Abstract

In integrated-optical directional couplers formed by two parallel waveguides we measure the difference Δβ = βevenβodd between the propagation constants of the supermodes. We couple them locally by heating a fine spot on one of the guides. When the spot is scanned along the coupler, the output power from one of the guides is found to vary periodically. The period of variation is the modal beat length Λ = 2πβ. We demonstrate this technique with directional couplers fabricated by K-ion exchange in glass. Beat lengths in the range 0.6–2.2 mm are measured with an accuracy of ±0.3%.

© 1996 Optical Society of America

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References

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  1. A. Miki, Y. Okamura, S. Yamamoto, J. Lightwave Technol. 7, 1912 (1989).
    [CrossRef]
  2. K. Kishioka, G. L. Yip, Appl. Opt. 31, 2807 (1992).
    [CrossRef] [PubMed]
  3. A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, Appl. Phys. Lett. 65, 947 (1994).
    [CrossRef]
  4. Y. Bourbin, A. Enard, M. Papuchon, K. Thyagarajan, J. Lightwave Technol. LT-5, 684 (1987).
    [CrossRef]
  5. N. Chinone, R. Ulrich, Opt. Lett. 6, 16 (1981).
    [CrossRef] [PubMed]
  6. R. Eckhardt, R. Ulrich, Appl. Phys. Lett. 63, 284 (1993).
    [CrossRef]
  7. R. Stolte, R. Ulrich, Opt. Lett. 20, 142 (1995).
    [CrossRef] [PubMed]
  8. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991), Chap. 6, p. 255.
  9. A. N. Miliou, R. Srivastava, R. V. Ramaswamy, J. Lightwave Technol. 11, 220 (1993).
    [CrossRef]

1995 (1)

1994 (1)

A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, Appl. Phys. Lett. 65, 947 (1994).
[CrossRef]

1993 (2)

A. N. Miliou, R. Srivastava, R. V. Ramaswamy, J. Lightwave Technol. 11, 220 (1993).
[CrossRef]

R. Eckhardt, R. Ulrich, Appl. Phys. Lett. 63, 284 (1993).
[CrossRef]

1992 (1)

1989 (1)

A. Miki, Y. Okamura, S. Yamamoto, J. Lightwave Technol. 7, 1912 (1989).
[CrossRef]

1987 (1)

Y. Bourbin, A. Enard, M. Papuchon, K. Thyagarajan, J. Lightwave Technol. LT-5, 684 (1987).
[CrossRef]

1981 (1)

Bourbin, Y.

Y. Bourbin, A. Enard, M. Papuchon, K. Thyagarajan, J. Lightwave Technol. LT-5, 684 (1987).
[CrossRef]

Boyd, J. T.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, Appl. Phys. Lett. 65, 947 (1994).
[CrossRef]

Chinone, N.

Choo, A. G.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, Appl. Phys. Lett. 65, 947 (1994).
[CrossRef]

De Brabander, G. N.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, Appl. Phys. Lett. 65, 947 (1994).
[CrossRef]

Eckhardt, R.

R. Eckhardt, R. Ulrich, Appl. Phys. Lett. 63, 284 (1993).
[CrossRef]

Enard, A.

Y. Bourbin, A. Enard, M. Papuchon, K. Thyagarajan, J. Lightwave Technol. LT-5, 684 (1987).
[CrossRef]

Jackson, H. E.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, Appl. Phys. Lett. 65, 947 (1994).
[CrossRef]

Kishioka, K.

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991), Chap. 6, p. 255.

Miki, A.

A. Miki, Y. Okamura, S. Yamamoto, J. Lightwave Technol. 7, 1912 (1989).
[CrossRef]

Miliou, A. N.

A. N. Miliou, R. Srivastava, R. V. Ramaswamy, J. Lightwave Technol. 11, 220 (1993).
[CrossRef]

Okamura, Y.

A. Miki, Y. Okamura, S. Yamamoto, J. Lightwave Technol. 7, 1912 (1989).
[CrossRef]

Papuchon, M.

Y. Bourbin, A. Enard, M. Papuchon, K. Thyagarajan, J. Lightwave Technol. LT-5, 684 (1987).
[CrossRef]

Ramaswamy, R. V.

A. N. Miliou, R. Srivastava, R. V. Ramaswamy, J. Lightwave Technol. 11, 220 (1993).
[CrossRef]

Srivastava, R.

A. N. Miliou, R. Srivastava, R. V. Ramaswamy, J. Lightwave Technol. 11, 220 (1993).
[CrossRef]

Stolte, R.

Thiel, U.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, Appl. Phys. Lett. 65, 947 (1994).
[CrossRef]

Thyagarajan, K.

Y. Bourbin, A. Enard, M. Papuchon, K. Thyagarajan, J. Lightwave Technol. LT-5, 684 (1987).
[CrossRef]

Ulrich, R.

Yamamoto, S.

A. Miki, Y. Okamura, S. Yamamoto, J. Lightwave Technol. 7, 1912 (1989).
[CrossRef]

Yip, G. L.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, Appl. Phys. Lett. 65, 947 (1994).
[CrossRef]

R. Eckhardt, R. Ulrich, Appl. Phys. Lett. 63, 284 (1993).
[CrossRef]

J. Lightwave Technol. (3)

Y. Bourbin, A. Enard, M. Papuchon, K. Thyagarajan, J. Lightwave Technol. LT-5, 684 (1987).
[CrossRef]

A. Miki, Y. Okamura, S. Yamamoto, J. Lightwave Technol. 7, 1912 (1989).
[CrossRef]

A. N. Miliou, R. Srivastava, R. V. Ramaswamy, J. Lightwave Technol. 11, 220 (1993).
[CrossRef]

Opt. Lett. (2)

Other (1)

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991), Chap. 6, p. 255.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: Light from the laser diode (LD) heats a spot on one of the guides. PD, photodiode; POL, linear polarizer.

Fig. 2
Fig. 2

(a) Directional coupler with an induced perturbation at z0, (b) representation of the transition and coupling elements (Ei and Am are modal amplitudes), (c) interpretation of the measurement principle as an interferometer.

Fig. 3
Fig. 3

Phasor diagrams of (a) undefined output signals V e , V o and (b) their superposition V 3 .

Fig. 4
Fig. 4

(a), (b) Measured beat signals of directional couplers for which (a) w = 2.3 μm, g = 1.5 μm. and (b) w = g = 2.3 μm (c) measured dependence of beat length on the gap width g; (d) modulation signal P3(y0) obtained by scanning the perturbation transversely across the coupler.

Equations (5)

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κ m n ( z ) = k 0 2 2 N m β m F m * Δ ( x , y , z ) F n d x d y ,
K m n = Δ z κ m n ( ζ ) exp [ j ( β n β m ) ζ ] d ζ ,
δ V m n = j K m n V n exp [ j ( β n β m ) z 0 ] ,
V e = V e + δ V e e + δ V o e ,
V o = V o + δ V e o + δ V o o .

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