JPH06147985A - Method and instrument for measuring complex index of refraction - Google Patents

Abstract

PURPOSE:To highly sensitively measure the variation of a refractive index at an arbitrary wavelength without noise by providing an electrooptic phase modulator, Mach- Zehnder interferometer, wave length plates, polarization beam splitters, and photoreceptor elements. CONSTITUTION:The title instrument is constituted mainly of an electrooptic phase modulator 2 polarization beam splitters 3-8 sample 9 to be measured, wavelength plates 16-18, and photoreceptor elements 19-26. The angles of the elements 19-26 are set and the expressions of the modulated signal components of two frequency components are finally obtained by aiming at the frequency components only. When the ratio between the signals is taken by performing lock-in detection, phase variation can be measured with extremely high sensitivity without receiving any disturbance from noise existing in the instrument and gain variation. This analysis is performed after making signal components of various kinds of frequencies generated when different kinds of frequency modulation is performed on a modulator 2 and a signal to be measured passes through the wavelength plates 16-18. Therefore, the variation of a refractive index at an arbitrary wavelength and a gain change which occurs in the sample 9 can be measured simultaneously but separately.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a complex refractive index measuring method and apparatus, and more particularly to a Mach-Zehnder interferometer,
The present invention relates to a complex refractive index measuring method and apparatus including a wave plate, a polarization beam splitter, and a light receiving element.

[0002]

2. Description of the Related Art The following methods have been known as conventional methods for measuring complex refractive index.

First, FIG. 3 shows the gain (absorption) of the sample to be measured.
2 shows a measurement system for measuring the dynamic change of In the figure, 1 is a probe light, 2 is a light receiving element, and 3 is a sample to be measured.

In such a configuration, if the change occurring in the sample 3 to be measured is ge ^ir , the probe light electric field after passing through the sample is

[0005]

[Equation 1]

It is represented by Then, the complex index of refraction of the sample 3 to be measured is adjusted by chopping the pump light or the like.

[0007]

[Equation 2]

When modulated as shown in FIG.

[0009]

[Equation 3]

Therefore, a signal proportional to the gain change can be obtained.

However, in the complex refractive index measuring method having such a structure, it is not possible to obtain information on the phase change, that is, the refractive index change, occurring in the sample 3 to be measured.

FIG. 4 shows a conventional Mach-Zehnder interferometer, and information on the phase change can be obtained by the measurement using this interferometer.

In the figure, 1 is probe light, 2 and 3
Is a half mirror, 4 and 5 are total reflection mirrors, 6 is a sample to be measured, 7 is a light receiving element, and 8 is a λ / 4 wavelength plate.

The output light power in such a configuration is

[0015]

[Equation 4]

[0016] Then, when modulation is applied to the signal under measurement, the phase change is expressed by the following equation, including the noise due to the fluctuation between the mirrors of the Mach-Zehnder interferometer.

[0017]

[Equation 5]

As a result, the modulation signal component is represented by the following equation.

[0019]

[Equation 6]

However, the equation (6) is a mixture of the signals of the phase change and the gain change, and Δg needs to be 0 to obtain a signal proportional to the phase change γ ₀ .

For this reason, conventionally, the wavelength of the probe light is set in a region which is completely transparent to the sample to obtain the change in the refractive index of the sample to be measured.

[0022]

However, in order to obtain a change in birefringence using the Mach-Zehnder interferometer configured as described above, as described above, the probe light wavelength is completely applied to the sample. Since it has to be set in a transparent region, there remains a problem that it is impossible to measure the change in refractive index at any wavelength.

Further, the fluctuation between the mirrors cannot be ignored with respect to the wavelength of the probe light, and since it is added to the signal as noise, there remains a problem that highly sensitive measurement cannot be expected. It was

The present invention has been made under such circumstances, and an object of the present invention is to provide a complex refractive index measuring method and apparatus capable of measuring a refractive index change at an arbitrary wavelength. Especially.

Another object of the present invention is to provide a complex refractive index measuring device capable of measuring the refractive index change at an arbitrary wavelength with high sensitivity without noise.

[0026]

In order to achieve such an object, the complex refractive index measuring method according to the present invention basically comprises an electro-optical phase modulator, a Mach-Zehnder interferometer, and a wave plate. , A polarization beam splitter and a light receiving element, wherein the probe light using the electro-optic phase modulator is polarization-modulated at a modulation frequency ω _m , and the signal under measurement is intensity-modulated at a modulation frequency ω _s. Then, the signal light electric field whose phase is inverted by the half-wave plate and the signal light electric field which is not inverted are combined, and the signal components ω _m + ω _s and ω _m or 2ω _m + ω _s and 2ω _m of various frequencies generated by modulation It is characterized by taking a ratio.

Further, in the apparatus for performing the above-mentioned complex refractive index measuring method, the polarization beam splitter is tilted at 45 ° with respect to the direction of the electric field of the probe light.

[0028]

[Operation] The complex refractive index measuring method configured in this way is
Modulations of different frequencies are applied to the electro-optical phase modulator and the signal under measurement, and signal components of various frequencies generated thereby are analyzed after passing through different wave plates.

That is, in this analysis, the real part and the imaginary part of the complex refractive index can be measured independently and simultaneously.

Therefore, the change in the refractive index at an arbitrary wavelength can be measured, and the change in the gain occurring in the sample to be measured can be measured simultaneously and separately.

Furthermore, by tilting the polarization beam splitter at 45 ° with respect to the direction of the electric field of the probe light,
Noise can be blocked by the polarization beam splitter, so that highly sensitive measurements can be achieved.

[0032]

1 is an explanatory view showing a general optical arrangement of a complex refractive index measuring method and its apparatus according to the present invention.

In the figure, 1 is a probe light electric field parallel to the X axis, 2 is an electro-optical phase modulator, 3 to 5 are polarization beam splitters (PBS), 6 is a sample to be measured (DUT),
Reference numerals 7 and 8 are total reflection mirrors, and 9 is a phase plate. And 2
The electro-optical phase modulators 3 and PBSs 3 and 5 are arranged at angles α, β, and θ with respect to the X axis. Further, X'is the direction of transmitting 5 PBS.
The direction of reflection is Y '.

With such a configuration, the output probe light electric field is expressed by the following equation.

[0035]

[Equation 7]

Where γ, Γ and ξ are DUT and
The retardation generated in the electro-optic phase modulator and the phase plate, g is the electric field gain in the DUT.

Now, the input probe optical field is

[0038]

[Equation 8]

Then, the light intensity in the X'and Y'directions is γ
Assuming that the terms that do not depend on Γ and Γ are ignored, the following equations are obtained.

[0040]

[Equation 9]

[0041]

[Equation 10]

Here, Φ = α-β-π / 4, Ψ = β-θ
It has been replaced by.

It is assumed that noise N due to birefringence fluctuation due to temperature change or driving voltage fluctuation is superimposed on the phase difference in the electro-optical phase modulator.

[0044]

[Equation 11]

Let's say.

Further, when the complex refractive index of the sample to be measured is modulated by chopping the pump light or the like, the complex refractive index is expressed by the following equation including the noise due to the fluctuation between the mirrors of the Mach-Zehnder interferometer.

[0047]

[Equation 12]

On the premise of such a thing, next, as shown in FIG.
An example of a complex refractive index measuring device will be described using.

In the figure, 1 is an incident probe light, 2 is an electro-optical phase modulator, 3 to 8 are polarized beam splitters, 9 is a sample to be measured, 10 to 12 are total reflection mirrors, 13
To 15 are variable mirrors, 16 to 18 are λ / 4 and λ, respectively.
1/2, -λ / 4 wave plate, 19 to 26 are light receiving elements, 27,
28 is a differential amplifier, and 29 and 30 are summing amplifiers. Here, the angles of the respective elements are set so that α → π / 4, Φ → 0, Ψ → π / 4, and the expressions (11) and (12) are substituted into the expression (9) to obtain the Bessel function. Expand, ω _m , ω _m + ω _s , 2
Focusing only on the frequency components of ω _m + ω _s and 2ω _m ,

[0050]

[Equation 13]

It becomes Here, Φ << 1 and co
The replacement is performed as s2Φ = 1 and sin2Φ = 2Φ.

Now, let us consider frequency components of ω _m , ω _m + ω _s , 2ω _m + ω _s , and 2ω _m for four ways of ξ = 0, ± π / 2, and π. In addition, assuming that Φ is sufficiently close to 0, the term of Φ is ignored.

(I) When ξ = 0,

[0054]

[Equation 14]

(Ii) When ξ = π / 2

[0056]

[Equation 15]

(Iii) When ξ = π,

[0058]

[Equation 16]

(Iv) When ξ = −π / 2

[0060]

[Equation 17]

Next, consider generating a necessary signal based on the above equation. In the following, γ, Δg, N, n ′ << 1
Considering that, the minute term with respect to the signal is ignored. First, equation (13, 2) and (15, 2)
By the equation and the differential amplification of the equations (14, 1) and (16, 1),

[0062]

[Equation 18]

Is obtained. Therefore, if these signals are lock-in detected and the ratio of these signals is calculated, the phase changes can be performed with extremely high sensitivity without being disturbed by various noises N, n ′ and gain changes Δg existing in the device. It becomes possible to measure the quantity γ ₀ .

That is,

[0065]

[Formula 19]

Further, equations (14,3) and (16,3),
And (13,4) and (15,4) are summed,

[0067]

[Equation 20]

Will be obtained. It is possible to obtain a gain change by performing lock-in detection on the signal of equation (19, 1), but if noise N is a problem, similarly (19, 1)
By taking the ratio with the lock-in signal in the equation (2), it is possible to measure the relative gain change with high sensitivity without being affected by noise. That is,

[0069]

[Equation 21]

It becomes

As described above, according to the complex refractive index measuring method shown in the above embodiment, the electro-optic phase modulator and the signal to be measured are modulated with different frequencies, and the signal components of various frequencies generated thereby are generated. , It is designed to analyze after passing through different wave plates.

That is, in the analysis, the real part and the imaginary part of the complex refractive index can be measured independently and simultaneously.

Therefore, the change in the refractive index at an arbitrary wavelength can be measured, and the change in the gain occurring in the sample to be measured can be measured simultaneously and separately.

Furthermore, by tilting the polarization beam splitter at 45 ° with respect to the direction of the electric field of the probe light,
Noise can be blocked by the polarization beam splitter, so that highly sensitive measurements can be achieved.

[0075]

As is apparent from the above description,
According to the complex refractive index measuring method and the apparatus thereof according to the present invention, it becomes possible to measure the refractive index change at an arbitrary wavelength.

Further, it becomes possible to measure the change in the refractive index at an arbitrary wavelength with extremely high sensitivity.

[Brief description of drawings]

FIG. 1 is an explanatory view showing a general optical system arrangement of a complex refractive index measuring method and its apparatus according to the present invention.

FIG. 2 is an explanatory diagram showing a configuration of an embodiment of a complex refractive index measuring method and apparatus according to the present invention.

FIG. 3 is a configuration diagram showing an example of a conventional gain change measurement system.

FIG. 4 is a configuration diagram showing an example of a conventional measurement system for measuring a change in refractive index.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Probe light, 2 ... Electro-optical phase modulator, 3-8 ... Polarization beam splitter, 9 ... Measured sample, 10-11 ...
Total reflection mirror, 12-15 ... Half mirror, 16-18
... Wave plate, 19-26 ... Light receiving element, 27-30 ... Operational amplifier.

Claims (3)

[Claims] 1. An electro-optical phase modulator, a Mach-Zehnder interferometer, a wave plate, a polarization beam splitter, and a light-receiving element, which are used for probe light using the electro-optical phase modulator. Polarization modulation of the modulation frequency ω _m , intensity modulation of the modulation frequency ω _s is applied to the signal under measurement, the signal light electric field whose phase is inverted by the half-wave plate and the signal light electric field which is not inverted are combined, and A complex refractive index measuring method, characterized in that a ratio of signal components of different frequencies ω _m + ω _s and ω _m or 2ω _m + ω _s and 2ω _m is taken. 2. An electro-optical phase modulator, a Mach-Zehnder interferometer, a wave plate, a polarization beam splitter, and a light-receiving element, the probe light using the electro-optical phase modulator. The polarization modulation of the modulation frequency ω _m and the intensity modulation of the modulation frequency ω _{s to} the signal under measurement are combined with the signal light electric field whose phase is inverted by the half-wave plate and the signal light electric field which is not inverted, and by the modulation. A complex refraction index measuring device comprising: means for calculating a ratio of generated signal components ω _m + ω _s and ω _m or 2ω _m + ω _s and 2ω _m . 3. The complex refractive index measuring device according to claim 2, wherein the polarization beam splitter is inclined at 45 ° with respect to the direction of the electric field of the probe light.