CN103487945A - Efficient polarization purifying device - Google Patents

Abstract

The invention provides an efficient polarization purifying device. The efficient polarization purifying device is composed of a wave plate heap, a quarter-wave plate and a reflector, wherein the wave plate heap is arranged obliquely, an Brewster angle is formed between the surface normal of the wave plate heap and the horizontal direction, then parallel light emitted by a laser can enter the wave plate heap with the Brewster angle, S polarized light is reflected, P polarized light is transmitted, and the quarter-wave plate is placed in the direction of S reflected light to enable the reflected S polarized light to shine on the quarter-wave plate vertically and the included angle between an optical axis and the horizontal direction to be 45 degrees; the reflector is placed behind the quarter-wave plate, the S polarized light is converted into the P polarized light after passing through the quarter-wave plate and the reflector, and then the P polarized light enters the wave plate heap with the Brewster angle. According to the efficient polarization purifying device, due to the fact that the reflector which is perpendicular to the wave plate heap is placed on the edge of the direction of emergent light formed after the reflected light passes through the wave plate heap, the emergent light is right in the horizontal direction; an extremely small number of elements are used, and single-direction-line polarized light with the high polarization degree, high polarization purity and high energy utilization rate is obtained.

Description

A kind of high-level efficiency polarization purification devices

Technical field

The present invention relates to the technical field of polarization converter, be specifically related to a kind of high-level efficiency polarization purification devices, its polarization converter that is high-polarization, high polarization purity, high conversion efficiency.

Background technology

Wave-plate stack is superimposed and is formed by one group of parallel plane glass sheet, when wave-plate stack surface normal and horizontal direction formation Brewster angle, when the natural light glancing incidence also passes through wave-plate stack, see through the refract light of wave-plate stack continuously with identical state incident and refraction, the per pass interface, all from refract light, reflect away the component (S component) of a part perpendicular to the paper vibration, finally make to approach by the transmitted light of wave-plate stack the linearly polarized light (P component) of the parallel plane of incidence.The light component of parallel plane of incidence vibration does not have reflection loss during by wave-plate stack, and the reflection loss that the light component of vertical paper vibration will produce up to 15% is that energy of reflection light is not utilized, cause the transmitted light energy later by wave-plate stack lower, just must increase the wave plate number and if obtain high-polarization, cause cost higher.

Summary of the invention

The present invention is directed to the deficiencies in the prior art and defect, a kind of device that comprises a tilted-putted wave-plate stack, a quarter-wave plate and two catoptrons is provided, take full advantage of reflected light to improve total degree of polarization and capacity usage ratio.

The technical solution used in the present invention is: a kind of high-level efficiency polarization purification devices, described purification devices is comprised of wave-plate stack, quarter-wave plate, the first catoptron and the second catoptron, wave-plate stack surface normal direction is from the horizontal by Brewster angle, quarter-wave plate and the first catoptron vertical reflection light direction are placed, reflection S polarized light passes through quarter-wave plate, the first catoptron and quarter-wave plate successively, convert the S polarized light to the P polarized light, the edge of the transmitted light direction at reflected light after wave-plate stack, vertical wave-plate stack is placed the second catoptron.

Wherein, the position of quarter-wave plate and the first catoptron can be according to debuging needs, at vertical reflection light direction parallel.

Wherein, quarter-wave plate equates with the size AH of the first mirror size JK, the second catoptron and all is more than or equal to beam diameter D, i.e. JK=AH >=D.

Wherein, what wave-plate stack adopted is fused quartz, or adopts CaF ₂, MgF ₂, the K9 ultraviolet can be saturating optical material.

Wherein, each size is determined relation:

l and θ, d, D are relevant, and the length L of wave-plate stack is by wave-plate stack material n ₂, wave-plate stack gross thickness d and beam diameter D determine, according to the specific requirement to degree of polarization, can determine that required wave plate counts N, by wave-plate stack gross thickness d and wave plate, counts the thickness that N can determine each piece wave plate

Principle of the present invention is:

The wave-plate stack surface normal, from the horizontal by Brewster angle, during directional light incident wave sheet pile, reflects the S polarized light, transmission P polarized light.Quarter-wave plate is placed perpendicular to S reflected light direction, makes S polarized light vertical irradiation quarter-wave plate, and the S polarized light becomes right-circularly polarized light through quarter-wave plate.Parallel quarter-wave plate is placed a catoptron, and the right-circularly polarized light after quarter-wave plate is reflected into to left circularly polarized light, and this left circularly polarized light vertically becomes the P polarized light through quarter-wave plate.The S polarized light converts the P polarized light to after quarter-wave plate and catoptron, along former reflection direction with the brewster angle incidence wave-plate stack.A catoptron perpendicular to wave-plate stack is placed by the edge of the transmitted light direction at reflected light after wave-plate stack, and the light positive after reflection is good along horizontal direction.Whole device simply is easy to realize, and conversion efficiency is high.

The present invention's advantage compared with prior art is:

1) polarization purification devices of the present invention only utilizes four elements, and the absorption loss in process seldom, obtains the one direction linearly polarized light of high-polarization, high polarization purity, high-energy utilization factor.

2) polarization purification devices of the present invention not only can be applied to the polarization purifying in polarized illumination system, also can be for the external cavity type gas laser.

3) polarization purification devices of the present invention has not only effectively utilized catoptrical energy, and ingenious making it through wave-plate stack, reaches energy and strengthens effect.

The accompanying drawing explanation

Fig. 1 is the main structure figure of efficient polarization purification devices;

Fig. 2 is the schematic diagram that the S polarized light converts the P polarized light to;

Fig. 3 is the catadioptric schematic diagram of light in wave-plate stack inside;

Fig. 4 is that transmitted light degree of polarization, total reflected light degree of polarization and total degree of polarization are counted change curve with wave plate;

Fig. 5 is that the marginal ray of determining concrete component size, beam diameter and wave plate thickness is propagated schematic diagram.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in further detail.

Fig. 1 is the main structure figure of efficient polarization purification devices.By wave-plate stack 1, quarter-wave plate 2, the first catoptron 3 and the second catoptron 4, formed.θ in figure _brepresent Brewster angle, different materials has different Brewster angles.In the present embodiment, for the 193nm wave band, to uv transmittance, fused quartz is as material preferably in wave-plate stack 1 employing, and refractive index is 1.560321, so Brewster angle is 57.344 °, wave-plate stack 1 surface normal is from the horizontal by 57.344 °.For CaF ₂, MgF ₂, other ultraviolet such as K9 can be saturating material or for the respective material (as the common quartz glass of visible light wave range) of its all band, the principle of this device is applicable equally.This tilted-putted wave-plate stack 1 of natural light glancing incidence, the S polarized light is reflected, the P polarized light transmission.In order to take full advantage of the energy of the S polarized light be reflected, in the reflected light direction, added S polarized light as shown in Figure 2 to convert the device of P polarized light to, by quarter-wave plate 2 and the first catoptron 3, formed.The S polarized light that all reflected light of wave-plate stack 1 are vertical paper vibration, the x direction of principal axis along the coordinate system defined vibrates, its vertical incidence quarter-wave plate 2, the optical axis of quarter-wave plate 2 and x axle angle at 45 °.Because the linearly polarized light process quarter-wave sector-meeting at 45 ° of direction of vibration and optical axis produces the circularly polarized light of a certain rotation direction, and the circularly polarized light of a certain rotation direction produces the linearly polarized light at 45 ° with optical axis through quarter-wave plate, can utilize so quarter-wave plate and arrangement of mirrors that the direction of vibration half-twist of S polarized light is become to the P polarized light, so the S polarized light produces right-circularly polarized light 5 through quarter-wave plate 2, become left circularly polarized light 6 through the first catoptron 3, left circularly polarized light 6 becomes the P polarized light through quarter-wave plate 2.The S polarized light of all reflections converts the P polarized light to after quarter-wave plate 2 and the first catoptron 3, with brewster angle incidence wave-plate stack 1.In addition, the position of quarter-wave plate 2 and the first catoptron 3 can be according to debuging needs, at vertical reflection light direction parallel.A end margin after wave-plate stack 1 is placed second catoptron 4 perpendicular to wave-plate stack 1, from Fig. 1 intermediate cam shape relation, is easy to draw, and after the second catoptron 4 reflections, the outgoing of P polarized light along continuous straight runs.

Angular relationship in Fig. 1, ∠ α=θ _b, incident ray i becomes Brewster angle θ with wave-plate stack 1 normal _bglancing incidence, after wave-plate stack 1, emergent ray is parallel with incident ray (becomes θ with wave-plate stack 1 normal direction _b), because reflected light after quarter-wave plate 2 and the first catoptron 3 equally with θ _bincident wave sheet pile 1, so the emergent ray of reflected light after wave-plate stack 1 becomes θ with wave-plate stack 1 normal direction _b, in figure, angular relationship is known: ∠ β=θ _b, ∠ γ=90 °-θ _b,

∠ α+∠ β+2 ∠ γ=θ _b+ θ _b+ 2 (90 °-θ _b)=180 °, the light i ' after the second catoptron 4 is parallel to incident ray i, so be the horizontal direction outgoing.

Fig. 3 is the catadioptric figure of light in sheet pile inside, for simplicity, only considers the reflection between wave plate, does not consider the reflection of wave plate inside.N ₁for the refractive index of air, n ₂refractive index for wave plate.The Stokes vector that V is incidence natural lights, with V _rNand V _tNmean respectively the Stokes vector of N bar reflected light and transmitted light, the catadioptric situation of three light of take in figure is example, has drawn inner catadioptric schematic diagram, by that analogy, can obtain the catadioptric figure of N bar light.N in Fig. 3 ₁layer does not represent the real air layer thickness, only draws for convenience the wherein propagation condition of light.

At first we derive transmission and the reflection Muller matrix of wave-plate stack 1, and then the degree of polarization of derivation natural light total reflected light after wave-plate stack 1, and the degree of polarization of transmitted light and the degree of polarization of all reflected light after wave-plate stack 1, finally obtain total degree of polarization.And, by the MATLAB calculating of programming, can obtain corresponding each degree of polarization result of the different wave plate numbers shown in table 1, and we have only provided the degree of polarization result of 1～20 block of wave plate, and total degree of polarization of 20 blocks of wave plates is very high, and degree of polarization afterwards is tending towards 100%.For the purpose of directly perceived, total draw the degree of polarization of all catoptrical degree of polarization as shown in Figure 4, transmitted light and the degree of polarization change curve with the wave plate number.

Each degree of polarization numerical result of table 1

The total degree of polarization of sheet number (piece) total reflected light degree of polarization transmitted light degree of polarization
	171.88%20.19%49.36%
282.05%38.79%65.98%
	387.99%54.70%76.45%
491.91%67.44%83.78%
	594.56%77.13%88.94%
696.35%84.20%92.52%
	797.56%89.22%94.97%
898.38%92.71%96.63%
	998.92%95.10%97.75%
1099.28%96.72%98.50%
	1199.52%97.81%99.00%
1299.68%98.54%99.34%
	1399.79%99.03%99.56%
1498.86%99.35%99.71%
	1599.91%99.57%99.80%
1699.94%99.71%99.87%
	1799.96%99.81%99.91%
1899.97%99.87%99.94%

19	99.98%	99.92%	99.96%
				20	99.99%	99.94%	99.97%

The mathematical derivation process of total degree of polarization:

The degree of polarization of the transmission Muller matrix of a wave plate and process N piece wave plate transmitted light:

The Muller matrix M of wave plate two interfaces ₁, M ₂for:

${\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="HDA0000391322470000021.png,HDA0000391322470000031.png"\; state="\{\{state\}\}">M</figure-callout>}}_1=\frac{{2n}_2}{n_1}{\left(\frac{\cos {\mathrm{\&theta;}}_1\sin {\mathrm{\&theta;}}_2}{\sin \mathrm{\&beta;}\cos \mathrm{\&alpha;}}\right)}^2\left(\begin{array}{cccc}{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}+1& {\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}-1& 0& 0\\ {\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}-1& {\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}+1& 0& 0\\ 0& 0& 2\cos \mathrm{\&alpha;}& 0\\ 0& 0& 0& 2\cos \mathrm{\&alpha;}\end{array}\right),\mathrm{\&alpha;}={\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2,\mathrm{\&beta;}={\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2$

${\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">M</figure-callout>}}_2=\frac{{2n}_1}{n_2}{\left(\frac{\cos {\mathrm{\&theta;}}_1\sin {\mathrm{\&theta;}}_2}{\sin \mathrm{\&beta;}\cos \mathrm{\&alpha;}}\right)}^2\left(\begin{array}{cccc}{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}+1& {\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}-1& 0& 0\\ {\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}-1& {\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}+1& 0& 0\\ 0& 0& 2\cos \mathrm{\&alpha;}& 0\\ 0& 0& 0& 2\cos \mathrm{\&alpha;}\end{array}\right)$

θ wherein ₁and θ ₂represent respectively incident angle and refraction angle.

The transmission Muller matrix M of a wave plate _tfor:

$M_t={\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">M</figure-callout>}}_2\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="HDA0000391322470000021.png,HDA0000391322470000031.png"\; state="\{\{state\}\}">M</figure-callout>}}_1=\frac{1}{2}{\left(\frac{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}{2\mathrm{\&theta;}}_1\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">sin</figure-callout>}{2\mathrm{\&theta;}}_2}{{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}\mathrm{co}{s}^2\mathrm{\&alpha;}}\right)}^2\left(\begin{array}{cccc}{\mathrm{<figure-callout\; id="4"\; label="cos"\; filenames="HDA0000391322470000022.png"\; state="\{\{state\}\}">cos</figure-callout>}}^4\mathrm{\&alpha;}+1& {\mathrm{<figure-callout\; id="4"\; label="cos"\; filenames="HDA0000391322470000022.png"\; state="\{\{state\}\}">cos</figure-callout>}}^4\mathrm{\&alpha;}-1& 0& 0\\ {\mathrm{<figure-callout\; id="4"\; label="cos"\; filenames="HDA0000391322470000022.png"\; state="\{\{state\}\}">cos</figure-callout>}}^4\mathrm{\&alpha;}-1& {\mathrm{<figure-callout\; id="4"\; label="cos"\; filenames="HDA0000391322470000022.png"\; state="\{\{state\}\}">cos</figure-callout>}}^4\mathrm{\&alpha;}+1& 0& 0\\ 0& 0& 2\mathrm{co}{s}^2\mathrm{\&alpha;}& 0\\ 0& 0& 0& 2\mathrm{<figure-callout\; id="2"\; label="co\; s"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">co</figure-callout>}{s}^{}{}^2\mathrm{\&alpha;}\end{array}\right)$

And then obtain N piece wave plate transmission Muller matrix M ⁿ _tfor:

${M^N}_t=M_t...M_t=A^N\left(\begin{array}{cccc}{\cos }^{4N}\mathrm{\&alpha;}+1& {\cos }^{4N}\mathrm{\&alpha;}-1& 0& 0\\ {\cos }^{4N}\mathrm{\&alpha;}-1& {\cos }^{4N}\mathrm{\&alpha;}+1& 0& 0\\ 0& 0& {\left({2\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}\right)}^N& 0\\ 0& 0& 0& {\left({2\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}\right)}^N\end{array}\right)$

Wherein $A=\frac{1}{2}{\left(\frac{\sin 2{\mathrm{\&theta;}}_1\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">sin</figure-callout>}2{\mathrm{\&theta;}}_2}{{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}}\right)}^2$

The transmitted light Stokes vector V of natural light after N piece glass sheet _tNfor:

$\begin{array}{c}{V}_{\mathrm{tN}}={M_t}^N*V\\ =A^N\left(\begin{array}{cccc}{\cos }^{4N}\mathrm{\&alpha;}+1& {\cos }^{4N}\mathrm{\&alpha;}-1& 0& 0\\ {\cos }^{4N}\mathrm{\&alpha;}-1& {\cos }^{4N}\mathrm{\&alpha;}+1& 0& 0\\ 0& 0& {\left({2\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}\right)}^N& 0\\ 0& 0& 0& {\left({2\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}\right)}^N\end{array}\right)\\ =A^N\left(\begin{array}{c}{\cos }^{4N}\mathrm{\&alpha;}+1\\ {\cos }^{4N}\mathrm{\&alpha;}-1\\ 0\\ 0\end{array}\right)=\left(\begin{array}{c}{S}_0\\ S_1\\ S_2\\ {\mathrm{<figure-callout\; id="3"\; label="S"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">S</figure-callout>}}_3\end{array}\right)\end{array}\left(\begin{array}{c}1\\ 0\\ 0\\ 0\end{array}\right)$

The degree of polarization of transmitted light: $P=\frac{\sqrt{{{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA0000391322470000021.png,HDA0000391322470000031.png"\; state="\{\{state\}\}">S</figure-callout>}}_1}^2+{{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">S</figure-callout>}}_2}^2+{{\mathrm{<figure-callout\; id="3"\; label="S"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">S</figure-callout>}}_3}^2}}{S_0}=\frac{1-{\cos }^{4N}\mathrm{\&alpha;}}{1+{\cos }^{4N}\mathrm{\&alpha;}},(\mathrm{\&alpha;}={\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)$

S wherein ₀, s ₁, s ₂and s ₃represent four components of Stokes vector.

The degree of polarization of transmitted light during with brewster angle incidence:

$P=\frac{\sqrt{{{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA0000391322470000021.png,HDA0000391322470000031.png"\; state="\{\{state\}\}">S</figure-callout>}}_1}^2+{{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">S</figure-callout>}}_2}^2+{{\mathrm{<figure-callout\; id="3"\; label="S"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">S</figure-callout>}}_3}^2}}{S_0}=\frac{1-{\cos }^{4\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">N</figure-callout>}}2{\mathrm{\&theta;}}_1}{1+{\cos }^{4\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">N</figure-callout>}}2{\mathrm{\&theta;}}_1}$

The reflection Muller matrix of a wave plate is derived:

Fresnel formula:

$\left\{\begin{array}{c}{r}_s=-\frac{\sin ({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)}{\sin ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}=\frac{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000391322470000021.png,HDA0000391322470000031.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\cos {\mathrm{\&theta;}}_1-{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2\cos {\mathrm{\&theta;}}_2}{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000391322470000021.png,HDA0000391322470000031.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\cos {\mathrm{\&theta;}}_1+{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2\cos {\mathrm{\&theta;}}_2}\\ r_p=\frac{\tan (\mathrm{\&theta;}1-{\mathrm{\&theta;}}_2)}{\tan ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}=\frac{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2\cos {\mathrm{\&theta;}}_1-{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000391322470000021.png,HDA0000391322470000031.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\cos {\mathrm{\&theta;}}_2}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2\cos {\mathrm{\&theta;}}_1+{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000391322470000021.png,HDA0000391322470000031.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\cos {\mathrm{\&theta;}}_2}\\ t_s=\frac{2\cos {\mathrm{\&theta;}}_1\sin {\mathrm{\&theta;}}_2}{\sin ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}=\frac{{2\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000391322470000021.png,HDA0000391322470000031.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\cos {\mathrm{\&theta;}}_1}{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000391322470000021.png,HDA0000391322470000031.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\cos {\mathrm{\&theta;}}_1+{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2\cos {\mathrm{\&theta;}}_2}\\ t_p=\frac{2\cos {\mathrm{\&theta;}}_1\sin {\mathrm{\&theta;}}_2}{\sin ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)\cos ({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)}=\frac{{2\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000391322470000021.png,HDA0000391322470000031.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\cos {\mathrm{\&theta;}}_1}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2\cos {\mathrm{\&theta;}}_1+{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000391322470000021.png,HDA0000391322470000031.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\cos {\mathrm{\&theta;}}_2}\end{array}\right.$

Incident light and catoptrical Stokes vector are expressed as:

$\left\{\begin{array}{c}I=E_S{E^{*}}_S+E_p{E^{*}}_p\\ M=E_S{E^{*}}_S-E_p{E^{*}}_p\\ C=E_S{E^{*}}_P+E_p{E^{*}}_S\\ S=E_S{E^{*}}_P-E_p{E^{*}}_S\end{array}\right.\left\{\begin{array}{c}{I}_r={r^2}_s{E}_S{E^{*}}_S+{r^2}_p{E}_p{E^{*}}_p\\ M_r={r^2}_s{E}_s{E^{*}}_S-{r^2}_p{E}_p{E^{*}}_p\\ C_r=r_S{r}_p(E_s{E^{*}}_P+E_p{E^{*}}_S)\\ S_r=r_s{r}_p(E_S{E^{*}}_P-E_P{E^{*}}_S)\end{array}\right.$

Reflected light and incident light connect by Muller matrix:

$\left(\begin{array}{c}{I}_r\\ M_r\\ C_r\\ S_r\end{array}\right)=\left(\begin{array}{cccc}{r^2}_s+{r^2}_p& {r^2}_s-{r^2}_p& 0& 0\\ {r^2}_s-{r^2}_p& {r^2}_s+{r^2}_p& 0& 0\\ 0& 0& {2r}_s{r}_p& 0\\ 0& 0& 0& {2r}_s{r}_p\end{array}\right)\left(\begin{array}{c}I\\ M\\ C\\ S\end{array}\right)$

The reflection Muller matrix of wave plate is Mr:

$M_r={r^2}_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000391322470000021.png,HDA0000391322470000031.png"\; state="\{\{state\}\}">p</figure-callout>}}\left(\begin{array}{cccc}1+{\mathrm{\&epsiv;}}^2& 1-{\mathrm{\&epsiv;}}^2& 0& 0\\ 1-{\mathrm{\&epsiv;}}^2& 1+{\mathrm{\&epsiv;}}^2& 0& 0\\ 0& 0& 2\mathrm{\&epsiv;}& 0\\ 0& 0& 0& 2\mathrm{\&epsiv;}\end{array}\right),\mathrm{\&epsiv;}=\frac{r_s}{r_p}$

The Stokes vector of the total reflected light of natural light after the N sheet is derived:

As shown in Figure 3, do not consider the reflection in wave plate inside, only consider the reflection of light between wave plate, can obtain the Stokes vector through N piece back reflection light:

V _r1＝M _rV，V _r2＝M _tM _rM _tV，V _r3＝M _tM _tM _rM _tM _tV，......V _rN＝M _t ^(N-1)M _rM _t ^(N-1)V

V wherein _rNmean the catoptrical Stokes vector of N bar, N=1,2,3

The transmission Muller matrix of known N piece wave plate, the Muller matrix M of (N-1) piece that is easy to get ^n-1 _tfor:

${M^{N-1}}_t=A^{N-1}\left(\begin{array}{cccc}{\cos }^{4(N-1)}\mathrm{\&alpha;}+1& {\cos }^{4(N-1)}\mathrm{\&alpha;}-1& 0& 0\\ {\cos }^{4(N-1)}\mathrm{\&alpha;}-1& {\cos }^{4(N-1)}\mathrm{\&alpha;}+1& 0& 0\\ 0& 0& {\left(2\mathrm{co}{s}^2\mathrm{\&alpha;}\right)}^{(N-1)}& 0\\ 0& 0& 0& {\left(2\mathrm{co}{s}^2\mathrm{\&alpha;}\right)}^{(N-1)}\end{array}\right)$

The catoptrical Stokes vector V after the N piece _rNfor:

$\begin{array}{c}{V}_{\mathrm{rN}}={M_t}^{(N-1)}{M}_r{M_t}^{(N-1)}V\\ =A^{N-1}\left(\begin{array}{cccc}{\cos }^{4(N-1)}\mathrm{\&alpha;}-1& {\cos }^{4(N-1)}\mathrm{\&alpha;}-1& 0& 0\\ {\cos }^{4(N-1)}\mathrm{\&alpha;}-1& {\cos }^{4(N+1)}\mathrm{\&alpha;}+1& 0& 0\\ 0& 0& {\left({2\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}\right)}^{(N-1)}& 0\\ 0& 0& 0& {\left({2\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}\right)}^{(N-1)}\end{array}\right)\&CenterDot;\\ {{\mathrm{<figure-callout\; id="2"\; label="r\; p"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_p}^2\left(\begin{array}{cccc}1+{\mathrm{\&epsiv;}}^2& 1-{\mathrm{\&epsiv;}}^2& 0& 0\\ 1-{\mathrm{\&epsiv;}}^2& 1+{\mathrm{\&epsiv;}}^2& 0& 0\\ 0& 0& 2\mathrm{\&epsiv;}& 0\\ 0& 0& 0& 2\mathrm{\&epsiv;}\end{array}\right)\&CenterDot;\\ A^{N-1}\left(\begin{array}{cccc}{\cos }^{4(N-1)}\mathrm{\&alpha;}+1& {\cos }^{4(N-1)}\mathrm{\&alpha;}-1& 0& 0\\ {\cos }^{4(N-1)}\mathrm{\&alpha;}-1& {\cos }^{4(N-1)}\mathrm{\&alpha;}+1& 0& 0\\ 0& 0& {\left({2\cos }^2\right)}^{(N-1)}& 0\\ 0& 0& 0& {\left({2\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}\right)}^{(N-1)}\end{array}\right)\left(\begin{array}{c}1\\ 0\\ 0\\ 0\end{array}\right)\end{array}$

The Stokes vector V of total reflected light _rfor: $V_r=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{V}_{\mathrm{ri}}={\mathrm{<figure-callout\; id="1"\; label="V\; r"\; filenames="HDA0000391322470000021.png,HDA0000391322470000031.png"\; state="\{\{state\}\}">V</figure-callout>}}_r+{\mathrm{<figure-callout\; id="2"\; label="V\; r"\; filenames="HDA0000391322470000012.png,HDA0000391322470000021.png"\; state="\{\{state\}\}">V</figure-callout>}}_r+...V_{\mathrm{rN}}$

The transmitted light Stokes vector of total reflected light after quarter-wave plate 2 and the first catoptron 3 enter wave-plate stack 1 again derived:

The Muller matrix M of the quarter-wave plate 2 that angle is 45 ° _{t (1/4)}(45 °) are:

the Muller matrix M of the first catoptron 3 _r(-) is: $M_r(-)=\left(\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& -1\end{array}\right)$

Total reflected light passes through quarter-wave plate 2, the first catoptron 3, quarter-wave plate 2 successively, again enters the transmitted light Stokes vector V after sheet pile 1 _rtn is: V _rtN=M _t ⁿm _{t (1/4}) M _r(-) M _{t (1/4}) _vr

Total Stokes vector:

Final total Stokes vector V _zong(not considering the reflection of last catoptron) again passes through the Stokes vector V of wave-plate stack 1 after conversion for total reflected light _rtNstokes vector V with transmitted light _tNsum, that is:

$\begin{array}{c}{V}_{\mathrm{zong}}=V_{\mathrm{rtN}}+V_{\mathrm{tN}}\\ ={M_t}^N{M}_{t(1/4)}{M}_r(-)M_{t(1/4)}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{V}_{\mathrm{ri}}+{M_t}^N*V\\ ={M_t}^N{M}_{t(1/4)}{M}_r(-)M_{t(1/4)}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left({M_t}^{(i=1)}{M}_r{M_t}^{(i=1)}V\right)+{M_t}^N*V\end{array}$

By V _zonfour component substitution formula of g:

can calculate total degree of polarization.

In Fig. 4,1 is the change curve of total degree of polarization with the wave plate number, the 2nd, and the degree of polarization of total reflected light is with the change curve of wave plate number, and the 3rd, the degree of polarization of transmitted light is with the change curve of wave plate number.As can be seen from Figure 4, along with the increase of wave plate number, each degree of polarization all increases, and finally trends towards 100%.And can find out, reflected light has very high degree of polarization by wave-plate stack 1 again, makes the degree of polarization of the relative transmitted light of total degree of polarization totally improve a lot.When reflected light not being used, only have the degree of polarization of transmitted light, 13 blocks of wave plates just can reach 99% degree of polarization, and, by apparatus of the present invention, after catoptrical degree of polarization is used, 11 blocks of wave plates just can make degree of polarization reach 99% degree of polarization.We can, according to the requirement to degree of polarization, select suitable wave plate number.

In Fig. 5, θ is refraction angle, and only the catadioptric light of the incident ray in two marginal rays as shown in Figure 5 (be incidence point must between an E, F) can be utilized fully.Consider marginal ray, suppose that wave-plate stack AB end length is L, gross thickness is d, beam effective diameter D, EF=L-2*d*tan θ, AG=L-2*d*tan θ, beam diameter D=EF*sin θ, the second catoptron 4 length A H=AG*tan θ, the length JK of quarter-wave plate 2 and the first catoptron equals beam diameter D, i.e. JK=D.By top derivation, can be obtained

and have

visible L and θ, d, D are relevant, and the length L of wave-plate stack 1 is by wave-plate stack material n ₂, wave-plate stack gross thickness d and beam diameter D determine.For non-marginal ray, provide the range of size of each device, beam effective diameter D≤EF*sin θ, the length A H of the second catoptron 4 >=AG*tan θ, the length JK of quarter-wave plate 2 and the first catoptron >=EF*sin θ.Due to

n ₁the refractive index of air, n ₂being the refractive index of material, is the attribute of material, and θ=90 °-θ _bthe size that can know beam diameter D, each device by inference is all relevant with the material of wave-plate stack.

Count N because can determine wave plate according to required degree of polarization, can be found out by top derivation, when wave plate is counted N mono-regularly, if the thickness of each piece wave plate

little, the gross thickness d of wave-plate stack 1 is little so, and beam diameter D is large, and the light that enters wave-plate stack 1 is many, and the light beam gross energy is large.So, when degree of polarization one timing, it is certain that wave plate is counted N, the gross energy of the outgoing beam of the thickness effect of each piece wave plate after wave-plate stack 1.

Those of ordinary skill in the art will be appreciated that, above embodiment is only for the present invention is described, and not be used as limitation of the invention, as long as in connotation scope of the present invention, the above embodiment is changed, and modification all will drop in the scope of the claims in the present invention book.

Claims (5)

1. a high-level efficiency polarization purification devices, it is characterized in that: described purification devices is by wave-plate stack (1), quarter-wave plate (2), the first catoptron (3) and the second catoptron (4) form, wave-plate stack (1) surface normal direction is from the horizontal by Brewster angle, quarter-wave plate (2) and the first catoptron (3) vertical reflection light direction are placed, reflection S polarized light passes through quarter-wave plate (2) successively, the first catoptron (3) and quarter-wave plate (2), convert the S polarized light to the P polarized light, the edge of the transmitted light direction at reflected light after wave-plate stack, vertical wave-plate stack (1) is placed the second catoptron (4).

2. high-level efficiency polarization purification devices according to claim 1, it is characterized in that: the position of quarter-wave plate (2) and the first catoptron (3) can be according to debuging needs, at vertical reflection light direction parallel.

3. high-level efficiency polarization purification devices according to claim 1 is characterized in that: quarter-wave plate (2) equates with the size AH of the first catoptron (3) size JK, the second catoptron (4) and all is more than or equal to beam diameter D, i.e. JK=AH >=D.

4. high-level efficiency polarization purification devices according to claim 1 is characterized in that: what wave-plate stack (1) adopted is fused quartz, or adopts CaF ₂, MgF ₂, the K9 ultraviolet can be saturating optical material.

5. high-level efficiency polarization purification devices according to claim 1, it is characterized in that: each size is determined relation:

l and θ, d, D are relevant, and the length L of wave-plate stack (1) is by wave-plate stack material n ₂, wave-plate stack gross thickness d and beam diameter D determine, according to the specific requirement to degree of polarization, can determine that required wave plate counts N, by wave-plate stack gross thickness d and wave plate, counts the thickness that N can determine each piece wave plate

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