MgF2-Ag tunable reflection retarder

Shuichi Kawabata and Masako Suzuki Gakushuin University, Physics Department, Mejiro, Toshima-ku, Tokyo, 171, Japan. Received 3 November 1979. 0003-6935/80/040484-02$00.50/0. © 1980 Optical Society of America. Zaghloul et al.1,2 have developed the design steps for

film-substrate external-reflection retarders that are angle-of-incidence tunable and have performed a computer-based analysis for the system SiO2-Si (SiO2 film on Si substrate). They have also verified the operation of this system experi­mentally.

We have carried out a similar analysis for the systems MgF2-Ag, Al, Cu, and Au and found that the best performance is exhibited by MgF2-Ag. The last-mentioned system is much superior to the system SiO2-Si at λ = 6328 Å.

Let ρ = tan Ψ exp(iΔ) represent the ratio of the amplitude reflection coefficients for light polarized parallel (p) and perpendicular (s) to the plane of incidence reflected from a film-substrate retarder. The essential requirement for an angle-of-incidence tunable retarder is that as the angle of incidence varies from 0 to 90°, tan Ψ remains as close to unity as possible, while Δ changes over a range of 180°. Accord­ingly, the maximum deviation of Ψ from 45° (δΨ)m to be

484 APPLIED OPTICS / Vol. 19, No. 4 / 15 February 1980

Fig. 1. δΨ = Ψ – 45° vs the angle of incidence computed for λ = 6328 Å, MgF2-Ag system. The optimum film thickness d0 is 910

Table I. Comparison of Substrate Metals for the System MgF2-Metal

The values of ñ for Ag and Au are determined from our measure­ments at 6328 Å. Those for Al and Cu are estimated using published values.5,6 The normal-incidence reflectance R is calculated from ñ.

observed in the whole range of will serve as a convenient measure for the suitability of a film-substrate system as a tunable retarder.

The value of (δΨ)m depends on the thickness d of the overlaid film. The optimum film thickness for which (δΨ)m becomes smallest will be denoted by d0. It is desirable to have (δΨ)m insensitive to the changes in d in the neighborhood of d0.

Figure 1 gives the computed values of δΨ = Ψ – 45° against the angle of incidence for the system MgF2-Ag. The results for three film thicknesses d = 800, 900, and 1000 Å are shown. The optimum thickness for this system was found to be 910 Å.

The same computations have been carried out for MgF2 films overlaid on Al, Cu, and Au. The results are summarized in Table I in which d0 and (δΨ)m are given for the respective metals and in Fig. 2 in which (δΨ)m is plotted against (d - d0). Figure 2 shows the sensitivity of (δΨ)m to the change in film thickness near d0. As seen in Table I and Fig. 2, the higher the substrate reflectance, the better the performance of the film-substrate tunable retarder, Ag giving the best result.

It is to be noted that there is more than one film thickness for a given film-substrate system at which (δΨ)m assumes a minimum, since tan Ψ is a periodic function of d. With MgF2-Ag, for instance, a second optimum thickness is found at ~1650 Å.

The reflectance (Rp ≅ Rs) of the MgF2-Ag retarder is about 96% for all the angles of incidence between 0-90° for either d = 910 Å or 1650 Å.

To verify the computational results, we have done the fol­lowing experiment. A silver film >1000 Å in thickness was evaporated onto a glass slide, and on it was overlaid a MgF2 film having a thickness of 1620 Å. Such a reflection-retarder

Fig. 2. Maximum deviation of Ψ from 45° (δΨ)m vs the deviation of film thickness from the optimum value (d – d0) computed for λ =

6328 Å.

Fig. 3. Experimental results. Ψ and Δ vs the angle of incidence , MgF2-Ag reflection retarder.

system was placed on the sample table of a return-path el-lipsometer3,4 to which a Babinet compensator had been added in the mirror arm. When, at a fixed angle of incidence , ex­tinction is achieved by adjusting the compensator and the polarizer, the reading of the Babinet compensator gives Δ, and the azimuth of the polarizer gives Ψ. The results are shown in Fig. 3. The solid curves represent the theoretical values. The value of Ψ could be determined to ±0.1°. The observed Ψ agreed with 45° within this accuracy throughout the range of . Note that at λ = 6328 Å (δΨ)m amounted to ~2.5°, with the SiO2-Si system having the optimum thickness (1000 Å), which has been studied by Zaghloul et al.1

We have also carried out similar calculations for the systems ZnS-Ag and ZnS-Au. For ZnS-Ag the optimum thickness d0 was found to be 300 Å, at which (δΨ)m was 0.144°. The values of (δΨ)m for ZnS-Au were greater (>0.5°).

Sincere thanks are due to K. Kinosita for valuable discus­sions and for reading the manuscript.

References 1. A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, J. Opt. Soc.

Am. 65, 1043 (1975). 2. A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, Opt.

Commun. 14, 260 (1975). 3. M. Yamamoto, Opt. Commun. 10, 200 (1974). 4. M. Yamamoto, Jpn. J. Appl. Phys. Suppl. 14-1, 413 (1975). 5. L. G. Schulz and F. R. Tangherlini, J. Opt. Soc. Am. 44, 362

(1954). 6. L. G. Schulz, J. Opt. Soc. Am. 44, 357 (1954).

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