JP7791563B2 - Electric field measurement method and electric field sensor - Google Patents

Description

The present invention relates to an electric field measurement method and an electric field sensor.

There are known electric field measurement methods that use nonlinear optical effects to measure the electric field of an object being measured (Patent Documents 1 and 2). In particular, in recent years, electric field measurement methods that use short-pulse lasers (wavelength: 800 nm or less), such as CARS (Coherent Anti-Stokes Raman Scattering) and E-FISH (Electric Field Induced Second Harmonic generation), have become popular (Non-Patent Documents 1 and 2). This type of electric field sensor uses a short-pulse laser to induce a nonlinear optical effect in the ambient gas, and the resulting response is detected as a signal.

Japanese Patent Application Publication No. 6-88840 Japanese Patent Application Laid-Open No. 2020-118498

CARS (Coherent Anti-stokes Raman Scattering): T. Ito, K. Kobayashi, U. Czarnetzki and Satoshi Hamaguchi: “Rapid formation of electric field profiles in repetitively pulsed high-voltage high-pressure nanosecond discharges”, J. Phys. D: Appl. Phys. 43 (2010) 062001 E-FISH (Electric Field Induced Second Harmonic generation): A. Dogariu, B. M. Goldberg, S. O'Byrne and R. B. Miles: “Species-Independent Femtosecond Localized Electric Field Measurement”, Phys. Rev. Applied 7 (2017) 024024

In the above-mentioned conventional electric field measurement methods, in order to increase the detection efficiency of the target nonlinear light (to increase the probability of nonlinear optical effects occurring), it is necessary to either strongly focus the incident laser on the measurement target or shorten the pulse time width of the incident laser to increase the number of photons incident per unit time and unit space. However, in this type of electric field measurement method, self-contraction or self-diffusion can occur as the incident laser propagates through space, making it difficult to achieve the desired focused state. In particular, when an incident laser with a high energy density both temporally and spatially, such as a short-pulse laser, is used, the number of photons incident per unit time increases, making self-contraction or self-diffusion more likely to occur. This results in the problem of not being able to achieve the desired focused state required to ensure practically sufficient measurement accuracy.

In light of these circumstances, the object of the present invention is to provide an electric field measurement method and electric field sensor that can obtain the spatial distribution of the measured electric field with practically sufficient measurement accuracy.

According to one aspect of the present invention, there is provided an electric field measurement method for determining, as a measurement target electric field, an electric field emitted from a measurement target portion using a nonlinear optical effect. In this electric field measurement method, an incident laser beam for irradiating the measurement target portion is focused on a focusing region where the measurement target portion is located and which extends over a predetermined length substantially perpendicular to the propagation direction of the incident laser beam. The nonlinear light to be measured is extracted from the transmitted light emitted from the measurement target portion, and the measurement target electric field is calculated based on the intensity of the extracted nonlinear light. Measurement parameters are then adjusted so that the intensity of the incident laser beam satisfies a first intensity condition that is equal to or greater than a predetermined lower intensity limit and equal to or less than a predetermined upper intensity limit, and so that the intensity of the incident laser beam satisfies a second intensity condition . The second intensity condition is determined based on the focusing angle of the light focused on the focusing region and the intensity of the incident laser beam. In particular, the lower intensity limit is predetermined as a minimum intensity value that ensures a conversion efficiency, i.e., the efficiency with which the incident laser beam irradiated on the measurement target portion is converted into nonlinear light, equal to or greater than a certain value . The upper intensity limit is predetermined as a maximum intensity value that suppresses plasma generation in the measurement space. The second intensity condition is defined as a relationship between the collection angle and the intensity of the incident laser beam that satisfies the first intensity condition and makes the Rayleigh length of the incident laser beam equal to or less than a certain value, and the power of the incident laser beam per unit area on a plane perpendicular to the direction of travel after passing through a focusing element used to focus the light onto the focusing region is used to determine whether the intensity of the incident laser beam satisfies the first intensity condition. Furthermore, the integrated value of the power on the plane is used as the intensity of the incident laser beam that defines the second intensity condition.

According to another aspect of the present invention, there is provided an electric field sensor that utilizes a nonlinear optical effect to determine an electric field emitted by a measurement target portion as a measurement target electric field. The electric field sensor includes a laser oscillator that emits an incident laser beam to be irradiated onto the measurement target portion, a focusing element that focuses the incident laser beam emitted from the laser oscillator onto a focusing region where the measurement target portion is located, an extractor that extracts the nonlinear light to be measured from the transmitted light emitted from the measurement target portion, and a computing unit that calculates the measurement target electric field based on the intensity of the extracted nonlinear light. In this electric field sensor, measurement parameters are adjusted so that the intensity of the incident laser beam satisfies a first intensity condition that is equal to or greater than a predetermined lower intensity limit and equal to or less than an upper intensity limit, and so that the intensity of the incident laser beam satisfies a second intensity condition . The second intensity condition is defined based on the focusing angle associated with focusing onto the focusing region and the intensity of the incident laser beam. In particular, the lower intensity limit is predetermined as the minimum intensity value that ensures a conversion efficiency, i.e., the efficiency with which the incident laser beam irradiated onto the measurement target portion is converted into nonlinear light, equal to or greater than a certain value. The upper intensity limit is predetermined as the maximum intensity value that suppresses plasma generation in the measurement space. The second intensity condition is defined as a relationship between the collection angle and the intensity of the incident laser that satisfies the first intensity condition and makes the Rayleigh length of the incident laser equal to or less than a certain value. Whether the intensity of the incident laser satisfies the first intensity condition is determined using the power of the incident laser per unit area on a plane perpendicular to the direction of travel of the incident laser after passing through a focusing element used to focus the laser onto the focusing region. Furthermore, the integrated value of the power on the plane is used as the intensity of the incident laser that defines the second intensity condition.

The present invention provides an electric field measurement method and electric field sensor that can acquire the spatial distribution of the measured electric field with practically sufficient measurement accuracy.

1 is a diagram illustrating the overall configuration of an electric field sensor according to an embodiment of the present invention. FIG. 2 is a block diagram illustrating the configuration of a measurement/calculation device. FIG. 2 is a side view (yz plan view) of the measurement stage. FIG. 2 is a plan view (zx plan view) of the measurement stage. FIG. 2 is a perspective view of a main part of a measurement stage. FIG. 1 is a diagram showing a high-resolution region. FIG. 10 is a diagram showing the depth resolution of the electric field sensor of the embodiment. FIG. 10 is a diagram showing the depth resolution of the electric field sensor of Example 2.

Embodiments of the present invention will be described below with reference to the drawings.

Figure 1 is a diagram illustrating the configuration of an electric field sensor 10 according to one embodiment of the present invention. The electric field sensor 10 of this embodiment focuses a pulsed laser (hereinafter also referred to as "incident laser IL") generated from a predetermined laser source and irradiates it onto the object to be measured O, detects the intensity of light (hereinafter also referred to as "nonlinear light EL") excited by the object to be measured O and contained in the light (hereinafter also referred to as "transmitted light TL") that passes through the object to be measured O, and determines the electric field emitted by the object to be measured O based on this intensity.

The electric field sensor 10 of this embodiment described below is assumed to be an E-FISH type electric field sensor in which an incident laser IL is irradiated onto the object to be measured O in a measurement space of atmospheric air, and in an environment in which an electrostatic field is applied to the object to be measured O. However, the configuration of the electric field sensor 10 of this embodiment is not limited to E-FISH type, and can be applied, with appropriate modifications, to other types of sensors that utilize nonlinear optical effects, such as CARS type.

In addition, in this embodiment, the coordinate axis along the direction in which the incident laser IL or nonlinear light EL travels (optical axis direction) is defined as the z-axis, the coordinate axis along the focusing region F (described below) where the incident laser IL is focused is defined as the y-axis, and the coordinate axis along the direction perpendicular to the y-axis and z-axis is defined as the x-axis.

As shown in the figure, the electric field sensor 10 of this embodiment mainly comprises a laser oscillator 20, a lens set 22, a measurement stage 24, a filter set 26, and a measurement/calculation device 28.

The laser oscillation device 20 outputs a laser pulse of a predetermined wavelength as the incident laser IL. Specifically, the laser oscillation device 20 outputs a short pulse laser (particularly, an ultrashort pulse laser or an extremely short pulse laser) such as a nanosecond pulse laser (ns pulse laser), a picosecond pulse laser (ps pulse laser), or a femtosecond pulse laser (fs pulse laser), more specifically an fs pulse laser, as the incident laser IL. Furthermore, the laser oscillation device 20 is configured to be able to arbitrarily adjust the wavelength λ _IL , pulse duration pd _IL , and pulse energy Ep _IL [J] of the incident laser IL.

The lens set 22 is composed of optical equipment for collimating the incident laser light IL emitted from the laser oscillator 20 and for suitably focusing the light onto a focusing region F within the measurement stage 24. More specifically, the lens set 22 in this embodiment is composed of a spherical concave lens 22a, a spherical convex lens 22b, and a cylindrical lens 22c, arranged in this order from the laser oscillator 20. In particular, the cylindrical lens 22c functions as a focusing element that focuses the incident laser light IL onto a linear region (hereinafter also referred to as "focusing region F") extending over a predetermined length in the y-axis direction at a predetermined position z (beam waist position _z0 , described later) that corresponds to the focal length f.

The measurement stage 24 is where the object to be measured, O, is placed. The measurement stage 24 also has electrodes 25 (see Figure 3) for applying an electric field (hereinafter also referred to as the "measurement electric field") from the positive to the negative y-axis direction to the object to be measured O. In other words, the object to be measured O is irradiated with the incident laser IL while the measurement electric field is applied.

The filter set 26 includes various filters for extracting nonlinear light EL having wavelength components to be measured from the transmitted light TL in response to irradiation with the incident laser IL. In particular, the filter set 26 of this embodiment is composed of a short-pass filter 26a that cuts long-wavelength components equal to or greater than a predetermined value, a long-pass filter 26b that cuts short-wavelength components equal to or less than a predetermined value after cutting the long-wavelength components, and a band-pass filter 26c that cuts components outside a predetermined frequency range (i.e., a predetermined wavelength range) after cutting the short-wavelength components.

More specifically, for example, the short-pass filter 26a is an optical filter that reflects wavelength components between 700 nm and 900 nm and transmits wavelength components between 350 nm and 700 nm. The long-pass filter 26b is an ultraviolet-cut filter that transmits only wavelength components of 400 nm or longer. The band-pass filter 26c is a narrow-band band-pass filter that transmits frequency components contained in the transmitted light TL that are twice the frequency of the incident laser light IL (i.e., wavelength components with half the wavelength λ _IL ) and cuts off other frequency components. Therefore, the filter set 26 mainly extracts the nonlinear light EL contained in the transmitted light TL, more specifically, the second harmonic generation (SHG) I _SHG with a wavelength λ _SHG that is half the wavelength λ _IL of the incident laser light IL.

In this embodiment, the second harmonic I _SHG is a component of the nonlinear light EL that is generated when the incident laser IL is irradiated onto the object O to be measured, thereby inducing a third-order nonlinear optical effect (the effect in which the object O to be measured absorbs two photons of wavelength λ _IL and emits one photon with twice the energy and wavelength λ _IL /2).

The measurement/calculation device 28 is a device that primarily receives as input the signal of the transmitted light TL filtered by the filter set 26 and the signal of the incident laser IL, and determines the electric field of the object to be measured O (hereinafter also referred to as the "electric field E to be measured").

2 is a block diagram illustrating the configuration of the measurement/calculation device 28. As shown in the figure, the measurement/calculation device 28 includes a laser intensity acquirer 28a that acquires the intensity _IIL of the incident laser IL, an SHG intensity extractor 28b that extracts the intensity of the SHG contained in the nonlinear light EL (hereinafter also referred to as "SHG intensity I ^{(2ω )} "), and an electric field calculator 28c that calculates the electric field E to be measured based on the acquired intensity _IIL of the incident laser IL and the extracted SHG intensity I ^{(2ω )} .

The laser intensity acquirer 28a is configured to detect or estimate the intensity I _IL of the incident laser IL, in particular the intensity I _IL at the position where the incident laser IL is most concentrated (i.e., the position of the focused area F) (hereinafter also referred to as the "maximum incident laser intensity I ⁽ ω ⁾ _probe "), or an intensity I _IL of a value close enough to be considered identical thereto.

In particular, in this embodiment, the laser intensity acquirer 28a obtains the intensity I _IL of the incident laser IL (particularly the maximum incident laser intensity I ⁽ ω ⁾ _probe ) as the power [W] of the incident laser IL per unit area [ ^cm2 ] of a cross section of a plane (x-y plane) perpendicular to the propagation direction (z-axis direction) of the incident laser IL in the measurement space. In other words, the intensity I _IL of the incident laser IL in this embodiment is a physical quantity that can be identified with the magnitude of the optical electric field generated by the incident laser IL.

The SHG intensity extractor 28b is composed of a spectrometer that disperses the nonlinear light EL from the filter set 26, a CCD imaging sensor consisting of a photomultiplier tube for obtaining the intensity spectrum of the dispersed nonlinear light EL, and a calculator that calculates the SHG intensity I ^{(2ω )} from the obtained intensity spectrum.

Then, the electric field calculator 28c calculates the electric field E to be measured from the following equation (1) based on the maximum incident laser intensity I ⁽ ω ⁾ _probe and the SHG intensity I ^{(2ω )} .

In the formula, "A" is a calibration constant, "N" is the number density of molecules in the measurement space (particularly the air atmosphere), "ω" is the angular frequency of the incident laser IL, and "χ ⁽³⁾ _i,j,k,l (-2ω,0,ω,ω)" is the third-order nonlinear susceptibility tensor. Note that the calibration constant A, number density N, and third-order nonlinear susceptibility tensor χ ⁽³⁾ _i,j,k,l (-2ω,0,ω,ω) may be determined in advance or may be determined appropriately depending on the measurement environment, etc.

Measurements performed by the electric field sensor 10 having the above-described configuration will now be described in further detail. The meanings of the parameters used in the following description are defined as follows.
"Beam diameter D": The size of the range (particularly the range on the xy plane) of the spatial distribution of the incident laser IL, within which the intensity _IIL substantially affects the measurement results relative to the optical axis r.
"Spot size w(z)": The size of the beam area (particularly the length of the beam area in the x-axis direction) that is equal to or greater than a predetermined ratio (e.g., 1/e or 1/ ^e2 ) of the intensity IIL of the incident laser _IL at position z on the optical axis r.
"Beam waist position z ₀ ": the position z on the optical axis r where the incident laser beam IL is most focused (i.e., the position of the focused region F).
"Beam waist diameter w ₀ ": Spot size w(z ₀ ) at beam waist position z ₀ .
"Rayleigh range z (Ra)": the range on the z-axis where the cross-sectional area of the beam (incident laser IL or transmitted light TL) is less than twice the cross-sectional area at the beam waist position _z0 .
"Rayleigh length Z _r ": the length on the z-axis from the beam waist position z ₀ to the end of the Rayleigh range z (Ra).
"Convergence angle θ": the angle between the optical axis r and the outer edge of the beam area, starting from the beam waist position _z0 (focusing area F). In other words, the convergence angle θ is a physical quantity that indicates the ease of focusing the incident laser IL in the focusing area F after passing through the cylindrical lens 22c.

In this embodiment, as shown in FIG. 5, which will be described later, the distribution of the incident laser IL after passing through the cylindrical lens 22c, which is the focusing element, has a substantially uniform shape along the x-z plane (more specifically, a triangle with the focusing area F as its vertex). In other words, in this embodiment, the size of the angle of the vertex of this triangle (i.e., a one-dimensional angle) is directly related to the ease of focusing the incident laser IL in the focusing area F, and so this is used as the focusing angle θ. On the other hand, depending on the shape of the distribution of the incident laser IL after focusing, if it is difficult to express the ease of focusing the incident laser IL in the focusing area F using only a one-dimensional angle, the focusing angle θ may be defined as an appropriate solid angle.

Figure 3 is a side view (y-z plan view) of the measurement stage 24, Figure 4 is a plan view (z-x plan view) of the measurement stage 24, and Figure 5 is a perspective view of the main parts of the measurement stage 24. Note that in Figure 5, the object to be measured O and electrode 25 have been omitted to simplify the drawing.

As shown in the figure, the incident laser IL is focused by the cylindrical lens 22c and irradiated onto the object to be measured O. The transmitted light TL, which includes the nonlinear light EL emitted from the object to be measured O, is then emitted toward the filter set 26.

In the electric field measurement method using the electric field sensor 10 of this embodiment described above, the incident laser IL is focused onto the focusing region F by the cylindrical lens 22c. Therefore, the electric field E to be measured of the object O can be determined as a spatial distribution in the direction in which the focusing region F extends (the y-axis direction) (hereinafter also simply referred to as the "electric field spatial distribution").

In particular, in this embodiment, by imposing a first condition (hereinafter also referred to as the "first intensity condition") on the intensity _IIL of the incident laser IL, it is possible to achieve practically sufficient measurement accuracy in the measurement of the above-mentioned electric field spatial distribution. Furthermore, by imposing a second condition (hereinafter also referred to as the "second intensity condition") on the intensity _IIL of the incident laser IL, on the premise that the above-mentioned first condition is satisfied, it is possible to achieve high depth resolution (the shortness of the area in the z-axis direction that can be distinguished during measurement) in the measurement of the electric field spatial distribution. The first intensity condition and the second intensity condition will be described in detail below.

[First strength condition]
The inventors have found that the main reasons why practically sufficient measurement accuracy cannot be obtained in measuring the spatial distribution of the electric field are a decrease in conversion efficiency due to self-diffusion of the incident laser IL, or the generation of ionization (plasma) of atoms or molecules in the measurement space due to self-contraction of the incident laser IL. As a result of extensive research, the inventors have found that the occurrence of self-diffusion or self-contraction, which are factors that reduce measurement accuracy, is strongly correlated with the distribution of the intensity _IIL of the incident laser IL in the measurement space.

Therefore, the first intensity condition in this embodiment is defined as a condition in which the intensity _IIL is equal to or greater than the lower intensity limit _Ilo determined from the viewpoint of maintaining conversion efficiency and equal to or less than the upper intensity limit _Iul determined from the viewpoint of suppressing plasma generation, and the measurement parameters are adjusted so that this first intensity condition is satisfied.

The intensity lower limit I _lo is determined in advance through experiments or the like as the minimum value of the intensity I _IL that serves as a criterion for determining whether the conversion efficiency has reached a level that allows for practically acceptable measurement accuracy. As can be understood by referring to the above formula (1), the SHG intensity I ^{(2ω )} to be detected depends on the intensity I _IL of the incident laser IL (particularly the maximum incident laser intensity I ⁽ ω ⁾ _probe ), the electric field E to be measured, and the type and state (pressure or temperature) of the atmospheric gas. Therefore, once the electric field E to be measured is set to a certain value and the type and state of the atmospheric gas are determined, the intensity lower limit I _lo can be determined as the lower limit of the intensity I _IL of the incident laser IL that corresponds to the minimum allowable detection sensitivity. The intensity lower limit I _lo is set, for example, in the range of 10 ¹⁰ [J/(s·cm ² )] to 10 ¹¹ [J/(s·cm ² )].

The upper intensity limit _Iul is determined in advance through experiments or the like as the maximum value of the intensity _IIL that suppresses the generation of plasma caused by the spatial propagation of the incident laser IL within a range that maintains practical measurement accuracy. In particular, the upper intensity limit _Iul is determined as the value of the maximum incident laser intensity I ⁽ ω ⁾ _probe that generates plasma emission. The specific value of the upper intensity limit _Iul can be determined appropriately depending on necessary parameters such as the type and state of the atmospheric gas. The upper intensity limit _Iul is set, for example, in the range of ¹⁰¹³ [J/(s· ^cm2 )] to ¹⁰¹⁵ [J/(s· ^cm2 )].

Furthermore, as the intensity _IIL of the incident laser beam IL used to determine whether the first intensity condition is satisfied, it is preferable to use a value that is as close as possible to the above-mentioned maximum incident laser intensity I ⁽ ω ⁾ _probe . More specifically, it is preferable to use a value obtained by sensors (not shown) that are provided to estimate or detect the intensity _IIL at a position close to the beam waist position _z0 (position of the focusing region F).

The measurement parameters are any one or more parameters that can affect the change in intensity _IIL of the incident laser IL and can be adjusted by arranging each device included in the electric field sensor 10 to perform the electric field measurement method and/or manipulating the control parameters of each device (such as manipulating the output).

In particular, the measurement parameters in this embodiment include one or more parameters selected from the group consisting of the beam diameter D, pulse width pd _IL , pulse energy Ep _IL , and wavelength λ _IL of the incident laser IL, and focal length f.

More specifically, in this embodiment, the intensity _IIL of the incident laser IL can be specifically determined by increasing the beam diameter D, decreasing the pulse width _pdIL , increasing the pulse energy _EpIL , shortening the wavelength _λIL , and/or decreasing the focal length f, within a range not exceeding the _intensity upper limit value Iul.

On the other hand, the beam diameter _D is reduced, the pulse width pd _IL is increased, the pulse energy Ep _IL is reduced, the wavelength λ IL is increased, and/or the focal length f is increased, within a range in which the intensity I _IL of the incident laser _IL does not fall below the intensity lower limit value I lo.

Here, the beam diameter D, which is also used as a measurement parameter, is preferably a value detected or estimated at a position immediately before incidence on the cylindrical lens 22c, which is the focusing element (in this embodiment, a position between the spherical convex lens 22b and the cylindrical lens 22c). In particular, the beam diameter D can be any value that correlates with the size of the cross-sectional shape of the incident laser IL (the extent of spread of the incident laser IL in the x-y plane). For example, if the cross-sectional shape of the incident laser IL is a polygon such as a square, the beam diameter D can be the length of one side, the length of the diagonal, or the area. Furthermore, if the cross-sectional shape of the incident laser IL is circular, the diameter, perimeter, or area can also be used as the beam diameter D. In particular, from the perspective of achieving the first intensity condition, the beam diameter D is preferably selected from the range of 0.1 mm to 50 mm, for example.

The beam diameter D can also be adjusted by placing any optical device (optical device that replaces or is used in conjunction with the spherical concave lens 22a and spherical convex lens 22b of this embodiment) in front of the cylindrical lens 22c that ultimately focuses the incident laser IL, and/or by adjusting the area of the exit surface of the incident laser IL from the laser oscillator device 20.

Furthermore, the pulse width pd _IL , pulse energy Ep _IL , and wavelength λ _IL , which are also used as measurement parameters, are adjusted to desired values as appropriate by selecting the specifications of the laser oscillation device 20 and manipulating the output settings of the laser oscillation device 20. The wavelength λ _IL of the incident laser IL may be adjusted by providing a predetermined filter element. In particular, from the viewpoint of realizing the first intensity condition, a preferable pulse width pd _IL is selected, for example, from the range of 10 fs to 1 ns. Furthermore, a preferable pulse energy Ep _IL is selected, for example, from the range of 0.1 mJ to 1 J. Furthermore, a preferable wavelength λ _IL is selected, for example, from the range of 0.8 μm to 5 μm.

The focal length f used as a measurement parameter is determined as the distance from the exit surface of the lens set 22 for incident light to the imaging position (beam waist position z ₀ ), which is determined according to the structure (thickness, material, radius of curvature, etc.) of the lens set 22 (particularly, the cylindrical lens 22c in this embodiment). In particular, a preferable focal length f from the viewpoint of realizing the first intensity condition is selected from the range of 10 mm to 1000 mm, for example.

As described above, by adjusting the measurement parameters so that the intensity IIL of the incident laser _IL satisfies the first intensity condition, it is possible to achieve practically sufficient measurement accuracy in measuring the electric field spatial distribution, even when using a high-intensity incident laser IL such as a short-pulse laser (particularly, an ultrashort-pulse or ultrashort-pulse laser).

[Second strength condition]
The inventors have come to the idea that by satisfying the first intensity condition, sufficient measurement accuracy can be achieved in measuring the electric field spatial distribution, and then by imposing a stricter second intensity condition on the intensities I and _{I L} , the depth resolution in the measurement can be further improved. The details of this will be explained below.

First, assuming that the incident laser beam IL follows the characteristics of an ideal Gaussian beam (an electromagnetic wave whose intensity distribution centered on the optical axis r is approximately a Gaussian distribution), the Rayleigh length _Zr is determined by the following equation (2) based on the beam waist diameter _w0 or the collection angle θ, and the wavelength _λIL of the incident laser beam IL.

The beam waist diameter w ₀ is expressed by the following equation (3).

In addition, "NA" in the formula (3) means the numerical aperture.

Therefore, theoretically, the incident laser beam IL behaves in accordance with the characteristics expressed by the above formulas (2) and (3). That is, by appropriately adjusting the measurement parameters, the beam diameter D, the wavelength λ _IL , or the focal length f included in formula (2) or (3), it is possible to appropriately control the shortness of the Rayleigh length _Zr (the high depth resolution).

On the other hand, as described above, when nonlinear effects such as plasma generation due to the use of a high-intensity incident laser IL occur, the focusing characteristics of the incident laser IL no longer follow equations (2) and (3). Therefore, it becomes difficult to adjust the Rayleigh length _Zr to a desired value by simply adjusting the measurement parameters based on equation (2) or (3). As a result, it is difficult to improve the depth resolution.

In response to this, the inventors, through extensive research, have come up with the idea that if the intensity _IIL of the incident laser IL further satisfies a second intensity condition, the occurrence of nonlinear effects that affect the control of the Rayleigh length _Zr can be suppressed, thereby improving the depth resolution.

Specifically, the second intensity condition in this embodiment is defined as a two-dimensional closed region (hereinafter also referred to as "high-resolution region R") defined by two variables: the collection angle θ and the intensity peak P _L of the incident laser IL. Note that the intensity peak P _L ([J/s]) in this embodiment is the maximum peak height (e.g., peak value) of the value obtained by integrating the intensity I _IL [J/(s·cm ² )] over a spread region in a plane perpendicular to the z-axis direction.

6 is a diagram showing a high-resolution region R. As shown in the figure, the high-resolution region R is defined so that, when the collection angle θ varies within a range between its minimum and maximum values, the range of intensity _IIL that is permissible from the viewpoint of improving depth resolution is more limited than the range of intensity _IIL that is determined from the viewpoint of satisfying the first intensity condition. This will be explained in more detail below.

5, when the incident laser beam IL is incident on the cylindrical lens 22c, if the converging angle θ is fixed, the area of the beam divergence region at the focal position (beam waist position z ₀ ) is H×w _0. Therefore, by using the above equations (2) and (3), the relationship between the converging angle θ and the maximum incident laser intensity I ⁽ ω ⁾ _probe at which the Rayleigh length Z _r is equal to or less than a certain value can be determined as shown in the following equation (4).

Here, applying the intensity lower limit I _lo associated with the first intensity condition to the maximum incident laser intensity I ⁽ ω ⁾ _probe in equation (4) determines the lower limit of the intensity peak P _L according to the collection angle θ (curve C1 in FIG. 6 ). On the other hand, applying the intensity upper limit I _ul associated with the first intensity condition to the maximum incident laser intensity I ⁽ ω ⁾ _probe in equation (4) determines the upper limit of the intensity peak P _L according to the collection angle θ (curve C2 in FIG. 6 ). That is, the high-resolution region R between curves C1 and C2 defines the range of intensity I _IL (more specifically, the range of the intensity peak P _L ) that satisfies both the first and second intensity conditions. Therefore, by adjusting the measurement parameters so that the intensity peak P _L is included in the high-resolution region R, it is possible to further improve the depth resolution while maintaining the required measurement accuracy.

Note that the specific means for adjusting the measurement parameters is not limited to the specific embodiments described above with reference to Figures 1 and 2, and can be replaced by any means known in the art.

The effects of the electric field measurement method according to this embodiment described above will now be explained.

In this embodiment, there is provided an electric field measurement method that utilizes a nonlinear optical effect to determine an electric field emitted by a measurement target portion (measurement target O) as a measurement target electric field E. This electric field measurement method focuses an incident laser IL to be irradiated onto the measurement target O in a light-focusing region F where the measurement target O is placed and which extends over a predetermined length substantially perpendicular to the traveling direction of the incident laser IL (along the y-axis direction), extracts a measurement target nonlinear light EL from a transmitted light TL emitted from the measurement target O, and calculates a measurement target electric field E based on the intensity (in particular, the SHG intensity I ^{(2ω )} ) of the extracted nonlinear light EL.

In particular, in this electric field measurement method, measurement parameters are adjusted so as to satisfy a first intensity condition in which the intensity IIL of the incident laser _IL is equal to _or greater than a predetermined intensity lower limit _Ilo and equal to or less than an intensity upper limit Iul. Furthermore, the intensity lower limit _Ilo is a value determined from the viewpoint of ensuring that the conversion efficiency, which is the efficiency with which the incident laser IL irradiated onto the object O is converted into nonlinear light EL, is equal to or greater than a certain value. Moreover, the intensity upper limit _Iul is a value determined from the viewpoint of suppressing the generation of plasma in the measurement space.

As a result, even if nonlinear optical phenomena such as self-contraction or self-diffusion occur during the propagation of the incident laser IL through the measurement space, making it difficult to predict the focusing state of the incident laser IL, the electric field E to be measured (particularly its spatial distribution) can be measured with high precision. In particular, even when a high-intensity incident laser IL is used, it is possible to ensure measurement precision sufficient for practical use.

Furthermore, in the electric field measurement method of this embodiment, a second intensity condition is set based on the collection angle θ of the light collection onto the light collection region F and the intensity _IIL of the incident laser IL, and measurement parameters are adjusted so that the intensity _IIL of the incident laser IL satisfies the second intensity condition. The second intensity condition is defined as a relationship between the collection angle θ and the intensity _IIL of the incident laser IL (intensity peak P _L ) that satisfies the first intensity condition and makes the Rayleigh length _Zr of the incident laser IL equal to or less than a certain value (high-resolution region R).

This makes it possible to improve depth resolution while ensuring practically sufficient measurement accuracy when measuring the electric field E to be measured.

Furthermore, to determine whether the intensity _IIL of the incident laser IL satisfies the first intensity condition, the power of the incident laser IL per unit area on a plane perpendicular to the propagation direction (z-axis direction) after passing through a focusing element (particularly the cylindrical lens 22c) used to focus the light onto the focusing region F (i.e., the maximum incident laser intensity I ⁽ ω ⁾ _probe ) is used. Furthermore, the integral value of the power of the incident laser IL on the above plane (intensity peak P _L ) is used as the intensity _IIL of the incident laser IL that defines the second intensity condition.

This realizes a specific embodiment that is preferable from the viewpoint of further improving measurement accuracy as a parameter related to the intensity _IIL used to determine whether the first intensity condition and the second intensity condition are satisfied.

In particular, by using a value as close as possible to the maximum incident laser intensity I ⁽ ω ⁾ _probe to determine whether the intensity IIL of the incident laser _IL satisfies the first intensity condition, the accuracy in the comparison with the intensity upper limit value _Iul (the accuracy in determining whether plasma is generated in the actual measurement space) can be further improved. As a result, the measurement accuracy is further improved.

The measurement parameters include one or more parameters selected from the group consisting of the beam diameter D, pulse width pd _IL , pulse energy Ep _IL , wavelength λ _IL , and focal length f of the incident laser IL.

This provides specific measurement parameters that are preferable for adjusting the intensity _IIL of the incident laser beam IL to satisfy the first and second intensity conditions.

Furthermore, the beam diameter D of the incident laser IL is detected or estimated at a position immediately before it enters the focusing element (particularly the cylindrical lens 22c).

This allows the beam diameter D of the incident laser IL to be a more specific measurement parameter used in actual measurements based on the specific configuration of the measurement system.

Furthermore, in this embodiment, the pulse width pd _IL , pulse energy Ep _IL , and wavelength λ _IL are adjusted by operating the laser oscillation device 20 that oscillates the incident laser IL.

This realizes a specific configuration for adjusting the pulse width pd _IL , pulse energy Ep _IL , and wavelength λ _IL to satisfy the first intensity condition and/or the high resolution region R.

In particular, it is preferable to use an ultrashort pulse laser (or extremely short pulse laser) as the incident laser IL. This makes it possible to more reliably achieve the desired conversion efficiency of the incident laser IL during measurement.

In the electric field measurement method of this embodiment, the second harmonic I _SHG is extracted as the nonlinear light EL, and the electric field E to be measured is calculated from the intensity of the second harmonic I _SHG (SHG intensity I ⁽² ω ⁾ ).

This makes it possible to achieve practically sufficient measurement accuracy and high depth resolution, assuming that the second harmonic I _SHG , which provides a relatively high signal strength, is detected to measure the electric field E to be measured.

Furthermore, this embodiment provides an electric field sensor 10 that utilizes a nonlinear optical effect to determine the electric field emitted by the measurement target (object O) as the electric field E to be measured.

In particular, this electric field sensor 10 comprises a laser oscillator 20 that emits an incident laser IL to be irradiated onto the object to be measured O, a focusing element (particularly a cylindrical lens 22c) that focuses the incident laser IL emitted from the laser oscillator 20 onto a focusing region F where the object to be measured O is located, an extraction device (SHG intensity extractor 28b) that extracts the nonlinear light EL to be measured from the transmitted light TL emitted from the object to be measured O, and a calculation device (electric field calculator 28c) that calculates the electric field E to be measured based on the intensity (particularly the SHG intensity I ^{(2ω )} ) of the extracted nonlinear light EL.

In this electric field sensor 10, the measurement parameters are adjusted so as to satisfy a first intensity condition in which the intensity _IIL of the incident laser IL is equal to or greater than a predetermined intensity lower limit _Ilo and equal to or less than an intensity upper limit _Iul . Furthermore, the intensity lower limit _Ilo is a value determined from the viewpoint of ensuring that the conversion efficiency, which is the efficiency with which the incident laser IL irradiated onto the object O is converted into nonlinear light EL, is equal to or greater than a certain value. Moreover, the intensity upper limit _Iul is a value determined from the viewpoint of suppressing the generation of plasma in the measurement space.

This provides an electric field sensor 10 with a configuration suitable for implementing an electric field measurement method that achieves practically sufficient measurement accuracy for the electric field E to be measured.

The electric field measurement method and electric field sensor 10 of the present embodiment described above can be suitably applied in a variety of fields, including medical cell analysis, analysis of natural phenomena such as lightning strikes, and monitoring of processing accuracy in precision processing such as semiconductor etching, even in cases where measurement using existing sensors (especially sensors that use laser sources with high photon density) is difficult.

The present invention will be explained in more detail below using Examples 1 and 2, but the present invention is not limited to these examples.

Example 1
Measurement accuracy was evaluated for the electric field measurement method based on the following equipment and measurement conditions.

[Device configuration]
Laser oscillator 20: PHAROS PH2-SP-1mJ (manufactured by Light Conversion)
Lens set 22 (22a: concave cylindrical lens (f=-20 mm), 22b and 22c: convex spherical lenses (f=80 mm))
Filter set 26 (26a: #84-714 (Edmund), 26b: #65-132 (Edmund), 26c: #39-349 (Edmund))

Measurement/Calculation Unit 28: istar DH320T-18F-03-LP (Andor)

[Measurement parameter settings]
The measurement parameters were adjusted so that the estimated value of the intensity _IIL of the incident laser IL near the focusing area F (≒ maximum incident laser intensity I ⁽ ω ⁾ _probe ) would satisfy the first intensity condition. The specific adjusted measurement parameters are as follows:

Pulse width: 190 fs
・Pulse energy 0.5 mJ
Wavelength of incident laser λ _IL : 1030 nm
Beam diameter D: 5 mm
・Focal length f: 80mm

[Evaluation of measurement accuracy]
Under the above conditions, the transmittance T(z) of the incident laser IL at each position z on the object O to be measured was measured. Meanwhile, the ideal value of the transmittance T(z) in the electric field measurement was determined based on the following formulas (5) and (6).

In the formula, "β" represents the two-photon absorption coefficient, "I ₀ (t)" represents the time profile of the maximum incident laser intensity I ⁽ ω ⁾ _probe , "L" represents the thickness of the object O (length along the z-axis), and "z" represents the position of the object O on the z-axis.

The plot in the graph in Figure 7 shows the measured values of transmittance T(z) in Example 1. Note that the solid line in Figure 7 is an approximation curve generated from equations (5) and (6) for transmittance T(z) under the measurement parameters in Example 1.

Furthermore, the Rayleigh length _zr was calculated based on the approximation curve, and twice this value ( _2zr ) was used as an index representing the depth resolution. As a result, the depth resolution _2zr was found to be 400 μm.

Example 2
The measurement accuracy and depth resolution were evaluated for the electric field measurement method based on the following equipment and measurement conditions.

[Device configuration]
The same as in Example 1 was used except that lens set 22 (22a: convex spherical lens f=-40 mm, 22b: convex spherical lens f=150 mm, 22c: convex cylindrical lens f=80 mm) was used.

[Measurement parameter settings]
(1) An appropriate collection angle θ was set in advance through experiments etc., assuming the same measurement parameters as in Example 1. Specifically, the collection angle θ was set to 0.25 [rad].

(2) With reference to the collection angle θ-intensity I _/L table (a table defining the second measurement conditions) shown in Fig. 6, the measurement parameters were adjusted so that the intensity peak P/ _L was included in the high-resolution region R from the set collection angle θ. The specific adjusted measurement parameters are as follows:

Pulse width: 190 fs
・Pulse energy 0.1 mJ
Wavelength of incident laser λ _IL : 1030 nm
Beam diameter D: 20 mm
・Focal length f: 80mm

[Evaluation of measurement accuracy]
The measurement accuracy was evaluated in the same manner as in Example 1.

The plot of the graph in Fig. 8 represents the measured values of transmittance T(z) in Example 2. The solid line in Fig. 8 is an approximation curve generated from Equation (5) and Equation (6) for the transmittance T(z) under the measurement parameters in Example 2. As shown in Fig. 8, the measured values in Example 2 generally follow the approximation curve for transmittance T(z). The depth resolution _2zr was calculated from the measured values. The depth resolution _2zr was 46 µm.

[Results and Discussion]
7 and 8, in Examples 1 and 2 that satisfy the first intensity condition, the transmittance T(z) generally follows the curve of the ideal value. That is, it is considered that the measurement method of Examples 1 or 2 ensures at least a practically sufficient measurement accuracy in measuring the electric field spatial distribution.

Furthermore, in Example 2, which satisfies the second intensity condition, the depth resolution is significantly improved compared to Example 1. This is thought to be due to Example 2 satisfying the second intensity condition.

The above describes embodiments of the present invention, but these embodiments merely illustrate some of the application examples of the present invention, and are not intended to limit the technical scope of the present invention to the specific configurations of the above embodiments.

For example, the electric field sensor 10 may be configured to include a polarization splitter that splits the nonlinear light EL to be measured into multiple polarization directions (e.g., the y-axis direction and the z-axis direction), and the measurement/calculation device 28 may determine the electric field E to be measured corresponding to the multiple polarization directions based on the nonlinear light EL split into multiple directions by the polarization splitter.

10 electric field sensor 20 laser oscillation device 22c cylindrical lens 28 measurement/calculation device 28a laser intensity acquisition device 28b SHG intensity extractor 28c electric field calculation device

Claims (7)

An electric field measurement method for determining an electric field emitted from a measurement target portion as a measurement target electric field by utilizing a nonlinear optical effect,
an incident laser beam for irradiating the measurement portion is focused on a focusing region in which the measurement portion is disposed and which extends over a predetermined length substantially perpendicular to the traveling direction of the incident laser beam;
extracting nonlinear light to be measured from transmitted light emitted from the measurement target portion;
calculating the electric field to be measured based on the extracted intensity of the nonlinear light;
adjusting measurement parameters so that the intensity of the incident laser satisfies a first intensity condition that is equal to or greater than a predetermined intensity lower limit value and equal to or less than a predetermined intensity upper limit value, and so that the intensity of the incident laser satisfies a second intensity condition ;
the second intensity condition is defined based on a collection angle related to collection of light onto the light collection region and an intensity of the incident laser,
the intensity lower limit value is predetermined as a minimum value of intensity that makes a conversion efficiency, which is an efficiency at which the incident laser irradiated on the measurement portion is converted into the nonlinear light, equal to or greater than a certain value,
the upper intensity limit value is predetermined as a maximum value of the intensity that suppresses the generation of plasma in the measurement space,
The second strength condition is
a relationship between the collection angle and the intensity of the incident laser that satisfies the first intensity condition and makes the Rayleigh length of the incident laser equal to or less than a certain value,
determining whether the intensity of the incident laser satisfies the first intensity condition using the power of the incident laser per unit area on a plane perpendicular to the traveling direction after passing through a focusing element used to focus the light onto the focusing region;
an integrated value of the power in the plane is used as the intensity of the incident laser that defines the second intensity condition;
Electric field measurement method. 2. The electric field measurement method according to claim 1 ,
The measurement parameters are:
The incident laser includes one or more parameters selected from the group consisting of a beam diameter, a pulse width, a pulse energy, and a wavelength of the incident laser, and a focal length at which light is focused on the focused region.
Electric field measurement method. 3. The electric field measurement method according to claim 2,
the measurement parameters include the beam diameter;
The beam diameter is detected or estimated at a position immediately before the beam is incident on a focusing element used to focus the beam onto the focusing region.
Electric field measurement method. The electric field measurement method according to any one of claims 1 to 3 ,
Furthermore, the nonlinear light is split into a plurality of polarization directions,
determining the electric field to be measured corresponding to the plurality of polarization directions;
Electric field measurement method. The electric field measurement method according to any one of claims 1 to 4 ,
The incident laser is an ultrashort pulse laser .
Electric field measurement method. The electric field measurement method according to any one of claims 1 to 5 ,
extracting a second harmonic as the nonlinear light;
calculating the electric field to be measured from the intensity of the incident laser and the intensity of the second harmonic;
Electric field measurement method. An electric field sensor that utilizes a nonlinear optical effect to determine an electric field emitted from a measurement target as a measurement target electric field,
a laser oscillator that emits an incident laser to be irradiated onto the measurement target portion;
a focusing element that focuses the incident laser emitted from the laser oscillator on a focusing region where the measurement target is located;
an extracting device that extracts nonlinear light to be measured from transmitted light emitted from the measurement target portion;
a calculation device that calculates the electric field to be measured based on the extracted intensity of the nonlinear light,
measurement parameters are adjusted so that the intensity of the incident laser satisfies a first intensity condition that is equal to or greater than a predetermined intensity lower limit value and equal to or less than a predetermined intensity upper limit value, and so that the intensity of the incident laser satisfies a second intensity condition ;
the second intensity condition is defined based on a collection angle related to collection of light onto the light collection region and an intensity of the incident laser,
the intensity lower limit value is predetermined as a minimum value of intensity that makes a conversion efficiency, which is an efficiency at which the incident laser irradiated on the measurement portion is converted into the nonlinear light, equal to or greater than a certain value,
the upper intensity limit value is predetermined as a maximum value of the intensity that suppresses the generation of plasma in the measurement space,
The second strength condition is
a relationship between the collection angle and the intensity of the incident laser that satisfies the first intensity condition and makes the Rayleigh length of the incident laser equal to or less than a certain value,
determining whether the intensity of the incident laser satisfies the first intensity condition using the power of the incident laser per unit area on a plane perpendicular to the direction of travel of the incident laser after passing through a focusing element used to focus the laser on the focusing region;
an integrated value of the power in the plane is used as the intensity of the incident laser that defines the second intensity condition;
Electric field sensor.