Preliminary study of the feasibility of quarter-wave retardation rhombs for SPIROU

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Erik Wiggins
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1 Preliminary study of the feasibility of quarter-wave retardation rhombs for SPIROU 1. Introduction: Fresnel rhombs exhibits the less chromatic effect and larger spectral range than other conventional quarter-wave retardation devices like crystalline plates. Using a thin-film coating of MgF2 on one face were occurs a total reflection, improves the achromacity of the rhomb This solution has been used with success in the two twin spectropolarimetric instruments Espadons at CFHT, Hawaii and Narval at Pic du Midi, France. The two instruments work in the spectral band µm. The present document gives the current results about the feasibility of this kind of coated rhombs in the IR bands covering µm 2. Model Given a material with an index of refraction n(λ) depending of the wavelength λ, the retardation between the two polarizations! and // occurring at total reflection in a dielectric can be expressed by (according to Born & Wolf) : " cos! i tan = 2 sin sin 2 2! # n! i i 2!! " = #! //! i : angle This relation is valid for a bare substrate (no thin film coating) The model of a reflection with thin film has been done in an Excel sheet. The details are not included in the document. This Excel sheet has already been used for the Espadons and Narval instruments, only the spectral range has been changed, corresponding refractive index for both the substrate and coating have been updated. 3. Solution with optical glasses and MgF2 coating The choice of glasses has been restricted to the OHARA glass catalog Valid range of refractive index: Minimum refractive index For non-coated glass, only a glass with an index greater than can have a retardation of 45 (quarter-wave retardation). For n>1.497 there is two solutions giving 45 : small angle (A1) and big angle (A2)

2 The solution A2 should be preferred than the A1 solution has it gives better results in term of sensitivity to angle Maximum refractive index With an MgF2 coating, the thin film formulas work if the index of refraction of the glass is inferior to Minimum internal transmission of glass The total path of light in a rhomb (with two total internal reflection) is equal to 2*h* tan(θ) with θ the angle of the Rhomb and h the aperture size of the rhomb. The aperture of the rhomb is close to 10 mm and the angle of the rhomb between 53 and 63 (A2 solution), the total path of light in the rhomb is between 26.5 and mm. As it is planned to have 1 quarter-wave rhomb and two half-waves rhombs for polarimetric analysis, this means 5 times the total path of a quarter-wave rhomb : at least 130 mm. In the OHARA catalog, the internal transmission is given for 10 mm thickness T 10 mm T 130 mm Available glasses for MgF2 coating Using the refractive index criteria the choice of glasses in the OHARA catalog are Glass Code(d) Code REFRACTIVE INDICES n2325 n1970 n1530 n1129 Abbe IR (IR) S-TIL S-FTM S-TIM S-TIM S-TIM PBM S-TIM INTERNAL TRANSMISSION (10mm Thick) Glass S-TIL S-FTM S-TIM S-TIM S-TIM PBM S-TIM

3 Only one glass exhibits an acceptable absorption: S-FTM16 in the nm band. In the IR, all these glasses have equivalent dispersion (except PBM3 but this is an obsolete glass). To have a comparison, in the visible (Espadons and Narval), the chosen glass for the rhomb was an equivalent to the S-BSL7 glass: nd=1.516, vd=64.1.the available glasses for SPIROU with an MgF2 coating are much more dispersive in comparison Performances of S-FTM16 rhomb rhomboèdre S-FTM16! /4+MgF2 angle : , e M gf2 = nm Thickness = 30.8 mm with an entrance aperture of 10 mm Performances of S-TIL2 rhomb rhomboèdre S -TIL2! /4+MgF2 angle : , e M gf2 = nm + - Thickness = 27.6 mm with an entrance aperture of 10 mm.

4 3.6. Performances of S-TIM8 rhomb rhomboèdre S -TIM8! /4+MgF2 angle : , e M gf2 = nm Thickness = 31 mm with an entrance aperture of 10 mm Performances of S-TIM5 rhomb rhomboèdre S -TIM5! /4+MgF2 angle : , e M gf2 = nm Thickness = 31.4 mm with an entrance aperture of 10 mm.

5 3.8. Performances of S-TIM2 rhomb rhomboèdre S -TIM2! /4+MgF2 angle : , e M gf2 = nm Thickness = 32 mm with an entrance aperture of 10 mm. 4. Solution with ZnSE A good IR coating on the entrance and exit face of the rhomb is mandatory due to the high index of ZnSe (n= 2.45 in the IR). The ZnSe Calculated Transmission Profiles Calculated transmission profiles of Zinc Selenide (ZnSe) at 293K for substrate thicknesses between 2.0 and 4.5mm 1µm = cm-1 ; 2µm = cm-1 ; 2.4 µm = 4166 cm-1

6 4.1. MgF2 coating Only the A1 solution is applicable rhomboèdre ZnSe!/4+MgF2 angle : , e MgF2 = 83.5 nm Thickness = 9.3 mm with an entrance aperture of 10 mm Diamond CVD A2 solution is applicable rhomboèdre ZnSe!/4+diamond CVD angle : , e MgF2 = nm Thickness = 43 mm with an entrance aperture of 10 mm

7 5. 5 Other possibilities A different coating with an index of refraction lower than the index of refraction of the substrate may widen the chose of OHARA glasses. For example : SiO2, Al2O3, HfF4 Other materials for thin films coating are available. An Applied Optics article ( Appl.Opt. 36, N 10 April 1997 p2157, Optical and durability properties of infrared transmitting thin films) gives some index of refraction in the Ir with some durability of the different coatings. The optical glass catalog is classified by decreasing transmission at 2400 nm. REFRACTIVE INDICES Glass Code(d) Code(IR) n2325 n1970 n1530 n1129 Abbe IR S-NPH S FTM S-TIM S-TIH S-TIH S-TIH S-TIH S-TIH S-TIH S-TIH S-TIM S-TIM S-TIH S-TIH S-TIH BAH LAM INTERNAL TRANSMISSION (10mm Thick) Glass Code(d) Code(IR) S-NPH S- FTM S-TIM S-TIH S-TIH S-TIH S-TIH S-TIH S-TIH S-TIH S-TIM S-TIM S-TIH S-TIH S-TIH BAH LAM

8 New materials arise but as the index of refraction increased, the angle of the rhomb increased with the thickness of the rhomb. Only the S-NPH2 material seems interesting by comparison with S-FTM16. So-far only NdF3 coating seems available rhomboèdre S-NPH2!/4+NdF3 angle : , e NdF3 = nm Thickness = 38 mm with an entrance aperture of 10 mm.

9 6. Comparison matrix The internal transmission is calculated with the thickness of the rhomb. For ZnSe transmission, the attenuation coefficient has been taken equal to cm-1 (conservative number, data given at 10.6 µm give < cm-1) Δδ is the difference between the maximal and minimal retard for a δ +i mean( ) is the mean value of the retardation for a + δ -i mean( ) is the mean value of the retardation for a - Material Coating Rhomb Angle( ) e coating (nm) rhomb thickness (mm) Internal transmission 2200 nm Internal transmission 2400 nm Δδ ( ) δ +i mean( ) δ i mean( ) ZnSe Diamond S-NPH2 NdF S-FTM16 MgF S-TIL2 MgF S-TIM8 MgF S-TIM2 MgF S-TIM5 MgF ZnSe MgF The best solution is to use a ZnSe rhomb with a diamond CVD coating.

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