JPWO2013077097A1 - Polarization analyzer, polarization analysis method, physical property measuring apparatus, and physical property measuring method - Google Patents

Abstract

A polarization analyzer capable of measuring the polarization direction and electric field amplitude of an electromagnetic wave at high speed and with high accuracy is provided. The polarization analyzer includes an electromagnetic wave generation source that generates an electromagnetic wave, a nonlinear optical crystal having an electro-optic effect, a rotation mechanism that rotates the crystal relative to incidence of the electromagnetic wave at an angular frequency ω, and the electromagnetic wave An optical system for injecting a probe light pulse into the crystal in synchronization with irradiation of the crystal by the detector, a detector for detecting an intensity difference signal of light components orthogonal to each other of the probe light pulse transmitted through the crystal, and the intensity difference And an analysis unit that extracts at least one of the ω component and the 3ω component from the signal and determines the polarization direction and the electric field amplitude of the electromagnetic wave based on the extracted ω component and / or 3ω component.

Description

  The present invention relates to a polarization analyzer and a polarization analysis method for determining the polarization direction and electric field amplitude of an electromagnetic wave at high speed and with high accuracy, and a configuration and method for measuring physical properties using the polarization analysis apparatus.

  Recent advances in ultra-short pulse laser technology have made it possible to generate and detect light (electromagnetic waves) in the terahertz band, which has been difficult in the past. A nonlinear optical crystal is used for generation and detection of terahertz waves. Specifically, a zinc flash structure crystal such as GaP or ZnTe is used as the non-linear optical crystal, and a coherent terahertz electromagnetic wave pulse is generated by irradiating the crystal with ultrashort pulse laser light. When terahertz electromagnetic waves are used for physical property measurement, the characteristics of the sample can be measured by guiding the generated terahertz electromagnetic waves to the sample to be measured and detecting the transmitted wave or reflected wave through the nonlinear optical crystal for detection. .

  FIG. 1 shows a general polarization direction analyzer 1000. A terahertz wave modulated by the frequency ω of the chopper 1001 by irradiating the nonlinear optical crystal S1 through the polarizer P1 and the optical chopper 1001 using an ultrashort pulse laser beam emitted from a laser light source (not shown) as a pump light pulse. Generate electromagnetic pulses. The polarization direction of the terahertz electromagnetic wave pulse can be arbitrarily set by appropriately rotating the polarizer P1 and the crystal S1. The terahertz electromagnetic wave pulse is guided to the beam cut element C by the mirror M1, and the pump light is cut. The beam that has passed through the element C is transmitted through the two wire grid polarizers WG1 and WG2, and the polarization direction dependency at the time of terahertz wave detection is eliminated by WG2. The first wire grid polarizer WG1 is normally manually rotated to cut out two orthogonal polarization direction electric field components of 45 degrees and -45 degrees. The second wire grid polarizer WG2 fixes the polarization direction of the cut out terahertz electric field by setting it to 0 degree or 90 degrees. The terahertz electromagnetic wave whose polarization direction is fixed is irradiated to the nonlinear optical crystal S2 through the mirror M2.

  In synchronization with the irradiation of the terahertz electromagnetic wave, the probe light pulse is incident on the nonlinear optical crystal S2 through the polarizer (P2). When a terahertz electric field is applied to the nonlinear optical crystal S2, birefringence occurs in the crystal S2 due to the electrooptic effect, and an intensity difference occurs in the electric field component of the probe light passing through the crystal S2. Since this intensity difference is proportional to the intensity of the terahertz electric field (proportional coefficient is known), the intensity of the terahertz electric field can be estimated by detecting the intensity difference with the detector 1010 and the lock-in amplifier 1011. Since the terahertz electric field is modulated at the frequency ω of the chopper 1001, lock-in detection can be performed with high accuracy.

  In order to determine the polarization direction of the electromagnetic wave, electric field components in two orthogonal directions are required. Therefore, the time waveform data of each terahertz electric field when the wire grid polarizer WG1 is set to 45 degrees and −45 degrees is acquired and analyzed. In order to acquire time waveform data, generally, the electric field intensity is measured while shifting the incident timing of the probe light or the pump light pulse on the delay stage, and the electric field measurement at different times is continued until the entire electric field waveform is obtained.

  When measuring surface irregularities of a sample using terahertz electromagnetic waves, the sample is irradiated with terahertz electromagnetic waves, and the surface level difference is obtained from the difference in arrival time when the reflected wave reaches the detection crystal. In order to obtain the difference in arrival time, it is necessary to specify the time indicating the peak value of the terahertz electromagnetic wave, and it is necessary to measure the time waveform at each measurement point.

  Regarding terahertz wave detection, there is known a document that expresses how the output signal of ΔI varies depending on the angle formed by the crystal orientation angle of the zinc flash structure crystal and the terahertz electric field polarization direction (for example, Non-patent document 1). This method requires that both the crystal and the polarizer be rotated at the same time so that the [001] direction of the crystal orientation and the polarization direction of the probe light pulse coincide with each other, and that the phase π is not in the determinable polarization direction. It is disadvantageous in that determinism remains.

  Also, the polarization direction of the probe light pulse, the crystal azimuth angle of the zinc flash structure crystal, and the angles of all optical elements (quarter wave plate, Wollaston prism, etc.) involved in terahertz electric field detection were rotated by arbitrary angles. It is known to derive a general expression for the output signal intensity of ΔI depending on the polarization direction of the terahertz electric field (see, for example, Non-Patent Document 2). This method is not suitable for practical use because it is only a theoretical calculation of a general formula.

  Further, the detection crystal is rotated so that the angle formed between the [001] axis of the zinc flash structure crystal and the polarization direction of the probe light pulse is 0 degree and 90 degrees, and based on the value of ΔI at the two angles. A method for determining the polarization direction of a terahertz electromagnetic wave has been proposed (see, for example, Non-Patent Document 3).

P.C.M.Planken et al., J. Opt. Soc. Am. B. Vol. 18, No. 3, 313-317 (2001). N.C.J.van der valk, T. Wenchebach, and P.C.M.Planken, J. Opt. Soc. Am. B, Vol. 21, No. 3 622-631 (2004) R. Zhang et al. Appl. Opt. Vol. 47, 6422-6427 (2008)

  Conventional polarization direction analysis and measurement methods have the following problems. First, the electric field strength and the polarization direction cannot be acquired independently at the same time. Further, in order to determine the polarization direction, it is necessary to measure the time waveform of the terahertz electromagnetic wave at each of the rotation positions of 45 degrees and −45 degrees of the wire grid polarizer WG1. That is, it takes time to scan the delay stage twice. When measuring the unevenness of the material surface, it is necessary to scan the delay stage for each measurement point to obtain a time waveform. Furthermore, the WG polarizer is a large element of 2 inches or more (about 4 inches for high-precision products), requires a large torque to rotate, and normally the WG polarizer is rotated manually. The WG polarizer is an expensive part. In a relatively inexpensive WG polarizer using a metal punching method, the usable bandwidth is limited to 1 THz or less. Further, the extinction ratio (ratio of the transmittance of light in the polarization direction orthogonal to the transmittance of light in the polarization direction desired to pass) does not increase, and highly accurate polarization analysis cannot be performed.

  In view of these problems, the present invention provides a polarization analysis apparatus and method that can determine the polarization direction and electric field amplitude of an electromagnetic wave simultaneously and independently from each other with high speed and high accuracy with a simple configuration. The task is to do.

  It is another object of the present invention to provide a physical property measuring apparatus and a physical property measuring method using the determination of the polarization direction.

  As a first aspect of the present invention, a polarization analyzer is provided. The polarization analyzer includes an electromagnetic wave generation source that generates an electromagnetic wave, a non-linear optical crystal having an electro-optic effect, a rotation mechanism that rotates the crystal relative to the incidence of the electromagnetic wave at an angular frequency ω, An optical system for injecting a probe light pulse into the crystal in synchronization with irradiation, a detector for detecting an intensity difference signal of light components orthogonal to each other of the probe light pulse transmitted through the crystal, and an ω component and 3ω from the intensity difference signal An analysis unit that extracts at least one of the components and determines a polarization direction and an electric field amplitude of the electromagnetic wave based on the extracted ω component and / or 3ω component;

  Thereby, the polarization direction and the electric field amplitude can be determined from the specific angular frequency component at high speed and with high accuracy.

In a good configuration example, the analysis unit
ΔI = C · E · [(1/2) cos (ωt + φ) + (3/2) cos (3ωt−φ)]
The phase information and the amplitude information of the ω component and / or the 3ω component of the electromagnetic wave are acquired based on the above, and the polarization direction and the electric field amplitude are determined based on the acquired phase information and amplitude information. Here, C is a coefficient, and E is the electric field amplitude of the electromagnetic wave.

  Thereby, phase information and amplitude information can be instantaneously and independently extracted from the detected difference signal.

  As a good configuration example, the angular frequency of the rotation mechanism is set so that an odd number of data points can be obtained on the crystal during one rotation of the crystal. With this configuration, noise can be effectively removed.

  As a second aspect of the present invention, a physical property measuring apparatus using the above-described polarization analysis is provided. The physical property measuring apparatus includes an electromagnetic wave generation source, a sample stage for holding a sample, a non-linear optical crystal for detection, a rotation mechanism for rotating the crystal relative to the incident electromagnetic wave at an angular frequency ω, and a crystal synchronized with the electromagnetic wave. Includes an optical system for injecting a probe light pulse, a detector, a polarization analysis unit, a correspondence information storage unit, and a sample analysis unit.

  The electromagnetic wave generation source generates circularly or elliptically polarized electromagnetic waves and irradiates the sample. The detection crystal detects a reflected electromagnetic wave from the sample. The detector detects an intensity difference signal of light components orthogonal to each other of the probe light pulse transmitted through the crystal. The polarization analyzer extracts at least one of the ω component and the 3ω component from the detected intensity difference signal, and the polarization angle of the circularly or elliptically polarized electromagnetic wave based on the extracted ω component and / or 3ω component To decide. The polarization angle-characteristic correspondence information storage unit obtains the polarization angle of the circularly or elliptically polarized electromagnetic wave acquired in advance for a specific substance (the polarization angle of the electromagnetic wave when the probe light pulse is incident on the detection crystal) and the characteristic of the substance. Correspondence information indicating a one-to-one correspondence relationship with is stored. The sample analyzer determines the characteristics of the sample based on the polarization angle of the electromagnetic wave determined by the polarization analyzer and the corresponding information.

  With this configuration, the electric field waveform scan for each measurement becomes unnecessary, and the characteristics of the sample can be measured immediately from the measured polarization direction.

  The polarization direction can be measured at high speed and with high accuracy. There is no need to use expensive WG polarizers. The polarization direction of electromagnetic waves can be determined with high speed and high accuracy over a wide band. In the physical property measurement using the polarization direction measurement, the characteristics of the sample can be directly acquired from the detected polarization direction without acquiring the time waveform of the electric field every time.

It is a schematic block diagram of the conventional general polarization direction analyzer. It is a schematic block diagram of the polarization analyzer of 1st Embodiment. It is the schematic of the detection optical system of FIG. It is a figure for demonstrating the principle of electro-optic sampling. FIG. 3 is a perspective view of the detection optical system in FIG. 2. It is a figure which shows the coordinate system of the nonlinear optical crystal rotated by a motor. It is a graph which shows the data value acquired with the apparatus and method of 1st Embodiment, and the function formula corresponding to this. It is a figure which shows the amplitude Fourier component of measurement data. It is a figure which shows the phase Fourier component of measurement data. It is a figure which shows deriving | leading a polarization angle directly from measurement data. It is a flowchart which shows a polarization direction analysis method. It is a graph which shows the effect of a 1st embodiment. It is a graph which shows the effect of 1st Embodiment, and is a figure which shows that an electric field amplitude and a polarization direction can be measured mutually independently and stably. It is a schematic block diagram of the polarization analyzer of 2nd Embodiment. It is explanatory drawing of noise cancellation. It is a schematic block diagram of the measuring apparatus of 3rd Embodiment. It is a conceptual diagram of a general surface level | step difference measurement. It is a conceptual diagram of the electromagnetic wave spectrum measurement by an optical delay stage. It is a figure explaining the relationship between the polarization angle of the electromagnetic waves for measurement, and a sample surface level | step difference. It is a figure explaining the relationship between the polarization angle of the electromagnetic waves for measurement, and a sample surface level | step difference. It is a flowchart which shows the measuring method of 3rd Embodiment. It is a schematic diagram of the correspondence acquisition of the surface level | step difference of Example 3, and a polarization angle. It is a measurement result of the correspondence between the polarization angle and the z-direction depth position. It is a figure which shows the measurement result which measured the sample using the measuring apparatus of embodiment. This is acquired data when the number of integrations N = 1 at each measurement point. It is a table | surface which shows the measurement result by the measuring apparatus of embodiment compared with a comparative example. It is a graph which shows depth resolution of 1 micrometer.

Hereinafter, embodiments of the invention will be described with reference to the drawings.
<First Embodiment>
FIG. 2 is a schematic configuration diagram of the polarization analyzer 10 of the first embodiment. A characteristic of the polarization analyzer 10 is that a non-linear optical crystal for detection (S2) 16 is rotated at high speed at an angular velocity ω, and at least one angular frequency component of ω and 3ω is extracted from the detected intensity difference signal ΔI. In other words, the electric field amplitude intensity Ea and the polarization direction γ of the irradiated electromagnetic wave are obtained simultaneously and independently of each other. In addition, compared with the conventional configuration, two wire grid (WG) polarizers and an optical chopper are unnecessary, and the configuration is simplified.

  The polarization analyzer 10 includes a nonlinear optical crystal (S2) 16, a motor 17 that rotates the nonlinear optical crystal 16 at an angular velocity ω, an electromagnetic wave generation source 19 that generates an electromagnetic wave that irradiates the nonlinear optical crystal 16, and an angular velocity ω. It includes an optical system 29 for injecting a probe light pulse into the rotated nonlinear optical crystal 16. In addition, a detector 20 that detects an intensity difference signal ΔI of two orthogonal components of the probe light that has passed through the nonlinear optical crystal 16, and frequency analysis of the detected intensity difference signal results in at least one of the ω component and the 3ω component. A polarization analysis unit 21 that extracts and determines the polarization direction and electric field amplitude of the electromagnetic wave based on the ω component and / or the 3ω component is included.

  The nonlinear optical crystal 16 is an electro-optic crystal whose refractive index becomes anisotropic when an electric field is applied. For example, the nonlinear optical crystal 16 is a zinc flash structure crystal, and GaP, ZnTe or the like can be used. In the example of FIG. 2, a GaP crystal having a crystal orientation plane of (110) is used. The GaP crystal 16 is held by a frame (not shown), and the frame is connected to the motor 17. As the motor 17 rotates, the GaP crystal 16 held on the frame rotates at an angular velocity ω.

  The electromagnetic wave generation source 19 is a terahertz electromagnetic wave generation source in the example of FIG. A pump light pulse (femtosecond light pulse) emitted from a laser (not shown) is incident on a nonlinear optical crystal (S1) 12 such as ZnTe through a polarizer (P1) 11 to generate a terahertz electromagnetic wave pulse. The generated terahertz electromagnetic wave is guided to the detection nonlinear optical crystal 16 through the mirror (M1) 13, the beam cut element (C) 14, and the mirror (M2) 15.

  On the other hand, the probe light pulse is guided to the detection nonlinear optical crystal 16 in synchronization with the irradiation of the terahertz electromagnetic wave by the optical system 29 including the polarizer (P2) 18 and the reflection mirror M3. The probe light pulse may be used by branching a part of the laser beam that generates the pump light pulse.

  The probe light pulse transmitted through the nonlinear optical crystal 16 is detected by the detector 20. The probe light pulse is detected by electro-optic sampling using the electro-optic effect of the nonlinear optical crystal 16. The electro-optic sampling will be described with reference to FIGS.

FIG. 3 is a schematic diagram showing the configuration of the detection system A of FIG. The probe light pulse that has been linearly polarized by the polarizer (P2) 18 is incident on the GaP crystal 16 having the (110) plane. The probe light pulse transmitted through the GaP crystal 16 is incident on the quarter-wave plate 22 to form circularly polarized light, and is separated into two linearly polarized beams orthogonal to each other using a Wollaston prism (WP) 23. The separated light beams (signal intensities I ₁ and I ₂ ) are detected by the photodetection photodiodes D1 and D2, respectively, and converted into current. The difference signal ΔI (ΔI = I ₁ −I ₂ ) can be extracted as a voltage signal by converting the difference between the currents generated in D1 and D2 into a voltage by a current / voltage amplifier (not shown).

  4 is a conceptual diagram of electro-optic sampling, and FIG. 5 is a perspective view of the detection system of FIG. As shown in FIG. 4A, when a terahertz electric field is not applied to the GaP crystal 16, the probe light LB passes through the GaP crystal 16 while maintaining linearly polarized light.

At this time, as shown in FIG. 5, the transmitted light of the GaP crystal is c axis (axis unique to the optical element) by π / 4 with respect to the reference axis of the laboratory system (coincident with the direction of the electric field Eb of the probe light pulse). ) Is transmitted through the quarter-wave plate 22 in a tilted state, the probe light becomes circularly polarized light. When the circularly polarized light is separated into the x component and the y component by the Wollaston prism 23, the intensity in any direction is the same, so I ₁ = I ₂ and the output signal (difference signal ΔI) becomes zero.

On the other hand, as shown in FIG. 4B, when the electric field E _THz is applied to the GaP crystal 16 having the electro-optic effect, the refractive index of the crystal changes to become refractive index anisotropy (Pockels effect). For this reason, the probe light transmitted through the GaP crystal 16 cannot maintain the polarization state before incidence, and the light transmitted through the quarter wavelength plate 22 becomes elliptically polarized light. In this case, the difference between the magnitudes (squares) of the x component and the y component is not zero. A difference occurs in the intensity detected by the photodiodes D1 and D2 of the detector 20, and a difference signal ΔI proportional to the terahertz electric field is obtained. In FIG. 5, U3 is the propagation direction of the probe light and is an axis perpendicular to the (110) plane of the GaP crystal 16, and U1 and U2 are the high refractive index direction and the low refractive index direction in the (110) plane. Indicates.

FIG. 6A and FIG. 6B are diagrams showing a coordinate system used in the first embodiment. The horizontal axis x and the vertical axis y are laboratory axes and are determined by the polarization direction of the probe light. The electric field polarization direction Eb of the probe light coincides with the x axis. The angle formed by the x axis and the polarization direction E _{THz of the} terahertz electric field is γ, and the angle formed by the x axis and the [−110] azimuth axis of the GaP crystal 16 is β. Since the GaP crystal 16 is rotated at the angular velocity ω by the motor 17, the angle β changes with ωt. In FIG. 6, for simplification, it is assumed that the [−110] azimuth axis of the GaP crystal 16 at time t = 0 coincides with the x axis. FIG. 6B is obtained by adding refractive index axes U1 and U2 to the coordinate system of FIG. 6A, and shows refractive index anisotropy due to application of a terahertz electric field.

The parameters to be measured are the polarization direction γ of the terahertz electric field with respect to the polarization direction Eb of the probe light pulse and the amplitude of the terahertz electric field (proportional to the magnitude of E _THz ).

  As the inventors of the present application change the angle β from moment to moment so as to satisfy β = ωt, the difference output signal ΔI of the detector 20 changes as a function of time according to the following equation (0). I found it.

ここで、Ｉはプローブ光パルスの強度、Ωはプローブ光パルスの角周波数、ｎとｒはそれぞれプローブ光パルスの波長におけるＧａＰ結晶１６の屈折率と非線形光学定数、ｄはＧａＰ結晶１６の厚さ、ｃは光速であり、すべて既知の値である。厳密には位相整合条件を加味する必要があるため若干の修正が必要とされるが、ｄの値が小さい結晶を用いれば、その効果を無視することができる。したがって、（Ｉ・Ω・ｎ³・ｒ・ｄ／２ｃ）を係数Ｃとおくことができる。式（０）の導出については、後述する。

Here, I is the intensity of the probe light pulse, Ω is the angular frequency of the probe light pulse, n and r are the refractive index and nonlinear optical constant of the GaP crystal 16 at the wavelength of the probe light pulse, respectively, and d is the thickness of the GaP crystal 16 , C are the speed of light, all known values. Strictly speaking, it is necessary to take into account the phase matching condition, so that slight correction is required. However, if a crystal having a small d value is used, the effect can be ignored. Therefore, (I · Ω · n ³ · r · d / 2c) can be set as the coefficient C. The derivation of Expression (0) will be described later.

The phase information φ in Expression (0) represents the polarization direction γ of the terahertz electric field in FIG. Further, since the amplitude signal is proportional to _ETHz , the absolute value of the terahertz electric field intensity can be extracted by applying an appropriate proportionality coefficient. By using the equation (0), a component that vibrates at an angular frequency ω and / or 3ω is extracted from the output ΔI of the detector 20 and information on the amplitude and phase is obtained to instantaneously change the polarization direction and amplitude of the terahertz electric field. In addition, each can be measured independently.

  The verification experiment actually performed is shown below. 3 was actually assembled, and the GaP crystal 16 was rotated using the motor 17 rotating at 94.73 Hz. The rotating GaP crystal was irradiated with terahertz electromagnetic waves, and in synchronization with this, a probe light pulse was incident on the GaP crystal 16. The laser used to generate the pump light pulse and the probe light pulse is a laser having a pulse width of 150 femtoseconds and a repetition frequency of 1.042 KHz.

  By setting the rotation of the motor 17 to 94.73 Hz, 11 data points are set on the rotating GaP crystal 16. That is, while the GaP crystal 16 makes one rotation (360 °), the crystal 16 is irradiated with terahertz electromagnetic waves 11 times, and ΔI is acquired from 11 data points. The number of data points is not limited to 11, and an arbitrary number can be set. As will be described later in connection with the second embodiment, it is desirable to set an odd number from the viewpoint of noise removal.

FIG. 7A is a diagram in which 11 consecutive acquired data points (white circles) are plotted. The horizontal axis represents the data point number (i), and the vertical axis represents the intensity of the difference signal ΔI. If the number of data points is 11, the angle between the data points is 360 ° / 11 = 32.73 °. The crystal angle β at the i-th data point (the angle β of the [−110] axis of the GaP crystal with respect to the polarization direction Eb of the incident probe light) is
β = (i−1) × 360 ° / 11 = (i−1) × 2π / 11 [rad]
It becomes.

  Eleven data points can be represented by equation (1).

図７（Ａ）の点線は、式（１）について以下のパラメータを用いて描いたものである。

The dotted line in FIG. 7 (A) is drawn using the following parameters for equation (1).

測定データは式（１）を非常によく再現している。図７（Ｂ）は、式（１）の右辺の２つの項を分解してプロットした図である。

The measurement data reproduces equation (1) very well. FIG. 7B is a diagram in which the two terms on the right side of Equation (1) are decomposed and plotted.

図７（Ｂ）からわかるように、３ω成分（曲線Ｂ）の最大振幅はω成分（曲線Ａ）の最大振幅の３倍であり、３倍の速さで時間変化する。ＡとＢを合波すると図７（Ａ）の波形になる。

As can be seen from FIG. 7B, the maximum amplitude of the 3ω component (curve B) is three times the maximum amplitude of the ω component (curve A), and changes with time at a speed of 3 times. When A and B are combined, the waveform of FIG.

  FIG. 8 shows the result of Fourier analysis of the 11 data points in FIG. 7A and extracting the amplitude Fourier components for the frequency components of β, 2β, 3β, 4β, 5β, and 6β. Amplitudes appear at β and 3β, and the amplitude Fourier components of 2β, 4β, 5β, and 6β are almost zero. The amplitude Fourier component of 3β is three times the amplitude Fourier component of β. The reason why the amplitude Fourier components of 2β, 4β, 5β, and 6β are not completely zero is that there is a slight error (nonlinearity) in the linearity of the detector 20.

  The ω component and the 3ω component shown in equation (1)

は、それぞれ以下の量を表している。

Represents the following quantities, respectively.

ここでβ₀は結晶の初期角度、γは求めたい偏光角度（図６の座標系のＥ_THzの偏光角γ）、ｎ₁、ｎ₂は任意の整数である。図７では便宜上、初期角度β₀をゼロとしていたが、実際にはセットアップ時に結晶がどの方向を向いているか（どの象限に［−１１０］方位軸があるか）わからないからである。

Here, β ₀ is the initial angle of the crystal, γ is the polarization angle to be obtained (E _THz polarization angle γ in the coordinate system of FIG. 6), and n ₁ and n ₂ are arbitrary integers. In FIG. 7, for the sake of convenience, the initial angle β ₀ is set to zero, but in reality it is not known which direction the crystal is oriented during setup (which quadrant has the [−110] azimuth axis).

From the equations (2) and (3), the initial angle β _{0 of the} crystal is determined. Suppose now that we know that the value of β ₀ is roughly between 45 ° and 135 °. That is, it is assumed that the [−110] crystal orientation axis of the GaP crystal is in the vicinity of 90 ° with respect to the polarization direction (x-axis) of the probe light pulse (β ₀ = 90 ± 45 °). In this case, the initial angle β ₀ can be expressed by Equation (4).

ただし、０≦Δβ≦π/２。このとき、式（２）と式（３）を足すと以下の式が得られる。

However, 0 ≦ Δβ ≦ π / 2. At this time, the following equation is obtained by adding the equations (2) and (3).

したがって、式（５）を用いてΔβの値を算出することができる。

Therefore, the value of Δβ can be calculated using Equation (5).

±４５°の範囲で当初の結晶の向きをラフに知ることができれば、上述した要領で式を簡単に作ることができ、Δβの値を正確に知ることができる。

If the initial crystal orientation can be roughly known within a range of ± 45 °, the equation can be easily made in the manner described above, and the value of Δβ can be accurately known.

  In the case of Example 1, according to the parameter (Equation 3) used in the graph of FIG.

あるから、式（５）の３番目の式が適用され、Δβ＝150.2°−135°＝15.2°が求められる。初期角度β₀は、式（４）からβ₀＝45°＋15.2°＝60.2°である。

Therefore, the third equation of equation (5) is applied to obtain Δβ = 150.2 ° −135 ° = 15.2 °. The initial angle β ₀ is β ₀ = 45 ° + 15.2 ° = 60.2 ° from the equation (4).

  By substituting the above values into Equations (2) and (3), they can be transformed into Equations (2) ′ and (3) ′.

γの範囲は０°＜γ＜３６０°である必要があるから、式(2)'、(3)'のｎ₁、ｎ₂の値は、それぞれ０、１でなければならない。したがって、

Since the range of γ needs to be 0 ° <γ <360 °, the values of n ₁ and n ₂ in equations (2) ′ and (3) ′ must be 0 and 1, respectively. Therefore,

となり、式(2)''と式(3)''のいずれを用いてもγ＝186.5°であることがわかる。

Thus, it can be seen that γ = 186.5 ° using either of the formulas (2) ″ and (3) ″.

9 and 10 are diagrams for explaining the above-described solving method using graphs. First, it was found from Equation (5) that β ₀ = 60.2 °. Therefore, from equation (2) '',

によりγを導出する。これは図９のω成分における濃いグレイの棒線（246.7°）から淡い灰色の棒線（60.2°）を引き算することに相当する（246°−60.2°＝186.5°）。

To derive γ. This corresponds to subtracting the light gray bar (60.2 °) from the dark gray bar (246.7 °) in the ω component of FIG. 9 (246 ° −60.2 ° = 186.5 °).

On the other hand, since 3β ₀ = 180.6 °, if n ₂ = 0 in equation (3) ′,

となり、負となってしまう。従って、３６０°を足して、

And become negative. Therefore, add 360 °

を計算すればよい。これは図９の３ω成分における白い棒線（3β₀＋360°＝540.6°）から濃いグレーの棒線（354.1°）を引き算することに相当する（540.6°−354.1°＝186.5°）。

Should be calculated. This corresponds to subtracting the dark gray bar (354.1 °) from the white bar (3β ₀ + 360 ° = 540.6 °) in the 3ω component of FIG. 9 (540.6 ° −354.1 ° = 186.5 °).

  FIG. 10 shows the calculation result. As a matter of course, γ = 186.5 ° can be derived by using equation (2) ″ and equation (3) ″.

If the initial angle β ₀ cannot be estimated because of the measurement device, 90 ° arbitraryness remains in the determination of the polarization angle. In that case, the arbitraryness of the initial angle can be eliminated by the following method.

First, an electromagnetic wave source that is roughly known as longitudinally polarized light or laterally polarized light is prepared. For example, a polarizer that can distinguish between longitudinally polarized light and laterally polarized light is placed in the middle of the optical path. As an example, if the silicon substrate is placed obliquely (at an angle of 45 ° with respect to the propagation direction of the terahertz electromagnetic wave), the transmittance of longitudinally polarized light and transversely polarized light is changed to distinguish between vertically polarized light and horizontally polarized light. be able to. Then, the polarization angle of light having a known polarization (whether vertical or horizontal) is determined by the above method. At this time, if a value of lateral polarization of γ = 186.5 ° appears even though it is longitudinal polarization, it can be determined that there is an error of 90 ° in determining β ₀ . Therefore, it is only necessary to newly replace β ₀ = (60.2 + 90) ° and continue the subsequent experiment.

  This method can suppress the 90 ° arbitraryness to the 180 ° arbitrary. With 180 ° arbitraryness, for example, the indefiniteness of whether the electric field vector in the horizontal direction (horizontal direction) points to the right or left is left, but indefiniteness in the horizontal direction is a problem in practice. It seems that there is no problem because there is almost no.

  FIG. 11 is a flowchart showing the polarization direction analysis method according to the first embodiment. In step S101, the detection nonlinear optical crystal is rotated at an angular frequency ω. In step S103, the nonlinear optical crystal is irradiated with the electromagnetic wave to be measured, and the probe light is incident in synchronization therewith. In step S105, the light beam transmitted through the crystal is separated into mutually orthogonal components, and a differential signal (intensity difference) ΔI is detected. In step S107, the difference signal ΔI is frequency-analyzed to extract the angular frequency ω component and the 3ω component. This process is expressed by equation (1) and is equivalent to equation (0). In step S107, the amplitude component and the phase component of the irradiation electromagnetic wave are acquired, and the polarization direction and the electric field amplitude are calculated. The polarization direction γ can be obtained from any phase information of ω and 3ω. In addition, by multiplying the amplitude information of the ω and 3ω components by an appropriate known coefficient, the absolute value of the electric field strength of the electromagnetic wave can be extracted.

12 and 13 are diagrams illustrating the effects of the first embodiment. FIG. 12 is a graph showing a deviation distribution from the average value when the polarization direction γ is measured by the method described above. One measurement was 22 milliseconds, and the measurement was repeated 10,000 times (N = 10000). The measurement result shows a Gaussian distribution, and the deviation σ from the average value of 75.00 ° is only 0.56 °. Since the standard error is expressed by σ / N ^1/2 , the accuracy is ± 0.0056 °.

  FIG. 13 is a graph showing the stability of the measurement method of the first embodiment. The upper part of FIG. 13 shows the electric field amplitude, and the lower part shows a deviation from the average value in the polarization direction. These two results were obtained independently and simultaneously from 1000 measurement points in the range of 42 seconds. In the upper measurement, the circular attenuating filter of the near-infrared laser pulse was manually rotated to intentionally change the amplitude Ea of the terahertz electric field in a range of ± 25% and normalize the maximum amplitude.

  In the lower measurement, the variation in the terahertz polarization direction γ (the polarization direction of the terahertz electric field with respect to the polarization direction of the probe light) within the same measurement period was acquired. The deviation from the average value of 75.00 ° at 1000 measurement points is shown. From this measurement result, it can be seen that the measurement variation in the polarization direction γ is very small regardless of the change in the electric field amplitude, and the polarization direction can be stably obtained without depending on the radio wave amplitude.

  As described above, by using the apparatus and method of the first embodiment, compared with the conventional method using a pair of wire grid polarizers and the method of manually rotating a crystal in two orthogonal directions, the following The effect is obtained.

First, the polarization direction and the electric field strength can be measured in real time with high speed (within 22 milliseconds) and high accuracy (below 1 degree) in one scan. Second, even if the polarization direction of the optical element is not accurately set, the absolute polarization direction of the irradiation electromagnetic wave with respect to the polarization direction of the probe light can be determined. Third, the electric field amplitude and polarization information can be acquired separately in one measurement, and the polarization information is independent of the influence of amplitude fluctuation. Fourth, the device configuration is simplified.

Second Embodiment
In the second embodiment, a noise removal function is added to the apparatus and method of the first embodiment. FIG. 14 is a schematic diagram of the polarization analyzer 50 of the second embodiment. The same components as those in the polarization analyzer 10 of FIG. 3 are denoted by the same reference numerals, and redundant description is omitted.

  14 includes an optical chopper 51 inserted in front of the polarizer (P1) 11 of the electromagnetic wave generation source 19 and a noise removal calculation unit 53. The optical chopper 51 and the noise removal calculation unit 53 are used to effectively remove noise that appears when the polarization direction is detected.

  Noise generated in the polarization analyzer 50 is caused by scattering of probe light or the like in the (110) zinc-blende structure crystal (GaP crystal in the second embodiment) 16 for detection. Noise appears even if there is no irradiation electromagnetic wave to be measured, and periodically changes as a function of the angle at each time when the GaP crystal 16 is rotated.

The optical chopper 51 modulates the generated electromagnetic wave with the frequency f ₁ . The modulation frequency f ₁ is set so as to satisfy the following relationship when the rotational frequency of the detection GaP crystal 16 is f ₂ .

f ₁ = (n / 2) × f ₂ (6)
Here, n is an odd number, which is the number of data points on the rotating GaP crystal 16.

  FIG. 15 is a diagram for explaining the principle of noise cancellation using the optical chopper 51. In this example, n = 5, that is, the number of irradiation points (data points) on the crystal 16 is five.

f ₁ = (5/2) × f ₂ (7)
The horizontal axis is a time axis, and j is an irradiation pulse number of electromagnetic waves. The generated electromagnetic wave is turned ON / OFF at the frequency f ₁ along the time axis by the optical chopper 51. On the other hand, the GaP crystal 16 rotating at the frequency f ₂ is designed to rotate once at 2.5 times the ON / OFF cycle of the generated electromagnetic wave.

  In the first rotation of FIG. 15, the generated electromagnetic wave is ON in an angle range of 0 to 72 ° (an angle obtained by dividing the initial angle by 5). In the same 0-72 ° angle range of the second rotation, the generated electromagnetic wave is OFF. Therefore, by subtracting the second rotation data from the first rotation data, noise that exists in common in the first rotation and the second rotation is subtracted, and only the electromagnetic wave signal to be obtained remains.

  In the subsequent angle range of 72 to 144 °, the generated electromagnetic wave is OFF at the first rotation, and the generated electromagnetic wave is ON at the second rotation. In this case, the first rotation data is subtracted from the second data. This process is repeated until it is rotated 360 ° to obtain a data string from which noise has been removed.

  The reason why the number n of data points is set to an odd number is to make sure that the number of data points is ON and OFF in the same angular region when two consecutive rotations are set as one set. This numerical processing is expressed as follows (example of n = 5).

ここで、ΔＩ（ｊ）はｊ番目に取得した差分信号ΔＩであり、ΔＩ'（ｊ）はＯＮ／ＯＦＦ処理でノイズを差し引いて得られた新しいデータ列である。

Here, ΔI (j) is the jth difference signal ΔI acquired, and ΔI ′ (j) is a new data string obtained by subtracting noise in the ON / OFF process.

  The noise removal calculation unit 53 performs the processing of Expression 16 based on the difference signal ΔI detected by the detector 52. By using ΔI ′ (j) obtained by the noise removal processing for subsequent frequency analysis (extraction of ω component and 3ω component), the polarization direction and electric field amplitude of the irradiated electromagnetic wave can be measured more accurately.

  In FIG. 14, the noise removal calculation unit 53 is inserted between the detector 52 and the analysis unit 21, but may be configured integrally with the detector 52 or integrated with the analysis unit 21. It may be configured. Alternatively, an external arithmetic device may be used.

An actual verification example will be described. Eleven data points are set on the GaP crystal 16. The repetition frequency of the laser system is 1.042 kHz. By dividing this by 11 using an electric circuit, f ₂ = 94.73 Hz
And The angular velocity ω of the motor 17 is controlled so as to have this f ₂ value. The frequency f ₁ of the optical chopper 51 is obtained from the equation (6):
f ₁ = (11/2) × 94.73 Hz = 521 Hz
It is. With this setting, the terahertz electromagnetic wave generated by the 1.042 kHz laser pulse hits the GaP crystal 16 at an angle obtained by dividing 360 ° into 11 equal parts.

  The noise removal calculation unit 53 of the detector 52 generates 11 new data strings using 22 data points (data points for two rotations).

偏波解析部２１は、得られたΔＩ'（ｊ）データ列の成分を周波数解析してω成分と３ω成分を抽出し、電磁波の偏波方向（偏光角度）と電場振幅を決定する。これにより、ノイズを効果的に抑制した偏波方向、電場振幅の決定が可能になる。

The polarization analysis unit 21 performs frequency analysis on the components of the obtained ΔI ′ (j) data string, extracts the ω component and the 3ω component, and determines the polarization direction (polarization angle) and the electric field amplitude of the electromagnetic wave. As a result, it is possible to determine the polarization direction and the electric field amplitude while effectively suppressing noise.

Since the method of the first embodiment and the second embodiment has very high polarization direction determination accuracy, high-precision magneto-optical measurement by minute Kerr rotation angle measurement (or Faraday rotation angle measurement) or polarization rotation by birefringence It can be applied to the detection of micro-stress and strain using microscopic and high-precision circular dichroism spectrum measurement of biomolecules. When measuring characteristics of a sample by irradiation with electromagnetic waves, it can be applied to various characteristics measurement such as surface shape, stress, internal state such as magnetism, and structure of biomolecules.

<Third Embodiment>
In the third embodiment, the characteristics of a substance are measured with high resolution using the polarization analyzer of the first embodiment or the second embodiment. In the third embodiment, the surface step (unevenness) of the sample is determined as an example of the material characteristic. In this example, the sample is irradiated with circularly or elliptically polarized electromagnetic waves, and the characteristics of the sample are measured directly from the polarization direction of the reflected electromagnetic waves from the sample.

  FIG. 16 is a schematic diagram of a physical property measuring apparatus 100 according to the third embodiment. The measuring apparatus 100 includes a laser 101, a stage 131 that holds a sample 130, a ZnTe crystal 115 for generating electromagnetic waves, an optical element 111 that converts the generated electromagnetic waves into circularly or elliptically polarized light, and detection that detects reflected electromagnetic waves from the sample 130. ZnTe crystal 116, a motor 117 that rotates the ZnTe crystal 116 at an angular frequency ω, and an optical system 129 that makes the probe light pulse LB incident on the ZnTe crystal 116 in synchronization with the irradiation of electromagnetic waves. The ZnTe crystals 115 and 116 are crystals having a zinc flash structure. The sample 130 is placed in a reflection system located between the ZnTe crystal 115 for generating electromagnetic waves and the ZnTe crystal 116 for detection.

  The physical property measuring apparatus 100 further includes a detector 152 that detects the differential signal ΔI of the probe light that passes through the detection ZnTe crystal 116, and frequency analysis of the differential signal ΔI to extract the ω component and the 3ω component, thereby A polarization analysis unit 121 that determines the wave direction and a sample analysis unit 122 that measures the characteristics of the sample 130 from the output of the polarization analysis unit 121 are included. The sample analysis unit 122 includes, for a specific substance, a polarization angle-characteristic correspondence information storage unit 123 that stores information indicating a correspondence relationship between a polarization direction (polarization angle) acquired in advance and characteristics of the substance, and a measured polarization. A characteristic determination unit 124 that determines the characteristic of the sample from the angle and the stored correspondence information is provided. When measuring the surface step, the correspondence relationship between the polarization angle and the step (surface depth) is acquired in advance and stored in the correspondence information storage unit 123. Here, the polarization angle acquired in advance is a polarization angle of the circularly polarized (or elliptically polarized) electromagnetic wave when the probe light pulse is incident on the detection crystal 116. The light emitted from the laser 101 is branched by a beam splitter (BS), part of which is guided to the electromagnetic wave generating ZnTe crystal 115 as a pump light pulse, and part of the light is guided to the detection ZnTe crystal 116 as a probe light pulse.

  The laser 101, the optical element (GL, HWP, reflection mirror, etc.), the ZnTe crystal 115, and the quarter wavelength plate 111 constitute an electromagnetic wave generation source. Optionally, an optical chopper 110 for noise removal may be inserted. The ZnTe crystal 115 is irradiated with a laser pulse that has passed through the linear polarizer GL and the half-wave plate HWP to generate an electromagnetic wave. In the example of FIG. 16, a terahertz wave is generated, and the generated electromagnetic wave is passed through the quarter wavelength plate 111 to be circularly polarized. Circularly polarized electromagnetic waves are guided to the sample 130 via parabolic mirrors (PM1-PM3). The electromagnetic wave reflected by the surface of the sample 130 enters the detection ZnTe crystal 116 via the parabolic mirror (PM4, PM5).

  On the other hand, the probe light LB branched by the beam splitter (BS) is guided to the detection ZnTe crystal 116 by the optical system 129. The optical system 129 includes a delay stage DS having an optical delay element 106. The delay stage DS can be fixed during the measurement of the sample 130. This is one of the advantageous features of the physical property measuring apparatus 100. The reason will be described below.

  In general, the change in the depth of the sample surface is measured by irradiating the sample with linearly polarized light and measuring the time until the reflected light from the sample is detected. This is shown in FIG. When there is a step of distance d between point A and point B of the sample, a difference of Δx = 2d occurs in the optical path length of the detected electromagnetic wave. This is detected as a time difference Δt (Δx = cΔt; c is the speed of light). In order to measure the change Δt in the arrival time, it is necessary to determine the time at which the amplitude of the electromagnetic wave exhibits a peak value. Therefore, as shown in FIG. 18, the delay stage must be driven.

  In FIG. 18, by moving the position of the optical delay element 106 by Δx, the optical path length of the electromagnetic wave changes by 2Δx. When the optical path length is increased by 2Δx, the incident timing of the electromagnetic wave to the detection ZnTe crystal 116 is shifted by Δt (Δt = 2Δx / c). By repeating the measurement of the reflected electromagnetic wave while moving the position of the optical delay element 106 with a constant step size, the entire time waveform of the electromagnetic wave incident on the detection ZnTe crystal 116 can be obtained, and the peak position can be specified. . However, in this method, the delay stage must be driven for each measurement point.

  Therefore, in the third embodiment, the irradiation electromagnetic wave is not linearly polarized light but circularly polarized light or elliptically polarized light, thereby making it unnecessary to drive the delay stage DS during measurement. In the case of circularly polarized light or elliptically polarized light, the step (unevenness) on the sample surface is measured by utilizing the fact that the polarization angle of the electric field changes continuously.

  FIG. 19 is a diagram for explaining the correspondence between the polarization angle of circularly polarized light and a step as an example. The z axis is the traveling direction of electromagnetic waves. The step d (position in the z direction) and the polarization angle of the electric field can be associated with the step of one wavelength or less of the electromagnetic wave in a one-to-one correspondence. In the method using linearly polarized light shown in FIG. 17, the step d between the points A and B is detected as a difference in arrival time of the electric field. On the other hand, in the method of FIG. 19, the step d can be detected as a change in the polarization angle of the electromagnetic wave.

  In general, when the change in the azimuth angle of the circularly polarized electric field vector is Δθ (deg.) And the wavelength is λ, the step d satisfies the relationship of Expression (10).

式（１０）から分かるように、物性測定装置１００の有利な特徴として、測定される段差ｄは電磁波の振幅と無関係である。これは光源強度の揺らぎがノイズとして入ってこないことを意味する。また、従来のように直線偏光を入射する場合と異なり、測定中に検出電磁波の時間波形全体をスキャンする必要がないため、サンプリング数を大幅に減らすことができる。

As can be seen from the equation (10), as an advantageous feature of the physical property measuring apparatus 100, the step d to be measured is independent of the amplitude of the electromagnetic wave. This means that the fluctuation of the light source intensity does not enter as noise. Further, unlike the conventional case where linearly polarized light is incident, it is not necessary to scan the entire time waveform of the detected electromagnetic wave during measurement, so that the number of samplings can be greatly reduced.

  FIG. 20A and FIG. 20B depict a snapshot of the electric field when the probe light pulse reaches the detection ZnTe crystal 116. The direction of travel of the electric field is the direction of the arrow in the figure (z direction), assuming counterclockwise circular polarization. In order to make the figure easier to see, the electric field of the x component is omitted.

  20A shows the electromagnetic wave reflected from the point A in FIG. 17, and FIG. 20B shows the electromagnetic wave reflected from the point B that is 10 μm deeper than the point A in FIG. In the case of the measuring apparatus 100 of FIG. 16, since the wavelength λ of the irradiated electromagnetic wave is 300 μm and d = 10 μm, Δθ = 24 ° is obtained according to the equation (10). Therefore, when the polarization angle of the reflected electromagnetic wave from the point A of the sample is calculated as 180 ° by the polarization analysis unit 121 (FIG. 16), as shown on the right side of FIGS. , The polarization angle of the reflected electromagnetic wave from the point B is 156 °.

  As described above, it is possible to measure a minute step (depth position) below the detection wavelength from the polarization angle of the light reflected by the sample 130 and detected by the nonlinear optical crystal 116. When the polarization analyzer 10 of the first embodiment or the polarization analyzer 50 of the second embodiment is used, the direction of polarization can be determined with an accuracy of ± 0.01 ° or less as shown in FIG. If Δθ = ± 0.01 ° is substituted into equation (10), d = ± λ / 72000. If the wavelength of the incident electromagnetic wave is a terahertz wave with λ = 300 μm, the sample surface can be measured with an accuracy of d = ± 4.2 nm.

  While the delay stage DS of FIG. 16 is fixed during measurement, the delay stage DS is driven in order to obtain a one-to-one correspondence between the polarization angle and the step. Even in this case, only one scan is required for each substance, and it is not necessary to scan a delay stage for acquiring a time waveform during measurement. The scanning of the delay stage here is different from the two-dimensional scanning of the electromagnetic wave on the sample surface.

  The measurement method using the linearly polarized light is the same as that of the third embodiment, that is, the electric field is obtained in advance as a function of the level difference d (E = E (d)), and d is determined from the measured E value. It is not impossible to apply the method of estimating However, the magnitude of the reflected electric field varies depending on the fluctuation of the laser and the reflectance of the measurement object, and in the case of linearly polarized light, there is a restriction that E and d generally do not correspond one-to-one. Not right. On the other hand, the circularly polarized light is very advantageous in that the polarization angle and the step can be made one-to-one correspondence without being affected by the laser fluctuation as shown in the equation (10). The same applies to elliptically polarized light.

  As a method for acquiring in advance the relationship between the polarization angle and the level difference d for each substance, the stage 131 holding the sample may be moved in the z direction instead of driving the delay stage DS. In this case, the correspondence relationship between the polarization angle and the level difference d is acquired while gradually changing the position of the sample 130 in the z direction with an electric micrometer or the like. In any method, the surface step can be directly determined from the polarization angle (polarization direction) of the electromagnetic wave reflected and detected on the surface of the sample 130.

  FIG. 21 is a flowchart of the physical property measurement method according to the third embodiment. In step S201, the sample is irradiated with circularly or elliptically polarized electromagnetic waves, and the relationship between the polarization angle of the reflected light detected by the nonlinear optical crystal and the sample characteristics (for example, surface step d) is acquired in advance. The acquired correspondence information is stored in the measuring apparatus 100. In step S203, the object to be measured is irradiated with circularly or elliptically polarized electromagnetic waves, and the reflected electromagnetic waves are detected with a nonlinear optical crystal. In step S205, the polarization angle (polarization direction) of the detected electromagnetic wave is determined by the method of the first embodiment or the second embodiment. In step S207, the characteristic (surface step d) of the measurement object is determined from the measured polarization direction and the stored correspondence.

  By this method, the surface shape of the substance can be measured at high speed and with high accuracy.

  Example 3 is presented as a specific example of characteristic measurement using the physical property measuring apparatus 100 of the third embodiment. In Example 3, the surface shape of the object is measured, and the measurement result is applied to the performance evaluation of the machine tool.

  First, step S201 in FIG. 21 is performed. Specifically, the linearly polarized terahertz electromagnetic wave generated by the (110) ZnTe crystal 115 is converted into elliptically polarized light by the QWP 111 using the apparatus of FIG. Next, an elliptically polarized terahertz electromagnetic wave pulse is incident on the stage 131 on which the sample 130 is mounted. The reflected wave from the sample is detected using the detection rotating crystal 116 and the balance detector system thereafter, and the amplitude and polarization state are measured based on the ω component and / or the 3ω component of the detected wave. This is repeated while changing the position of the stage 131 in the height direction (z direction).

  FIG. 22 is a schematic diagram for acquiring the correspondence between the surface step of the sample S and the polarization angle of the detected electromagnetic wave. While moving the stage 131 on which the sample 130 is mounted by 10 μm in the z direction of the schematic diagram (A) of FIG. 22, the amplitude and polarization state of the detected electromagnetic wave are measured at each position. The polarization state and amplitude obtained from the measurement result are associated with measurement points and stored in advance in a correspondence table (corresponding to the correspondence information storage unit 123 in FIG. 16). The polarization state of the electromagnetic wave reflected at the position where the level difference is low in the z-position direction (FIG. 22C) is Δθ compared to the polarization state of the electromagnetic wave reflected at the position where the level difference of the sample S is high (FIG. 22B). Therefore, the depth position of the sample can be found from the measured value of the polarization state by referring to the correspondence table, and the step shape of the object can be determined by scanning in the xy plane for measurement. can get.

  FIG. 23 shows the measurement result of the correspondence between the polarization state and the depth position in the z direction. FIG. 23A is a polar plot of the result of simultaneous measurement of the amplitude and polarization of the terahertz electromagnetic wave while moving the stage 131. Each white circle point is a point obtained by moving the z coordinate in the + z direction (the height direction in FIG. 22A) at intervals of 10 μm and stopping the stage 131 during measurement. FIG. 23B is a diagram in which the result of FIG. 23A is re-plotted in the relationship between the z coordinate (horizontal axis) and the polarization angle γ (vertical axis). The absolute value of the z coordinate is a relative value, and the point where z = 0 can be used anywhere. In FIG. 23B, as will be described later, the z coordinate position at x = 0, y = 0 in FIG.

  As shown in FIG. 23B, it can be seen that the detected polarization angle γ monotonously increases with increasing z coordinate value in the range of z = −240 μm to z = 80 μm. That is, in the range of 80 − (− 240) = 320 μm in the z direction, there is a one-to-one correspondence between the z coordinate value and the polarization angle γ, and the z coordinate value is determined from the experimentally obtained polarization angle γ. It can be determined uniquely. In FIG. 23B, it seems that there is no change in the polarization angle in the range of −240 to −200 μm and 70 to 80 μm. However, when this region is enlarged, the value of γ increases monotonously with the increase of the z coordinate. A one-to-one correspondence is ensured.

  In the example of FIG. 23, since the measurement point of the z coordinate is one point at 10 μm, linear interpolation is performed between the measurement points when considering the (z vs. γ) correspondence between the z coordinate and the polarization angle. By doing so, calibration curve data was created.

Next, step S203 in FIG. 21 is performed. Specifically, the object to be measured is irradiated with electromagnetic waves, and the reflected electromagnetic waves are detected by the optical crystal 116. As a measurement sample, a logo mark shown in FIG. This is a 30 mm square aluminum plate engraved with a pen mark having a depth of about 17 μm using a numerically controlled milling machine. The engraving method is as follows.
(A) An aluminum plate of 30 mm × 30 mm × 10 mm is prepared and set on a numerically controlled milling machine.
(B) Using this milling machine, a 30 mm × 30 mm portion of the aluminum plate surface is flattened using a φ50 mm milling cutter.
(C) Engraving a logo mark programmed in advance on a numerically controlled milling machine with a depth of 10 μm. For three engraving parts A, B1, and B2, a circle is drawn from the center of each part at a depth setting value of 10 μm, and engraving is performed while increasing the diameter of the circle. The engraving order of the three parts A, B1, and B2 is first engraved from the upper left to the lower right of the part A. Next, the lower left part B1 is engraved. Finally, the upper right part B2 is engraved. The diameter of the end mill used in each process is 1 mm.
(D) Wash the finished aluminum plate with aerosol.
(E) Next, relative depth measurement was performed using a contact-type thickness meter (resolution: ± 2 μm), and the numerical values shown in FIG. Specifically, when the z-coordinate when the entire aluminum plate is made flat (step (b)) is the reference value (z = 0 μm) and the depth of the part A is measured, the depth of the lower right portion is − It was 16 μm. The measured value of the part B1 (lower left part) was −17 μm. Since the resolution of the contact thickness gauge used for measurement is ± 2 μm, the difference in depth between the two points is within the range of error. Moreover, although it is deeper than the machine setting value (depth 10 μm), this is an error in machining a machine tool.

  For the same sample, thickness measurement was performed using a terahertz elliptically polarized pulse using the apparatus 100 of FIG. The stage 131 was moved at a pitch of 1 mm in the xy direction, and the polarization was measured with the stage 131 stopped during measurement.

  Next, steps S205 and S207 in FIG. 21 are performed. The detection value of the reflected electromagnetic wave from each measurement point (x, y) is analyzed by the polarization analysis unit 121 of the measurement apparatus 100 to obtain the polarization angle γ. The obtained polarization angle γ is sequentially stored in the memory. Then, using the (z vs γ) correspondence (calibration curve) obtained in FIG. 23, the value of z is derived from the measured γ value. Therefore, the final data is the value z (x, y) of the depth z at each (x, y) coordinate. If this is displayed in two-dimensional contour lines, the surface shape of the sample can be displayed in two dimensions. The image shown in FIG. 24B can be obtained by arbitrarily performing tilt correction on the actually acquired data.

  FIG. 24C shows the change in the depth of the cross section along the line CC ′ in FIG. 24B, and FIG. 24D shows the change in the depth in the DD ′ cross section of FIG. As shown in the cross-sectional profile of FIG. 24C or FIG. 24D, we succeeded in obtaining quantitative depth information of about 16 μm.

  From the above, the measuring apparatus 100 according to the third embodiment can be used in a non-contact inspection method for a machining board. Displacement measurement using a laser can be considered as a non-contact measurement method, but there is a risk of blindness when the laser enters the eye. By conducting this with terahertz waves, it becomes possible to conduct a safe and secure investigation. As will be described later, the apparatus 100 in FIG. 16 has a measurement speed / depth resolution comparable to or higher than that of a laser displacement meter.

  The measurement speed will be described below. In obtaining the image of FIG. 24B, integration is performed 10 times at each point. It takes 22ms × 10 = 0.22s per point. Since a total of 841 measurement points (28 mm × 28 mm range scanned at 1 mm pitch), the measurement time is substantially 185 seconds, that is, the measurement is completed in about 3 minutes.

  FIG. 25A shows acquired data when measurement is performed with the number of integrations N = 1. FIG. 25B is a graph showing a cross-sectional shape along the line EE ′ of FIG. As can be seen from the graph, although the resolution is slightly lowered, sufficiently quantitative imaging measurement can be performed. In the case of FIG. 25, the measurement time at each point is only 22 ms. Accordingly, the total measurement time for a total of 8411 points is about 19 seconds, and in principle, the surface unevenness image can be acquired at a very high speed. The measurement is completed within 20 minutes even when the movement time of the stage 131 between each point is included in the actual measurement. If the measurement apparatus 100 of FIG. 16 is combined with a CCD camera capable of measuring a wide range at once, polarization imaging is performed, the measurement time can be dramatically reduced.

  FIG. 26 is a table showing a result of comparing the measurement time of the measurement apparatus 100 of FIG. 16 with a commercially available laser displacement meter using visible laser light. In the comparative example, LK-H085 manufactured by Keyence Corporation having a reference distance (distance between the sample and the laser emission surface or the condenser lens) equivalent to that of the measuring apparatus 100 in FIG. 16 was used.

  With regard to the measurement range, terahertz spectroscopy can adjust the range as much as possible by separately using the so-called Time-of-Flight method of when the peak of the electric field waveform arrives. Since the unevenness can be measured within a range of ± 0.16 mm at the determined position, there is no inferiority compared to the laser displacement meter. Regarding the spot diameter, the apparatus 100 according to the embodiment that is reduced to a circle having a diameter of 1 mm is more convenient than the comparison apparatus that is reduced to a rectangle.

  The principle accuracy of the device 100 of the third embodiment is higher. FIG. 27 shows data indicating what determines the depth resolution of the measurement system of the third embodiment. This is a set of M = 0 to 9 (the position is fixed during this time), and the polarization angle is continuously measured, and then M = 10, the stage 131 is shifted by 1 μm in the −z direction, and M = 10 to 19 (the position is fixed during this time) ), And the polarization angle was measured continuously. As shown in FIG. 27, a depth resolution of 1 μm is sufficiently achieved.

  Finally, the fundamental resolution of the measuring apparatus 100 according to the third embodiment will be considered. From FIG. 27, when the sample is moved by 1 μm, the polarization angle is rotated by 2 °. As described with reference to FIG. 12, a polarization angle determination accuracy of approximately 1 ° is realized in one measurement of 22 ms. Therefore, in principle, a depth determination accuracy of 0.5 μm can be realized in 22 ms. In addition, since the determination accuracy of 0.1 ° can be obtained by 100 times integration (2.2 s), a depth determination accuracy of 0.05 μm can be realized in 2.2 seconds. This means that quicker and more accurate measurement can be performed as compared with the laser displacement meter described in the table of FIG. Furthermore, with 10,000 times integration (220 s), a depth determination accuracy of 0.005 μm can be realized.

Thus, it is considered that the depth determination accuracy is further improved by increasing the number of integrations, applying imaging measurement using a CCD camera, or the like, or a combination thereof.
<Mathematical verification>
Finally, the derivation of equation (0) will be described with reference to the coordinate system of FIG. In FIG. 6, U <b> 1 and U <b> 2 are the refractive index principal axes of the GaP crystal 16. Let β be the angle formed between the [−110] azimuth axis (X axis) of the GaP crystal having the (100) plane and the x axis of the experimental system. The polarization direction of the terahertz electric field E _THz with respect to the x axis is represented by γ = α + β. As shown in FIG. 6B, one refractive index principal axis U1 of the GaP crystal 16 forms an angle of (Ψ + β) with respect to the x axis.

  The angle Ψ is expressed as a function in the polarization direction α of the terahertz electric field with respect to the X crystal azimuth axis, as shown in the formula (A1).

ＧａＰ結晶１６を透過するプローブ光パルスのＵ１方向成分とＵ２方向成分の相対位相シフトは、式（Ａ２）で表される。

The relative phase shift between the U1 direction component and the U2 direction component of the probe light pulse transmitted through the GaP crystal 16 is expressed by the equation (A2).

ここで、ω₀はプローブ光パルスの中心角周波数、Ｅaは電磁波の電場振幅（図６のＥ_THzに対応）、ｄ、ｎ₀、ｒ₄₁はそれぞれＧａＰ結晶の厚さ、屈折率、非線形電気光学定数である。

Here, ω ₀ is the central angular frequency of the probe light pulse, E a is the electric field amplitude of the electromagnetic wave (corresponding to E _THz in FIG. 6), d, n ₀ , and r ₄₁ are the thickness, refractive index, and nonlinear electric power of GaP crystal, respectively. It is an optical constant.

  Since the probe light pulse Eb is always polarized in the x-axis direction, it is represented by the vector of the formula (A3).

ＧａＰ結晶を透過し、１／４波長板（２つの主軸がｘ軸に対して±４５°傾いている）を通過したプローブ光パルスは、式（Ａ４）で表される。

A probe light pulse that has passed through the GaP crystal and passed through a quarter-wave plate (the two principal axes are inclined by ± 45 ° with respect to the x-axis) is expressed by the formula (A4).

ここで、Ｒ（θ）は回転角θでの座標変換行列であり、式（Ａ５）で表される。

Here, R (θ) is a coordinate transformation matrix at the rotation angle θ, and is represented by Expression (A5).

式（Ａ４）において、

In formula (A4),

は実験系での１／４波長板のジョーンズ行列を表す。

Represents the Jones matrix of the quarter-wave plate in the experimental system.

また、Ｇ（α）は電場の印加により生じたＧａＰ結晶の複屈折の行列である。

G (α) is a birefringence matrix of the GaP crystal generated by applying an electric field.

ここでφはプローブ光の偏光の平均位相変化（位相因子）であるが、電場強度の計算が目的であるため省略する。式（Ａ４）を計算すると式（Ａ８）のようになる。

Here, φ is the average phase change (phase factor) of the polarization of the probe light, and is omitted because it is intended to calculate the electric field strength. When formula (A4) is calculated, formula (A8) is obtained.

式（Ａ８）のプローブ光パルス（１／４波長板通過後のプローブ光パルス）をウォラストンプリズムでｘ成分とｙ成分に分離すると、強度の差分は式（Ａ９）で表される（図５参照）。

When the probe light pulse of the formula (A8) (the probe light pulse after passing through the quarter wavelength plate) is separated into the x component and the y component by the Wollaston prism, the difference in intensity is expressed by the formula (A9) (FIG. 5). reference).

ＧａＰ結晶１６を透過するプローブ光パルスのＵ１方向成分とＵ２方向成分の相対位相シフトは、式（Ａ２）で表される。ここでテラヘルツ電場がそれほど強くないとすると、sinΓ(α)二アリーイコールΓ(α)と近似することができる。式（Ａ１）、（Ａ２）、およびα＝γ−βを式（Ａ９）に代入すると、式Ａ（１０）が得られる。これは式（１）すなわち式（０）に対応する。

The relative phase shift between the U1 direction component and the U2 direction component of the probe light pulse transmitted through the GaP crystal 16 is expressed by the equation (A2). If the terahertz electric field is not so strong, it can be approximated as sin Γ (α) two equal Γ (α). Substituting Equations (A1) and (A2) and α = γ−β into Equation (A9) yields Equation A (10). This corresponds to the equation (1), that is, the equation (0).

以上の計算では、ＧａＰ結晶の厚さｄは小さいものと仮定している。

In the above calculation, it is assumed that the thickness d of the GaP crystal is small.

  Polarization analysis using equation (0) or equation (1) is advantageous because the polarization direction and electric field amplitude can be determined instantaneously without being affected by each other. The principle of this polarization analysis is not limited to the analysis of terahertz electromagnetic waves, but is also effective for the polarization analysis of near-infrared rays and visible rays.

  By combining a recent ultrashort pulse laser technology with an appropriate nonlinear optical crystal such as ZnTe, GaP, GaSe, etc., electromagnetic waves can be detected in the same manner as in the embodiment up to frequencies of several tens of GHz and above of about 100 THz. It is. That is, the polarization direction of light from the gigahertz band to the mid to near infrared band can be determined with high speed and high accuracy. In the future, it can be considered that the same detection can be performed for light in the visible band.

  When this polarization analysis is used for material measurement, it is not necessary to acquire a time waveform for each measurement point, and the surface step can be immediately determined from the polarization direction of the reflected electromagnetic wave.

  In the first to third embodiments described above, the generation of electromagnetic waves is not limited to pulse irradiation on the nonlinear optical crystal, and may be generated using a photoconductive antenna or photoexcited plasma. The rotation of the crystal for detection is not limited to the use of an electric motor, and any rotation mechanism such as a rotary actuator or a servo motor can be used. Further, since the detection optical crystal may be rotated relative to the incident electromagnetic wave, the incident electromagnetic wave may be rotated instead of rotating the detection optical crystal.

  This international application claims priority based on Japanese Patent Application No. 2011-258104 filed on November 25, 2011, the entire contents of which are incorporated herein by reference.

10, 50 Polarization analyzer 12, 115 Non-linear optical crystal 16, 116 for electromagnetic wave generation Non-linear optical crystal 17, 117 for detection Motor (rotation mechanism)
19 Electromagnetic wave generation source 20, 52, 152 Detector 21 Polarization analysis unit 29 Optical system 51, 110 for probe light pulse incidence Optical chopper 53, 153 Noise removal calculation unit 100 Physical property measurement device 101 Laser 121 Polarization analysis unit 122 Sample Analysis unit 123 Polarization angle-characteristic correspondence information storage unit 124 Characteristic determination unit

Claims (20)

An electromagnetic wave source that generates electromagnetic waves;
A nonlinear optical crystal having an electro-optic effect;
A rotation mechanism for rotating the crystal relative to the incidence of the electromagnetic wave at an angular frequency ω,
An optical system for injecting a probe light pulse into the crystal in synchronization with irradiation of the crystal with the electromagnetic wave;
A detector for detecting an intensity difference signal of light components orthogonal to each other of the probe light pulse transmitted through the crystal;
An analysis unit that extracts at least one of a ω component and a 3ω component from the intensity difference signal, and determines a polarization direction and an electric field amplitude of the electromagnetic wave based on the extracted ω component and / or the 3ω component;
A polarization analyzer. The analysis unit
ΔI = C · E · [(1/2) cos (ωt + φ) + (3/2) cos (3ωt−φ)]
The phase information and the amplitude information of the ω component and / or the 3ω component of the electromagnetic wave are acquired based on the phase information, and the polarization direction and the electric field amplitude are determined based on the acquired phase information and amplitude information. The polarization analyzer according to 1,
Here, C is a coefficient, and E is the electric field amplitude of the electromagnetic wave.   2. The polarization analyzer according to claim 1, wherein an angular frequency of the rotation mechanism is set so that an odd number of data points are obtained on the crystal during one rotation of the crystal. An optical chopper for turning on and off the irradiation of the electromagnetic wave on the crystal at a predetermined frequency;
An arithmetic unit for calculating a new difference signal by taking a difference between two difference signals obtained at data points at the same angular position on the crystal in two successive rotations of the crystal;
The polarization analyzer according to claim 3, further comprising: When the frequency of the optical chopper is f ₁ , the rotation frequency of the crystal is f ₂ , and the number of data points on the crystal is n (n is an odd number),
f ₁ = (n / 2) · f ₂
The polarization analyzer according to claim 4, wherein: An electromagnetic wave source that generates circularly or elliptically polarized electromagnetic waves;
A nonlinear optical crystal having an electro-optic effect;
A rotation mechanism for rotating the crystal relative to the incidence of the electromagnetic wave at an angular frequency ω,
A first optical system for injecting a probe light pulse into the crystal in synchronization with irradiation of the crystal with the electromagnetic wave;
A sample stage for holding a sample between the electromagnetic wave source and the crystal;
A second optical system for guiding the electromagnetic wave to the sample and guiding the reflected electromagnetic wave reflected by the sample to the crystal;
A detector for detecting an intensity difference signal of light components orthogonal to each other of the probe light pulse transmitted through the crystal;
A polarization analyzer that extracts at least one of a ω component and a 3ω component from the intensity difference signal, and determines a polarization angle of the circularly polarized electromagnetic wave based on the extracted ω component and / or the 3ω component;
A correspondence information storage unit for storing correspondence information indicating a one-to-one correspondence relationship between a polarization angle at the time of incidence of a probe light pulse in the crystal of the electromagnetic wave and a sample characteristic, obtained in advance;
A sample analyzer that determines the characteristics of the sample based on the polarization angle of the reflected electromagnetic wave determined by the polarization analyzer and the correspondence information;
An apparatus for measuring physical properties, comprising:   The physical property measuring apparatus according to claim 6, wherein the first optical system further includes a delay stage having an optical delay element, and the delay stage is driven when the correspondence information is acquired in advance.   The physical property measuring apparatus according to claim 6, wherein the sample stage for holding the sample is driven in the z direction when the correspondence information is acquired in advance.   The electromagnetic wave generation source includes a non-linear optical crystal for generating an electromagnetic wave by applying a light pulse, and an optical element for converting the electromagnetic wave generated by the non-linear optical crystal for generating an electromagnetic wave into circularly polarized light or elliptically polarized light. The physical property measuring apparatus according to claim 6. The characteristic of the sample is the surface shape of the sample,
The physical property measuring apparatus according to claim 6, wherein the correspondence information is information indicating a one-to-one correspondence relationship between a surface position of the sample and a polarization angle of the electromagnetic wave. Irradiating a nonlinear optical crystal having an electro-optic effect with an electromagnetic wave, and rotating the crystal relative to the irradiated electromagnetic wave at an angular frequency ω,
A probe light pulse is incident on the crystal in synchronization with the irradiation of the electromagnetic wave,
Detecting an intensity difference signal of optical components orthogonal to each other of the probe light pulse transmitted through the crystal;
Polarization analysis characterized in that at least one of ω component and 3ω component is extracted from the intensity difference signal, and the polarization direction and electric field amplitude of the electromagnetic wave are determined based on the extracted ω component and / or 3ω component. Method. The determination step includes
ΔI = C · E · [(1/2) cos (ωt + φ) + (3/2) cos (3ωt−φ)]
The phase information and the amplitude information of the ω component and / or the 3ω component of the electromagnetic wave are acquired based on the phase information, and the polarization direction and the electric field amplitude are determined based on the acquired phase information and amplitude information. 11. Polarization analysis method according to 11,
Here, C is a coefficient, and E is the electric field amplitude of the electromagnetic wave.   12. The polarization analysis method according to claim 11, wherein the angular frequency of the crystal is set so that an odd number of data points are obtained on the crystal during one rotation of the crystal. On / off modulation of the irradiation of the electromagnetic wave on the crystal at a predetermined frequency,
In two successive rotations of the crystal, a new difference signal is calculated by taking the difference between two difference signals obtained at data points at the same angular position on the crystal.
Further comprising a step,
The polarized wave according to claim 13, wherein the determining step determines a polarization direction and an electric field amplitude of the electromagnetic wave based on an ω component and / or a 3ω component extracted based on the new difference signal. analysis method. When the frequency of the on / off modulation is f ₁ , the rotation frequency of the crystal is f ₂ , and the number of data points on the crystal is n (n is an odd number),
f ₁ = (n / 2) · f ₂
The polarization analysis method according to claim 14, wherein: For a specific substance, a one-to-one correspondence between the polarization angle of a circularly polarized light or an elliptically polarized electromagnetic wave that irradiates the substance at the time of probe light pulse incidence in the detection nonlinear optical crystal and the characteristics of the substance is shown. Acquire and store correspondence information in advance,
Irradiating the sample with the circularly polarized or elliptically polarized electromagnetic wave, and reflecting the reflected electromagnetic wave reflected on the sample surface to the nonlinear optical crystal for detection rotating at an angular frequency ω,
In synchronization with the irradiation of the crystal by the electric wave, a probe light pulse is incident on the nonlinear optical crystal for detection,
Detecting an intensity difference signal of light components orthogonal to each other of the probe light pulse transmitted through the nonlinear optical crystal for detection;
Extracting at least one of the ω component and the 3ω component from the intensity difference signal, and determining a polarization angle of the circularly or elliptically polarized electromagnetic wave based on the extracted ω component and / or 3ω component;
A physical property measurement method, comprising: determining characteristics of the sample based on the determined polarization angle and the correspondence information.   The physical property measurement method according to claim 16, wherein the correspondence information is obtained by driving an optical delay element disposed on an optical path of the probe light pulse.   The physical property measurement according to claim 16, wherein the correspondence information is acquired by measuring a polarization angle of the electromagnetic wave while driving a stage holding the sample in the z-axis direction.   The circularly or elliptically polarized electromagnetic wave is generated by applying a light pulse to a nonlinear optical crystal for generating an electromagnetic wave to generate the electromagnetic wave and passing the generated electromagnetic wave through a quarter-wave plate. Item 17. The physical property measurement method according to Item 16. The characteristic of the sample is the surface shape of the sample,
The physical property measurement method according to claim 16, wherein the correspondence information is acquired as information indicating a one-to-one correspondence relationship between a surface position of the sample and a polarization angle of the electromagnetic wave.

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