JP3227783B2 - Pile of plates - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a pile of plates used in the ultraviolet region, particularly among polarizers required for extracting linearly polarized light in various spectrometers and optical experiments.

[0002]

2. Description of the Related Art A dichroic polarizing filter and a birefringent crystal of an anisotropic crystal are used as polarizers for extracting linearly polarized light oscillating in a specific direction such as in a spectrometer or an optical experiment. Polarizers, grid polarizers in which a large number of conductor wire grids are arranged, and pile-of-plates utilizing differences in P-polarized light transmittance and S-polarized light transmittance to a transparent plate.

[0003] Each polarizer has advantages and disadvantages in terms of usable wavelength region, degree of polarization (extinction ratio), aperture, and price.

[0004] Of these, only the pile of plates can be used in a wide wavelength range from the ultraviolet region to the visible and infrared regions, but in particular, they can be used in the ultraviolet region. ing. In addition, although a relatively large aperture can be manufactured, the degree of polarization is inferior to that of a polarizing prism.

[0005] As shown in Fig. 1, the pile of plates is formed by arranging a number of transparent plates inclined symmetrically.

When light is obliquely incident on a semi-infinite medium,
Assuming that the refractive indices of the outside and the medium are N and n, the incident angle is α, and the refractive angle is β, the S-polarized reflectance R _s and the P-polarized reflectance R _p can be written as follows.

R _s = [(N cos α−n cos β) / (N cos α + n cos β)] ² (1-a) R _p = [(n cos α−N cos β) / (n cos α + N cos β)] ² (1-b) ) Where N sinα = n sinβ (Snell's law) (2)
Holds.

Since the relationship of R _s > R _p is generally established between R _s and R _p , P-polarized light is transmitted more than S-polarized light. In particular, when the incident angle becomes the Brewster angle α _B , R _p = 0, so that there is no reflection loss of P-polarized light. A pile of plates is a polarizer in which a large number of plates are arranged so that an incident angle becomes a Brewster angle and only P-polarized light is transmitted.

When light is incident on one parallel plate, the effects of interference are averaged, and considering the effect of internal multiple reflection, the S-polarized light transmittance T _1s and the P-polarized light transmittance T _1p are as follows.

T _1s = (1−R _s ) / (1 + R _s ) (3-a) T _1p = (1−R _p ) / (1 + R _p ) (3-b) Next, m plates are placed in parallel. When arranged, ignoring multiple reflection between the plates, the S-polarized light transmittance T _ms and the P-polarized light transmittance T _mp are respectively T _ms = T _1s ^m = [(1−R _s ) / (1 + R _s )] ^m (4 ^{_{-a) T mp = T 1p m}} = [(1-R p) / (1 + R p)] polarization P since the ^m (4-b) is as follows (Walter G. DRIS
coll & William Vanghan, “Handbook of Optics” P10-
89 1978 by Mc Graw. Hill).

[0011]

(Equation 5) FIG. 2 shows the dependency of T _{mp on} the incident angle at m = 2, 4, 8 when N = 1, n = 1.546, and FIG. 3 shows the dependency of the P on the incident angle.

Further, when N = 1 and n = 1.814, T
FIG. 4 shows the dependence of _{mp on} the incident angle, and FIG. 5 shows the dependence of P on the incident angle.

[0013]

As apparent from FIGS. 2 to 5, a substrate having a low refractive index can obtain a high transmittance at a relatively wide angle of incidence, but has a high degree of polarization even when a large number of substrates are stacked. Not very high. On the other hand, in the case of a substrate having a high refractive index, the degree of polarization is significantly increased when the number of substrates is increased, but the range of incident angles at which a high transmittance is obtained is narrow.

If a high degree of polarization is required, a material having a high refractive index may be selected. However, in the infrared region, the refractive index is 3 or 4.
There is a substrate having a high refractive index, but none of the substrates transmitting ultraviolet light has such a high refractive index. For example, λ = 25
Refractive index in the vicinity of 0nm is 1.47 fluorite (C _a F _2),
And so on 1.51 of quartz (S _i O _2).

The present invention has been made in view of the above-mentioned drawbacks of the conventional pile of plates, and has as its object to provide a pile of plates that simultaneously satisfies a high degree of polarization and a wide angle of incidence.

[0016]

The construction of the pile of plates of the present invention is shown in FIGS. A birefringent material is used for the flat plate, and is arranged such that the refractive index of S-polarized light of incident light is larger than the refractive index of P-polarized light.

[0017] That is, the refractive index n ₀ of the refractive index n _e is the ordinary ray of extraordinary ray when using uniaxial positive crystal as a material
As shown in FIG. 6, the direction of the optical axis is perpendicular to the plane of incidence.

On the other hand, when a negative crystal is used, since n _e <n ₀ , the direction of the optical axis is in the plane of incidence as shown in FIG.

[0019]

When the refractive index of S-polarized light is n _s , the refractive angle is β _s , the refractive index of P-polarized light is n _p , and the refractive angle is β _p , when N = 1
(1) than _{R s = [(cos α-} n s cos β s) / (cosα + n s cos β s)] 2 (6-a) R p = [(n p cos α-cos β p) / (n _p cos α + cos β _p )] ² (6-b), and especially when the incident angle is Brewster's angle α _B , R _p = 0, so that if Snell's law (2) is used, sin ² α _B = n _p ² / (n _p ² +1), cos ² α _B = 1 / (n _p ² +1) (7)

In order to widen the incident angle with a high P-polarized light transmittance, the rate of change of T _1P with respect to the incident angle at the Brewster angle should be small. Therefore, it is better that | ∂ ² T _1P / 小 さ い α ² | is small.

From (1-b), (4-b), (7), etc.

[0022]

(Equation 8)

[0023]

[Equation 9] Since (n _p > 1), the smaller the n _p , the better the usable incident angle can be obtained.

As is apparent from (5), the degree of polarization is higher when T _1s / T _1p is smaller, that is, when T _1s is smaller.

[0025]

(Equation 10) Than

[0026]

[Equation 11] And T _1s to decreases it can be seen that better n _s is greater because becomes.

From the above, it can be seen that the condition for increasing the degree of polarization is opposite to the condition for increasing the incident angle.
In conventional pile-of-plates using isotropic materials, n _s
= N _p , so that giving priority to one of the characteristics results in the other being inferior.

In the present invention, since a birefringent material having anisotropy is used for the material, the condition of n _s > n _p is satisfied, and two characteristics which are contrary to the conventional product can be simultaneously satisfied. First, the incident angle existence of the transmittance when a uniaxial negative crystal is used as a material will be described with reference to FIG.

The main refractive index of the ordinary ray of the crystal is n _ω , the refractive index is n ₀ , the refraction angle is β ₀ , the main refractive index of the extraordinary ray is n _ε , the refractive index is n _e , and the refraction angle is β _e . .

[0030] n _0> n _e so n _s may Taking the arrangement as n _p is n _e to n ₀ is a negative crystal. That is,
The optical axes may be arranged so that S-polarized light becomes an ordinary ray and P-polarized light becomes an extraordinary ray. However, it is assumed that the direction of the optical axis is inclined by an angle よ り from the crystal surface.

N ₀ = n _ω (12) 1 / _ne ² = (1 / n _ω ² ) sin ² (β _e −ψ) + (1 / n _ε ² ) cos ² (β _e −ψ) (13 ) sin α = n ₀ sin β ₀ = _ne sin β _e (14), sin β ₀ = (1 / n _ω ) sin α (15)

[0032]

(Equation 16) _{n e = sin α / sin β} e (17) where ^{a = (1 / sin 2 α} ) + cos2ψ [(1 / n ε 2) - (1 / n ω 2)] b = (1 / n ω 2) ^{+ cos 2 ψ [(1 /} n ε 2) - (1 / n ω 2)] c = sin2α [(1 / n ε 2) - (1 / n ω 2)] (12), (15), ( 16), ₍₀ β from _{17), n 0, β e} , n e is Motomari T _1p, T _1s is determined from the following equation _{T 1p = 2n e cos αcos β} e / (n e 2 cos 2 α + cos 2 β e _{) (18) T 1s = 2n} 0 cos αcos β 0 / (n o 2 cos 2 β 0 + cos 2 α) (19) (18), Motomari is T _mp, T _ms by substituting (19) into (4) Further, by substituting into (5), the degree of polarization P is obtained.

Next, the incident angle dependence of the transmittance when a uniaxial positive crystal is used as a material will be described with reference to FIG.

[0034] n _p may Taking an arrangement such that n ₀ to n _e> n _0, so n _s is a positive crystal n _e. That is, S
The optical axis may be arranged so that the polarized light is an extraordinary ray and the P-polarized light is an ordinary ray.

In the arrangement as shown in FIG. 6, since n ₀ = n _ω (20) _ne = n _ε (21), the refraction angles β ₀ and β _e are sin α = n _ε sin β _e = n _ω sin β ₀ (22), T _1p and T _1s are as follows.

T _1p = 2n _ω cos αcos β ₀ / (n _ω ² cos ² α + cos ² β ₀ ) (23) T _1s = 2n _ε cos αcos β _e / (n _ε ² cos ² β _e + cos ² α) ( 24) T _mp , T _ms , and P are obtained from (4) and (5) based on (22) to (24) as in the case of the negative crystal.

[0037]

EXAMPLES select calcite as uniaxial negative crystal, n ω ₌ 1.814 Taking design wavelength 250 nm, the n ε = _1.546.
The dependence of T _{mp on} the incident angle when ψ = 0 ° is shown in the graph of FIG. 8, and the dependence of P on the incident angle is shown in the graph of FIG.

However, the number of plates (m) is 2, 4,
Calculations were made for each of the eight sheets.

First, comparing FIGS. 2 and 8, the pile of plates of the present invention has an incident angle as wide as that of a conventional pile of plates made of a material having an isotropic and low refractive index (1.546). It can be seen that the P-polarized light transmittance is high in the range.

However, comparing FIG. 3 and FIG. 9, it can be seen that the degree of polarization is always higher than that of the same pile of plates of the conventional product.

On the other hand, comparing FIGS. 5 and 9, the pile of plates of the present invention is isotropic and has a high refractive index (1.814).
It can be seen that the degree of polarization is as high as that of a conventional pile of plates made of a material having

However, comparing FIGS. 4 and 8, it can be seen that the P-polarized light transmittance is always higher in a wider incident angle range than the same pile of plates of the conventional product.

[0043]

According to the present invention, it is possible to simultaneously satisfy a high P-polarized light transmittance and a high degree of polarization, which were incompatible with conventional products.

[Brief description of the drawings]

FIG. 1 is a diagram showing a cross section of a conventional pile of plates.

FIG. 2 is a graph showing the incident angle dependency of the P-polarized light transmittance of a conventional pile of plates made of an isotropic material having a refractive index of 1.546.

FIG. 3 is a graph showing the incident angle dependence of the degree of polarization.

FIG. 4 is a graph showing the incident angle dependence of the P-polarized light transmittance of a conventional pile of plates made of an isotropic material having a refractive index of 1.814.

FIG. 5 is a graph showing the dependence of the degree of polarization on the incident angle.

FIG. 6 is a diagram illustrating a cross section of a pile of plates of the present invention when a uniaxial positive crystal is used as a material.

FIG. 7 is a diagram showing a cross section of the pile of plates of the present invention when a uniaxial negative crystal is used as a material.

FIG. 8 is a graph showing the incident angle dependence of the P-polarized light transmittance at a wavelength of 250 nm of a pile of plates using calcite (uniaxial negative crystal) as a material in an example of the present invention.

FIG. 9 is a graph showing the incident angle dependence of the degree of polarization.

Claims (1)

(57) [Claims] 1. A pile of plates in which a large number of flat plates are arranged at a Brewster angle, wherein the flat plate is made of a birefringent material and the refractive index of S-polarized light is larger than that of P-polarized light. A pile of plates characterized by being arranged in such a manner.