng. Fract. Mech. 4, 865–876 (1972).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshtein, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), Secs. 1.441.1 and 1.441.4.

Sano, H.

J.-P. Weber, B. Stoltz, H. Sano, M. Dasler, O. Oberg, J. Wolz, “An integratable polarization-independent tunable filter for WDM systems: the multigrating filter,” J. Lightwave Technol. 14, 2719–2735 (1996).
[CrossRef]

Schablitsky, S. J.

Z. Yu, S. J. Schablitsky, S. Y. Chou, “Nanoscale GaAs metal–semiconductor–metal photodetectors fabricated using nanoimprint lithography,” Appl. Phys. Lett. 74, 2381–2383 (1999).
[CrossRef]

Stoltz, B.

J.-P. Weber, B. Stoltz, H. Sano, M. Dasler, O. Oberg, J. Wolz, “An integratable polarization-independent tunable filter for WDM systems: the multigrating filter,” J. Lightwave Technol. 14, 2719–2735 (1996).
[CrossRef]

Suhara, T.

T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[CrossRef]

Sun, D.

Weber, J.-P.

J.-P. Weber, B. Stoltz, H. Sano, M. Dasler, O. Oberg, J. Wolz, “An integratable polarization-independent tunable filter for WDM systems: the multigrating filter,” J. Lightwave Technol. 14, 2719–2735 (1996).
[CrossRef]

Wolz, J.

J.-P. Weber, B. Stoltz, H. Sano, M. Dasler, O. Oberg, J. Wolz, “An integratable polarization-independent tunable filter for WDM systems: the multigrating filter,” J. Lightwave Technol. 14, 2719–2735 (1996).
[CrossRef]

Yeh, C.

C. Elachi, C. Yeh, “Periodic structures in integrated optics,” J. Appl. Phys. 44, 3146–3152 (1973).
[CrossRef]

Yu, Z.

Z. Yu, S. J. Schablitsky, S. Y. Chou, “Nanoscale GaAs metal–semiconductor–metal photodetectors fabricated using nanoimprint lithography,” Appl. Phys. Lett. 74, 2381–2383 (1999).
[CrossRef]

Zhao, C.

Appl. Opt.

Appl. Phys. Lett.

Z. Yu, S. J. Schablitsky, S. Y. Chou, “Nanoscale GaAs metal–semiconductor–metal photodetectors fabricated using nanoimprint lithography,” Appl. Phys. Lett. 74, 2381–2383 (1999).
[CrossRef]

Eng. Fract. Mech.

M. A. Hussain, S. L. Pu, “Dynamic stress intensity factor for an unbounded plate having collinear cracks,” Eng. Fract. Mech. 4, 865–876 (1972).
[CrossRef]

IEEE J. Quantum Electron.

T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[CrossRef]

J. Appl. Phys.

C. Elachi, C. Yeh, “Periodic structures in integrated optics,” J. Appl. Phys. 44, 3146–3152 (1973).
[CrossRef]

J. Lightwave Technol.

J.-P. Weber, B. Stoltz, H. Sano, M. Dasler, O. Oberg, J. Wolz, “An integratable polarization-independent tunable filter for WDM systems: the multigrating filter,” J. Lightwave Technol. 14, 2719–2735 (1996).
[CrossRef]

E. N. Glytsis, T. K. Gaylord, M. G. Moharam, “Electric field, permittivity, and strain distributions induced by interdigitated electrodes of electrooptic waveguides,” J. Lightwave Technol. LT-5, 668–681 (1987).
[CrossRef]

Opt. Lett.

Other

M. J. Weber, ed., CRC Handbook of Laser Science and Technology (CRC Press, Boca, Raton, Fla., 1986), Vol. IV, Part 2.

I. S. Gradshtein, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), Secs. 1.441.1 and 1.441.4.

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 (6)

Fig. 1
Fig. 1

General definition of the problem to be studied.

Fig. 2
Fig. 2

Examples of the normalized electric potential distribution inside the buffer layer: (a) a/ l = 0.7, ΔV = -V 0; (b) a/ l = 0.4, ΔV = 0.

Fig. 3
Fig. 3

Psuedocapacitance as function of (a) the normalized electrode width for 2h = l/2, d = h/2 (dotted curve); 2h = l, d = h/4 (solid curve); (b) the normalized spatial frequency for a/ l = 0.5, d = h/4, ΔV = -V 0 (solid curve); a/ l = 0.5, d = h/4, ΔV = -V 0 (dotted curve); a/ l = 0.5, d = h/2, ΔV = -2V 0 (dashed curve); (c) the normalized bias voltage for a/ l = 0.5, 2h = l, d = h/2.

Fig. 4
Fig. 4

Contour plots of the refractive-index distribution inside the waveguide for (a) ΔV = 0 and (b) ΔV = -0.5V 0. The data were calculated for the following parameter set: r 33 = 30.8 × 10-12 m/V, 2h = l, d = h/4, a = 0.5l, n e = 2.17.

Fig. 5
Fig. 5

First (solid curves) and second (dashed curves) spatial harmonics of the refractive-index distribution in the waveguide region as functions of (a) the normalized bias voltage for V 0 = 1V, 2h = 2 µm, a = 0.5l, 2h = l/2, d = 0.25h, (b) the normalized electrode width (ΔV = 0), and (c) the constant component versus the normalized electrode width: 2h = l, d = 0.05h, ΔV = 0.

Fig. 6
Fig. 6

Structure of the all-fiber tunable and switchable filter: (a) top view, (b) cross-sectional view.

Equations (35)

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

ε33i2φix, zz2+ε11i2φix, zx2=0,
φ1x, z=V0Bh+Bd ε33wε33b+n=1 Cn exp-nkzcosnkx,
φ2x, z=V0Bh+Bz-hε33wε33b+n=1 Ensinhnkhδ2coshnkδ1z-h+ε33wε11wε33bε11b1/2 coshnkhδ2×sinhnkδ1z-hcosnkx,
φ3x, z=V0Bz+n=1 En sinhnkδ2zcosnkx,
Bh+Bd ε33wε11b+n=1 En* Fn cosnkxε11bε33b1/2Gn+εaFn=1+ΔVV0,  0x<a2,
Bh+Bd ε33wε11b+n=1 En* Fn cosnkxε11bε33b1/2Gn+εaFn=1,l-a2x<l,
ε33wBh+n=1 nkhEn* cosnkx=0,  a2x<l-a2,
En*=Enε11bε33b1/2Gn+εaFn,Fn=coshnkdδ1sinhnkhδ2+ε11wε33wε11bε33b1/2 sinhnkdδ1coshnkhδ2,Gn=sinhnkdδ1sinhnkhδ2+ε11wε33wε11bε33b1/2 coshnkdδ1coshnkhδ2.
n=1 En* cosnkx=-1+ΔVV0-Bh1+ε33wε33b d×εa+ε33Bε11B1/2+n=1N En*Rn×cosnkx,  0x<a2,
n=1 En* cosnkx=-1-Bh1+ε33wε33b d×εa+ε33Bε11B1/2+n=1N En*Rn×cosnkx,  l-a2x<l,
Rn=ε11bε33b1/2+εaFnε11bε33b1/2Gn+εaFn,  limnRn=0.
ρx=ε33wBh+n=1 nkhEn* cosnkx=ρ1x0<x<a/20a/2<x<l-a/2ρ2xl-a/2<x<l.
ε33wBh=1l0a/2 ρ1ξdξ+1l0a/2 ρ2l-ξdξ=a01+a02,
nkhEn*=2l0a/2 ρ1ξcosnkξdξ+-1n×2l0a/2 ρ2l-ξcosnkξdξ.
n=1cosnkxcosnkξn=-12×ln2|coskx-coskξ|, n=1-1n cosnkxcosnkξn=-12×ln2|coskx+coskξ|.
-1πh0a/2 ρ1ξln2|coskx-coskξ|dξ-1πh0a/2×ρ2ξln2|coskx+coskξ|dξ=1+ΔVV0-Bh1+ε33wε33bdhε11bε33b)1/2+εa+2πh×n=1Rnncosnkx0a/2 ρ1ξcosnkξdξ+-1n0a/2 ρ2l-ξcosnkξdξ,  0x a2,
-1πh0a/2 ρ1ξln2|coskx-coskξ|dξ-1πh0a/2×ρ2ξln2|coskx+coskξ|dξ=1-Bh1+ε33wε33bdhε11bε33b1/2+εa+2πhn=1×Rnncosnkx0a/2 ρ1ξcosnkξdξ+-1n0a/2×ρ2l-ξcosnkξdξ,  l-a2x<l.
coskx=cos2ka/4+sin2ka/4coskζ,coskξ=cos2ka/4+sin2ka/4coskη;
coskx=-cos2ka/4-sin2ka/4coskζ,coskξ=cos2ka/4+sin2ka/4coskη.
-ln2|coskx-cosξ|=-lnsin2ka4+2 m=1cosmkζcosmkηm,ln2|coskx+cosξ|=ln4 cos2ka4-m=1-1m12tanka42mcoskζ+coskηmm, cosnkx=s=0n bmn cosmkζ.
-1πhlnsin2ka40l ρ1ηdξdηdη+2πh0l ρ1ηdξdηm=1cosmkζcosmkηmdη-1πhlncos2ka40l ρ2ηdξdηdη+1πh0l ρ2ηdξdηm=1-1m12tanka42mcoskζ+coskηmmdη=1+ΔVV0-Bh1+ε33wε33bdhε11bε33b)1/2+εa+2πhn=1Rnnm=0n bmn cosmkζ×0l ρ1ηdξdηp=0n bpn cospkηdη+-1n0l ρ2ηdξdηp=0n bpn cospkηdη,  0ζ<l,
-1πhlnsin2ka40l ρ2ηdξdηdη+2πh0l ρ2ηdξdηm=1cosmkζcosmkηmdη-1πhlncos2ka40l ρ1ηdξdηdη+1πh0l ρ1ηdξdηm=1-1m12tanka42mcoskζ+coskηmmdη=1-Bh1+ε33wε33bdhε11bε33b1/2+εa+2πhn=1Rnnm=0n bmn cosmkζ×-1n0l ρ1ηdξdηp=0n bpn cospkηdη+0l ρ2ηdξdηp=0n bpn cospkηdη,  0ζ<l.
ρ1ξηdξdη=i=0 ai1 cosikη,ρ2l-ξηdξdη=i=0 ai2 cosikη.
0lcosikζcosjkζdζ=l/2δij,
-a01 lnsin2ka4-a02 ln4 cos2ka4+2a02m=1-1mm12tanka42m1l20l0lcoskζ+coskηmdζdη=1+ΔVV0-Bh1+ε33wε33bdhkhε11bε33b1/2+εa+2a01n=1Rnnb0n2+2a02n=1-1nRnnb0n2+p=1nap1n=1Rnn bpnb0n+ap2n=1-1nRnn bpnb0n,
-a01 ln4 cos2ka4-a02 lnsin2ka4+2a01m=1-1mm12tanka42m1l20l0lcoskζ+coskηmdζdη=1-Bh1+ε33wε33bdhkhε11bε33b1/2+εa+2a01n=1-1nRnnb0n2+2a02n=1Rnnb0n2+p=1nap1n=1-1nRnn bpnb0n+ap2n=1Rnn bpnb0n;
m=1Gmp2+δmpm-2Ampxm=2Ap-Gp2x0,m=1Gmp2-δmpm-2Bmpym=-2Bp+Gp2y0,
x0=2+ΔVV0khεa+ε11bε33b1/2+2 m=1Am-Gm8xm2kh εa+ε11bε33b1/2ε33w1+ε33wε33bdh-lnsin2ka2+G04-2 n-1R2n2nb02n2,
y0=-ΔVV0 khεa+ε11bε33b1/2+2 m=1Bm+Gm8ymln14tan2ka4+G04+2 n-1R2n-12n-1b02n-12,
Amp=n=1R2n2n bm2nbp2n,  Ap=n=1R2n2n bp2nb02n,Bmp=n=1R2n-12n-1 bm2n-1bp2n-1,  Bp=n=1R2n-12n-1 bp2n-1b02n-1,
Gmp=n=1-1nαmpnn12tanka42n,  Gp=n=1-1nβpnn12tanka42n,  G0=Gp, p=0.
Bh=x0ε33w,nkhEn*=2b02nx0+m=1n bm2nxm2b02n-1y0+m=1n bm2n-1ym.
C=QV0=2V00a/2 ρ2xdx=2V00l ρ2xηdxdηdη=2πx0-y0kh.
Ezx, z=V0hx0ε33w+n=1 nkhδ2En*×coshnkδ2zcosnkxε11bε33b1/2Gn+εaFn.
neff=ne+Δn=ne-V0hx0ε33w,

Metrics