Abstract

We show theoretically that for a two-photon photosensitivity process a channel waveguide can be self-written in a planar slab of photosensitive germanosilicate glass. We further analyze features of this process using both numerical and analytical techniques and compare waveguides formed by this two-photon process to those formed by a one-photon process.

© 1996 Optical Society of America

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References

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  1. K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: applications to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
    [Crossref]
  2. V. Mizrahi, P. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, and R. M. Atkins, “Ultraviolet laser fabrication of ultrastrong optical fiber gratings and of germania-doped channel waveguides,” Appl. Phys. Lett. 63, 1727–1729 (1993).
    [Crossref]
  3. T. M. Monro, C. M. de Sterke, and L. Poladian, “Self-writing a waveguide in glass using photosensitivity,” Opt. Commun. 119, 523–526 (1995).
    [Crossref]
  4. V. Mizrahi, S. LaRochelle, G. I. Stegeman, and J. E. Sipe, “Physics of photosensitive-grating formation in optical fibers,” Phys. Rev. A 43, 433–438 (1991).
    [Crossref] [PubMed]
  5. J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. E. Smith, “Experimental observation of spatial soliton in interactions,” Opt. Lett. 16, 15–17 (1991).
    [Crossref] [PubMed]
  6. A. S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Lett. 21, 24–26 (1996).
    [Crossref] [PubMed]
  7. S. J. Frisken, “Light-induced optical waveguide uptapers,” Opt. Lett. 18, 1035–1037 (1993).
    [Crossref] [PubMed]
  8. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 16.
  9. C. M. de Sterke and J. E. Sipe, “Ideal mode expansion for planar optical waveguides: application to the TM-TM coupling coefficient for grating structure,” J. Opt. Soc. Am. A 7, 636–645 (1990).
    [Crossref]
  10. C. M. de Sterke, S. An, and J. E. Sipe, “Growth dynamics of phase gratings in optical fibers,” Opt. Commun. 83, 315–321 (1991).
    [Crossref]
  11. D. A. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, “Production of in-fiber gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993).
    [Crossref]
  12. G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of Bragg graftings in optical fibers by a transverse holographic method,” Opt. Lett. 14, 823–825 (1989).
    [Crossref] [PubMed]
  13. J. Albert, B. Malo, F. Bilodeau, D. C. Johnson, and K. O. Hill, “Photosensitivity in Ge-doped silica optical waveguides and fibers with 193-nm light from an ArF excimer laser,” Opt. Lett. 19, 387–389 (1994).
    [PubMed]
  14. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).
  15. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
    [Crossref]
  16. E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970).
  17. E. Caglioti, B. Crosignani, and P. Di Porto, “Hamiltonian description of nonlinear propagation in optical fibers,” Phys. Rev. A 38, 4036–4042 (1988).
    [Crossref] [PubMed]
  18. T. Ueda and W. L. Kath, “Dynamics of coupled solitons in nonlinear optical fibers,” Phys. Rev. A 42, 563–571 (1990).
    [Crossref] [PubMed]
  19. D. P. Hand and P. St. J. Russell, “Photoinduced refractive-index changes in germanosilicate fibers,” Opt. Lett. 15, 102–104 (1990).
    [Crossref] [PubMed]

1996 (1)

1995 (1)

T. M. Monro, C. M. de Sterke, and L. Poladian, “Self-writing a waveguide in glass using photosensitivity,” Opt. Commun. 119, 523–526 (1995).
[Crossref]

1994 (1)

1993 (3)

V. Mizrahi, P. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, and R. M. Atkins, “Ultraviolet laser fabrication of ultrastrong optical fiber gratings and of germania-doped channel waveguides,” Appl. Phys. Lett. 63, 1727–1729 (1993).
[Crossref]

S. J. Frisken, “Light-induced optical waveguide uptapers,” Opt. Lett. 18, 1035–1037 (1993).
[Crossref] [PubMed]

D. A. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, “Production of in-fiber gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993).
[Crossref]

1991 (3)

V. Mizrahi, S. LaRochelle, G. I. Stegeman, and J. E. Sipe, “Physics of photosensitive-grating formation in optical fibers,” Phys. Rev. A 43, 433–438 (1991).
[Crossref] [PubMed]

J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. E. Smith, “Experimental observation of spatial soliton in interactions,” Opt. Lett. 16, 15–17 (1991).
[Crossref] [PubMed]

C. M. de Sterke, S. An, and J. E. Sipe, “Growth dynamics of phase gratings in optical fibers,” Opt. Commun. 83, 315–321 (1991).
[Crossref]

1990 (3)

1989 (1)

1988 (1)

E. Caglioti, B. Crosignani, and P. Di Porto, “Hamiltonian description of nonlinear propagation in optical fibers,” Phys. Rev. A 38, 4036–4042 (1988).
[Crossref] [PubMed]

1978 (1)

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: applications to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).

Aitchison, J. S.

Albert, J.

An, S.

C. M. de Sterke, S. An, and J. E. Sipe, “Growth dynamics of phase gratings in optical fibers,” Opt. Commun. 83, 315–321 (1991).
[Crossref]

Anderson, D. A.

D. A. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, “Production of in-fiber gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993).
[Crossref]

Atkins, R. M.

V. Mizrahi, P. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, and R. M. Atkins, “Ultraviolet laser fabrication of ultrastrong optical fiber gratings and of germania-doped channel waveguides,” Appl. Phys. Lett. 63, 1727–1729 (1993).
[Crossref]

Bilodeau, F.

Caglioti, E.

E. Caglioti, B. Crosignani, and P. Di Porto, “Hamiltonian description of nonlinear propagation in optical fibers,” Phys. Rev. A 38, 4036–4042 (1988).
[Crossref] [PubMed]

Crosignani, B.

E. Caglioti, B. Crosignani, and P. Di Porto, “Hamiltonian description of nonlinear propagation in optical fibers,” Phys. Rev. A 38, 4036–4042 (1988).
[Crossref] [PubMed]

de Sterke, C. M.

T. M. Monro, C. M. de Sterke, and L. Poladian, “Self-writing a waveguide in glass using photosensitivity,” Opt. Commun. 119, 523–526 (1995).
[Crossref]

C. M. de Sterke, S. An, and J. E. Sipe, “Growth dynamics of phase gratings in optical fibers,” Opt. Commun. 83, 315–321 (1991).
[Crossref]

C. M. de Sterke and J. E. Sipe, “Ideal mode expansion for planar optical waveguides: application to the TM-TM coupling coefficient for grating structure,” J. Opt. Soc. Am. A 7, 636–645 (1990).
[Crossref]

Di Porto, P.

E. Caglioti, B. Crosignani, and P. Di Porto, “Hamiltonian description of nonlinear propagation in optical fibers,” Phys. Rev. A 38, 4036–4042 (1988).
[Crossref] [PubMed]

DiGiovanni, D. J.

V. Mizrahi, P. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, and R. M. Atkins, “Ultraviolet laser fabrication of ultrastrong optical fiber gratings and of germania-doped channel waveguides,” Appl. Phys. Lett. 63, 1727–1729 (1993).
[Crossref]

Erdogan, T.

V. Mizrahi, P. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, and R. M. Atkins, “Ultraviolet laser fabrication of ultrastrong optical fiber gratings and of germania-doped channel waveguides,” Appl. Phys. Lett. 63, 1727–1729 (1993).
[Crossref]

D. A. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, “Production of in-fiber gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993).
[Crossref]

Frisken, S. J.

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: applications to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[Crossref]

Glenn, W. H.

Hand, D. P.

Hill, K. O.

J. Albert, B. Malo, F. Bilodeau, D. C. Johnson, and K. O. Hill, “Photosensitivity in Ge-doped silica optical waveguides and fibers with 193-nm light from an ArF excimer laser,” Opt. Lett. 19, 387–389 (1994).
[PubMed]

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: applications to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[Crossref]

Jackel, J. L.

Johnson, D. C.

J. Albert, B. Malo, F. Bilodeau, D. C. Johnson, and K. O. Hill, “Photosensitivity in Ge-doped silica optical waveguides and fibers with 193-nm light from an ArF excimer laser,” Opt. Lett. 19, 387–389 (1994).
[PubMed]

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: applications to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[Crossref]

Kath, W. L.

T. Ueda and W. L. Kath, “Dynamics of coupled solitons in nonlinear optical fibers,” Phys. Rev. A 42, 563–571 (1990).
[Crossref] [PubMed]

Kawasaki, B. S.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: applications to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[Crossref]

Kewitsch, A. S.

LaRochelle, S.

V. Mizrahi, S. LaRochelle, G. I. Stegeman, and J. E. Sipe, “Physics of photosensitive-grating formation in optical fibers,” Phys. Rev. A 43, 433–438 (1991).
[Crossref] [PubMed]

Leaird, D. E.

Lemaire, P. J.

V. Mizrahi, P. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, and R. M. Atkins, “Ultraviolet laser fabrication of ultrastrong optical fiber gratings and of germania-doped channel waveguides,” Appl. Phys. Lett. 63, 1727–1729 (1993).
[Crossref]

Malo, B.

Meltz, G.

Merzbacher, E.

E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970).

Mizrahi, V.

V. Mizrahi, P. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, and R. M. Atkins, “Ultraviolet laser fabrication of ultrastrong optical fiber gratings and of germania-doped channel waveguides,” Appl. Phys. Lett. 63, 1727–1729 (1993).
[Crossref]

D. A. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, “Production of in-fiber gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993).
[Crossref]

V. Mizrahi, S. LaRochelle, G. I. Stegeman, and J. E. Sipe, “Physics of photosensitive-grating formation in optical fibers,” Phys. Rev. A 43, 433–438 (1991).
[Crossref] [PubMed]

Monro, T. M.

T. M. Monro, C. M. de Sterke, and L. Poladian, “Self-writing a waveguide in glass using photosensitivity,” Opt. Commun. 119, 523–526 (1995).
[Crossref]

Morey, W. W.

Oliver, M. K.

Poladian, L.

T. M. Monro, C. M. de Sterke, and L. Poladian, “Self-writing a waveguide in glass using photosensitivity,” Opt. Commun. 119, 523–526 (1995).
[Crossref]

Reed, W. A.

V. Mizrahi, P. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, and R. M. Atkins, “Ultraviolet laser fabrication of ultrastrong optical fiber gratings and of germania-doped channel waveguides,” Appl. Phys. Lett. 63, 1727–1729 (1993).
[Crossref]

Russell, P. St. J.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[Crossref]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 16.

Silberberg, Y.

Sipe, J. E.

V. Mizrahi, S. LaRochelle, G. I. Stegeman, and J. E. Sipe, “Physics of photosensitive-grating formation in optical fibers,” Phys. Rev. A 43, 433–438 (1991).
[Crossref] [PubMed]

C. M. de Sterke, S. An, and J. E. Sipe, “Growth dynamics of phase gratings in optical fibers,” Opt. Commun. 83, 315–321 (1991).
[Crossref]

C. M. de Sterke and J. E. Sipe, “Ideal mode expansion for planar optical waveguides: application to the TM-TM coupling coefficient for grating structure,” J. Opt. Soc. Am. A 7, 636–645 (1990).
[Crossref]

Smith, P. W. E.

Stegeman, G. I.

V. Mizrahi, S. LaRochelle, G. I. Stegeman, and J. E. Sipe, “Physics of photosensitive-grating formation in optical fibers,” Phys. Rev. A 43, 433–438 (1991).
[Crossref] [PubMed]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[Crossref]

Ueda, T.

T. Ueda and W. L. Kath, “Dynamics of coupled solitons in nonlinear optical fibers,” Phys. Rev. A 42, 563–571 (1990).
[Crossref] [PubMed]

Weiner, A. M.

White, A. E.

D. A. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, “Production of in-fiber gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993).
[Crossref]

Yariv, A.

Appl. Phys. Lett. (2)

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: applications to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[Crossref]

V. Mizrahi, P. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, and R. M. Atkins, “Ultraviolet laser fabrication of ultrastrong optical fiber gratings and of germania-doped channel waveguides,” Appl. Phys. Lett. 63, 1727–1729 (1993).
[Crossref]

Electron. Lett. (1)

D. A. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, “Production of in-fiber gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

C. M. de Sterke, S. An, and J. E. Sipe, “Growth dynamics of phase gratings in optical fibers,” Opt. Commun. 83, 315–321 (1991).
[Crossref]

T. M. Monro, C. M. de Sterke, and L. Poladian, “Self-writing a waveguide in glass using photosensitivity,” Opt. Commun. 119, 523–526 (1995).
[Crossref]

Opt. Lett. (6)

Phys. Rev. A (3)

E. Caglioti, B. Crosignani, and P. Di Porto, “Hamiltonian description of nonlinear propagation in optical fibers,” Phys. Rev. A 38, 4036–4042 (1988).
[Crossref] [PubMed]

T. Ueda and W. L. Kath, “Dynamics of coupled solitons in nonlinear optical fibers,” Phys. Rev. A 42, 563–571 (1990).
[Crossref] [PubMed]

V. Mizrahi, S. LaRochelle, G. I. Stegeman, and J. E. Sipe, “Physics of photosensitive-grating formation in optical fibers,” Phys. Rev. A 43, 433–438 (1991).
[Crossref] [PubMed]

Other (4)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 16.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[Crossref]

E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970).

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Figures (9)

Fig. 1
Fig. 1

Top view of a slab of glass with dashed curves showing the initial diffraction and the solid curves showing schematically how the light is guided after the channel waveguide has formed.

Fig. 2
Fig. 2

Intensity contour plot for the two-photon case at T=2 on axis (η=0). The primary eye is the maximum at ζ ≈ 3000.

Fig. 3
Fig. 3

Solid curve is the position of the intensity eye as given by the simulation for the two-photon case. The dashed curve is this position as found by the series-expansion technique, Eq. (13), with terms up to order ζ4. The dotted curve shows results found by use of terms up to order ζ10.

Fig. 4
Fig. 4

Intensity contour plot for the two-photon case at T=6 on axis (η=0). Here the primary eye is at ζ1700, and the secondary eyes are at ζ approximately equal to 2500, 3400, 4700, 6700, and 11000.

Fig. 5
Fig. 5

Results of WKB analysis for the waveguide for the one-photon case. The solid curves (left scale) correspond to the propagation constants of the lowest two even modes at T=0.248. The dashed curve (right scale) shows m, as found by Eq. (7). The dimensionless propagation constant shown in this figure (β) is related to the actual propagation constant (βact) by the scaling βact=k(1+β), where k is the wave number in the unexposed glass.

Fig. 6
Fig. 6

Results of WKB analysis for the waveguide for the two-photon case. The solid curves (left scale) are the propagation constants of the lowest two even modes at T=6. The dotted curve (right scale) is m [see Eq. (7)]. The dimensionless propagation constant shown in this figure (β) is related to the actual propagation constant (βact) by the scaling βact=k(1+β), where k is the wave number is the unexposed glass.

Fig. 7
Fig. 7

Intensity contour plot for the two-photon case at T=8 on axis (η=0).

Fig. 8
Fig. 8

Refractive-index contour plot for the two-photon case at T=10 on axis (η=0). This shows that a fairly uniform channel waveguide has formed. The refractive-index primary eye is at ζ2500 at this time.

Fig. 9
Fig. 9

Intensity along the ζ axis at different times for the one-photon case. The solid curves correspond to the numerical simulation, and the dashed curves correspond to semianalytic results.

Equations (22)

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

E(x,y,z,t)=F(x)(y,z,t)exp[i(kz-ωt)]yˆ+c.c.,
(η,0,t)=1wexp-η22w2,
iddζ+12d2dη2+Δnn=0,
Δn(T)n=-T(*)pdT,
(ζ,η,T;w)=w0wζw02w2,ηw0w,Tww02-p;w0,
Δn(ζ,η,T;w)=w0w2Δnζw02w2,ηw0w,Tww02-p;w0.
-Δn(η,ζ,T)ndη=π2m(ζ,T)+12,
abΔn(η,ζ,T)n-β dη=π2q+12,
Δn(η,ζ,T)n=(00*)pT,
ζB=2π|β1-β2|.
m(λ)=m(λ0)λ0λ.
I(ζ,T)=(0,ζ,T)*(0,ζ,T),
Iζ,TI0,T=1+2T-12ζ2w4+38-19T+20T23ζ4w8+-516+991T4-1206T25+3424T3135ζ6w12+35128-31427T8+659163T270-2079976T3945+96952T4945ζ8w16+-63256+22193927T320-525271781T21260+40850324T3225-895316T4525+10157296T523625ζ10w20,
Δnζ,TΔn0,T=1+2T-1ζ2w4+1-20T+52T29ζ4w8+-1+258T-8476T245+2612T3135ζ6w12+1-4060T+143020T221-148196T3105+12288T4175ζ8w16+-1+357098T5-54715148T2189+490773272T34725-222997088T423625+56998688T5212625ζ10w20,
T=14T0,
T=12,
N=hσexp-η2σ2,
=β1/4 exp-βη22,
-EηE*ηdη.
Δn=n2k2W2
Δn=n4k2W2.
zR=kW22,

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