Properties of multicomponent achromatic and superachromatic zero-order wave plates

INTRODUCTION

The design of multicomponent zero-order wave plates is described in Ref. 1. References 2 and 3 present the calculated and experimentally measured spectral dependences of the phase shift for three-component (achromatic) and five- component (superachromatic) wave plates.

The spectral achromatization region can be broadened by increasing the number of components in the plate.4 The goal of this paper was to fabricate a seven-component zero- order quarter-wave plate and to measure its spectral response. The wavelength dependences of the position of the optical axis were also measured for three-, five- and seven- component wave plates. Besides this, the dependences of the phase shift of the wave plates on temperature and angle of incidence of the rays were investigated, along with the trans- mission spectra of the plates.

DESIGN

The design of the seven-component wave plate is shown in Fig. 1.

By comparison with the five-component design, an ad- ditional pair of components is added between the end com- ponents. The optic axes of the pairs of components, which are symmetrical relative to the central one, are parallel. The phase shifts T₂ of the central components equal 180°, while the end components have T₁ <= 180° in zero order for the central wavelength A₀. The value of T₁ for A₀ and angles QI₁, QI₂, and QI₃ is calculated for the required equivalent phase shift in such a way that, for an identical phase-shift variation of the components from the specified value, regardless of how it is caused (by varying the wavelength, temperature, or angle of incidence), the equivalent phase shift of the entire design remains constant within certain limits.⁴

At Astropribor Production Cooperative (PK Astropribor) at the Main Astronomical Observatory, National Academy of Sciences of Ukraine, achromatic (APAV) and superachro- matic (APCSAV-5, APSAV-7) zero-order wave plates have been fabricated from three, five, and seven anisotropic poly- meric plates, respectively, cemented between two glass (or quartz) windows. Such a design ensures good quality of the transmitted wave front, as well as minimizing the ray devia- tion (with controlled cementing) and the surface reflection losses.

SPECTRAL DEPENDENCES OF THE PHASE SHIFT AND ORIENTATION OF THE OPTIC AXIS. SPECTRAL DEPENDENCE OF THE TRANSMISSION

Figure 2 shows typical spectral dependences of the phase shift for three-, five-, and seven-component wave plates. The normalized wavelength A  A₀ is plotted on the horizontal axis, where A₀ is the central wavelength, and the phase shift in waves is plotted on the vertical axis. With an allowance on the phase shift of ±0.01A, the region in which the plates can be used ranges from A₁  A₀ to A₂  A₀. The ratio of the limiting wavelengths A₂  A₁ is shown in Table I for the wave plates whose curves are shown in Fig. 2.

It can be seen from Fig. 2 and Table I that the achroma- tization region is substantially greater in the seven- component than in the five-component quarter-wave plate, and this makes is promising to fabricate and use them. The addition of the two supplementary components to the APSAV-5 half-wave plate also broadens the achromatization region. However, regions appear inside the spectral range in which the phase shift substantially differs (by as much as 15°) from 180°.⁴ Such a deviation can hardly be considered acceptable, and this makes it inexpedient to fabricate and use seven-component half-wave plates. These results show that five-component half-wave plates are wider in their achroma- tization region than their counterpart quarter-wave plates and have virtually the same width as seven-component quarter- wave plates.

The azimuth of the optic axis depends on the wavelength in multicomponent wave plates. Figure 3 shows these depen- dences for three-, five- and seven-component wave plates. In the achromatic region, the oscillation of the orientation of the optic axis is insignificant, but, if necessary, this phenomenon needs to be taken into account.

Figure 4 shows the spectral dependence of the transmis- sion of the superachromatic wave plate (with antireflection- coated outer windows). In the short-wavelength region, the transmission threshold is determined by the transmission threshold of polymethyl methacrylate (PMMA) (when quartz windows are used). In the long-wavelength region, there are two absorption bands that are characteristic of PMMA. How- ever, if necessary, wave plates can be fabricated and used that operate all the way to 1600 nm by taking into account the transmission features of the plates in the IR region.

DEPENDENCE OF THE PHASE SHIFT ON THE ANGLE OF INCIDENCE

Figure 5 shows how the deviation of the phase shift of APSAV-5 quarter- and half-wave plates depends on the angle of incidence for various azimuths of incidence of the rays, measured from the direction of the optic axis (a), as well as the dependence of the deviation of the phase shift on the azimuth of incidence of the rays relative to the optic axis for a fixed angle of incidence of 10° (b). The studies were car- ried out at a wavelength of 0.63 µm, using the polarimetric methods described in Refs. 5 and 6 to measure and process the data. It turned out that there are azimuths at which the phase shift does not depend in general on the angle of inci- dence of the rays (for a quarter-wave plate: 22.5°, 112.5°, 202.5°, and 292.5°; for a half-wave plate: 45°, 135°, 225°, and 315°), and there are azimuths at which this dependence is strongest (for a quarter-wave plate: 67.5°, 157.5°, 247.5° and 337.5°; for a half-wave plate: 0°, 90°, 180°, and 270°). Moreover, as the angle of incidence increases, the phase shift can either increase (azimuths 67.5° and 247.5°) or decrease (157.5° and 337.5°).

For the APSAV-7 seven-component quarter-wave plate (the character of the dependences are similar to those of APSAV-5 in Fig. 5), the azimuths are not sensitive to an angle of incidence lying in the region of 12°, 102°, 192°, and 282°, while the azimuths at which the dependence on the angle of incidence is a maximum are 57°, 147°, 237°, and 327°.

Thus, when an actual beam containing oblique rays of various amplitudes is incident on a plate, the deviations of the phase shift can be either positive or negative. However, when the angle of incidence is ±9° for a quarter-wave plate and ±11° for a half-wave plate, the phase-shift deviations do not exceed ±3.6° (i.e., ±0.01A). These values determine the angular aperture of the superachromatic wave plates.

TEMPERATURE DEPENDENCE OF THE PHASE SHIFT

Varying the temperature has an identical effect on the phase shifts of the individual components of the plates (as does varying the wavelength). Therefore, it can be expected that the temperature dependence of the phase shift of a mul- ticomponent phase plate will be similar to the wavelength dependence of the phase shift.

Table II shows the data of measurements of the tempera- ture dependence of the phase shift of the APSAV-5 quarter- wave plate. There is a region inside the measured interval in which the phase shift is virtually independent of the tempera- ture. Extrapolation of this dependence makes it possible to conclude that the phase-shift variation does not exceed 0.01A in the working region of temperatures (−20 ° C to + 50 ° C).

TECHNICAL CHARACTERISTICS OF MULTICOMPONENT WAVE PLATES

Tables III and IV show the technical characteristics of achromatic and superachromatic zero-order wave plates fab- ricated at PK Astropribor. In the collection of their proper- ties, the achromatic and superachromatic zero-order wave plates are some of the best, and, in their size (up to 60 mm), they are unique.