Abstract

The design steps for film—substrate single-reflection retarders are briefly stated and applied to the SiO<sub>2</sub>—Si film—substrate system at wavelength 6328 Å. The criterion of minimum-maximum error of the ellipsometric angle ψ is used to choose angle-of-incidence-tunable designs. Use is made of the (Φ-<i>d</i>) plane (angle of incidence versus thickness) to determine whether a given film—substrate system with known optical properties and film thickness can operate as a reflection retarder and to determine the associated angles of incidence and retardation angles. This leads to the concept of permissible-thickness bands and forbidden gaps for operation of a film—substrate system as a reflection retarder. Experimental measurements on one of the proposed designs proved the validity of the method.

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  1. J. M. Bennett and H. E. Bennett, in Handbook of Optics, edited by W. G. Driscoll and W. Vaughan (McGraw—Hill, New York, 1975).
  2. The magnitude of the attenuation is independent of the incident polarization.
  3. R. M. A. Azzam, A. -R. M. Zaghloul, and N. M. Bashara, J. Opt. Soc. Am. 65, 252 (1975).
  4. Note that, whereas the use of a film—substrate system as a reflection retarder is new, its use as a reflection polarizer is well known. See, for example, M. Ruiz-Urbieta and E. M. Sparrow, J. Opt. Soc. Am. 62, 1188 (1972) and other papers in this series.
  5. Ellipsometric Tables of the Si—SiO2 System for Mercury and He—Ne Laser Spectral Lines, edited by G. Gergely (Akademiai Kiado, Budapest, 1971).
  6. In step 1, instead of using ρ = eƒΔ, we use the general form ρ = tanψe; steps 2–5 remain unchanged.
  7. The derivation of Eqs. (2) and (3) is given in Ref. 3.
  8. Alternatively, the angle of incidence φ′ can be obtained by anynumerical method (e.g., successive bisection) to find the rootof the equation | X | = 1.
  9. Our investigation of the effect of substrate absorption on the results of the film-substrate single-reflection retarder designs has shown that the mirror symmetry of the two branches B+ and B- occurs exactly only when the substrate is totally transparent. Deviation from exact symmetry increases with substrate absorption.
  10. Angle-of-incidence-tunable retarders are those with the least thickness. By adding multiples of Dφ, the performance of the retarder gets worse, refer to Fig. 11(left).
  11. An alternative procedure would be to add the appropriate multiple of Dφ, at each φ, to the image of the unit circle and to obtain the intersection points of this vertically translated image with the straight line d = const. In general, the first method is more convenient.
  12. The existence of exact reflection-retardation modes depends, for a particular system at a given wavelength, on the film thickness only.
  13. dmin and dmax are obtained by extrapolation to Δ= 0° and ° = ∓180° of the branches shown in Fig. 4.

Azzam, R. M. A.

R. M. A. Azzam, A. -R. M. Zaghloul, and N. M. Bashara, J. Opt. Soc. Am. 65, 252 (1975).

Bashara, N. M.

R. M. A. Azzam, A. -R. M. Zaghloul, and N. M. Bashara, J. Opt. Soc. Am. 65, 252 (1975).

Bennett, H. E.

J. M. Bennett and H. E. Bennett, in Handbook of Optics, edited by W. G. Driscoll and W. Vaughan (McGraw—Hill, New York, 1975).

Bennett, J. M.

J. M. Bennett and H. E. Bennett, in Handbook of Optics, edited by W. G. Driscoll and W. Vaughan (McGraw—Hill, New York, 1975).

Ruiz-Urbieta, M.

Note that, whereas the use of a film—substrate system as a reflection retarder is new, its use as a reflection polarizer is well known. See, for example, M. Ruiz-Urbieta and E. M. Sparrow, J. Opt. Soc. Am. 62, 1188 (1972) and other papers in this series.

Sparrow, E. M.

Note that, whereas the use of a film—substrate system as a reflection retarder is new, its use as a reflection polarizer is well known. See, for example, M. Ruiz-Urbieta and E. M. Sparrow, J. Opt. Soc. Am. 62, 1188 (1972) and other papers in this series.

Zaghloul, A. -R. M.

R. M. A. Azzam, A. -R. M. Zaghloul, and N. M. Bashara, J. Opt. Soc. Am. 65, 252 (1975).

Other (13)

J. M. Bennett and H. E. Bennett, in Handbook of Optics, edited by W. G. Driscoll and W. Vaughan (McGraw—Hill, New York, 1975).

The magnitude of the attenuation is independent of the incident polarization.

R. M. A. Azzam, A. -R. M. Zaghloul, and N. M. Bashara, J. Opt. Soc. Am. 65, 252 (1975).

Note that, whereas the use of a film—substrate system as a reflection retarder is new, its use as a reflection polarizer is well known. See, for example, M. Ruiz-Urbieta and E. M. Sparrow, J. Opt. Soc. Am. 62, 1188 (1972) and other papers in this series.

Ellipsometric Tables of the Si—SiO2 System for Mercury and He—Ne Laser Spectral Lines, edited by G. Gergely (Akademiai Kiado, Budapest, 1971).

In step 1, instead of using ρ = eƒΔ, we use the general form ρ = tanψe; steps 2–5 remain unchanged.

The derivation of Eqs. (2) and (3) is given in Ref. 3.

Alternatively, the angle of incidence φ′ can be obtained by anynumerical method (e.g., successive bisection) to find the rootof the equation | X | = 1.

Our investigation of the effect of substrate absorption on the results of the film-substrate single-reflection retarder designs has shown that the mirror symmetry of the two branches B+ and B- occurs exactly only when the substrate is totally transparent. Deviation from exact symmetry increases with substrate absorption.

Angle-of-incidence-tunable retarders are those with the least thickness. By adding multiples of Dφ, the performance of the retarder gets worse, refer to Fig. 11(left).

An alternative procedure would be to add the appropriate multiple of Dφ, at each φ, to the image of the unit circle and to obtain the intersection points of this vertically translated image with the straight line d = const. In general, the first method is more convenient.

The existence of exact reflection-retardation modes depends, for a particular system at a given wavelength, on the film thickness only.

dmin and dmax are obtained by extrapolation to Δ= 0° and ° = ∓180° of the branches shown in Fig. 4.

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