Abstract

Starting with an accurate linear electromagnetic theory of a totally reflecting prism coupled to a dielectric waveguide, we implement a numerical technique to take into account optogeometric perturbations in stratified media. We calculate both the reflected fields in intensity on the prism base (near field) and in infinity (far field) for an incident Gaussian beam. The study of the variations of the intensity in the reflected beam (near and far fields) versus light power shows thermoinduced dilation of the prism and an intensity-dependent refractive index of thin films composed of tantalium pentoxyde and titanium dioxide.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. K. Tien, R. Ulrich, “Theory of prism–film coupler and thin-film light guides,” J. Opt. Soc. Am. 60, 1325–1337 (1970).
    [Crossref]
  2. R. Ulrich, “Theory of prism–film coupler by plane wave analysis,” J. Opt. Soc. Am. 60, 1337–1350 (1970).
    [Crossref]
  3. Y. Shah, T. Tamir, “Absorption and lateral shift of beams incident upon lossy multilayered media,” J. Opt. Soc. Am. 73, 37–44 (1983).
    [Crossref]
  4. Y. Levy, C. Imbert, “Amplification des déplacements à la réflexion totale,” Opt. Commun. 13, 43–47 (1975).
    [Crossref]
  5. R. Petit, M. Cadillac, “Théorie électromagnétique du coupleur à prisme,” J. Opt. (Paris) 8, 41–49 (1977).
    [Crossref]
  6. G. M. Carter, Y. J. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
    [Crossref]
  7. C. Liao, G. I. Stegeman, “Nonlinear prism coupler,” Appl. Phys. Lett. 44, 164–166 (1984).
    [Crossref]
  8. R. M. Fortenberry, G. Assanto, R. Moshrefzadeh, C. T. Seaton, G. I. Stegeman, “Pulsed excitation of nonlinear distributed coupling into zinc oxide optical waveguides,” J. Opt. Soc. Am. B 5, 425–431 (1988); G. Assanto, R. M. Fortenberry, C. T. Seaton, G. I. Stegeman, “Theory of pulsed excitation of nonlinear distributed prism couplers,” J. Opt. Soc. Am. B 5, 432–442 (1988).
    [Crossref]
  9. G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
    [Crossref]
  10. G. Vitrant, R. Reinisch, J. Cl. Paumier, G. Assanto, G. I. Stegeman, “Nonlinear prism coupler with nonlocality,” Opt. Lett. 14, 898–902 (1989).
    [Crossref] [PubMed]
  11. W. Lukosz, P. Pirani, V. Briguet, “Optical bistability by photothermal displacement in prism coupling into planar waveguides,” Opt. Lett. 12, 263–265 (1987).
    [Crossref] [PubMed]
  12. C. Falco, A. Azema, J. Botineau, D. B. Ostrowsky, “Infrared prism coupling characterization and optimization via near-field m-line scanning,” Appl. Opt. 21, 1847–1850 (1982).
    [Crossref] [PubMed]
  13. J. Goodman, Introduction à l’Optique de Fourier (Masson, Paris, 1972), pp. 53–71.
  14. P. Vincent, N. Paraire, M. Nevière, A. Koster, R. Reinisch, “Gratings in nonlinear optics and optical bistability,” J. Opt. Soc. Am. B 2, 1106–1116 (1985).
    [Crossref]
  15. M. Haelterman, G. Vitrant, R. Reinisch, “Transverse effects in nonlinear planar resonators. I. Modal theory,” J. Opt. Soc. Am. B 7, 1309–1318 (1990); G. Vitrant, M. Haelterman, R. Reinisch, “Transverse effects in nonlinear planar resonators. II. Modal analysis for normal and oblique incidence,” J. Opt. Soc. Am. B 7, 1319–1327 (1990).
    [Crossref]
  16. F. Flory, H. Rigneault, N. Maythaveekulchai, F. Zamkostian, “Characterization by guided wave of instabilities of optical coatings submitted to high-power flux: thermal and third-order nonlinear properties of dielectric thin films,” Appl. Opt. 32, 5628–5639 (1993).
    [Crossref] [PubMed]
  17. H. K. Pulker, Coatings on Glass (Elsevier, Amsterdam, 1984), pp. 247–256.
  18. E. D. Palik, Handbook of Optical Constant of Solids (Academic, Orlando, Fla., 1985), 795–798.
  19. M. Commandré, L. Bertrand, G. Albrand, E. Pelletier, “Measurement of absorption losses of optical thin film components by photothermal deflection spectroscopy,” in Optical Components and Systems, A. Masson, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 805, 128–135 (1987).
  20. S. Ogura, H. A. Macleod, “Water sorption phenomena in optical thin films,” Thin Solid Films 34, 371–375 (1986).
    [Crossref]
  21. H. A. Macleod, “The microstructure of optical thin films,” in Optical Thin Films, R. I. Seddon, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 325, 21–28 (1982).

1993 (1)

1990 (1)

1989 (1)

1988 (2)

1987 (1)

1986 (1)

S. Ogura, H. A. Macleod, “Water sorption phenomena in optical thin films,” Thin Solid Films 34, 371–375 (1986).
[Crossref]

1985 (1)

1984 (1)

C. Liao, G. I. Stegeman, “Nonlinear prism coupler,” Appl. Phys. Lett. 44, 164–166 (1984).
[Crossref]

1983 (2)

G. M. Carter, Y. J. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
[Crossref]

Y. Shah, T. Tamir, “Absorption and lateral shift of beams incident upon lossy multilayered media,” J. Opt. Soc. Am. 73, 37–44 (1983).
[Crossref]

1982 (1)

1977 (1)

R. Petit, M. Cadillac, “Théorie électromagnétique du coupleur à prisme,” J. Opt. (Paris) 8, 41–49 (1977).
[Crossref]

1975 (1)

Y. Levy, C. Imbert, “Amplification des déplacements à la réflexion totale,” Opt. Commun. 13, 43–47 (1975).
[Crossref]

1970 (2)

Albrand, G.

M. Commandré, L. Bertrand, G. Albrand, E. Pelletier, “Measurement of absorption losses of optical thin film components by photothermal deflection spectroscopy,” in Optical Components and Systems, A. Masson, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 805, 128–135 (1987).

Assanto, G.

Azema, A.

Bertrand, L.

M. Commandré, L. Bertrand, G. Albrand, E. Pelletier, “Measurement of absorption losses of optical thin film components by photothermal deflection spectroscopy,” in Optical Components and Systems, A. Masson, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 805, 128–135 (1987).

Botineau, J.

Briguet, V.

Cadillac, M.

R. Petit, M. Cadillac, “Théorie électromagnétique du coupleur à prisme,” J. Opt. (Paris) 8, 41–49 (1977).
[Crossref]

Carter, G. M.

G. M. Carter, Y. J. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
[Crossref]

Chen, Y. J.

G. M. Carter, Y. J. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
[Crossref]

Commandré, M.

M. Commandré, L. Bertrand, G. Albrand, E. Pelletier, “Measurement of absorption losses of optical thin film components by photothermal deflection spectroscopy,” in Optical Components and Systems, A. Masson, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 805, 128–135 (1987).

Falco, C.

Flory, F.

Fortenberry, R. M.

Goodman, J.

J. Goodman, Introduction à l’Optique de Fourier (Masson, Paris, 1972), pp. 53–71.

Haelterman, M.

Imbert, C.

Y. Levy, C. Imbert, “Amplification des déplacements à la réflexion totale,” Opt. Commun. 13, 43–47 (1975).
[Crossref]

Koster, A.

Levy, Y.

Y. Levy, C. Imbert, “Amplification des déplacements à la réflexion totale,” Opt. Commun. 13, 43–47 (1975).
[Crossref]

Liao, C.

C. Liao, G. I. Stegeman, “Nonlinear prism coupler,” Appl. Phys. Lett. 44, 164–166 (1984).
[Crossref]

Lukosz, W.

Macleod, H. A.

S. Ogura, H. A. Macleod, “Water sorption phenomena in optical thin films,” Thin Solid Films 34, 371–375 (1986).
[Crossref]

H. A. Macleod, “The microstructure of optical thin films,” in Optical Thin Films, R. I. Seddon, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 325, 21–28 (1982).

Maythaveekulchai, N.

Moshrefzadeh, R.

Nevière, M.

Ogura, S.

S. Ogura, H. A. Macleod, “Water sorption phenomena in optical thin films,” Thin Solid Films 34, 371–375 (1986).
[Crossref]

Ostrowsky, D. B.

Palik, E. D.

E. D. Palik, Handbook of Optical Constant of Solids (Academic, Orlando, Fla., 1985), 795–798.

Paraire, N.

Paumier, J. Cl.

Pelletier, E.

M. Commandré, L. Bertrand, G. Albrand, E. Pelletier, “Measurement of absorption losses of optical thin film components by photothermal deflection spectroscopy,” in Optical Components and Systems, A. Masson, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 805, 128–135 (1987).

Petit, R.

R. Petit, M. Cadillac, “Théorie électromagnétique du coupleur à prisme,” J. Opt. (Paris) 8, 41–49 (1977).
[Crossref]

Pirani, P.

Pulker, H. K.

H. K. Pulker, Coatings on Glass (Elsevier, Amsterdam, 1984), pp. 247–256.

Reinisch, R.

Rigneault, H.

Seaton, C. T.

Shah, Y.

Stegeman, G. I.

Tamir, T.

Tien, P. K.

Ulrich, R.

Vincent, P.

Vitrant, G.

Zamkostian, F.

Zanoni, R.

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

G. M. Carter, Y. J. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
[Crossref]

C. Liao, G. I. Stegeman, “Nonlinear prism coupler,” Appl. Phys. Lett. 44, 164–166 (1984).
[Crossref]

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
[Crossref]

J. Opt. (Paris) (1)

R. Petit, M. Cadillac, “Théorie électromagnétique du coupleur à prisme,” J. Opt. (Paris) 8, 41–49 (1977).
[Crossref]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

Y. Levy, C. Imbert, “Amplification des déplacements à la réflexion totale,” Opt. Commun. 13, 43–47 (1975).
[Crossref]

Opt. Lett. (2)

Thin Solid Films (1)

S. Ogura, H. A. Macleod, “Water sorption phenomena in optical thin films,” Thin Solid Films 34, 371–375 (1986).
[Crossref]

Other (5)

H. A. Macleod, “The microstructure of optical thin films,” in Optical Thin Films, R. I. Seddon, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 325, 21–28 (1982).

J. Goodman, Introduction à l’Optique de Fourier (Masson, Paris, 1972), pp. 53–71.

H. K. Pulker, Coatings on Glass (Elsevier, Amsterdam, 1984), pp. 247–256.

E. D. Palik, Handbook of Optical Constant of Solids (Academic, Orlando, Fla., 1985), 795–798.

M. Commandré, L. Bertrand, G. Albrand, E. Pelletier, “Measurement of absorption losses of optical thin film components by photothermal deflection spectroscopy,” in Optical Components and Systems, A. Masson, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 805, 128–135 (1987).

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 (12)

Fig. 1
Fig. 1

Principle of the m-line technique.

Fig. 2
Fig. 2

System and coordinate frame.

Fig. 3
Fig. 3

Plot of 2πα c /k 0 in the complex plane with air-layer thickness (given in micrometers beside each point). The structure is prism (rutile)–air–8H–glass, where H denotes a high-refractive-index (n H ) layer of optical thickness λ1/4 (λ1 = 1.064 μm, n H = 2.2, n p = 2.997, n s = 1.52, polarization TE, mode TE4). The calculation wavelength is λ0 = 2π/k 0 = 0.5145 μm.

Fig. 4
Fig. 4

Profile in intensity of the incident Gaussian beam (A), the resulting profiles in intensity of the near (B) and the far (C) fields, and the field distribution in intensity for z > 0 (D). The structure considered here is prism–air–8H–glass, as already mentioned in Fig. 3; the air-layer thickness is 0.117 μm. The guided-wave propagates in accordance with decreasing x on Figs. 4(A), 4(B), and 4(D). The origin of the x axis according to Fig. 2 is located at 500 μm in Fig. 4(D).

Fig. 5
Fig. 5

Maximum coupling efficiency for the TE4 mode versus the air-layer thickness. The structure considered here is the same as the one considered in Fig. 3.

Fig. 6
Fig. 6

m-lines experimental setup.

Fig. 7
Fig. 7

Dependence of calculated [(a), (c), (e)] and measured [(b), (d), (f)] profiles in the intensity of the near field with air-layer thickness. The structure is the same as the one already considered in Fig. 3. For the calculation of the profile the air-layer thickness is (a) 0.117 μm, (c) 0.114 μm, and (e) 0.09 μm.

Fig. 8
Fig. 8

Near-field intensity distribution as recorded with the digital imaging system. This picture corresponds to the profile given in Fig. 7(b); λ0 = 0.5145 μm.

Fig. 9
Fig. 9

Dependence of calculated [(a), (c), (e)] and measured [(b), (d), (f)] profiles in the intensity of the far field with air-layer thickness. The structure is the same as the one already considered in Fig. 3. For the calculation of the profile the air-layer thickness is (a) 0.21 μm, (c) 0.14 μm, and (e) 0.125 μm.

Fig. 10
Fig. 10

Low coupling efficiency. Far-field intensity evolution when the incident power rises from 20 to 920 mW and is lowered back to 20 mW. The structure is the same as the one considered in Fig. 3.

Fig. 11
Fig. 11

Calculated [(a), (c), (e)] and measured (from Fig. 9) [(b), (d), (f)] profiles in the intensity of the far field. For the calculation of the profiles we consider a localized decrease of the air-layer thickness that follows the light intensity on the prism base. The largest air-layer-thickness decrease is of (a) ~0 nm for 20 mW, (c) ~1 nm for 150 mW, and (e) ~2 nm for 310 mW; λ0 = 0.5145 μm.

Fig. 12
Fig. 12

Calculated [(a), (c)] and corresponding measured [(b), (d)] profiles in the intensity of the near and the far fields when the incident light power is 20 mW. The air-layer thickness is 0.11 μm; λ0 = 0.5145 μm. Also shown are calculated [(e), (g)] and corresponding measured (f), (h)] profiles in the intensity of the near and the far fields when the incident light power is 650 mW. In the calculation we consider an intensity-dependent refractive index in the guide (n 2 = 6 × 10−9 cm2/kW). The air-layer thickness is 0.099 μm; λ0 = 0.5145 μm.

Tables (1)

Tables Icon

Table 1 Nonlinear Refractive-Index Coefficients and Associated Rise Times

Equations (20)

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

U i = exp ( 2 i π α x + i χ p z ) ,
χ p = ( n p 2 k 0 2 - 4 π 2 α 2 ) 1 / 2 = n p k 0 cos θ .
U ( x , z ) = u ( z ) exp ( 2 i π α x ) ,
u ( z ) = A j + exp ( i χ j z ) + A j - exp ( - i χ z ) ,
M X = S ,
det [ M ( α ) ] = 0.
U i ( x , z ) = - + P ^ ( α - α ) exp [ 2 i π α x + i χ p ( α ) z ] d α .
U i ( x , 0 ) = P ( x ) = - + P ^ ( α - α ) exp ( 2 i π α x ) d α .
U ( x , z ) = - + P ^ ( α - α ) u ( α , z ) exp ( 2 i π α x ) d α .
u ( α , z ) = r ( α ) exp [ - i χ p ( α ) z ]
U r ( x , z ) = - + P ^ ( α - α ) r ( α ) exp [ - i χ p ( α ) z ] × exp ( 2 i π α x ) d α .
U r ( x , 0 ) = | - + P ^ ( ζ ) r ( ζ + α ) exp ( 2 i π ζ x ) d ζ | ,
I ff : | - + U r ( x , 0 ) exp ( - 2 i π f x x ) d x | 2 ,
U ( x , z ) = | - + P ^ ( ζ ) u ( ζ + α , z ) exp ( 2 i π ζ x ) d ζ | .
ρ ( x ) = α π g 2 ( x ) - + P ( x ) 2 d x ,
1 2 π d g ( x ) d x + α g ( x ) = P ( x ) .
n ( 1 ) ( z ) = n 0 ( z ) + n 2 ( z ) I ( 1 ) ( α 1 - α , z ) ,
I ( 1 ) ( α 1 - α , z ) = 1 2 0 μ 0 n 0 ( z ) P ^ ( α 1 - α ) u ( α 1 , z ) 2 ,
n ( 2 ) ( z ) = n 0 ( z ) + n 2 ( z ) I ( 2 ) ( α 2 - α , z ) ,
I ( 2 ) ( α 2 - α , z ) = 1 2 0 μ 0 n ( 1 ) ( z ) P ^ ( α 2 - α ) u ( α 2 , z ) 2 ,

Metrics