Abstract

The purpose of this work is to describe a direct method for determining thermal dependence of the refractive indices of bulk materials and waveguiding film structures. The technique is alternative to standard ones, which require prism-shaped specimens, and decidedly simple than other new methods based on planar grating structures.

© 1997 Optical Society of America

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References

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  1. P. Martin et al., “Accurate refractive index measurements of doped and undoped InP by a grating coupling technique,” Appl. Phys. Lett 67 (7), 881–883 (1995).
    [CrossRef]
  2. E. Gini et al., “Thermal dependence of the refractive index of InP measured with integrated optical demultiplexer,” J. Appl. Phys. 79 (8), 4335–4337 (1996).
    [CrossRef]
  3. S. Waldenstrom, K. Razi Naqvi, “Measurement of refractive indices of prismatic materials,” Eng. Lab. Notes in Opt. Phot. News 7 (2), S1–S2 (1996), and references herein enclosed.
  4. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon Press, Oxford, 1989).
  5. G. Cocorullo et al., “New Possibilities for efficient silicon integrated electro-optical modulators,” Opt. Comm. 86 (2), 228–235 (1991).
    [CrossRef]
  6. G. Cocorullo, I. Rendina, “Thermo-optical modulation at 1.5 mm in silicon étalon,” Electron. Lett. 28 (1), 83–84 (1992).
    [CrossRef]
  7. Solimeno et al., Guiding, Diffraction and Confinement of the Optical Radiation (Academic Press, Orlando, 1986).
  8. G. Cocorullo et al., “Thermo-optical modulation at 1.5 mm in an a-SiC—a-Si—a-SiC planar guided-wave structure,” IEEE Phot. Tech. Lett. 8 (7), 900–902 (1996).
    [CrossRef]

1996

E. Gini et al., “Thermal dependence of the refractive index of InP measured with integrated optical demultiplexer,” J. Appl. Phys. 79 (8), 4335–4337 (1996).
[CrossRef]

S. Waldenstrom, K. Razi Naqvi, “Measurement of refractive indices of prismatic materials,” Eng. Lab. Notes in Opt. Phot. News 7 (2), S1–S2 (1996), and references herein enclosed.

G. Cocorullo et al., “Thermo-optical modulation at 1.5 mm in an a-SiC—a-Si—a-SiC planar guided-wave structure,” IEEE Phot. Tech. Lett. 8 (7), 900–902 (1996).
[CrossRef]

1995

P. Martin et al., “Accurate refractive index measurements of doped and undoped InP by a grating coupling technique,” Appl. Phys. Lett 67 (7), 881–883 (1995).
[CrossRef]

1992

G. Cocorullo, I. Rendina, “Thermo-optical modulation at 1.5 mm in silicon étalon,” Electron. Lett. 28 (1), 83–84 (1992).
[CrossRef]

1991

G. Cocorullo et al., “New Possibilities for efficient silicon integrated electro-optical modulators,” Opt. Comm. 86 (2), 228–235 (1991).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon Press, Oxford, 1989).

Cocorullo, G.

G. Cocorullo et al., “Thermo-optical modulation at 1.5 mm in an a-SiC—a-Si—a-SiC planar guided-wave structure,” IEEE Phot. Tech. Lett. 8 (7), 900–902 (1996).
[CrossRef]

G. Cocorullo, I. Rendina, “Thermo-optical modulation at 1.5 mm in silicon étalon,” Electron. Lett. 28 (1), 83–84 (1992).
[CrossRef]

G. Cocorullo et al., “New Possibilities for efficient silicon integrated electro-optical modulators,” Opt. Comm. 86 (2), 228–235 (1991).
[CrossRef]

Gini, E.

E. Gini et al., “Thermal dependence of the refractive index of InP measured with integrated optical demultiplexer,” J. Appl. Phys. 79 (8), 4335–4337 (1996).
[CrossRef]

Martin, P.

P. Martin et al., “Accurate refractive index measurements of doped and undoped InP by a grating coupling technique,” Appl. Phys. Lett 67 (7), 881–883 (1995).
[CrossRef]

Razi Naqvi, K.

S. Waldenstrom, K. Razi Naqvi, “Measurement of refractive indices of prismatic materials,” Eng. Lab. Notes in Opt. Phot. News 7 (2), S1–S2 (1996), and references herein enclosed.

Rendina, I.

G. Cocorullo, I. Rendina, “Thermo-optical modulation at 1.5 mm in silicon étalon,” Electron. Lett. 28 (1), 83–84 (1992).
[CrossRef]

Solimeno,

Solimeno et al., Guiding, Diffraction and Confinement of the Optical Radiation (Academic Press, Orlando, 1986).

Waldenstrom, S.

S. Waldenstrom, K. Razi Naqvi, “Measurement of refractive indices of prismatic materials,” Eng. Lab. Notes in Opt. Phot. News 7 (2), S1–S2 (1996), and references herein enclosed.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon Press, Oxford, 1989).

Appl. Phys. Lett

P. Martin et al., “Accurate refractive index measurements of doped and undoped InP by a grating coupling technique,” Appl. Phys. Lett 67 (7), 881–883 (1995).
[CrossRef]

Electron. Lett.

G. Cocorullo, I. Rendina, “Thermo-optical modulation at 1.5 mm in silicon étalon,” Electron. Lett. 28 (1), 83–84 (1992).
[CrossRef]

Eng. Lab. Notes in Opt. Phot. News

S. Waldenstrom, K. Razi Naqvi, “Measurement of refractive indices of prismatic materials,” Eng. Lab. Notes in Opt. Phot. News 7 (2), S1–S2 (1996), and references herein enclosed.

IEEE Phot. Tech. Lett.

G. Cocorullo et al., “Thermo-optical modulation at 1.5 mm in an a-SiC—a-Si—a-SiC planar guided-wave structure,” IEEE Phot. Tech. Lett. 8 (7), 900–902 (1996).
[CrossRef]

J. Appl. Phys.

E. Gini et al., “Thermal dependence of the refractive index of InP measured with integrated optical demultiplexer,” J. Appl. Phys. 79 (8), 4335–4337 (1996).
[CrossRef]

Opt. Comm.

G. Cocorullo et al., “New Possibilities for efficient silicon integrated electro-optical modulators,” Opt. Comm. 86 (2), 228–235 (1991).
[CrossRef]

Other

Solimeno et al., Guiding, Diffraction and Confinement of the Optical Radiation (Academic Press, Orlando, 1986).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon Press, Oxford, 1989).

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Figures (2)

Figure 1
Figure 1

Thermal dependence of the measured (dotted) and calculated (solid) light intensity transmitted acrossa 300-µm-thick silicon wafer working as an étalon interferometer. The radiation wavelength is 1.52 µm.

Figure 2
Figure 2

Light intensity interferometric pattern at 1.55 µm produced by the temperature variation in a 1650-µm-long planar etalon cavity made of a α-SiC/α-Si/α-SiC waveguiding multilayer deposited on a Si crystal substrate.

Equations (8)

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I t = I 0 1 1 + 4 F 2 π 2   sin 2   φ
F = π R / 1 - R
C = I max t I min t = 1 + 4 F 2 π 2
M = I max t - I min t / I max t = 1 - 1 C
φ = 2 π l   cos θ λ δ n + 2 π n   cos θ λ δ l δ φ t h e r m o o p t i c + δ φ t h e r m o   exp   a n s i o n
n T = λ 4 l Δ T π 2 - n k
λ = 1523 ± 0.003   nm ,   l = 300 ± 1   µ m ,   n = 3.5 ± 0.1 ,   and   k = 2.6 × 10 - 6 ° K - 1 ,   gives   n T = 1.86 ± 0.08 × 10 - 4 ° K - 1 .
F I 2 = F - 2 + F exp - 2 ,   w h e r e   F e x p

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