^{1,a)}, M. Salewski

^{1}, A. S. Jacobsen

^{1}, M. Jessen

^{1}, S. B. Korsholm

^{1}, P. K. Michelsen

^{1}, S. K. Nielsen

^{1}and M. Stejner

^{1}

### Abstract

Radiation from magnetized plasmas is in general elliptically polarized. In order to convert the elliptical polarization to linear polarization, mirrors with grooved surfaces are currently employed in our collective Thomson scattering diagnostic at ASDEX Upgrade. If these mirrors can be substituted by birefringent windows, the microwave receivers can be designed to be more compact at lower cost. Sapphire windows (a-cut) as well as grooved high density polyethylene windows can serve this purpose. The sapphire window can be designed such that the calculated transmission of the wave energy is better than 99%, and that of the high density polyethylene can be better than 97%.

I. INTRODUCTION

II. THEORETICAL BACKGROUND

III. EXPERIMENTAL SETUP

IV. RESULTS

A. Sapphire window

B. High density polyethylene window

C. Transmission through the sapphire window

D. Transmission through the HDPE window

V. DISCUSSION

VI. CONCLUSION

### Key Topics

- Sapphire
- 31.0
- Electric fields
- 20.0
- Mirrors
- 18.0
- Refractive index
- 16.0
- Polarization
- 10.0

## Figures

Sapphire is a birefringent material and can be used for polarization purposes. The inherent optical axis lies within the window plane (a-cut). α symbolizes the phase shift between E x and E y of E out . α = ψ, if ϕ = 0 and the electric field components E x and E y of E in are in phase. The dashed arrows depict the principal axes and the local coordinate system of the window if it is rotated around the z-axis by the angle Φ.

Sapphire is a birefringent material and can be used for polarization purposes. The inherent optical axis lies within the window plane (a-cut). α symbolizes the phase shift between E x and E y of E out . α = ψ, if ϕ = 0 and the electric field components E x and E y of E in are in phase. The dashed arrows depict the principal axes and the local coordinate system of the window if it is rotated around the z-axis by the angle Φ.

Staggered HDPE plates can serve as birefringent window and be used for polarization purposes. α symbolizes the phase shift between E x and E y of E out . The bi-directional arrows indicate the grooved section of the material. The center section between the bi-directional arrows does not contribute to polarization effects.

Staggered HDPE plates can serve as birefringent window and be used for polarization purposes. α symbolizes the phase shift between E x and E y of E out . The bi-directional arrows indicate the grooved section of the material. The center section between the bi-directional arrows does not contribute to polarization effects.

Photos of the grooved HDPE window (left) and the sapphire window with anti-reflection coatings mounted in an optical holder (right). The diameter of the HDPE window is 90 mm, and the diameter of the sapphire window is 25 mm.

Photos of the grooved HDPE window (left) and the sapphire window with anti-reflection coatings mounted in an optical holder (right). The diameter of the HDPE window is 90 mm, and the diameter of the sapphire window is 25 mm.

A linearly polarized (x-direction) microwave beam (98 GHz) with a beam waist of 28 mm was focussed by means of a focusing mirror to a beam waist of 7.8 mm. A two-channel heterodyne detector was used to measure the electric field components E x and E y and the phase shift, α, in between. Test windows can be placed at A and B and rotated around the z-axis.

A linearly polarized (x-direction) microwave beam (98 GHz) with a beam waist of 28 mm was focussed by means of a focusing mirror to a beam waist of 7.8 mm. A two-channel heterodyne detector was used to measure the electric field components E x and E y and the phase shift, α, in between. Test windows can be placed at A and B and rotated around the z-axis.

Measurement of the electric field E x (triangles), E y (diamonds), and the phase, α, between E x and E y (circles). The symbols represent the measurements, and the solid lines show the calculation. The best fit between measurements and calculations was found for ψ = 77.5° in the calculation.

Measurement of the electric field E x (triangles), E y (diamonds), and the phase, α, between E x and E y (circles). The symbols represent the measurements, and the solid lines show the calculation. The best fit between measurements and calculations was found for ψ = 77.5° in the calculation.

Measurement of the electric field E x (triangles), E y (diamonds), and the phase, α, between E x and E y (circles). The symbols represent the measurements, and the solid lines show the calculation. The best fit between measurements and calculations was found for ψ = 87° in the calculation.

Measurement of the electric field E x (triangles), E y (diamonds), and the phase, α, between E x and E y (circles). The symbols represent the measurements, and the solid lines show the calculation. The best fit between measurements and calculations was found for ψ = 87° in the calculation.

Transmission of the sapphire window for o-mode (black) and x-mode (grey) with suprasil windows as anti-reflection layer. The transmission in the wavelength range of interest (100–110 GHz) is calculated to be better than 99%. Losses in the sapphire are not considered in this calculation.

Transmission of the sapphire window for o-mode (black) and x-mode (grey) with suprasil windows as anti-reflection layer. The transmission in the wavelength range of interest (100–110 GHz) is calculated to be better than 99%. Losses in the sapphire are not considered in this calculation.

Calculation of the transmission of the wave energy of the o-mode (black) and x-mode (grey), when the HDPE window is designed as a λ/4 plate. Losses in the HDPE are not considered in this calculation.

Calculation of the transmission of the wave energy of the o-mode (black) and x-mode (grey), when the HDPE window is designed as a λ/4 plate. Losses in the HDPE are not considered in this calculation.

Calculation of the transmission of the wave energy of the o-mode (black) and x-mode (grey), when the HDPE window is designed for ψ = 100° between the ordinary and extraordinary mode. Losses in the HDPE are not considered in this calculation.

Calculation of the transmission of the wave energy of the o-mode (black) and x-mode (grey), when the HDPE window is designed for ψ = 100° between the ordinary and extraordinary mode. Losses in the HDPE are not considered in this calculation.

## Tables

Refractive indices of sapphire, suprasil, and HDPE at room temperature. Here, tan(δ) is the ratio of the imaginary and the real part of the dielectric susceptibility.

Refractive indices of sapphire, suprasil, and HDPE at room temperature. Here, tan(δ) is the ratio of the imaginary and the real part of the dielectric susceptibility.

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