JP6632059B2 - Polarimetry apparatus and polarization measurement method using dual-com spectroscopy - Google Patents

Description

  The present invention relates to a polarization measurement device and a polarization measurement method using dual-com spectroscopy.

  In the field of chemistry or life science, a circular dichroism dispersometer is used to identify the configuration of an optical isomer of a molecule. Although optical isomers of a molecule cannot be identified by ordinary spectrum measurement, identification is possible by using a circular dichroism dispersometer utilizing a difference in change in polarization information.

  As a circular dichroism dispersometer, a circular dichroism dispersometer in which a photoelastic modulator (PEM) is incorporated in a monochromator or a Fourier transform infrared (FTIR) spectrometer is known (for example, see Patent Document 1). .

  In recent years, Dual Comb spectroscopy has attracted attention in the near-infrared and mid-infrared frequency regions. The dual-com spectroscopy is a technique for performing high-accuracy and high-speed spectroscopic measurement using an interference signal of two femtosecond lasers having slightly different repetition frequencies (for example, see Patent Document 2). Compared to FTIR spectrometry using an incoherent lamp light source, dual-com spectroscopy has higher frequency resolution and shorter measurement time.

JP 2012-202812 A U.S. Patent Application Publication No.US 2011/0069309 A1

  High-resolution and high-speed dual-com spectroscopy is expected as a technology that will replace FTIR spectroscopy in the future. However, there is no report on precise polarization measurement by dual-com spectroscopy.

  Therefore, it is an object of the present invention to provide a new configuration and method of polarization measurement using dual-com spectroscopy.

In order to solve the above problems, a first aspect of the present invention provides a polarization measuring device. Polarimeter is
A first optical frequency comb light source having a first repetition frequency;
A second optical frequency comb light source having a second repetition frequency;
A modulation element that is arranged on the light exit side of the sample on the optical path of the first optical frequency comb light source and that periodically modulates a polarization state;
Means for polarization-modulating the modulation element with a modulation frequency that is a fractional multiple of the repetition frequency difference between the first optical frequency comb light source and the second optical frequency comb light source;
Light output from the first optical frequency comb light source and transmitted through the sample and the modulation element, and a detector that detects interference light of light output from the second optical frequency comb light source;
An analyzer that measures a polarization state of light transmitted through the sample based on the interference light,
Having.

As a second aspect of the present invention, a polarization measurement method is provided. The polarization measurement method is
A first optical frequency comb light source having a first repetition frequency and a second optical frequency comb light source having a second repetition frequency constitute a light source for dual comb spectrometry,
Irradiating the sample with output light from the first optical frequency comb light source;
A modulation element, which is arranged on the emission side of the sample and periodically modulates a polarization state, is modulated at a modulation frequency that is a fractional multiple of a repetition frequency difference between the first optical frequency comb light source and the second optical frequency comb light source. Polarization modulated,
Detecting output light from the first optical frequency comb light source transmitted through the sample and the modulation element, and interference light of light output from the second optical frequency comb light source,
Measuring a polarization state of light transmitted through the sample based on the interference light.

  With the above configuration and method, high-speed and high-resolution polarization measurement is realized.

It is a schematic diagram of a polarization measuring device of an embodiment using dual-com spectroscopy. 6 is a modified example of the polarization measurement device of FIG. 9 is another modification of the polarization measurement device of FIG. 1. It is a figure which represents the polarization state of sample transmission light mathematically. It is a figure explaining the basic concept of an optical frequency comb. FIG. 2 is a conceptual diagram of polarization measurement by the dual-comb spectroscopy of FIG. 1. It is a figure explaining the principle of dual-comb spectroscopy seen in a time domain. FIG. 3 is a schematic diagram of a spectrum of an interference signal detected by the configuration of the embodiment. FIG. 4 is a schematic diagram of a spectrum in a frequency domain when ω = (6/5) Δfr, and shows a case where light transmitted through a sample is elliptically polarized light. FIG. 4 is a schematic diagram of a spectrum in a frequency domain when ω = (6/5) Δfr, and shows a case where light transmitted through a sample is linearly polarized light. The spectrum in the frequency domain when ω = (6/5) Δfr is also a schematic diagram, and shows a case where the light transmitted through the sample is circularly polarized light. FIG. 3 is a diagram of an optical system used for a verification experiment. It is a measurement result of the interference signal when the sample transmitted light is linearly polarized light. It is a measurement result of the interference signal when the sample transmitted light is elliptically polarized light. It is a measurement result of the interference signal when the sample transmitted light is elliptically polarized light close to circularly polarized light. It is a measurement result of the interference signal when the sample transmitted light is circularly polarized light. FIG. 11 is a diagram in which Stokes parameters when rotated using a quarter-wave plate as a substitute for a sample are plotted on a Poincare sphere. It is a power spectrum of an interference signal when rotated using a half-wave plate as a substitute for a sample. It is the figure which plotted the Stokes parameter at the time of rotating using the half wave plate as a substitute of a sample on a Poincare sphere.

An embodiment of the present invention will be described below with reference to the drawings.
<Apparatus configuration>
FIG. 1 is a schematic diagram of a polarization measuring device 10A using dual-com spectroscopy. The polarization measuring device 10A of the embodiment has a signal comb 11 as a first optical frequency comb light source and a local comb 12 as a second optical frequency comb light source.

  The signal comb 11 and the local comb 12 use femtosecond lasers having slightly different repetition frequencies. Assuming that the repetition frequency of the signal comb 11 is fr, the repetition frequency of the local comb 12 is described as fr-Δfr. Here, Δfr is a repetition frequency difference between two femtosecond lasers. As an example, both the signal comb 11 and the local comb 12 have a repetition frequency near 48 MHz, and the difference (Δfr) is 70 Hz. The signal comb 11 and the local comb 12 are collectively referred to as a “dual-com light source” for convenience.

  In the configuration example of FIG. 1, the light output from the signal comb 11 is superimposed on the output light from the local comb 12 by the mirror 19 and the polarizing beam splitter (PBS) 13. The sample (sample) 20 is irradiated with the superimposed light, and the light transmitted through the sample 20 is detected by the detector 21 through the rotation compensator 15.

  As a feature of the polarization measurement device 10A, a modulation element that periodically modulates the polarization state is disposed immediately after the emission surface of the sample 20. The modulation element is, for example, a rotation compensator 15 that optically rotates the direction of polarized light. As the rotation compensator 15, a quarter-wave plate can be used. In the following example, the rotation compensator 15 is used as a modulation element, but any element or mechanism may be used as long as the polarization state can be periodically modulated at a modulation frequency that is a fractional multiple of the repetition frequency difference between the two optical frequency comb light sources. Can be. For example, the polarization state may be periodically modulated using an element that electrically controls polarization, such as an electro-optic modulator or a photoelastic modulator.

  The rotation frequency of the rotation compensator 15 is controlled by the rotation control unit 25 so as to satisfy a predetermined condition. Specifically, the rotation frequency of the rotation compensator 15 is controlled so as to be a fractional multiple (1/10, 6/5, etc.) of the repetition frequency difference Δfr of the dual comb light source. The value of the fraction is selected to satisfy certain conditions, as described below.

When the value of the fraction is 6/5, the rotation frequency ω of the rotation compensator 15 is
ω = (6/5) Δfr
Is described. Here, ω is a frequency described in units of “Hz”, and can be converted, though distinguished from an angular frequency expressed in radians. When the repetition frequency difference Δfr is 70 Hz, the rotation frequency ω of the rotation compensator 15 is 84 Hz.

  What is detected by the detector 21 is the interference light of the light from the signal comb 11 transmitted through the sample 20 and the rotation compensator 15 and the light from the local comb 12. In general, radio frequency (microwave frequency) combs are regularly detected as interference light at intervals of Δfr in the frequency domain.

  In the embodiment, the rotation between the signal comb 11 and the local comb 12 is modulated by inserting a rotation compensator 15 rotating at a rotation frequency that is a fractional multiple of Δfr on the emission surface side of the sample 20 and modulating the polarization of the sample transmitted light. A new comb component containing information on the polarization state of light transmitted through the sample 20 is detected between the combs as signals. The details of the detection of this new comb component will be described later.

  The polarization measurement device 10A further includes a first polarizer (P1) 14 disposed on the incident side of the sample and a second polarizer (P2) 16 disposed on the output side of the rotation compensator 15. The first polarizer 14 adjusts light incident on the sample 20 to linearly polarized light. When the output light of the signal comb 11 and the output light of the local comb 12 are adjusted to linearly polarized light in advance, the first polarizer 14 does not necessarily need to be used.

  The second polarizer 16 adjusts light incident on the detector 21 to linearly polarized light. When the detector 21 has the capability of detecting linearly polarized light, the second polarizer 16 does not necessarily have to be used.

  The output of the detector 21 is connected to the analyzer 30. The analysis device 30 includes a comb analysis unit 31 and a polarization state calculation unit 32. The comb analyzer 31 analyzes the magnitude and phase of a new comb component appearing between the interference signals of the signal comb 11 and the local comb 12. The polarization state calculator 32 calculates the polarization state of the light transmitted through the sample 20 from the magnitude and phase of the newly appearing comb component. The method of calculating the polarization state will also be described later.

  The polarization state includes the type of polarization (circularly polarized light, linearly polarized light, or elliptically polarized light) and the direction of polarization (clockwise, counterclockwise, or linear direction), and is represented by, for example, (Δ, Ψ). The parameter Δ is the phase difference between the photoelectric field vector components orthogonal to each other, and represents the type of polarization. The parameter Ψ is a declination from a reference axis (eg, the y-axis), and thereby represents the direction of polarization. The analysis device 30 that analyzes the comb component and calculates the polarization state can be realized by, for example, a personal computer (PC).

  FIG. 2 shows a polarization measurement device 10B as a modification of FIG. The same components as those in FIG. 1 are denoted by the same reference numerals, and redundant description will be omitted.

  In the polarization measuring device 10B, only the output light from the signal comb 11 is incident on the sample 20, and the output light from the signal comb 11 after passing through the sample and the output light from the local comb 12 are superimposed on each other. Lead.

  More specifically, the output light of the signal comb 11 transmitted through the first polarizer 14 and the sample 20 is superimposed on the output light of the local comb 12 using the mirror 19 and the PBS 13. The output light of the local comb 12 is adjusted to linearly polarized light by the third polarizer (P3) 17 before entering the PBS 13. The light superimposed by the PBS 13 passes through the rotation compensator 15. As in FIG. 1, the rotation frequency ω of the rotation compensator 15 is controlled by the rotation control unit 25 to be a fractional multiple of the repetition frequency difference Δfr. The output light of the rotation compensator 15 is detected by the detector 21 via the second polarizer 16. The output of the detector 21 is input to the analyzer 30 and the polarization state (Δ, Ψ) of the transmitted light of the sample 20 is measured.

  FIG. 3 shows a polarization measurement device 10C as still another modification. The same components as those in FIG. 1 are denoted by the same reference numerals, and redundant description will be omitted.

  In the polarization measurement device 10C, only the output light from the signal comb 11 passes through the sample 20 and the rotation compensator 15. On the optical path of the signal comb 11, a first polarizer 14, a sample 20, a rotation compensator 15, and a second polarizer 16 are arranged in this order. 1 and 2, the rotation frequency ω of the rotation compensator 15 is controlled by the rotation control unit 25 to be a fractional multiple of the repetition frequency difference Δfr.

  The light from the signal comb 11 that has passed through the sample 20 and the rotation compensator 15 and has been adjusted to linearly polarized light by the second polarizer 16 is superimposed on the output light of the local comb 12 by the mirror 19 and the PBS 13. The output light of the local comb 12 is adjusted to linearly polarized light by the third polarizer (P3) 17 before entering the PBS 13. Light superimposed by the PBS 13 is detected by the detector 21. The output of the detector 21 is input to the analyzer 30 and the polarization state (Δ, Ψ) of the transmitted light of the sample 20 is measured.

  1 to 3, the output light of the signal comb 11 transmitted through the sample 20 is detected through the rotation compensator 15 whose rotation frequency is controlled to be a fractional multiple of the repetition frequency difference Δfr. As described below, the polarization state of the light transmitted through the sample 20 can be measured at high speed and with high accuracy by looking at the Fourier coefficient of a new comb component appearing between the interference signals regularly arranged in the detection light. .

The optical element for superimposing the light from the signal comb 11 and the light from the local comb 12 is not limited to the PBS, and a coupler or the like may be used.
<Principle of the present invention>
Next, the principle of the present invention will be described.

FIG. 4 is a diagram that mathematically represents the polarization state of the transmitted light of the sample 20. Consider a case where light passes through the sample 20 toward the front side (z direction) of the paper surface. The component of the photoelectric field vector transmitted through the sample 20 in the x-axis direction is defined as Ex, and the component in the y-axis direction is defined as Ey. Ex and Ey are usually
Ex = E _xo exp (iδx)
Ey = E _yo exp (iδy)
Is represented by Linear polarized light is a light that travels without vibrating at the same frequency in a state where there is no phase difference (Δ) between the initial phase δx of the Ex component and the initial phase δy of the Ey component. When the magnitudes of the Ex component and the Ey component are the same and there is a phase difference of π / 2 between δx and δy, the direction of the photoelectric field (composite vector) rotates along a circle when viewed in the xy plane. It becomes circularly polarized light. When the phase difference between δx and δy is other than 0 or π / 2, the light becomes elliptically polarized light. The angle between the direction of the photoelectric field (combined vector of Ex and Ey) and the y-axis is the declination (Ψ). In other words, the argument Ψ is an ellipticity angle measured from the y-axis direction.

  The polarization state of the transmitted light of the sample 20 is expressed by using two parameters (Δ, Ψ) of the phase difference Δ between the x-axis direction component (Ex) and the y-axis direction component (Ey) component of the photoelectric field and the deflection angle Ψ. Is done.

  FIG. 5 is a diagram illustrating the basic concept of the optical frequency comb. In the time domain, the ultrashort pulses output at the period Δt are arranged as a pulse train at intervals Δt on the time axis, as shown in the left diagram of FIG. When this pulse train is subjected to Fourier transform to obtain a spectrum in the frequency domain, an optical frequency train arranged at a constant interval fr is obtained as shown in the right diagram of FIG. Since the rows of optical frequencies are arranged like a "comb", they are called "optical frequency combs". The interval fr at which the comb is generated is the repetition frequency, and Δt and fr have an inverse relationship to each other.

The n-th frequency comb is represented by f (n) = f _CEO + n × fr, using the carrier envelope offset, ie, the starting frequency f _CEO .

  FIG. 6 is a conceptual diagram of the polarization measurement by the dual-com spectroscopy of FIG. Two lights having repetition frequencies different from each other by Δfr, that is, light from the signal comb 11 and light from the local comb 12 are superimposed by the mirror 19 and the PBS 13 and incident on the sample 20. The light transmitted through the sample 20 passes through the rotation compensator 15 that rotates at a rotation frequency ω that is a fractional multiple of the repetition frequency difference Δfr, and is detected by the detector 21. What is detected by the detector 21 is the interference light of the light from the signal comb 11 and the light from the local comb 12. The light from the signal comb 11 carries the polarization information received by passing through the sample 20. The light from the local comb 12 reads the spectral information of the sample 20 included in the light from the signal comb 11.

  In this example, the local light from the local comb 12 also passes through the sample 20, but since the signal comb 11 and the local comb 12 have very close repetition frequencies, it can be considered that the two lights undergo substantially the same change in the sample 20. . Therefore, the repetition frequency difference Δfr between the two lights is maintained, and the detector 21 properly detects the interference light.

  As shown in FIGS. 2 and 3, the polarization information of the sample contained in the light from the signal comb 11 may be read using the output light of the local comb 12 that does not pass through the sample 20.

  FIG. 7 is a diagram illustrating the principle of dual-comb spectroscopy viewed from the time domain. The signal comb 11 and the local comb 12 output pulses with a slight difference in repetition frequency. The pulse interval Δt of the signal comb 11 is equal to the reciprocal (1 / fr) of the repetition frequency fr. The pulse interval Δt ′ of the local comb 12 is equal to the reciprocal of the repetition frequency (1 / (fr−Δfr)).

  The detector 21 detects an interference signal U (t) between the signal comb 11 and the local comb 12. The interval between the interference signals U (t), that is, the time required from when the pulse of the signal comb 11 coincides with the pulse of the local comb 12 to the next coincidence is 1 / Δfr. In the dual-com spectroscopy, a resolution of fr is achieved in a measurement time of one cycle (1 / Δfr).

Let's replace this with the frequency domain. And _{n S-th} frequency comb signal comb 11, _{if n L-th} frequency comb of the local comb 12 are matched, the frequency difference is 0Hz, it appears as 0Hz signal at the detector 21. Similarly, the difference between the (n _S +1) -th frequency of the signal comb 11 and the (n _L +1) -th frequency of the local comb 12 is Δfr. This difference appears at the output of the detector 21 as a signal of Δfr. By repeating this, the interference signals U (t) of the signal comb 11 and the local comb 12 appear at intervals of Δfr in the radio frequency (or microwave frequency) region.

  As described above, in the dual-com spectroscopy, information on the optical frequency at fr intervals can be down-converted into information in the radio frequency domain at Δfr intervals.

  The present inventors combine the dual-comb spectroscopy of FIG. 7 with a polarization modulating means (for example, a rotation compensator 15 rotating at a rotation frequency of a certain condition) that satisfies a certain condition, so that the comb of the interference signal and the comb of the interfering signal are combined. In between, a new comb representing the polarization information of the sample 20 was found to stand.

  FIG. 8 is a schematic diagram of the spectrum of the interference signal detected by the configuration of the embodiment. This spectrum is a schematic diagram when the interference signal U (t) detected by the detector 21 is Fourier-transformed and viewed in the frequency domain. Here, the rotation frequency ω of the rotation compensator 15 is set to 1/10 (ω = Δfr / 10) of the repetition frequency difference Δfr between the signal comb 11 and the local comb 12.

  Focusing on the n-th oscillation mode, in addition to the comb signal Cn (nΔfr component) by the original dual-comb spectroscopy, new comb components a1, a2, b1, and b2 are located at nΔfr ± 2ω and nΔfr ± 4ω. Appears.

  When the state of the sample 20 indicates circular polarization, a new comb component a1 appears at a position ± 2ω from the original comb signal Cn.

  When the state of the sample 20 is linearly polarized light, new comb components b1 and b2 appear at positions ± 4ω from the comb signal Cn.

  When the sample 20 is elliptically polarized light, new comb components a1, a2, b1, and b2 appear at the positions of nΔfr ± 2ω and nΔfr ± 4ω because both the circularly polarized light component and the linearly polarized light component are included.

  By rotating the rotation compensator 15 at a rotation frequency that is a fractional multiple of the repetition frequency difference Δfr, a new comb component including the polarization information of the sample 20 is prevented from overlapping the comb signal Cn by the original dual-com spectroscopy. Control.

  Based on the position where the new comb component stands, it is possible to determine whether the sample 20 is circularly polarized light, linearly polarized light, or elliptically polarized light. As described later, the polarization state (Δ, Ψ) can be obtained by performing Fourier analysis on the interference signal U (t).

In order to separate and extract the four new comb components from the original comb signal Cn by dual comb spectroscopy, not only the four comb components a1, a2, b1, and b2 do not overlap each other, but also other comb signals. , For example, new comb components a4, b4, etc., generated in the adjacent comb signal C _{n + 1} need to be selected so as not to overlap.

For example, it half a + 2 [omega component of comb signal _{C n} of interest, there is a possibility that the overlap following four comb _{signal; C n + 1} of -2Omega _component, -2Omega component of _{C n + 2,} the _{C n + 3} - 4ω component, and + 4ω component of C _n−1 . That's 1/4, and + 2 [omega component of comb signal _{C n} of interest, there is a possibility that -2ω components of adjacent comb signal _{C n + 1} overlap. 1/10 times satisfies the condition that four newly appearing comb components can be extracted without overlapping. However, if the rotation frequency ω is 1/10 times Δfr, it may be difficult to sufficiently increase the measurement speed.

  On the other hand, if the rotation speed of the rotation compensator 15 is too high, the rotation of the rotation compensator 15 may become unstable. Therefore, as an example of a value that satisfies the condition that the rotation compensator 15 stably rotates and the four new comb components do not overlap, 6/5 is selected in the embodiment. This value is a value determined in consideration of the fact that the repetition frequency difference Δfr is about 70 Hz in the embodiment and that the upper limit of the frequency at which the motor used for rotating the rotation compensator 15 can rotate stably is about 100 Hz. It is. In this case, the rotation frequency ω is ω = (6/5) Δfr = 84 Hz.

  9 to 11 are schematic diagrams of the power spectrum in the frequency domain when the rotation frequency ω is (6/5) Δfr.

  FIG. 9 is a schematic diagram of a spectrum when light after passing through the sample is elliptically polarized light. For the n-th interference signal (com signal) Cn of interest, both the nΔfr ± 2ω component and the nΔfr ± 4ω component are detected.

  Since the rotation frequency ω is set to 6/5 times the repetition frequency difference Δfr, the position where the nΔfr ± 2ω component stands and the position where the nΔfr ± 4ω component stands are different from those in FIG. In FIG. 9, as indicated by the asterisk, the nΔfr ± 2ω component representing circularly polarized light appears outside the comb signal that is two away from the comb signal of interest Cn. The nΔfr ± 4ω component representing linearly polarized light appears outside the comb signal four distances from the comb signal of interest Cn.

  These four new comb components do not overlap with each other, nor do they overlap with the original dual-com spectroscopy comb signal. Also, it does not overlap with a new comb component generated in another comb signal.

  FIG. 10 is a schematic diagram of a spectrum in the case where the light after passing through the sample is linearly polarized light. In FIG. 10, only nΔfr ± 4ω components are detected. Similarly to FIG. 9, the nΔfr ± 4ω component indicated by the star appears outside the comb signal four away from the comb signal of interest Cn. This nΔfr ± 4ω component does not overlap with the comb signal by the original dual-com spectroscopy nor with a new comb component generated in another comb signal.

  FIG. 11 is a schematic diagram of a spectrum in the case where light after transmission through a sample is circularly polarized light. In FIG. 11, only nΔfr ± 2ω components are detected. Similarly to FIG. 9, the nΔfr ± 2ω component indicated by the star appears outside the comb signal two away from the comb signal of interest Cn. This nΔfr ± 2ω component does not overlap with the comb signal by the original dual-com spectroscopy or a new comb component generated in another comb signal.

When the rotation frequency of the rotation compensator 15 is ω = (6/5) Δfr, the correspondence between the original nΔfr component comb signal and the new comb representing polarization information is as follows:
± 2ω = ± (2 + 2/5) Δfr
± 4ω = ± (4 + 4/5) Δfr
It becomes. The circularly polarized information of the nΔfr comb signal Cn appears at a position of ± (2 + 2/5) Δfr counted from nΔfr. Similarly, information on the linear polarization of the nΔfr component comb signal Cn appears at a position of ± (4 + 4/5) Δfr, counting from the nΔfr component.

As described below, the polarization state of the sample transmitted light can be calculated from the magnitude and phase of the 2ω component and the 4ω component included in the detection light.
<Mathematical support>
As described above, the polarization state is represented by (Δ, Ψ). On the other hand, Stokes parameters S1 to S3 are used as quantities representing the polarization state. The Stokes parameter is represented by equation (0).

S1 = -cos2Ψ
S2 = sin2Ψ · cosΔ
S3 = −sin2Ψ · sinΔ (0)
In general, S3 = 0 for linearly polarized light and S1 = S2 = 0 for circularly polarized light.

  The optical electric fields of the signal comb 11 and the local comb 12 before passing through the sample 20 are expressed by Expressions (1) and (2), respectively.

Here, fr is the repetition frequency of the signal comb 11, f _CEO is the carrier envelope offset frequency of the signal comb 11, and φn is the phase of the signal comb 11. (Fr-.DELTA.fr) is the repetition frequency, f _'CEO local Com 12 carrier envelope offset frequency of the local comb 12, Fai'n is the phase of the local comb 12. Further, n _S and n _L are the first comb numbers of the signal comb signal and the local comb signal to be measured, respectively. The carrier envelope offset frequency between the signal comb 11 and the local comb 12 may be matched.

In general, the intensity I of the interference signal between the signal comb 11 and the local comb 12 is proportional to the square of the absolute value of the electric field obtained by adding E (t) and E ′ (t) (I∝ | E (t ) + E '(t) | ² ).

In embodiments, light transmitted through the sample 20 passes the rotation compensator (quarter wave plate) 15 and a second polarizer (P2) 16, subjected to intensity modulation E _A represented by the formula (3) (Fujiwara Hiroyuki, "Spectroscopic Ellipsometry", Maruzen Co., Ltd., pp. 91).

When the configuration of FIG. 1 is used, both the output light of the signal comb 11 and the output light of the local comb 12 pass through the sample 20, the rotation compensator 15, and the second polarizer 16. Accordingly, the light from the signal comb 11 and the local comb 12 each _E A * _E (t) and _E A * _E '(t) becomes, the interference signal at the detector 21 is detected. The interference signal U (t) detected by the detector 21 is
U (t) = <| E A E (t) + E A E '(t) | 2> = E A 2 <| E (t) + E' (t) | 2> and composed.

  This is expressed by Expression (4) using the Stokes parameters S1 to S3 of Expression (0).

Here, _{EnS + nE'nL + n} is the product of the amplitudes of the electric fields of the signal comb 11 and the local comb 12, and _{φnS + n-} φ'nL _{+ n} is the phase difference.

  As described above, when the sample 20 is linearly polarized light, S3 = 0, and when the sample 20 is circularly polarized light, S1 = S2 = 0. Substituting S1 = S2 = 0 into Equation (4) for circularly polarized light leaves nΔfr ± 2ω components. Substituting S = 0 into Equation (4) for linearly polarized light leaves nΔfr ± 4ω components. When the sample is elliptically polarized light, both nΔfr ± 2ω and nΔfr ± 4ω remain in equation (4). This principle matches the state schematically shown in FIG.

The value of U (t) can be obtained from the output of the detector 21. The value of Δfr is known. Although details are omitted, the Stokes parameters S1 to S3 can be obtained by the following procedures (1) to (5).
(1) | E _{ns + n} E ′ _{nL + n} S3 | is obtained from the amplitude of the nΔfr + 2ω component.
(2) When the phase of the corresponding nΔfr + 2ω component is subtracted from the phase of the nΔfr + 4ω component, the phase difference φ is obtained from the equation (4).
cosφ = S2 / (S1 ² + S2 ² ) ^1/2
sinφ = S1 / (S1 ² + S2 ² ) ^1/2
Becomes
φ = tan ⁻¹ (S1 / S2) = tan ⁻¹ (−cos2Ψ / sin2ΨcosΔ)
It is.
(3) The value obtained by multiplying the amplitude of the nΔfr + 4ω component by sinφ is (E _{ns + n} E ' _{nL + n} S1) / 2, and the value obtained by multiplying cos φ is (E _{ns + n} E' _{nL + n} S2) / 2 And
(4) | E _{ns + n} E ' _{nL + n} S3 |, (E _{ns + n} E' _{nL + n} S1) / 2, (E _{ns + n} E ' _{nL +} S1, S2, and S3 are determined by dividing _n S2) / 2 by | E _{ns + n} E ′ _{nL + n} | (S1 ² + S2 ² + S3 ² ) ^1/2 and normalizing the result.
(5) The sign of S3 is determined from a change in φ ′ (ie, the phase of the term of the nΔfr + 2ω component minus the phase of the nΔfr component). If there is a change of π or more, the sign of S3 is opposite to (1). It is also considered as necessary that φ has an indefiniteness of ± mπ / 2 (m is an integer).
When the Stokes parameters S1 to S3 are obtained, the polarization state (Δ, Ψ) can be obtained from equation (0).
<Verification experiment>
(1) Setup of Optical System FIG. 12 shows an optical system used in a verification experiment of the above-described principle. The configuration is basically the same as that of FIG. 1, and the same components are denoted by the same reference numerals, and redundant description will be omitted. The signal comb 11 and the local comb 12 are composed of erbium-doped fiber lasers, and the length of the resonator is controlled at high speed by an electro-optic modulator (EOM) to keep the line width of the comb at 1 Hz or less.

  The repetition frequency of the signal comb 11 is 48.35020 MHz, the repetition frequency of the local comb 12 is 48.35013 MHz, and the repetition frequency difference Δfr is about 70 Hz.

The signal comb 11 and the local comb 12 are controlled by the function generators 26 to 29 so that the beat frequency between the 1.54 μm stabilizing laser 23 and the comb having the mode number closest to the stabilizing laser 23 is 30 MHz. Also, the carrier envelope offset frequencies (f _CEO ) of the signal comb 11 and the local comb 12 are controlled by the function generators 28 and 29 so that the beat frequency becomes 30 MHz.

  Output light from the signal comb 11 is superimposed on output light from the local comb 12 by the mirror 19 and the PBS 13, and is incident on the sample 20 through the first polarizer 14. The first polarizer 14 is fixed at an angle of 45 °.

A quarter wave plate is used as the rotation compensator 15, and the rotation generator ω is controlled by a function generator as the rotation control unit 25 so that the rotation frequency ω becomes 1.2 times (6/5 times) the repetition frequency (Δfrep). I have. The light that has passed through the sample 20, the rotation compensator 15, and the second polarizer 16 is collected by a lens 18 into an input port (not shown) of a detector 21. The second polarizer 16 was set at an angle at which the detected power level was maximized when the second polarizer 16 was rotated with respect to the first polarizer 14 fixed at 45 °.
(2) Use of a quarter-wave plate as a sample A quarter-wave plate is arranged at the position of the sample 20 in FIG. 12 as a substitute for the sample. The quarter-wave plate is an optical element having a property of changing the polarization of incident light by using a difference in refractive index between the slow axis and the fast axis. By changing the angle θ of the 波長 wavelength plate as a sample, the polarization state of incident light can be converted into circularly polarized light or linearly polarized light. That is, it is possible to simulate the change in the polarization of the incident light received by a sample such as a biomolecule.

  The optical system shown in FIG. 12 is adjusted so as to be linearly polarized light when the angle θ of the 波長 wavelength plate as a sample is θ = 48 °, and circularly polarized light when θ = 93 °. When the angle θ of the 波長 wavelength plate is 48 °, light is considered to be incident along the fast axis (or the slow axis).

  The quarter-wave plate as a sample is rotated 180 ° from the position of θ = 48 ° in increments of 5 °. At each angle, an interference waveform (interferogram) is taken for 15 pulses.

  In the ordinary dual-com spectroscopy, if an interferogram for one pulse is recorded, the resolution becomes Δfr in the radio frequency domain. In the embodiment, since up to four sidebands (comb components) appear between the combs at intervals of Δfr, a resolution five times that of the related art is required. In the polarization measurement of the embodiment using the dual-com spectroscopy, it is necessary to measure at least 5 pulses, and measure 15 pulses with a margin.

  13 to 16 show power spectra obtained by performing discrete Fourier transform on an actually measured interferogram. The horizontal axis is the data number, and the vertical axis is the power.

  FIG. 13 is a power spectrum when the angle of the quarter-wave plate at the sample position is θ = 48 °. Side bands are observed at both ends of the region between the combs that appear regularly. In the verification experiment, since the rotation frequency of the rotation compensator 15 is set to ω = 1.2Δfr, these sidebands are ± 4ω components of the comb signal separated by four. This state shows a case where the transmitted light of the sample (1/4 wavelength plate) is completely linearly polarized light.

  FIG. 14 is a power spectrum when the angle of the quarter-wave plate at the sample position is θ = 63 °. In addition to the sidebands at both ends of the area between the combs, two sidebands also appear in the central area. The side band in the central region is a ± 2ω component of the comb signal separated by two. A total of four sidebands are observed between the combs, showing a case where the transmitted light of the sample (1/4 wavelength plate) is elliptically polarized light.

  FIG. 15 is a power spectrum when the angle of the quarter-wave plate at the sample position is θ = 78 °. The appearance of four sidebands between the combs is the same as in FIG. Compared to FIG. 14, the case where the nΔfr ± 2ω component is large and the transmitted light of the sample (1/4 wavelength plate) is elliptically polarized light close to circularly polarized light is shown.

  FIG. 16 is a power spectrum when the angle of the quarter-wave plate at the sample position is θ = 93 °. Two sidebands appear in the central area of the area between the combs. This shows a case where the transmitted light of the sample (1/4 wavelength plate) is circularly polarized light.

  As described in the above “Mathematical Support”, the polarization state (Δ, Ψ) of the sample transmitted light is obtained by obtaining the Stokes parameters S1 to S3 from the magnitudes and phases of the nΔf ± 2ω component and the nΔf ± 4ω component. be able to.

FIG. 17 is a diagram in which Stokes parameters S1 to S3 at respective angles of a 波長 wavelength plate as a sample are plotted on a Poincare sphere. When the quarter-wave plate is rotated from 48 ° to 5 ° in increments of 5 °, it starts near the equator (ie, linearly polarized light), passes through the vicinity of the North Pole in a figure eight shape, and returns to the vicinity of the equator again. I understand. This means that rotating the quarter-wave plate changes the polarization state of the transmitted light in the order of linearly polarized light → elliptically polarized light → circularly polarized light → elliptically polarized light → linearly polarized light. In FIG. 17, the rotation of 90 ° is depicted. However, when the quarter-wave plate is rotated by 180 °, as in the Northern Hemisphere, the Southern Hemisphere returns to the equator through the vicinity of the South Pole, and the figure of 8 is formed. Complete.
(3) Use of 波長 Wavelength Plate as Sample Next, a と wavelength plate is placed at the sample position in FIG. 12, and the same experiment as when a た wavelength plate is placed is performed. The optical system of FIG. 12 is adjusted so that light enters along the fast axis (or slow axis) when the angle of the half-wave plate is 84 °.

The half-wave plate is rotated 180 ° in steps of 15 ° from 84 °, and the power spectrum at each angle is measured. FIG. 18 shows only a part (for angles of rotation θ _{λ / 2} of 84 °, 54 °, 24 °, 354 °), but nΔfr between the combs over a range of rotation of 180 °. Only the ± 4ω component appears.

  FIG. 19 is a plot of Stokes parameters S1 to S3 at each angle of the half-wave plate on a Poincare sphere. (A) is a view of the whole Poincare sphere, (b) is a view of S1 to S3 when the angle θ of the half-wave plate is 84 ° to 9 °, viewed from the North Pole, and (c) is a half-wavelength. S1 to S3 when the angle θ of the plate is from 354 ° to 279 ° as viewed from the North Pole, and FIG.

  From FIG. 19, it can be seen that S1 to S3 move on the equator at substantially equal intervals. On the equator of the Poincare sphere, the inclination of the straight line is rotated by 90 ° at a diagonal position, and the rotation of the straight line is rotated by 180 ° around the equator. This is consistent with the result of the plot of FIG.

  An experiment using a half-wave plate as a sample confirmed that the technique of the embodiment can be effectively applied even when the change generated in the sample is rotation (change in inclination) of the plane of linearly polarized light.

  As described above, according to the polarization measurement of the embodiment, the measurement is performed by using the dual-com spectroscopy and arranging a rotation compensator whose rotation frequency is controlled to satisfy a predetermined condition on the emission side of the measurement target. The polarization state of the transmitted light of the target can be measured at high speed and with high accuracy. This technique can be applied, for example, to the measurement of circular dichroism of a substance.

10A, 10B, 10C Polarimeter 11 Signal comb (first optical frequency comb light source)
12. Local comb (second optical frequency comb light source)
13 Polarizing beam splitter (PBS)
14 polarizer 15 rotation compensator 16 polarizer 20 sample (sample)
21 Detector 25 Rotation control unit (rotation means)
30 analysis device 31 comb analysis unit 32 polarization state calculation unit

Claims (9)

A first optical frequency comb light source having a first repetition frequency;
A second optical frequency comb light source having a second repetition frequency;
A modulation element that is arranged on the light exit side of the sample on the optical path of the first optical frequency comb light source and that periodically modulates a polarization state;
Means for polarization-modulating the modulation element at a frequency that is a fractional multiple of the repetition frequency difference between the first optical frequency comb light source and the second optical frequency comb light source;
Light output from the first optical frequency comb light source and transmitted through the sample and the modulation element, and a detector that detects interference light of light output from the second optical frequency comb light source;
An analyzer that measures a polarization state of light transmitted through the sample based on the interference light,
A polarization measuring device comprising:   When the repetition frequency difference is Δfr and a frequency that is a fractional multiple of the repetition frequency difference is ω, the analysis apparatus calculates nΔfr ± 2ω and nΔfr for the nth (n is a natural number) interference signal in the frequency domain. The polarization measuring device according to claim 1, wherein at least one component of ± 4ω is detected, and a polarization state of light transmitted through the sample is calculated based on the detected component.   The polarization measurement device according to claim 2, wherein the value of the fraction times the fraction is set to a value in which four components of nΔfr ± 2ω and nΔfr ± 4ω do not overlap each other.   The polarization measurement device according to claim 2, wherein the analysis device determines the type of polarization and the direction of polarization based on the detected component.   The polarization measurement device according to claim 1, wherein the modulation element includes a rotation compensator, an electro-optic modulator, and a photoelastic modulator. An optical element that superimposes light output from the first optical frequency comb light source and light output from the second optical frequency comb light source;
The polarization measurement device according to any one of claims 1 to 5, further comprising: A first polarizer disposed on an incident surface side of the sample, and / or a second polarizer disposed on an output side of the modulation element;
The polarization measurement device according to any one of claims 1 to 6, further comprising: A first optical frequency comb light source having a first repetition frequency and a second optical frequency comb light source having a second repetition frequency constitute a light source for dual comb spectrometry,
Irradiating the sample with output light from the first optical frequency comb light source;
A modulation element, which is disposed on the emission side of the sample and periodically modulates the polarization state, is polarized at a frequency that is a fractional multiple of the repetition frequency difference between the first optical frequency comb light source and the second optical frequency comb light source. Modulate and
Detecting output light from the first optical frequency comb light source transmitted through the sample and the modulation element, and interference light of light output from the second optical frequency comb light source,
A polarization measurement method comprising: measuring a polarization state of light transmitted through the sample based on the interference light. When the repetition frequency difference is Δfr and a frequency that is a fractional multiple of the repetition frequency difference is ω, at least nΔfr ± 2ω and nΔfr ± 4ω for the nth (n is a natural number) interference signal in the frequency domain. Detect one component,
9. The polarization measurement method according to claim 8, wherein a polarization state of light transmitted through the sample is calculated based on the detected components.