2.1

Birefringence VPH grating

In the VPH grating, when an optically anisotropic medium such as liquid crystal (LC) and an isotropic medium or two kinds of optically anisotropic media are combined as a hologram recording material, the refractive index of an optically anisotropic medium and isotropic medium or two kinds of optically anisotropic media are adjusted so that the diffraction efficiency characteristics of the S and P polarizations at the first diffraction order coincide with each other, it is possible to achieve high diffraction efficiency even for a natural polarization and circular polarization. Figure 4 shows a numerical calculation of the diffraction efficiency of a birefringence VPH grating by using our own software of the rigorous coupled-wave analysis (RCWA) method [19, 20] modified for an anisotropic medium [2, 7].

Figure 4

Calculated polarized diffraction efficiencies versus grating thickness t of birefringence VPH grating at λ = 1.41 μm (upper panel), and polarized spectral diffraction efficiencies on t = 12.5 μm (left). n₁=1.55, n_{S max} = 1.60, n_{S min} = 1.50, n_{P max} = 1.653, n_{P min} = 1.50, = 1.0 μm, θ₀ = 45° (right) [2, 7].

We mixed an ultraviolet (UV) curable LC (no=1.55, ne=1.72) and normal LC (no=1.5, ne=1.65), sandwiched between two glass substrates in CITIZEN WATCH Co. Ltd., and the B-VPH grating was prototyped by an exposure optical system of a two-beams interferometer with an ultraviolet (325nm) laser. As shown on the left in figure 5, this B-VPH grating has diffraction efficiencies of up to 66%, 27% and 42% for S, P and natural polarizations, respectively. In addition, a visible light curable resin (n=1.51) and the UV-curable LC (no=1.55, ne=1.72) were mixed and sandwiched between two glass substrates, and the B-VPH grating was prototyped by an exposure optical system of a two-beams interferometer with a visible (532 nm) laser. As shown on the right in figure 5, this B-VPH grating achieves diffraction efficiencies of up to 80% and 86% for S and P polarizations, respectively.

Figure 5

Diffraction efficiency of B-VPH grating. Combination of UV-curable LC (no=1.55, ne=1.72) and normal LC (no=1.5, ne=1.65), Λ~ 0.45 μm (t=10μm, 2,240 groove/mm), t=10 μm (left), and combination of visible-curable resin (n=1.51) and UV-curable LC (no=1.55, ne=1.72), Λ~ 1.6 μm (616 groove/mm), t=20 μm (right)

2.2

Reflector facet transmission grating and hybrid grism

The RFT grating is a SR transmission grating with a new lattice structure of sawtooth shaped ridges with an acute vertex angle in which an incident beam from one facet of a ridge is reflected on the other facet of the ridge and the beam is exited from the rear surface of the ridge as shown on the left in figure 6 [7]. In the case of the incident and the diffraction angle are 45 °, and the refractive index of ridges is n=1.54, the vertex angle of the ridges is 38.8°. It was found that the RFT grating is able to achieve diffraction efficiency of above 80% from the 4th to higher diffraction orders by numerical calculations using the RCWA method [7]. We had planed to prototype a RFT grating for the WFOS (Wide Field Optical Spectrograph) [21] of the TMT by a replica from a mold in which V grooves were processed on a work of nickel-phosphorus alloy by shaper cutting with our ultra-high precision machine and a single-crystal diamond tool (Fig. 6 right). Since ridges of RTF gratings for the WFOS have the small vertex angles from 35° to 44°, difficulties are expected in the process of the mold machining and the replication. So we decided to prototype a SR transmission grating for a hybrid grism of the MOIRCS to clarify the problem in fabrication of the RTF grating for the WFOS. The grating period of the SR transmission grating is 10.8μm and the vertex angle is about 60°.

Figure 6

Schematic representation of RFT grating (left), and fabrication process of SR transmission grating with ridges of acute angle (right) [7].

The medium dispersion (R1300) grism for MOIRCS with saw tooth ridges is directly machined onto a prism of KRS-5 (mixed crystal of thallium chloride and thallium bromide) by a ruling engine. However, fine cracks have seen on the surface and the efficiency is remarkably deteriorated because this grism was repeated heat cycle between room temperature and 100 K when the enclosure of the MOIRCS was opened and closed. So we decided to develop a hybrid grism combining SR transmission grating of replica (n~1.5) with acute ridge angle and ZnSe (n=2.45@1.65 μm) prism (Fig. 7 left). The mold of a surface relief grating for the hybrid grism was successfully fabricated on to a work of Ni-P alloy by shaper cutting with our ultra-precision machine and a single-crystal diamond bite (Fig 7 middle and right).

Figure 7

Schematic representation of hybrid grism [7] (left), mold for replication experiment with work piece size of 50×50 [mm] (middle), wave-front error and interferogram of mold (right).

Then, experiments of replication were made 5 times by a company of nanoimprint manufactures. Until the 1st to the 4th experiments UV curable resin was used, however it was not practical because peelings and large wavefront error of transmission due to the shrinkage at the curing. In the 5th experiment, a two-part resin with small curing shrinkage mixed with silica was used, however the most of replica peeled off from the glass substrate, despite the use of a coupling agent. The replication process is currently being improved.

The peak diffraction efficiencies of the first replica prototype were about 45% (Fig. 8 left). Numerical calculations of the spectral characteristics for this SR transmission grating by the RCWA method revealed that the diffraction efficiency was lowered because the wavelength range shifted to the shorter wavelength (Fig. 8 left). Therefore, we investigated the spectral characteristics of the diffraction efficiency by changing the angle of the facet (β) from which the beam exits and the vertex angle (γ) of the ridge. As a result, in the case of the lattice shape β = 65.5 ° and γ = 55.0 °, it was found that the wavelength range and the diffraction efficiency are optimal (Fig. 8 right).

Fig. 8

Diffraction efficiency of MOIRCS hybrid grism. Left: current design, β=64.8 °, γ=61.8°. Right: optimal design, β = 65.5 °, γ= 55.0°.

2.3

Quasi-Bragg grating and volume binary grating

Quasi-Bragg (QB) grating is a transmission grating with a new structure in which rectangular metal films or low refractive index layers as mirror surfaces are aligned in parallel at an equal interval like a window shade or an armor window [2, 7, 11]. It is confirmed by numerical calculations using the RCWA method, that a QB grating can achieve high diffraction efficiency up to 80% in higher diffraction orders [22]. As in a VPH grism, a QB grism as shown on the left in figure 9 has a structure in which a QB grating is sandwiched between two prisms, so that the limitation of the critical angle at the interface between the high-index prism and the QB grating is less strict compared with a hybrid grism (Fig. 7 left), it is suitable for a high dispersion spectroscopy and becomes a promising dispersing optical element for an astronomical imaging instrument if it is put into practical use.

Figure 9

Schematic representation of QB grism (left) and VB grating (center), diffraction efficiency of VB grating for echelle grism of nu-MOIRCS (right: θ₀=28.4°, n₁=1.33, n₂ = n₃ =1.6, Λ= 5.1 μm, L&S = 4.6:0.5 [μm], t = 16 μm).

We decided to develop a QB grism for the high dispersion grism of nu-MOIRCS. The nu-MOIRCS is scheduled as the first light instrument for the ULTIMATE Subaru. The ULTIMATE Subaru plans to install a new ground-layer adaptive optics (GLAO) onto the Subaru telescope, improve the limiting magnitude and the spatial resolution by reducing the size of the star image by correcting the wavefront error due to the atmospheric turbulences. The echelle grism for the spectra from the third to the sixth diffraction orders combined with a direct vision prism as a cross disperser installs in the nu-MOIRCS, it can simultaneously covert the wavelength range of 0.8 to 1.8μm with large angular dispersion by folding the spectra on the detector, and it is the key to improve performance of the nu-MOIRCS.

By numerical calculations using the RCWA method, a QB grating uses the total reflection by the medium of a low refractive index as the mirror surface as shown on the center in figure 9, that is, a VB grating with a high aspect ratio functioning as a QB grating, we found that high diffraction efficiencies can be achieved by the grating [2, 7, 23]. We decided to develop a VB grating for the echelle grism of the nu-MOIRCS. On the right in figure 9 shows the diffraction efficiency of the VB grating (lattice period Λ=5.1μm, L & S=4.6: 0.5 [μm], thickness t=16μm) for the echelle grism. The echelle grism is fabricated by sandwiching the VB grating between two ZnSe prisms.

We develop a fabrication method for a VB grating as a mold of silicon with ridges of high aspect ratio in Toyoda Institute of Technology. By numerous trial fabrications, we found the process which oxygen is slightly added to the etching gas and the passivation gas, etching and sidewall protection (Bosch process) are performed while cleaning, and the amount of an etching volume is reduced. As a result, the scallops (irregularities formed every etching cycle) on the sidewall of the ridges successfully reduced to about 40 nm. Further, silicon oxide layers are formed on both sides of the ridge (sidewalls) surfaces of the silicon, and then the oxide layers are etched (Fig. 10 left). By repeating this process several times, it was possible to obtain extremely smooth surfaces with little scattering even in visible light. Specifically, a resist was formed on a silicon substrate by using a mask with a line & space of 2.0μm: 3.1μm. Deep grooves formed by the cycle etching onto the silicon substrates (two kind of depths with 10μm and 20μm). Silicon oxide layers are formed and removed twice. Where oxygen diffuses from a surface of the silicon is about 400 nm by the oxidation process when an oxide layer having a thickness of about 1μm. As a result, lattices of ridges with widths of 0.44 and 0.8 μm, respectively, which surfaces are extremely smooth, are obtained (Fig. 10 middle and right).

Figure 10

Fabrication process for silicon VB grating (left to middle) as a mold, central right: Λ= 5.1μm, t=10μm, s = 0.44μm, most right: Λ= 5.1μm, t=20μm, s = 0.80μm.

2.4

Quasi-Bragg immersion grating

An immersion grating is a reflection grating filled with a high-refractive index medium in its optical path, and angular dispersion of the immersion grating is proportional to the refractive index of the medium [24, 25]. In other words, since the size of an immersion grating can be reduced in inverse proportion to the refractive index of the medium compared with a conventional reflection grating with the same angular dispersion.

The QB immersion grating [11] was fabricated by combination of an inclined QB grating, Littrow prism and surface reflection mirror as shown on the right in figure 11 and on the left and middle in figure 12. The block of 60 seats of silica substrates was stacked by room temperature bonding of gold in Tohoku University (Fig. 11 left) [26]. The QB grating was cut with inclination of 30° from the block of silica substrates (Fig. 11 middle). We assembled a spectroscopic optical system of the Littrow mount (angle between incident and diffracted beams is small), and observed a diffraction image of the QB immersion grating using a He-Ne laser as a light source. As a result, although the order could not be separated because the point source image of the pinhole was larger than the interval of the diffraction orders, the diffraction intensity was highly concentrated (blazed) as shown in the right of figure 12, we confirmed the QB immersion grating functions as an immersion grating. It is difficult to fabricate a QB immersion grating for visible to near infrared wavelength by lamination of mirror substrates. On the other hand, it is relatively easy to fabricate a QB immersion grating of silicon or germanium for mid and far infrared wavelength by the lamination of mirror substrates.

Figure 11

Block of silica substrate stacked by room temperature bonding of gold (left), inclined QB grating of QB immersion grating (middle) and schematic representation of prototype of QB immersion grating (right).

Figure 12

Prototype of QB immersion grating (left), camera lens image of diffraction beam gazed from square surface of Littrow prism (middle) and diffraction pattern of QB immersion grating (right).