Abstract

We propose a new class of optical wave-front transformer based on a different mechanism that uses the multiple-reflection interference effect in a Gires–Tournois resonator (GTR) as the physical mechanism for phase modification. By coating the front surface of a GTR with a predefined graded reflectivity profile, one can synthesize various optical elements. We present the basic concept of our proposal by synthesizing a lenslike element as a proof-of-principle example. One unique feature of this element is that it can function as a reflecting mirror, a converging lens, or a diverging lens, depending on the resonator length. Other applications are briefly discussed.

© 1997 Optical Society of America

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References

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  1. M. W. Farn, in Handbook of Photonics, R. Stern, ed. (CRC, Boca Raton, Fla., 1995).
  2. T. Kotzer, J. Rosen, and J. Shamir, Appl. Opt. 31, 1126 (1992).
    [CrossRef] [PubMed]
  3. J. A. Neff, R. A. Athale, and S. H. Lee, Proc. IEEE 78, 826 (1990).
    [CrossRef]
  4. F. Gires and P. Tournois, C. R. Acad. Sci. 258, 612 (1964).
  5. A. Yariv and P. Yeh, Optical Waves in Crystal (Wiley, New York, 1990), p. 219.
  6. S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, Opt. Lett. 12, 84 (1987).
    [CrossRef] [PubMed]
  7. A. E. Siegman, Lasers (Oxford U. Press, Oxford, 1986), Chap.  11.
  8. A. Piegbari, Appl. Opt. 3555091996; P. Verly, J. Dobrowolski, A. Waldorf, and S. Bussiere, Appl. Opt. 32, 1145 (1993).

1996 (1)

1992 (1)

1990 (1)

J. A. Neff, R. A. Athale, and S. H. Lee, Proc. IEEE 78, 826 (1990).
[CrossRef]

1987 (1)

1964 (1)

F. Gires and P. Tournois, C. R. Acad. Sci. 258, 612 (1964).

Athale, R. A.

J. A. Neff, R. A. Athale, and S. H. Lee, Proc. IEEE 78, 826 (1990).
[CrossRef]

De Silvestri, S.

Farn, M. W.

M. W. Farn, in Handbook of Photonics, R. Stern, ed. (CRC, Boca Raton, Fla., 1995).

Gires, F.

F. Gires and P. Tournois, C. R. Acad. Sci. 258, 612 (1964).

Kotzer, T.

Laporta, P.

Lee, S. H.

J. A. Neff, R. A. Athale, and S. H. Lee, Proc. IEEE 78, 826 (1990).
[CrossRef]

Magni, V.

Neff, J. A.

J. A. Neff, R. A. Athale, and S. H. Lee, Proc. IEEE 78, 826 (1990).
[CrossRef]

Piegbari, A.

Rosen, J.

Shamir, J.

Siegman, A. E.

A. E. Siegman, Lasers (Oxford U. Press, Oxford, 1986), Chap.  11.

Svelto, O.

Tournois, P.

F. Gires and P. Tournois, C. R. Acad. Sci. 258, 612 (1964).

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystal (Wiley, New York, 1990), p. 219.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystal (Wiley, New York, 1990), p. 219.

Appl. Opt. (2)

C. R. Acad. Sci. (1)

F. Gires and P. Tournois, C. R. Acad. Sci. 258, 612 (1964).

Opt. Lett. (1)

Proc. IEEE (1)

J. A. Neff, R. A. Athale, and S. H. Lee, Proc. IEEE 78, 826 (1990).
[CrossRef]

Other (3)

A. Yariv and P. Yeh, Optical Waves in Crystal (Wiley, New York, 1990), p. 219.

M. W. Farn, in Handbook of Photonics, R. Stern, ed. (CRC, Boca Raton, Fla., 1995).

A. E. Siegman, Lasers (Oxford U. Press, Oxford, 1986), Chap.  11.

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of the proposed device using a GTR with a GRM used as front mirror M1. (b) Two reflectance profiles coated onto M1 that can be used to synthesize a converging lens.

Fig. 2
Fig. 2

Calculated reflected phase distribution and its corresponding normalized intensity distribution when the resonator spacing is set so the device functions as (a) a diverging lens, d1=3λ0/10; (b) a plane mirror, d2=λ0/2; (c) a converging lens, d3=λ0/5.

Fig. 3
Fig. 3

Calculated normalized intensity distributions of the diverging lens and the converging lens for two different bandwidths Δλ (1 and 20  nm). The effect of chromatics on the intensity pattern is not observable.

Equations (6)

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S=ρ expiψτ expiψτ expiψ-ρ expiψ,
β expiΘ=ErefEinc=expiψρ+expjψ-2θ1+ρ expjψ-2 θ,
Θ=-2 tan-1tankdcosψ+R+cosψtanψcosψ-R-cosψtanψtankd,
Θ-2 tan-11+R1-R tankd.
Rr, f, d, λ=[tankr24f-tankdtankd+tankr24f]2=[sinkr24f-kdsinkr24f+kd]21.
Θr, f0, z0, λ0, d-2 tan-1[tank0r24f0tank0z0 tank0d]

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