EUV SPECTROSCOPIC POLARIMETER

Abstract

We have invented an EUV spectroscopic polarimeter including a light receiving element, a first polarizing modulation element, a second polarizing modulation element, an energy splitting element and a light detecting and analyzing apparatus. The light receiving element is for receiving a target light. The first polarizing modulation element is rotatably connected to the light receiving element for generating a first polarized light. The second polarizing modulation element is rotatably connected to the first polarizing modulation element for generating a second polarized light. The energy splitting element receives the second polarized light so as to generate a modulated-polarization and energy-resolved light. The light detecting and analyzing apparatus receiving the polarization-modulated and energy-resolved light and providing a spectrum information by an analyzing algorithm which is able to retrieve the helicity, ellipticity, tilt angle and the degree of polarization for the whole spectrum of the target light.

Claims

1. An EUV spectroscopic polarimeter, which is operated in a vacuum-based environment, comprising: a light entrance for receiving a target light; a first polarizing modulation element rotatably connected to the light entrance, wherein the target light passes through the first polarizing modulation element so as to generate a first polarized light; a second polarizing modulation element rotatably connected to the first polarizing modulation element, wherein the first polarized light passes through the second polarizing modulation element so as to generate a second polarized light; dispersive element receiving the second polarized light so as to generate a polarization-modulated and wavelength-resolved light; and a light detecting and analyzing apparatus receiving the polarization-modulated and wavelength-resolved light and providing a spectrum information, wherein the spectrum information comprises at least one energy information.

2. The EUV spectroscopic polarimeter of claim 1, wherein the first polarizing modulation element comprises: a vacuum chamber connected to the light entrance; at least one reflection member located in the vacuum chamber; and a motor for rotating the vacuum chamber or the at least one reflection member.

3. The EUV spectroscopic polarimeter of claim 2, wherein a number of the at least one reflection member of the first polarizing modulation element is three.

4. The EUV spectroscopic polarimeter of claim 2, wherein the second polarizing modulation element comprises: a vacuum chamber connected to the vacuum chamber of the first polarizing modulation element; at least one reflection member located in the vacuum chamber of the second polarizing modulation element; and a motor for rotating the vacuum chamber of the second polarizing modulation element or the at least one reflection member of the second polarizing modulation element.

5. The EUV spectroscopic polarimeter of claim 4, wherein a number of the at least one reflection member of the second polarizing modulation element is three.

6. The EUV spectroscopic polarimeter of claim 4, wherein each of the at least one reflection member of the first polarizing modulation element and the at least one reflection member of the second polarizing modulation element is a gold mirror.

7. The EUV spectroscopic polarimeter of claim 1, wherein the dispersive element is a grating.

8. The EUV spectroscopic polarimeter of claim 1, wherein the dispersive element is a prism.

9. The EUV spectroscopic polarimeter of claim 1, wherein the target light is EUV or soft X-ray beams.

10. The EUV spectroscopic polarimeter of claim 1, wherein the light detecting and analyzing apparatus provides wavelength-resolved Stoke parameters.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0007] FIG. 1 shows a schematic view of an EUV spectroscopic polarimeter according to one embodiment of the present disclosure.

[0008] FIG. 2 is a schematic view of the first polarizing modulation element and a horizontal plane according to the embodiment of FIG. 1.

[0009] FIG. 3 shows the polarization states at the four photon energies of the target light depicted in the polar plots.

[0010] FIG. 4 shows polarization states of the target light measured by the EUV spectroscopic polarimeter (Retrieval) according to FIG. 1 and an EUV polarizor result (Polarizor).

DETAILED DESCRIPTION

[0011] FIG. 1 shows a schematic view of an EUV spectroscopic polarimeter 100 according to one embodiment of the present disclosure. In FIG. 1, the EUV spectroscopic polarimeter 100 includes a light receiving element 110, a first polarizing modulation element 120, a second polarizing modulation element 130, an energy splitting element 140 and a light detecting and analyzing apparatus 150. The light receiving element 110 is for receiving a target light. The first polarizing modulation element 120 is rotatably connected to the light receiving element 110, wherein the target light passes through the first polarizing modulation element 120 so as to generate a first polarized light. The second polarizing modulation element 130 is rotatably connected to the first polarizing modulation element 120, wherein the first polarized light passes through the second polarizing modulation element 130 so as to generate a second polarized light. The energy splitting element 140 receives the second polarized light so as to generate a polarization-modulated and energy-resolved light. The light detecting and analyzing apparatus 150 receives the polarization-modulated and energy-resolved light and providing a spectrum information, wherein the spectrum information includes at least one energy information. Therefore, the EUV spectroscopic polarimeter 100 can measure the polarization properties of wide bandwidth light simultaneously so as to increase the measuring speed.

[0012] In detail, the target light can be EUV or soft X-ray beams, but will not be limited thereto.

[0013] The first polarizing modulation element 120 can include a vacuum chamber 121, at least one reflection member and a motor 123, wherein, according to the embodiment of FIG. 1, a number of the at least one reflection member of the first polarizing modulation element 120 is three, which are reflection members 122a, 122b, 122c, but the present disclosure will not be limited thereto. The vacuum chamber 121 is connected to the light receiving element 110, the reflection members 122a, 122b, 122c are located in the vacuum chamber 121. The motor 123 is for rotating the vacuum chamber 121 or the at least one reflection member; specifically, according to the embodiment of FIG. 1, the motor 123 is for rotating the vacuum chamber 121, but the present disclosure will not be limited thereto. Further, each of the reflection members 122a, 122b, 122c can be gold mirrors, but the present disclosure will not be limited thereto.

[0014] The second polarizing modulation element 130 can include a vacuum chamber 131, at least one reflection member and a motor 133, wherein, according to the embodiment of FIG. 1, a number of the at least one reflection member is three, which are reflection members 132a, 132b, 132c, but the present disclosure will not be limited thereto. The vacuum chamber 131 is connected to the vacuum chamber 121 of the first polarizing modulation element 120. The reflection members 132a, 132b, 132c are located in the vacuum chamber 131 of the second polarizing modulation element 130. The motor 133 is for rotating the vacuum chamber 131 of the second polarizing modulation element 130 or the at least one reflection member of the second polarizing modulation element 130; specifically, according to the embodiment of FIG. 1, the motor 133 is for rotating the vacuum chamber 131 of the second polarizing modulation element 130. Further, each of the reflection members 132a, 132b, 132c can be gold mirrors, but the present disclosure will not be limited thereto.

[0015] According to the embodiment of FIG. 1, the energy splitting element 140 is a grating, and is made of gold coating. However, in other embodiments of the present disclosure, the energy splitting element 140 can be any diffraction element, such as prisms and gratings, and the present disclosure will not be limited thereto.

[0016] According to the arrangement of the light receiving element 110, the first polarizing modulation element 120, the second polarizing modulation element 130 and the energy splitting element 140, the polarization of the target light can be modulated, so that the light detecting and analyzing apparatus 150 can provide the spectrum information of the target light, and also resolve their polarization informations (energy-resolved polarization informations). Each energy information can include the ellipticity (the ratio of the minor axis to the major axis of elliptically polarized light), the helicity (left-handed or right-handed circular polarization), the tilt angle, and the degree of polarization (energy portion of pulses that is polarized) of the target light. In the meanwhile, both amplitude and phase modulations given by the first polarizing modulation element 120 and the second polarizing modulation element 130, together with the amplitude modulation of the energy splitting element 140 between s-polarization and p-polarization can be solved simultaneously.

[0017] The light detecting and analyzing apparatus 150 can provide polarization states, Stoke parameters, for whole spectrum, that is, the light detecting and analyzing apparatus 150 can provide spectrum and also their polarization states according to the nine parameters (the nine unknowns), which are four Stoke parameters of the target light, an amplitude modulation of the first polarizing modulation element 120, a phase retarder of the first polarizing modulation element 120, an amplitude modulation of the second polarizing modulation element 130, a phase retarder of the second polarizing modulation element 130, and an amplitude modulation of the energy splitting element 140. Please refer to FIG. 2, which is a schematic view of the first polarizing modulation element 120 and a horizontal plane X according to the embodiment of FIG. 1. In detail, in FIG. 1 and FIG. 2, due to the independent rotating structure (the motors 123, 133) of the first polarizing modulation element 120 and the second polarizing modulation element 130, the first polarizing modulation element 120 can be rotated along a rotating direction α, the second polarizing modulation element 130 can be rotated along a rotating direction β, and the rotating angles can be defined as the angle of each of the first polarizing modulation element 120 and the second polarizing modulation element 130 respective to the horizontal plane X.

[0018] In one example of the embodiment of FIG. 1, the photon energies of the target light are 23 eV, 26 eV, 29 eV and 32 eV, and each of the first polarizing modulation element 120 and the second polarizing modulation element 130 provides four angles, so that 16-(α,β) combinations are applied, such as (0, 0), (0, π/4), (0, π/2), (0, 3π/4), (π/ 4, 0), (π/4, π/4), (π/4, π/2), (π/4, 3π/4), (π/2, 0) (π/2, π/4), (π/2, π/2), (π/2, 3π/4), (3π/4, 0), (3π/4, π/4), (3π/4, π/2), and (3π/4, 3π/4).

[0019] Each of the Stoke parameters of the target light is S.sub.in. After the target light passing through the first polarizing modulation element 120, the second polarizing modulation element 130 and the energy splitting element 140, the light detecting and analyzing apparatus 150 can provide the Stoke vector of the output target light S.sub.out as the formulas (1), (2) and (3).

[00001]$\begin{array}{cc}{S}_{\mathrm{out}}=M\left({\gamma }_3,{\Delta }_3\right)R\left(\beta \right)M\left({\gamma }_2,{\Delta }_2\right)R\left(-\beta \right)R\left(\alpha \right)M\left({\gamma }_1,{\Delta }_1\right)R\left(-\alpha \right)S_{in};& \left(1\right)\\ M\left(\gamma ,\Delta \right)=\left[\begin{array}{cccc}1& \cos 2\gamma & 0& 0\\ \cos 2\gamma & 1& 0& 0\\ 0& 0& \sin 2\gamma \cos \Delta & -\sin 2\mathrm{\gamma cos}\Delta \\ 0& 0& \sin 2\mathrm{\gamma sin}\Delta & \sin 2\mathrm{\gamma cos}\Delta \end{array}\right];\mathrm{and}& \left(2\right)\\ R\left(\theta \right)=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos 2\theta & \sin 2\theta & 0\\ 0& -\sin 2\theta & \cos 2\theta & 0\\ 0& 0& 0& 1\end{array}.\right]& \left(3\right)\end{array}$

[0020] Wherein M is Mueller matrix defined to transform the incident Stoke vector into the exiting Stoke vector, R is rotation matrix, γ.sub.1 is the amplitude modulation of the first polarizing modulation element 120, γ.sub.2 is the amplitude modulation of the second polarizing modulation element 130, γ.sub.3 is the amplitude modulation of the energy splitting element 140, Δ.sub.1 is the phase retarder of the first polarizing modulation element 120, Δ.sub.2 is the phase retarder of the second polarizing modulation element 130, α and β are the angles of the first polarizing modulation element 120 and the second polarizing modulation element 130, respectively.

[0021] After expanding the whole matrix chains, S.sub.out can be obtained as the formula (4):

[00002]$\begin{array}{cc}\begin{array}{c}{S}_{\mathrm{out}}=S_0=K\times F\left(S_1/S_0,S_2/S_0,S_3/S_0,{\gamma }_1,{\gamma }_2,{\gamma }_3,{\Delta }_1,{\Delta }_2;\alpha ,\beta \right),\\ =K+\cos 2{\gamma }_3\{\left(\cos 2\beta \sin 2\beta -\cos 2\beta \sin 2\beta \sin 2{\gamma }_2\cos {\Delta }_2\right)\times \\ [S_1/S_0\left(\cos 2\alpha \sin 2\alpha -\cos 2\alpha \sin 2\alpha \sin 2{\gamma }_1\cos {\Delta }_1\right)+\\ K\sin 2\alpha \cos 2{\gamma }_1+S_2/S_0\left[{\left(\sin 2\alpha \right)}^2+{\left(\cos 2\alpha \right)}^2\sin 2{\gamma }_1\cos {\Delta }_1\right]-\\ S_3/S_0\cos 2\alpha \sin 2{\gamma }_1\sin {\Delta }_1]+[{\left(\cos 2\beta \right)}^2+{\left(\sin 2\beta \right)}^2\left(\sin 2{\gamma }_2\cos {\Delta }_2\right]\times \\ [K\cos 2\alpha \cos 2{\gamma }_1+S_2/S_0\left[\cos 2\alpha \sin 2\alpha -\cos 2\alpha \sin 2\alpha \sin 2{\gamma }_1\cos {\Delta }_1\right]+\\ S_1/S_0\left[{\left(\cos 2\alpha \right)}^2+{\left(\sin 2\alpha \right)}^2\sin 2{\gamma }_1\cos {\Delta }_1\right]+S_3/S_0\sin 2\alpha \sin 2{\gamma }_1\sin {\Delta }_1]+\\ \cos 2\beta \cos 2{\gamma }_2\left[K+S_1/S_0\cos 2\mathrm{\alpha cos}2{\gamma }_1+S_2/S_0\sin 2\mathrm{\alpha cos}2{\gamma }_1\right]+\\ \sin 2\mathrm{\beta sin}2{\gamma }_2\sin {\Delta }_2[S_3/S_0\sin 2{\gamma }_1\cos {\Delta }_1+S_2/S_0\cos 2{\mathrm{\alpha sin2\gamma }}_1\sin {\Delta }_1-\\ S_1/S_0\sin 2\mathrm{\alpha sin}2{\gamma }_1\sin {\Delta }_1]\}+\cos 2\beta \cos 2{\gamma }_2\{K\cos 2\alpha \cos 2{\gamma }_1+\\ S_2/S_0\left(\cos 2\alpha \sin 2\alpha -\cos 2\alpha \sin 2\alpha \sin 2{\gamma }_1\cos {\Delta }_1\right)+\\ S_1/S_0\left[{\left(\cos 2\alpha \right)}^2+{\left(\sin 2\alpha \right)}^2\sin 2{\gamma }_1\cos {\Delta }_1\right]+S_3/S_0\sin 2\alpha \sin 2{\gamma }_1\cos {\Delta }_1\}+\\ \sin 2\beta \cos 2{\gamma }_2\{S_1/S_0\left(\cos 2\alpha \sin 2\alpha -\cos 2\alpha \sin 2\alpha \sin 2{\gamma }_1\cos {\Delta }_1\right)+\\ K\sin 2\alpha \cos 2{\gamma }_1+S_2/S_0\left[{\left(\sin 2\alpha \right)}^2+{\left(\cos 2\alpha \right)}^2\sin 2{\gamma }_1\cos {\Delta }_1\right]-\\ S_3/S_0\cos 2\alpha \sin 2{\gamma }_1\sin {\Delta }_1\}+S_1/S_0\cos 2\alpha \cos 2{\gamma }_1+S_2/S_0\sin 2\alpha \cos 2{\gamma }_1;\end{array}& \left(4\right)\end{array}$

where K is a constant of the broadband EUV spectroscopic polarimeter 100. Thus, there are nine unknowns, K, S.sub.1/S.sub.0, S.sub.2/S.sub.0, S.sub.3/S.sub.0, γ.sub.1, γ.sub.2, γ.sub.3, Δ.sub.1, Δ.sub.2, and nine different equations by changing the angle α of the first polarizing modulation element 120 and the β of the second polarizing modulation element 130 are needed to solve the nine unknowns. In addition, an energy splitting element 140 and a light detecting and analyzing apparatus 150 obtain the spectrum. According to the example, 16-(α, β) combination angles of (0, 0), (0, π/4), (0, π/2), (0, 3π/4), (π/4,0), (π/4, π4), (π/4, π/2), (π/4, 3π/4), (π/2, 0), (π/2, π/4), (π/2, π/2), (π/ 2, 3π/4), (3π/4, 0), (3π/4, π/4), (3π/4, π/2), and (3π/4, 3π/4) respective to the horizontal plane X are selected.

[0022] Nine equations are applied to the genetic algorithm to minimize the deviation between those 16-(α, β) theoretical values by using equation (4) and the experimental observations. Hence, the Stoke parameters S.sub.1, S.sub.2, S.sub.3 can be solved by the above 16 equations, so as to further calculate the ellipticity ϵ the degree of polarization p, and the tilt angle θ as the formulas (5), (6) and (7):

[00003]$\begin{array}{cc}\mathrm{.Math.}=\tan \left[\frac{1}{2}a\tan \left(\frac{S_3}{\sqrt{S_1^2+S_2^2}}\right)\right];& \left(5\right)\\ p=\frac{\sqrt{S_1^2+S_2^2+S_3^2}}{S_0};\mathrm{and}& \left(6\right)\\ \theta =\frac{1}{2}\mathrm{atan}\left(\frac{S_2}{S_1}\right).& \left(7\right)\end{array}$

[0023] Please refer to FIG. 3 and Table 1, wherein FIG. 3 represents the polarization states of the four photon energies of the target light depicted in the polar plots, and Table 1 is the polarization information of each of the photon energies of the target light which are characterized by the light detecting and analyzing apparatus 150.

TABLE-US-00001 TABLE 1 Photon Degree of energy Tilt angle polarization (eV) Helicity Ellipticity (degrees) (%) 23 R 0.761 −8.8 100.9 26 R 0.72 −18.9 100.2 29 R 0.663 −25.2 85 32 R 0.584 −29.2 81.3

[0024] According to the FIG. 3 and Table 1, it is known that the EUV spectroscopic polarimeter 100 can provide energy-resolved polarization information of the target light.

[0025] FIG. 4 shows polarization states of the target light (EUV) measured by an EUV polarizer (Polarizor mode), and the broadband EUV spectroscopic polarimeter 100 (Retrieval mode) according to FIG. 1. For the validity confirmation of the energy-resolved polarimeter, a comparison was made by delivering two individual experiments. The first experiment (Polarizor mode) is to record the transmission of EUV light in one certain rotating sequence of α and β. In this example, we sample 24 points of the transmission of 32 eV light source by rotating two chambers incrementally in 360 degrees at the condition of α=β. The solid line in FIG. 4 presents the EUV transmission as a function of the rotating angle α. The following second experiment (Retrieval mode) is delivered to measure the EUV transmissions at the 16-(α, β) combinations of [0, 0], [0, π/4], [0, π/2], [0, 3π/4], [π/4,0], [π/4, π/4], [π/4, π/2], [π/4,3π/4], [π/2,0], [π/2, π/4], [π/2, π/2], [π/2,3π/4], [3π/4, 0], [3π/4, π/4], [3π/4, π/2] and [3π/4,3π/4]. Then listing these 16 equations based on equation (4), we solve and retrieve the polarization state of the 32 eV light source using a genetic algorithm, while also obtaining all unknowns parameters of amplitude and phase modulations from two rotating sets, and the amplitude modulation of the EUV grating between s- and p-polarizations. Based on those retrieval parameters, the dashed line is generated from the Mueller matrix calculation (equation (1)), following the angle sequence of the first experiment, in which α=β. Two curves match with each other very well in the polar diagram, directly proving the validity of the energy-resolved EUV polarimeter.

[0026] Hence, according to the present disclosure, the EUV spectroscopic polarimeter can be taken as an energy-resolved polarimeter, which includes two rotatable sets of reflective polarizer (that is, the first polarizing modulation element and second polarizing modulation element) and one diffraction element (that is, energy splitting element), has extended the spectral range of the EUV spectroscopic polarimeter to the EUV and soft X-ray spectral region with unprecedented sensitivity because of their short wavelengths.

[0027] Although the present disclosure has been described in considerable detail with reference to certain embodiments thereof, other embodiments are possible. Therefore, the spirit and scope of the appended claims should not be limited to the description of the embodiments contained herein.

[0028] It will be apparent to those skilled in the art that various modifications and variations can be made to the structure of the present disclosure without departing from the scope or spirit of the disclosure. In view of the foregoing, it is intended that the present disclosure covers modifications and variations of this disclosure provided they fall within the scope of the following claims.