Abstract

We present general optimization arguments for resonator-based all-optical switching. Several generic resonator geometries, namely Fabry-Perot resonators, circular gratings as well as micro-ring resonators, are discussed and their particular features highlighted. We establish analytical models which allow a direct comparison of the different all-optical switch geometries. For the parameter range investigated, we find a clear advantage of photonic band-gap resonators (based on Bragg-type reflection) over micro-ring resonators (based on total internal reflection).

© 2005 Optical Society of America

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References

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  1. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, New York, 2002).
  2. R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 2003).
  3. G. I. Stegeman and A. Miller, �??Physics of all-optical switching devices,�?? in Photonics in Switching, Vol. 1, J. E. Midwinter, ed. (Academic Press, San Diego, 1993).
  4. U. Peschel, T. Peschel, and F. Lederer, �??Optimization of bistable planar resonators operated near half the band gap,�?? IEEE J. Quantum Electronics 30, 1241-1249 (1994).
    [CrossRef]
  5. J. E. Heebner and R. W. Boyd, �??Enhanced all-optical switching by use of a nonlinear fiber ring resonator,�?? Opt. Lett. 24, 847-849 (1999).
    [CrossRef]
  6. G. Priem, I. Notebaert, P. Bienstman, G. Morthier, and R. Baets, �??Resonator-based all-optical Kerr-nonlinear phase shifting: Design and limitations,�?? J. Appl. Phys. 97, 023104-1 (2005)
    [CrossRef]
  7. M. F. Yanik, S. Fan, M. Soljacic, and J. D. Joannopoulos, �??All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,�?? Opt. Lett. 28, 2506-2508 (2003).
    [CrossRef] [PubMed]
  8. B. Luther-Davies and M. Samoc, �??Third-order nonlinear optical organic materials for photonic switching,�?? Curr. Opin. Solid State Mater. Sci. 2, 213-219 (1997).
    [CrossRef]
  9. D. Vujic and S. John, �??Pulse reshaping in photonic crystal waveguides and microcavities with Kerr nonlinearity: Critical issues for all-optical switching,�?? Phys. Rev. A 72, 013807-1 (2005).
    [CrossRef]
  10. D. I. Babic and S.W. Corzine, �??Analytic Expressions for the Reflection Delay, Penetration Depth, and Absorptance of Quarter-Wave Dielectric Mirrors,�?? IEEE J. Quantum Electronics 28, 514-524 (1992).
    [CrossRef]
  11. The reflection phase Φ used in this paper is related to the reflection phase θ used in Ref. [10] by Φ = -θ.
  12. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, �??Photonic crystals: putting a new twist on light,�?? Nature 386, 143-149 (1997).
    [CrossRef]
  13. A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G.-L. Bona, W. Bächtold, �??Lasing in organic circular grating structures,�?? J. Appl. Phys. 96, 3043-3049 (2004).
    [CrossRef]
  14. J. Scheuer, W. M. J. Green, G. A. DeRose, and A. Yariv, �??InGaAsP Annular Bragg Lasers: Theory, Applications, and Modal Properties,�?? IEEE J. Sel. Top. Quantum Electron. 11, 476-484 (2005).
    [CrossRef]
  15. G. A. Turnbull, A. Carleton, G. F. Barlow, A. Tahraouhi, T. F. Krauss, K. A. Shore, and I. D. W. Samuel, �??Influence of grating characteristics on the operation of circular-grating distributed-feedback polymer lasers,�?? J. Appl. Phys. 98, 023105-1 (2005).
    [CrossRef]
  16. J. Scheuer, W. M. J. Green, G. A. DeRose, and A. Yariv, �??Lasing from a circular Bragg nanocavity with an ultrasmall modal volume,�?? Appl. Phys. Lett. 86, 251101-1 (2005).
    [CrossRef]
  17. D. Ochoa, R. Houdre, M. Ilegems, H. Benisty, T. F. Krauss, and C. J. M. Smith, �??Diffraction of cylindrical Bragg reflectors surrounding an in-plane semiconductor microcavity,�?? Phys. Rev. B 61, 4806-4812 (2000).
    [CrossRef]
  18. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  19. C. Manolatou and H. A. Haus, Passive Components for Dense Optical Integration (Kluwer Academic Publishers, Boston, 2002).
    [CrossRef]
  20. E. A. J. Marcatili, �??Bends in Optical Dielectric Guides,�?? The Bell System Technical Journal, September issue, 175 2103-2132 (1969).

Appl. Phys. Lett.

J. Scheuer, W. M. J. Green, G. A. DeRose, and A. Yariv, �??Lasing from a circular Bragg nanocavity with an ultrasmall modal volume,�?? Appl. Phys. Lett. 86, 251101-1 (2005).
[CrossRef]

Curr. Opin. Solid State Mater. Sci.

B. Luther-Davies and M. Samoc, �??Third-order nonlinear optical organic materials for photonic switching,�?? Curr. Opin. Solid State Mater. Sci. 2, 213-219 (1997).
[CrossRef]

IEEE J. Quantum Electronics

U. Peschel, T. Peschel, and F. Lederer, �??Optimization of bistable planar resonators operated near half the band gap,�?? IEEE J. Quantum Electronics 30, 1241-1249 (1994).
[CrossRef]

D. I. Babic and S.W. Corzine, �??Analytic Expressions for the Reflection Delay, Penetration Depth, and Absorptance of Quarter-Wave Dielectric Mirrors,�?? IEEE J. Quantum Electronics 28, 514-524 (1992).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. Scheuer, W. M. J. Green, G. A. DeRose, and A. Yariv, �??InGaAsP Annular Bragg Lasers: Theory, Applications, and Modal Properties,�?? IEEE J. Sel. Top. Quantum Electron. 11, 476-484 (2005).
[CrossRef]

J. Appl. Phys.

G. A. Turnbull, A. Carleton, G. F. Barlow, A. Tahraouhi, T. F. Krauss, K. A. Shore, and I. D. W. Samuel, �??Influence of grating characteristics on the operation of circular-grating distributed-feedback polymer lasers,�?? J. Appl. Phys. 98, 023105-1 (2005).
[CrossRef]

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G.-L. Bona, W. Bächtold, �??Lasing in organic circular grating structures,�?? J. Appl. Phys. 96, 3043-3049 (2004).
[CrossRef]

G. Priem, I. Notebaert, P. Bienstman, G. Morthier, and R. Baets, �??Resonator-based all-optical Kerr-nonlinear phase shifting: Design and limitations,�?? J. Appl. Phys. 97, 023104-1 (2005)
[CrossRef]

Nature

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, �??Photonic crystals: putting a new twist on light,�?? Nature 386, 143-149 (1997).
[CrossRef]

Opt. Lett.

Photonics in Switching

G. I. Stegeman and A. Miller, �??Physics of all-optical switching devices,�?? in Photonics in Switching, Vol. 1, J. E. Midwinter, ed. (Academic Press, San Diego, 1993).

Phys. Rev. A

D. Vujic and S. John, �??Pulse reshaping in photonic crystal waveguides and microcavities with Kerr nonlinearity: Critical issues for all-optical switching,�?? Phys. Rev. A 72, 013807-1 (2005).
[CrossRef]

Phys. Rev. B

D. Ochoa, R. Houdre, M. Ilegems, H. Benisty, T. F. Krauss, and C. J. M. Smith, �??Diffraction of cylindrical Bragg reflectors surrounding an in-plane semiconductor microcavity,�?? Phys. Rev. B 61, 4806-4812 (2000).
[CrossRef]

The Bell System Technical Journal

E. A. J. Marcatili, �??Bends in Optical Dielectric Guides,�?? The Bell System Technical Journal, September issue, 175 2103-2132 (1969).

Other

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

C. Manolatou and H. A. Haus, Passive Components for Dense Optical Integration (Kluwer Academic Publishers, Boston, 2002).
[CrossRef]

The reflection phase Φ used in this paper is related to the reflection phase θ used in Ref. [10] by Φ = -θ.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, New York, 2002).

R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 2003).

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Figures (5)

Fig. 1.
Fig. 1.

Four generic optical resonator geometries: (a) an ideal FP resonator where the mirror planes have zero thickness; (b) a FP resonator with dielectric mirrors, i.e. quarter wave stacks; (c) a circular grating resonator consisting of concentric rings of alternating refractive index, and (d) a micro-ring resonator made of single-mode waveguides. The Kerr nonlinear material is indicated in red in all cases.

Fig. 2.
Fig. 2.

The function f = I input/I 0 for several types of mirrors which are characterized by their D-values. The D = 0 curve corresponds to the ideal FP resonator. The other curves represent FP resonators with dielectric mirrors. In all cases, the refractive index of the nonlinear material filling the cavity is taken to be n = n LI = 1.7 (representing e.g. a nonlinear polymer) and the low-index material of the dielectric stack has n L = 1.45 (e.g. quartz). The difference between the curves lies in the high-index material of the dielectric stack: D = 0.8 corresponds to n H = 3.5 (silicon in the IR), D = 2.3 corresponds to n H = 2.2 (a very high refractive index dielectric in the NIR), D = 3.1 corresponds to n H = 2.0 (a high refractive index dielectric in the VIS/NIR).

Fig. 3.
Fig. 3.

“Power ratio” of a circular grating for the resonance orders m = 0 and m = 1 of TM polarization. The order m describes the number of azimuthal nodal lines of the mode, i.e. its rotational symmetry. The grating parameters are: n H = 1.95, n = n L = 1.6, q = q opt, rc = 0.81a. It shows that for these example parameters there is a m = 0 resonance but no m = 1 resonance inside the band-gap.

Fig. 4.
Fig. 4.

Electric field amplitude in arbitrary units of the lowest-order (m = 0) TM resonance of a circular grating resonator (see text for geometric parameters).

Fig. 5.
Fig. 5.

The value of Γ = Iinputopt/I 0 of different resonator geometries as a function of the refractive index contrast D. Γ describes the switch intensity of an optimized geometry in units of the geometry-independent intensity I 0. Squares represent a selection of micro-rings (see text); the dotted line is a guide to the eye. The solid line represents DMFP cavities of the same refractive index contrasts [Eq. (43)]. Note that the point {D = 0, Γ = 1}, marked by a green circle, corresponds to the ideal FP resonator.

Tables (1)

Tables Icon

Table 1. Q-values of corresponding circular grating resonators (Q 0) and DMFP resonators [Q(1)]. Z denotes the number periods of the grating or the dielectric mirrors, respectively.

Equations (45)

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

n ( I ) = n + n 2 I .
Q = ν res δν .
τ switch = 1 δν = Q ν res = Q λ res c .
ν N = c 2 nL N ,
d ν N = ν N n dn .
Δ n = I c n 2 = 2 p I input n 2 ,
I input = n 2 p n 2 δν ν N = n 2 pQ n 2 .
Q N = F π 1 R 1 ,
p = 1 1 R Q πN 1 .
I input = I 0 N ,
I 0 = πn 2 Q 2 n 2 .
τ = ϕ ω ,
τ = π ω D ,
D = n LI n HI n H n H n L .
ϕ = ϕ 0 + ( ω ω 0 ) τ .
φ = 2 ( nLω c + ϕ ) = 2 ( nLω c + ( ω ω 0 ) τ ) ,
nLω c + ( ω ω 0 ) τ = πN .
= 2 ( nL c + τ ) .
= 2 ( N π ω 0 + τ ) .
κ = 1 + τω N π = 1 + D N .
d ν N = dn ν N n 1 κ .
Q = N π 1 R κ .
p = Q πN 1 κ .
I input = I 0 f ( N ) ,
f ( N ) = N κ 2 = ( N + D ) 2 N .
I input opt = I 0 × ( 1 + D ) 2 .
I input opt = I 0 × 4 D .
Q = ω Res W P .
q = d H d L
q opt = n L n H , ω 0 = 2 πc a n H + n L 4 · n H · n L ,
κ ν = ( dn n ν ) 1
ν N = c 2 π n eff r m N ,
I input = n eff pQ n 2 .
1 Q = 1 Q 0 + 1 Q e .
T = 1 1 + Q e Q o 2 ,
T = 1 Q Q 0 2 .
Q 0 Q .
p Q πN .
I input = π n eff Q 2 n 2 N .
I input opt = I 0 × 2 N ( Q , T , n i ) .
N ( Q , T , n i ) = 2 π n eff r m λ
I input opt = I 0 × Γ ,
Γ = { ( 1 + D ) 2 for D 1 4 D for D 1 .
Γ = 2 N ( Q , T , n i ) .
D = n L n H n L .

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