Cryogenic Performance of High-efficiency Germanium Immersion
Grating
Yuki Sarugakua, Yuji Ikedab,c, Sayumi Kajid , Naoto Kobayashia,b,e, Takashi Sukegwaf,Takayuki Arasakic, Sohei Kondoc, Kenshi Nakanishic, Chikako Yasuig, and Hideyo Kawakitaa,ca

Kiso Observatory, Institute of Astronomy, University of Tokyo, 10762-30 Mitaka, Kiso-machi,
Kiso-gun, Nagano 397-0101, Japan;b
Laboratory of Infrared High-resolution spectroscopy (LIH), Koyama Astronomical Observatory,Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-855, Japan;
cPhotocoding, 460-102 Iwakura-Nakamachi, Sakyo-ku, Kyoto 606-0025, Japan;
dDepartment of Physics, Faculty of Science, Kyoto-Sangyo University, Motoyama, Kamigamo,Kita-ku, Kyoto 603-8555, Japan;eInstitute of Astronomy, University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-0015, Japan;fOptical Products Operations, Canon Inc., 20-2, Kiyohara-Kogyodanchi, Utsunomiya, Tochigi 3213292, Japan;gNational Astronomical Observatory of Japan (NAOJ), 2-21-1 Osawa, Mitaka, Tokyo 181-8588,Japan;
ABSTRACT
Immersion gratings will play important roles for infrared astronomy in the next generation. We have been developing
immersion gratings with a variety of kinds of materials and have succeeded in fabricating a high-efficiency germanium(Ge) immersion grating with both a reflection coating on the grating surface and an AR coating on the entrance surface.
The grating will be installed in a K-, L-, and M-bands (2-5um) high-resolution (R=80,000) spectrograph, VINROUGE,
which is a prototype for the TMT MIR instrument. In this paper, we report the preliminary results on the evaluation ofthe Ge immersion grating. We confirmed that the peak absolute diffraction efficiency was in the range of 70-80 %,which was as expected from the design, at both room and cryogenic temperatures.
Keywords: immersion grating, infrared, high-resolution spectroscopy, VINROUGE, TMT

1. INTRODUCTION
Immersion grating is a diffraction grating wherein the diffraction surface is immersed in a material with a highrefractive index (n > 2, see Figure 1).1 The maximum spectral resolution of an immersion grating at a wavelength λ isgiven by!!" !"# !

𝑅!"#    =   𝜆/(∆𝜆)!"#    =   !
!!" !"# !
!"              (diffraction-­‐limited  case)                    (slit − limited  case)                            ,(1)whereφ is the collimated beam diameter, θ is the incident angle to the grating surface (which corresponds to the blaze
angle θB under the Littrow condition), s is the slit width measured in celestial coordinates, and D is the entrance pupil
diameter of the telescope. These equations indicate that immersion grating can provide n times higher spectral resolution
compared to classical reflective grating of the same clear aperture, thus it enables us to realize compact spectrographs
without changing the spectral resolution. This new device will play important roles for infrared astronomy in the next
generation (see Intro. in Ikeda et al.1).
Although immersion gratings are invaluable for infrared astronomy, realizing a practical immersion grating with highdiffraction efficiency is challenging. Since high grating efficiency is as effective as large telescope diameter, diffraction
efficiency is the critical indicator of gratings for astronomical use. Recently, we succeeded in fabricating a cadmium zinc

Figure 1. Classical reflective grating and immersion grating. n: refractive index, φ: collimated beam diameter, θ: blazed angle, d:groove pitch.

telluride (CdZnTe) immersion grating with perfect groove shapes,1 which showed the theoretically predicted relative
diffraction efficiency, by planing process with an ultrahigh-precision five-axis processing machine developed by Canon
Inc.2 This technique enables us to process ideal groove shapes on any kind of infrared materials including Ge. As a nextstep, practical Ge immersion gratings with both a reflection coating on the grating surface and an AR coating on theentrance surface have been completed.3 We are going to install a Ge immersion grating in a K-, L-, and M-bands (25um) high-resolution (R=80,000) spectrograph, VINROUGE,4 which is a prototype for the TMT MIR instrument. Since
Ge has very high refractive index (n = 4), which is the highest among the available infrared optical materials for
immersion grating, the optical system of the spectrograph is designed unprecedentedly compact (600 mm x 600 mm x600 mm) for the spectral resolution in this wavelength region. In this paper, we report the preliminary results on
measuring diffraction efficiency of the Ge immersion grating at both the room and cryogenic temperatures.

2. GE IMMERSION GRATING
Figure 2 shows the appearance of the Ge immersion grating for VINROUGE and Table 1 summarizes properties of thegrating. We set the apex angle to 86° to maximize the integrated diffraction efficiency as a result of a simulation basedon the rigorous coupled-wave analysis. The entrance/exit surface was tilted at 5° from the optical axis so that the ghost
ray generated at this surface deviates from the correct optical path. There are recesses with a width of 2 mm at both sidesof the diffraction surface for holing the grating without any thermal stresses on the diffraction surfaces.

Table 1. Properties of Ge immersion grating
Geometrical parameters
Material
Blaze angle
Apex angle
Groove Pitch
Tilt angle of entrance/exit surface
Area of entrance/exit surface
Area of diffraction surface
Diffraction surface
Surface roughness
Surface irregularity

Figure 2. Ge immersion grating for VINROUGE.
(a) Diffraction surface. (b) Schematic diagram.
(c) Entrance/exit surface. (d) Diffraction surface (topview)

Rowland’s ghost
Coating
Entrance/exit surface
Surface irregularity
Coating

Single-crystal Ge (n = 4.0)
75°
86°57.1 µm
5°32.0 mm x 32.0 mm
31.0 mm x 104.0 mm< 8 nm (RMS)< 65.6 nm (PV),< 18.7 nm (RMS)< 0.1 %
Ag (with protective coating)< 175 nm (PV)Broadband anti-reflective coating3. MEASUREMENT SYSTEM
Figure 3 shows an in-house equipment to measure the light diffracted by immersion gratings in the infrared wavelength
range under both the immersion and reflection configurations at room and cryogenic temperatures. For the light source,
this system employs a single-mode quantum cascade tunable laser (TLS-41047, Daylight Solutions, Inc.), whose
wavelength range is 4.30-5.11µm and the band width is < 6.8 x 10-6 µm. Linearly polarized beam is emitted from thelaser, and TE or TM modes can be selected by rotating a half-wave plate. The selected beam is cleaned up, expanded,and collimated by a spatial filter. The diameter of the collimated beam is reduced by a variable diaphragm aperture. Weset the diameter of the collimated beam to 3 mm for this experiment. The reduced beam is split by a beam splitter of a
CaF2 plate, which is wedged to prevent interferences within it and ghosts. One of the split beams enters and is diffracted
back by the immersion grating in the Littrow configuration, being focused on a two-dimensional (80 x 80 arrays)
photoconductive detector (Tachyon 6400 core, New Infrared Technologies, Ltd), whose wavelength detection range is 15 µm. The other split beam enters and is reflected back by a mirror, being also focused on the detector, but at thedifferent location. By monitoring the reflected beam and the diffracted beam simultaneously, we can compensate thetime variation of the laser output. Both an immersion grating and a reference mirror are switchable without changing thelight path. Comparing the intensities of beams diffracted by the immersion grating and reflected by the reference mirror,
we obtain the absolute diffraction efficiency of the immersion grating. When we measure the diffraction efficiency at thecryogenic temperature, the immersion grating and the reference mirror are installed in a cryostat, and they aremechanically switchable without breaking the vacuum condition with a motion feedthrough. The detail of the cryostat is
described in Kaji et al.5 From measurements at various wavelengths, we obtained the wavelength dependence of thediffraction efficiency. Since the direction of the diffracted beam changes with the wavelength, we put the IR detector andthe focusing lens on a movable plate to be able to follow it.

Figure 3. An in-house equipment to measure the diffraction efficiency of immersion gratings. (a) Schematic diagram of the opticalconfiguration. (b) Setup for measurement at the room temperature. (c) Setup for measurement at the cryogenic temperature. (d) The
Ge immersion grating and the reference mirror on the cold plate. (e) Motion feedthrough.

4. DIFFRACTION EFFICIENCY
We measured the diffraction efficiency of the Ge immersion grating at room and cryogenic (~28 K) temperatures. The
measurements were made at λ~ 4.25µm for both TE/TM modes. A beam with a diameter of 3 mm entered at the centerof the entrance/exit surface. The entrance/exit surface of the grating was tilted by 10° relative to the beam axis so that thebeam was diffracted back by the diffraction surface in the Littrow configuration when the wavelength was a blazewavelength.
Figure 4 shows the diffraction efficiency of the Ge immersion grating. We measured beam intensities at several
positions of the IR detector and took the average of them to reduce the uncertainty due to the pixel-to-pixel sensitivity
variation. The error bars in the figure show the standard deviations of the measured efficiency. The horizontal line shows
the peak efficiency expected from the designs of grooves and coating. The Ge immersion grating is found to have highefficiencies (80% for TE and 70% for TM) as expected from the design at both room and cryogenic temperatures. The
data measured at the cryogenic temperature is under detailed analysis, but the efficiency at the cryogenic temperature isroughly the same as that at room temperature.

Figure 4. Measured absolute diffraction efficiency at room and cryogenic temperatures (left: TE mode, right: TM mode). The
horizontal line shows the peak efficiency expected from the design.

ACKNOWLEDGMENTS
This study is financially supported by JSPS KAKENHI (16684001) Grant-in-Aid for Young Scientists (A), JSPS
KAKENHI (20340042) Grant-in-Aid for Scientific Research (B), JSPS KAKENHI (21840052) Grant- in-Aid for Young
Scientists (Start-up), and MEXT Supported Program for the Strategic Research Foundation at Private Universities, 2008–2012 (No. S0801061) and 2014–2018 (No. S1411028).

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