Abstract

The use of total reflection at the boundary between the guiding region and the substrate (or another guiding region) to implement waveguide achromatic elements is discussed. Two geometries of the boundary, parabolic and elliptical, are proposed and analyzed. The parabolic boundary was fabricated by selective ion exchange, and both its focusing capabilities and the compatibility of its numerical aperture with optical fibers are demonstrated.

© 1998 Optical Society of America

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References

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  1. J. Sochacki, “Gradient-index geodesic lenses for integrated optics: a uniform theory. I. Full aperture solutions,” J. Mod. Opt. 35, 891–906 (1988).
    [CrossRef]
  2. B. Chen, E. Marom, R. J. Morrison, “Diffraction-limited geodesic lens for integrated optics circuits,” Appl. Phys. Lett. 33, 511–513 (1978).
    [CrossRef]
  3. G. C. Righini, G. Molesini, “Design of optical-waveguides homogeneous refracting lenses,” Appl. Opt. 27, 4193–4199 (1988).
    [CrossRef] [PubMed]
  4. P. J. R. Laybourn, G. Molesini, G. C. Righini, “Homogeneous refracting lenses for integrated optical circuits,” J. Mod. Opt. 35, 1029–1048 (1988).
    [CrossRef]
  5. G. H. Chartier, P. J. R. Laybourn, A. Girod, “Masking process for double-ion-exchanged glass optical waveguides,” Electron. Lett. 22, 925–926 (1986).
    [CrossRef]
  6. J. Liñares, G. C. Righini, J. E. Alvarellos, “Modal coupling analysis for integrated optical components in glass and lithium niobate,” Appl. Opt. 31, 5292–5298 (1992).
    [CrossRef] [PubMed]
  7. X. Prieto, C. Montero, J. Liñares, “Three-step diffused surface waveguides for fabricating and designing integrated optical components,” J. Mod. Opt. 42, 2159–2163 (1995).
    [CrossRef]
  8. J. Saarinen, S. Honkanen, S. I. Najafi, J. Hutunen, “Double-ion exchange process in glass for the fabrication of computer-generated waveguide holograms,” Appl. Opt. 33, 3353–3359 (1994).
    [CrossRef] [PubMed]
  9. R. März, C. Cremer, “On the theory of planar spectrographs,” J. Lightwave Technol. 10, 2017–2220 (1992).
    [CrossRef]
  10. P. C. Clemens, G. Heise, R. März, H. Michel, A. Reichelt, H. W. Schneider, “8-Channel optical demultiplexer realized as SiO2/Si flat-field spectrograph,” IEEE Photon. Technol. Lett. 6, 1109–1111 (1994).
    [CrossRef]
  11. P. K. Tien, “Integrated optics and new phenomena in optical waveguides,” Rev. Mod. Phys. 49, 361–420 (1977).
    [CrossRef]
  12. J. Albert, “Ion exchange from salt melts,” in Introduction to Glass Integrated Optics, S. I. Najafi, ed. (Artech, London, 1992), Chap. 2.
  13. T. Tamir, ed., Guided-Wave Optoelectronics, Vol. 26 of Springer Series in Electronics and Photonics (Springer-Verlag, Berlin, 1988).
    [CrossRef]
  14. H. C. Cheng, R. V. Ramaswamy, “Symmetrical directional coupler as a wavelength multiplexer–demultiplexer: theory and experiment,” IEEE J. Quantum Electron. 27, 567–574 (1991).
    [CrossRef]
  15. K. Kishioka, G. L. Yip, “A novel three-wavelength demultiplexer utilising the two- and three-guide couplers,” J. Lightwave Technol. 11, 234–240 (1993).
    [CrossRef]
  16. A. Tervonen, S. Honkanen, “Model for waveguide fabrication in glass by two-step ion exchange with ionic masking,” Opt. Lett. 13, 71–73 (1988).
    [CrossRef] [PubMed]
  17. S. D. Fantone, “Refractive index and spectral models for gradient-index materials,” Appl. Opt. 22, 432–440 (1983).
    [CrossRef] [PubMed]
  18. A. N. Miliou, R. Srivastava, R. V. Ramaswamy, “Modeling of the index change in K+–Na+ ion-exchanged waveguides,” Appl. Opt. 30, 674–681 (1991).
    [CrossRef] [PubMed]
  19. R. A. Betts, F. Lui, “Broadband polarisation splitting couplers in ion-exchanged glass,” Electron. Lett. 26, 450–452 (1990).
    [CrossRef]

1995 (1)

X. Prieto, C. Montero, J. Liñares, “Three-step diffused surface waveguides for fabricating and designing integrated optical components,” J. Mod. Opt. 42, 2159–2163 (1995).
[CrossRef]

1994 (2)

J. Saarinen, S. Honkanen, S. I. Najafi, J. Hutunen, “Double-ion exchange process in glass for the fabrication of computer-generated waveguide holograms,” Appl. Opt. 33, 3353–3359 (1994).
[CrossRef] [PubMed]

P. C. Clemens, G. Heise, R. März, H. Michel, A. Reichelt, H. W. Schneider, “8-Channel optical demultiplexer realized as SiO2/Si flat-field spectrograph,” IEEE Photon. Technol. Lett. 6, 1109–1111 (1994).
[CrossRef]

1993 (1)

K. Kishioka, G. L. Yip, “A novel three-wavelength demultiplexer utilising the two- and three-guide couplers,” J. Lightwave Technol. 11, 234–240 (1993).
[CrossRef]

1992 (2)

1991 (2)

H. C. Cheng, R. V. Ramaswamy, “Symmetrical directional coupler as a wavelength multiplexer–demultiplexer: theory and experiment,” IEEE J. Quantum Electron. 27, 567–574 (1991).
[CrossRef]

A. N. Miliou, R. Srivastava, R. V. Ramaswamy, “Modeling of the index change in K+–Na+ ion-exchanged waveguides,” Appl. Opt. 30, 674–681 (1991).
[CrossRef] [PubMed]

1990 (1)

R. A. Betts, F. Lui, “Broadband polarisation splitting couplers in ion-exchanged glass,” Electron. Lett. 26, 450–452 (1990).
[CrossRef]

1988 (4)

A. Tervonen, S. Honkanen, “Model for waveguide fabrication in glass by two-step ion exchange with ionic masking,” Opt. Lett. 13, 71–73 (1988).
[CrossRef] [PubMed]

J. Sochacki, “Gradient-index geodesic lenses for integrated optics: a uniform theory. I. Full aperture solutions,” J. Mod. Opt. 35, 891–906 (1988).
[CrossRef]

G. C. Righini, G. Molesini, “Design of optical-waveguides homogeneous refracting lenses,” Appl. Opt. 27, 4193–4199 (1988).
[CrossRef] [PubMed]

P. J. R. Laybourn, G. Molesini, G. C. Righini, “Homogeneous refracting lenses for integrated optical circuits,” J. Mod. Opt. 35, 1029–1048 (1988).
[CrossRef]

1986 (1)

G. H. Chartier, P. J. R. Laybourn, A. Girod, “Masking process for double-ion-exchanged glass optical waveguides,” Electron. Lett. 22, 925–926 (1986).
[CrossRef]

1983 (1)

1978 (1)

B. Chen, E. Marom, R. J. Morrison, “Diffraction-limited geodesic lens for integrated optics circuits,” Appl. Phys. Lett. 33, 511–513 (1978).
[CrossRef]

1977 (1)

P. K. Tien, “Integrated optics and new phenomena in optical waveguides,” Rev. Mod. Phys. 49, 361–420 (1977).
[CrossRef]

Albert, J.

J. Albert, “Ion exchange from salt melts,” in Introduction to Glass Integrated Optics, S. I. Najafi, ed. (Artech, London, 1992), Chap. 2.

Alvarellos, J. E.

Betts, R. A.

R. A. Betts, F. Lui, “Broadband polarisation splitting couplers in ion-exchanged glass,” Electron. Lett. 26, 450–452 (1990).
[CrossRef]

Chartier, G. H.

G. H. Chartier, P. J. R. Laybourn, A. Girod, “Masking process for double-ion-exchanged glass optical waveguides,” Electron. Lett. 22, 925–926 (1986).
[CrossRef]

Chen, B.

B. Chen, E. Marom, R. J. Morrison, “Diffraction-limited geodesic lens for integrated optics circuits,” Appl. Phys. Lett. 33, 511–513 (1978).
[CrossRef]

Cheng, H. C.

H. C. Cheng, R. V. Ramaswamy, “Symmetrical directional coupler as a wavelength multiplexer–demultiplexer: theory and experiment,” IEEE J. Quantum Electron. 27, 567–574 (1991).
[CrossRef]

Clemens, P. C.

P. C. Clemens, G. Heise, R. März, H. Michel, A. Reichelt, H. W. Schneider, “8-Channel optical demultiplexer realized as SiO2/Si flat-field spectrograph,” IEEE Photon. Technol. Lett. 6, 1109–1111 (1994).
[CrossRef]

Cremer, C.

R. März, C. Cremer, “On the theory of planar spectrographs,” J. Lightwave Technol. 10, 2017–2220 (1992).
[CrossRef]

Fantone, S. D.

Girod, A.

G. H. Chartier, P. J. R. Laybourn, A. Girod, “Masking process for double-ion-exchanged glass optical waveguides,” Electron. Lett. 22, 925–926 (1986).
[CrossRef]

Heise, G.

P. C. Clemens, G. Heise, R. März, H. Michel, A. Reichelt, H. W. Schneider, “8-Channel optical demultiplexer realized as SiO2/Si flat-field spectrograph,” IEEE Photon. Technol. Lett. 6, 1109–1111 (1994).
[CrossRef]

Honkanen, S.

Hutunen, J.

Kishioka, K.

K. Kishioka, G. L. Yip, “A novel three-wavelength demultiplexer utilising the two- and three-guide couplers,” J. Lightwave Technol. 11, 234–240 (1993).
[CrossRef]

Laybourn, P. J. R.

P. J. R. Laybourn, G. Molesini, G. C. Righini, “Homogeneous refracting lenses for integrated optical circuits,” J. Mod. Opt. 35, 1029–1048 (1988).
[CrossRef]

G. H. Chartier, P. J. R. Laybourn, A. Girod, “Masking process for double-ion-exchanged glass optical waveguides,” Electron. Lett. 22, 925–926 (1986).
[CrossRef]

Liñares, J.

X. Prieto, C. Montero, J. Liñares, “Three-step diffused surface waveguides for fabricating and designing integrated optical components,” J. Mod. Opt. 42, 2159–2163 (1995).
[CrossRef]

J. Liñares, G. C. Righini, J. E. Alvarellos, “Modal coupling analysis for integrated optical components in glass and lithium niobate,” Appl. Opt. 31, 5292–5298 (1992).
[CrossRef] [PubMed]

Lui, F.

R. A. Betts, F. Lui, “Broadband polarisation splitting couplers in ion-exchanged glass,” Electron. Lett. 26, 450–452 (1990).
[CrossRef]

Marom, E.

B. Chen, E. Marom, R. J. Morrison, “Diffraction-limited geodesic lens for integrated optics circuits,” Appl. Phys. Lett. 33, 511–513 (1978).
[CrossRef]

März, R.

P. C. Clemens, G. Heise, R. März, H. Michel, A. Reichelt, H. W. Schneider, “8-Channel optical demultiplexer realized as SiO2/Si flat-field spectrograph,” IEEE Photon. Technol. Lett. 6, 1109–1111 (1994).
[CrossRef]

R. März, C. Cremer, “On the theory of planar spectrographs,” J. Lightwave Technol. 10, 2017–2220 (1992).
[CrossRef]

Michel, H.

P. C. Clemens, G. Heise, R. März, H. Michel, A. Reichelt, H. W. Schneider, “8-Channel optical demultiplexer realized as SiO2/Si flat-field spectrograph,” IEEE Photon. Technol. Lett. 6, 1109–1111 (1994).
[CrossRef]

Miliou, A. N.

Molesini, G.

G. C. Righini, G. Molesini, “Design of optical-waveguides homogeneous refracting lenses,” Appl. Opt. 27, 4193–4199 (1988).
[CrossRef] [PubMed]

P. J. R. Laybourn, G. Molesini, G. C. Righini, “Homogeneous refracting lenses for integrated optical circuits,” J. Mod. Opt. 35, 1029–1048 (1988).
[CrossRef]

Montero, C.

X. Prieto, C. Montero, J. Liñares, “Three-step diffused surface waveguides for fabricating and designing integrated optical components,” J. Mod. Opt. 42, 2159–2163 (1995).
[CrossRef]

Morrison, R. J.

B. Chen, E. Marom, R. J. Morrison, “Diffraction-limited geodesic lens for integrated optics circuits,” Appl. Phys. Lett. 33, 511–513 (1978).
[CrossRef]

Najafi, S. I.

Prieto, X.

X. Prieto, C. Montero, J. Liñares, “Three-step diffused surface waveguides for fabricating and designing integrated optical components,” J. Mod. Opt. 42, 2159–2163 (1995).
[CrossRef]

Ramaswamy, R. V.

H. C. Cheng, R. V. Ramaswamy, “Symmetrical directional coupler as a wavelength multiplexer–demultiplexer: theory and experiment,” IEEE J. Quantum Electron. 27, 567–574 (1991).
[CrossRef]

A. N. Miliou, R. Srivastava, R. V. Ramaswamy, “Modeling of the index change in K+–Na+ ion-exchanged waveguides,” Appl. Opt. 30, 674–681 (1991).
[CrossRef] [PubMed]

Reichelt, A.

P. C. Clemens, G. Heise, R. März, H. Michel, A. Reichelt, H. W. Schneider, “8-Channel optical demultiplexer realized as SiO2/Si flat-field spectrograph,” IEEE Photon. Technol. Lett. 6, 1109–1111 (1994).
[CrossRef]

Righini, G. C.

Saarinen, J.

Schneider, H. W.

P. C. Clemens, G. Heise, R. März, H. Michel, A. Reichelt, H. W. Schneider, “8-Channel optical demultiplexer realized as SiO2/Si flat-field spectrograph,” IEEE Photon. Technol. Lett. 6, 1109–1111 (1994).
[CrossRef]

Sochacki, J.

J. Sochacki, “Gradient-index geodesic lenses for integrated optics: a uniform theory. I. Full aperture solutions,” J. Mod. Opt. 35, 891–906 (1988).
[CrossRef]

Srivastava, R.

Tervonen, A.

Tien, P. K.

P. K. Tien, “Integrated optics and new phenomena in optical waveguides,” Rev. Mod. Phys. 49, 361–420 (1977).
[CrossRef]

Yip, G. L.

K. Kishioka, G. L. Yip, “A novel three-wavelength demultiplexer utilising the two- and three-guide couplers,” J. Lightwave Technol. 11, 234–240 (1993).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

B. Chen, E. Marom, R. J. Morrison, “Diffraction-limited geodesic lens for integrated optics circuits,” Appl. Phys. Lett. 33, 511–513 (1978).
[CrossRef]

Electron. Lett. (2)

R. A. Betts, F. Lui, “Broadband polarisation splitting couplers in ion-exchanged glass,” Electron. Lett. 26, 450–452 (1990).
[CrossRef]

G. H. Chartier, P. J. R. Laybourn, A. Girod, “Masking process for double-ion-exchanged glass optical waveguides,” Electron. Lett. 22, 925–926 (1986).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. C. Cheng, R. V. Ramaswamy, “Symmetrical directional coupler as a wavelength multiplexer–demultiplexer: theory and experiment,” IEEE J. Quantum Electron. 27, 567–574 (1991).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

P. C. Clemens, G. Heise, R. März, H. Michel, A. Reichelt, H. W. Schneider, “8-Channel optical demultiplexer realized as SiO2/Si flat-field spectrograph,” IEEE Photon. Technol. Lett. 6, 1109–1111 (1994).
[CrossRef]

J. Lightwave Technol. (2)

K. Kishioka, G. L. Yip, “A novel three-wavelength demultiplexer utilising the two- and three-guide couplers,” J. Lightwave Technol. 11, 234–240 (1993).
[CrossRef]

R. März, C. Cremer, “On the theory of planar spectrographs,” J. Lightwave Technol. 10, 2017–2220 (1992).
[CrossRef]

J. Mod. Opt. (3)

X. Prieto, C. Montero, J. Liñares, “Three-step diffused surface waveguides for fabricating and designing integrated optical components,” J. Mod. Opt. 42, 2159–2163 (1995).
[CrossRef]

J. Sochacki, “Gradient-index geodesic lenses for integrated optics: a uniform theory. I. Full aperture solutions,” J. Mod. Opt. 35, 891–906 (1988).
[CrossRef]

P. J. R. Laybourn, G. Molesini, G. C. Righini, “Homogeneous refracting lenses for integrated optical circuits,” J. Mod. Opt. 35, 1029–1048 (1988).
[CrossRef]

Opt. Lett. (1)

Rev. Mod. Phys. (1)

P. K. Tien, “Integrated optics and new phenomena in optical waveguides,” Rev. Mod. Phys. 49, 361–420 (1977).
[CrossRef]

Other (2)

J. Albert, “Ion exchange from salt melts,” in Introduction to Glass Integrated Optics, S. I. Najafi, ed. (Artech, London, 1992), Chap. 2.

T. Tamir, ed., Guided-Wave Optoelectronics, Vol. 26 of Springer Series in Electronics and Photonics (Springer-Verlag, Berlin, 1988).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Parabolic boundary: the bold portions of the curves are the relevant sectors where total reflection can be obtained for beams propagating parallel to the Z axis in the negative direction.

Fig. 2
Fig. 2

Elliptical boundary: the bold portions of the curves are the relevant sectors where total reflection can be obtained for beams originating from the origins of the coordinates.

Fig. 3
Fig. 3

Diagram of a 1 × 2 wavelength (de)multiplexer. By changing the properties of the low-index region one can fabricate other devices.

Fig. 4
Fig. 4

(a) Image of the scattered light from the integrated reflective element (two parabolic mirrors) taken by a CCD camera. (b) Ray-tracing diagram of this element.

Fig. 5
Fig. 5

Scattered light from the fundamental mode; we can see the total internal reflection on a straight boundary. Some small scratches (bright dots) were produced in previous attempts at prism coupling. The white corners delimit the rectangle (1.6 cm × 0.42 cm) that we used to evaluate the losses. The image at the right of the rectangle was rejected because the intensity of the scattered light there was not large in comparison with the background light.

Fig. 6
Fig. 6

Average over each column of pixels of the rectangle shown in Fig. 5 versus the column number. The zone where the light is reflected is shown. By taking into account the propagation direction and the fit result, we estimated the propagation losses. The reflection losses are smaller than the noise of the pixel averages (∼0.6 dB).

Equations (10)

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

sin   ϕ n s N 0 = sin   ϕ c ,
z = y 2 4 d - d     r   sin 2 θ 2 = d d > 0 r   cos 2 θ 2 = d d < 0 .
tan   ϕ = 1 r d r d θ = tan θ - π 2     2 ϕ = π - | θ | , 0 ϕ < π 2 ,     - π θ < π .
| θ | < 2   arccos n s / N 0 ,     θ 0 ,     - π θ < π ,
y 2 a 2 + z - b 2 - a 2 2 b 2 = 1 ,
r 2 sin 2   θ a 2 + cos 2   θ b 2 - 2 b 2 - a 2 b 2   r   cos   θ - a 2 b 2 = 0 .
tan   ϕ = 1 r d r d θ = sin   ε   sin   θ 1 - sin   ε   cos   θ ,
ε = arccos a / b .
cos   θ - n s 2 N 0 2 sin   ε 1 - n s 2 N 0 2 1 / 2 1 - n s 2 N 0 2 sin 2   ε 1 / 2 ,
ϕ > ϕ c ν ,   λ = arcsin n s λ N ν λ ;

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