JP2012063214A - Data analysis method in total reflection spectroscopic measurement - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a data analysis method in total reflection spectroscopic measurement capable of accurately and simply deriving a desired optical constant.SOLUTION: In the data analysis method in the total reflection spectroscopic measurement, a value q based on a ratio P of reference amplitude Rto sample amplitude Rand a phase difference Δ between a reference phase Φand a sample phase Φis found out. A complex refractive index of an object 34 to be measured is found out by combining the value q with a Fresnel's reflection equation and a Snell's formula and the desired optical constant of the object 34 to be measured can be accurately and simply derived.

Description

  The present invention relates to a data analysis method in total reflection spectroscopic measurement using terahertz waves.

Conventionally, a total reflection spectroscopic measurement method using visible light and near infrared light is widely known. Usually, the optical constant of the object to be measured is represented as a complex number. For example, when the dielectric constant is ε, ε = ε ₁ + iε ₂ . Thus, when the optical constant has two variables, two relational expressions are required to derive the optical constant. However, in the conventional total reflection spectroscopic measurement method using visible light and near infrared light, only the light intensity can be obtained by the first measurement, and the incident angle, polarization direction, and prism of the light with respect to the total reflection surface are obtained. It was necessary to change the parameters such as the material of the second time and perform the second measurement (for example, see Non-Patent Document 1).

  As a method for deriving two variables by one measurement, for example, there is a method using the Klarmas-Kronig relationship shown in Non-Patent Document 1, but this method is only an approximate expression. In contrast to the conventional total reflection spectroscopic measurement method, there is a total reflection spectroscopic measurement method using a terahertz wave (see, for example, Patent Document 1). In this total reflection spectroscopic measurement method using terahertz waves, both information relating to the intensity of terahertz waves and information relating to the phase can be obtained by one measurement, so that it is possible to measure an optical constant having two variables by one measurement. It is possible.

JP 2004-354246 A

Francis M.M. Mirabella Jr. and N.N. J. et al. Harrick, “Internal Reflection Spectroscopy: Review and Supplement” Abstracts of the 2007 Symposium of the Japan Spectroscopic Society Terahertz Spectroscopy Division p. 8-p. 13 M.M. Born and E.M. By Toru Kusagawa, “Principle of optics I” by Wolf

  However, Patent Document 1 described above does not disclose any method for deriving a desired optical constant from a measurement result of a total reflection spectroscopic measurement method using a terahertz wave. Further, in Non-Patent Document 2, Fresnel's reflection formula is shown as a formula used for data analysis, but such formula is a basic formula of optics shown in Non-Patent Document 3 and the like, It does not represent a data analysis method in a total reflection spectroscopic measurement method using terahertz waves. Therefore, in the total reflection spectroscopic measurement method using terahertz waves, establishment of a method for accurately and simply deriving a desired optical constant from the measurement result is required.

  The present invention has been made to solve the above-described problems, and an object of the present invention is to provide a data analysis method in total reflection spectrometry capable of accurately and easily deriving a desired optical constant.

In order to solve the above problems, a data analysis method in total reflection spectroscopic measurement according to the present invention is a total reflection spectroscopic measurement in which an object to be measured is arranged on a total reflection surface and a terahertz wave totally reflected on the total reflection surface is measured. The reference amplitude R _ref , the reference phase Φ _ref , and the sample amplitude R _sig are obtained by performing Fourier transform on the reference measurement result T _ref and the sample measurement result T _sig obtained by total reflection spectroscopy, respectively. obtains a sample phase [Phi _sig respectively, the reference amplitude _{R ref} and sampled amplitude ratio P between _{R sig,} and the reference phase [Phi _ref and the sample phase [Phi value obtained by the following equation using a phase difference delta (1) with _sig It is characterized in that the optical constant of the object to be measured is derived using q.

In the data analysis method in the total reflection spectroscopy, seeking the reference amplitude R _ref and sampled amplitude ratio P between R _sig, and the reference phase [Phi _ref and the sample phase [Phi value q based on the phase difference Δ between the _sig. By combining this value q with the Fresnel reflection formula and Snell formula, the complex refractive index of the object to be measured can be obtained, and the desired optical constant of the object to be measured can be derived accurately and simply.

  According to the data analysis method in the total reflection spectroscopic measurement according to the present invention, a desired optical constant can be accurately and easily derived.

It is a figure which shows one Embodiment of the total reflection spectroscopic measurement system which implement | achieves the data analysis method in the total reflection spectroscopic measurement which concerns on this invention. It is a side view of the integral prism which is an example of the total reflection prism used for the total reflection spectroscopy measurement system shown in FIG. It is a flowchart which shows the procedure which derives | leads-out the optical constant of a to-be-measured object.

  Hereinafter, preferred embodiments of a data analysis method in total reflection spectroscopy measurement according to the present invention will be described in detail with reference to the drawings.

  FIG. 1 is a diagram showing an embodiment of a total reflection spectroscopic measurement system for realizing a data analysis method in total reflection spectroscopic measurement according to the present invention. As shown in the figure, a total reflection spectroscopic measurement system 1 includes an integrated prism 3 in which a laser light source 2 that emits laser light, a terahertz wave generating element 32, a total reflection prism 31, and a terahertz wave detecting element 33 are integrated. And a detection unit 4 that detects terahertz waves. Further, the total reflection spectroscopic measurement system 1 includes a control unit 5 that controls the operation of the above components, a data analysis unit 6 that performs data analysis based on an output from the detection unit 4, and a processing result in the data analysis unit 6. And a display unit 7 for displaying.

  The laser light source 2 is a light source that generates a femtosecond pulse laser. For example, a femtosecond pulse laser with an average power of 120 mW and a repetition rate of 77 MHz is output from the laser light source 2. The femtosecond pulse laser emitted from the laser light source 2 is divided into pump light and probe light by the beam splitter 13 through the mirrors 11 and 12. Mirrors 14 and 15 and a lens 16 are provided in the probe light optical path C1 through which the probe light propagates. The probe light is collected by the lens 16 and enters a terahertz wave detection element 33 described later.

  On the other hand, a delay unit 21 and a modulator 22 are provided in the optical path C2 for pump light through which the pump light propagates. The delay unit 21 includes a pair of mirrors 23 and 24 and a reflecting prism 25 installed on the movable stage 26. The position of the reflecting prism 25 is moved back and forth with respect to the pair of mirrors 23 and 24, thereby pump light. The delay can be adjusted. The modulator 22 is a part that switches between transmission and blocking of the pump light by, for example, an optical chopper. Based on the signal from the control unit 5, the modulator 22 modulates transmission and interception of pump light at 1 kHz, for example.

  The pump light propagating through the optical path C2 for pump light is condensed by the lens 27 via the mirror 28 and enters the integrated prism 3. As shown in FIG. 2, the total reflection prism 31 constituting the integrated prism 3 is made of, for example, Si, a terahertz wave generating element 32 is fixed on the incident surface side, and terahertz wave detection is performed on the output surface side. Element 33 is fixed. The upper surface of the total reflection prism 31 is a flat surface, and an object to be measured 34 on which various optical constants such as a refractive index, a dielectric constant, and an absorption coefficient are measured is placed.

  As the terahertz wave generating element 32, for example, a nonlinear optical crystal such as ZnTe, an antenna element such as an optical switch using GaAs, a semiconductor such as InAs, a superconductor, or the like can be used. The pulse of the terahertz wave generated from these elements is generally about several picoseconds. When a nonlinear optical crystal is used as the terahertz wave generating element 32, when pump light is incident on the terahertz wave generating element 32, the terahertz wave generating element 32 is converted into a terahertz wave by the nonlinear optical effect. The generated terahertz wave is totally reflected by the upper surface of the total reflection prism 31 and enters the terahertz wave detection element 33.

  As the terahertz wave detecting element 33, for example, an antenna element such as an electro-optic crystal such as ZnTe or an optical switch using GaAs can be used. When an electro-optic crystal is used as the terahertz wave detecting element 33, when the terahertz wave and the probe light are simultaneously incident on the terahertz wave detecting element 33, the probe light receives birefringence due to the Pockels effect. The amount of birefringence of the probe light is proportional to the electric field strength of the terahertz wave. Therefore, the terahertz wave can be detected by detecting the birefringence amount of the probe light.

  As shown in FIG. 1, the detection unit 4 that detects a terahertz wave includes, for example, a λ / 4 wavelength plate 41, a polarizing element 42, a pair of photodiodes 43 and 43, and a differential amplifier 44. . The probe light reflected by the terahertz wave detection element 33 is guided to the detection unit 4 side by the mirror 45, condensed by the lens 46, passes through the λ / 4 wavelength plate 41, and then is polarized by the polarization element 42 such as a Wollaston prism. It is separated into a vertical linearly polarized light component and a horizontal linearly polarized light component. The vertical linearly polarized light component and the horizontal linearly polarized light component of the probe light are converted into electric signals by the pair of photodiodes 43 and 43, respectively, and the difference is detected by the differential amplifier 44. The output signal from the differential amplifier 44 is amplified by the lock-in amplifier 47 and then input to the data analysis unit 6.

  When the terahertz wave and the probe light are simultaneously incident on the terahertz wave detection element 33, a signal having an intensity proportional to the electric field intensity of the terahertz wave is output from the differential amplifier 44, and the terahertz wave and the probe light are output to the terahertz wave detection element 33. Are not incident at the same time, no signal is output from the differential amplifier 44. Further, the evanescent wave radiated when the terahertz wave is reflected by the upper surface of the total reflection prism 31 interacts with the object to be measured 34 placed on the upper surface of the total reflection prism 31, and the object to be measured 34 is placed. The reflectance of the terahertz wave changes as compared with the case where the antenna is not placed. Therefore, the spectral characteristic of the DUT 34 can be evaluated by measuring the change in the reflectance of the terahertz wave.

  The data analysis unit 6 is a part that performs data analysis processing of total reflection spectroscopic measurement based on, for example, a dedicated analysis program for the total reflection spectroscopic measurement system 1, and physically includes a CPU (central processing unit), memory, and input. It is a computer system having an apparatus, a display unit 7 and the like. The data analysis unit 6 executes data analysis processing based on the signal input from the lock-in amplifier 47 and causes the display unit 7 to display the analysis result. Details of the data analysis processing will be described later.

  Subsequently, a data analysis method in the above-described total reflection spectroscopic measurement system 1 will be described. FIG. 3 is a flowchart showing a procedure for deriving the optical constant of the DUT 34. In the following description, it is assumed that a terahertz wave is incident on the upper surface of the total reflection prism 31 as P-polarized light.

As shown in FIG. 3, first, reference measurement and sample measurement are performed using the total reflection spectroscopic measurement system 1 (steps S01 and S02). In the reference measurement, a substance (for example, air) whose optical constant is known is measured, and in the sample measurement, a substance whose optical constant is desired to be measured is measured. Then, a reference amplitude R _ref , a reference phase Φ _ref , a sample amplitude R _sig , and a sample phase Φ _sig are respectively obtained by _performing Fourier transform on the reference measurement result T _ref and the sample measurement result T _sig (step S03).

さらに、上述した比Ｐと位相差Δとを用いて値ｑを式（３）のように定める（ステップＳ０５）。

Next, a ratio P between the reference amplitude R _ref and the sample amplitude R _sig is obtained by the equation (1), and a phase difference Δ between the reference phase Φ _ref and the sample phase Φ _sig is obtained by the equation (2) (step S04).

Further, using the ratio P and the phase difference Δ described above, a value q is determined as shown in Expression (3) (step S05).

Here, the incident angle of the terahertz wave to the total reflection prism 31 is θ _i (see FIG. 2), and the refraction angles obtained from Snell's law in the reference measurement and the sample measurement are θ _ref and θ _sig , respectively. Further, using the Fresnel reflection equation, Pe ⁻ⁱ Δ in the equation (3) can be expressed by the following equation (4).

By substituting the above equation (4) into equation (3) and modifying the equation, the following equation (5) is obtained.

Further, when the complex refractive index of the material constituting the total reflection prism 31 is n _prism and the complex refractive index of the object to be measured 34 is n _sample , Snell's law is expressed by the following equation (6), The square of the complex refractive index of the measurement object 34 is expressed by Expression (7). Therefore, by substituting equation (5) into equation (7), the complex refractive index of the device under test 34 can be obtained, and thereby the desired optical constant of the device under test 34 is derived (step S06). ).

As described above, in the data analysis method in the total reflection spectroscopy, the reference amplitude R _ref and sampled amplitude R _sig ratio of P, and the reference phase [Phi _ref and the sample phase [Phi value based on a phase difference Δ between the _sig q Seeking. Then, by combining this value q with the Fresnel reflection formula and Snell formula, the complex refractive index of the device under test 34 can be obtained, and the desired optical constant of the device under test 34 can be derived accurately and simply.

  DESCRIPTION OF SYMBOLS 1 ... Total reflection spectroscopy measurement system, 2 ... Laser light source, 3 ... Integrated prism, 4 ... Detection part, 5 ... Control part, 6 ... Data analysis part, 7 ... Display part, 31 ... Total reflection prism, 32 ... Terahertz wave Generation element, 33... Terahertz wave detection element, 34.

Claims (1)

A data analysis method in total reflection spectroscopic measurement in which an object to be measured is arranged on a total reflection surface and a terahertz wave totally reflected on the total reflection surface is measured,
A reference amplitude R _ref , a reference phase Φ _ref , a sample amplitude R _sig , and a sample phase Φ _sig are respectively obtained by _performing Fourier transform on the reference measurement result T _ref and the sample measurement result T _sig obtained by the total reflection spectroscopic measurement. Seeking
Using the value q obtained by the following equation (1) using the ratio P between the reference amplitude R _ref and the sample amplitude R _sig and the phase difference Δ between the reference phase Φ _ref and the sample phase Φ _sig A data analysis method in total reflection spectrometry, characterized by deriving an optical constant of an object to be measured.

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