31 is parallel to the horizontal direction, the direction of the polarization of the laser light LR in the polarization modulation region 38 is in a circumferential direction about the polarization singularity region 36, that is, the optical axis LY and is aligned with a tangent in the circumferential direction, as shown in FIG. 6. Such a directional distribution of the laser light LR is referred to as a second example of a directional distribution (predetermined directional distribution). The laser light LR having the second example of the directional distribution is referred to as an azimuthally polarized (A-pol) light beam.

Examples of a third example of a directional distribution and a third example of an intensity distribution different to those of the first example and the second example include a case in which the polarization direction of the laser light LR emitted from the wavelength plate 31 is circular when viewed along the optical axis LY, that is, a case in which the laser light LR emitted from the wavelength plate 31 is circularly polarized light, as shown in FIG. 7. In this case, the laser light LR in the polarization modulation region 38 includes circularly polarized light at positions corresponding to each of the plurality of small regions 33 of the liquid crystal optical element 32.

The type and necessity of the wavelength plate 31 are selected in accordance with the directional distribution of the laser light LR emitted from the liquid crystal optical element 32 and the linearly polarized light of the laser light LR emitted from the light source 20. For example, as shown in FIG. 3, when the linearly polarized light of the laser light LR emitted from the light source 20 is parallel to the horizontal direction and the laser light LR having the first example of R-pol directional distribution is desirably emitted from the liquid crystal optical element 32, a λ/2 wavelength plate (that is, a half-wavelength plate) can be used as the wavelength plate 31 to make the direction of polarization of the laser light LR prior to incidence on the liquid crystal optical element 32 parallel to the vertical direction. In the example shown in FIG. 3, the wavelength plate 31 can be omitted as long as the linearly polarized light of the laser light LR emitted from the light source 20 is parallel to the vertical direction, and the laser light LR emitted from the light source 20 may be directly incident on the liquid crystal optical element 32.

Similarly, as shown in FIG. 5, when the linearly polarized light of the laser light LR emitted from the light source 20 is parallel to the vertical direction and the laser light LR having the A-pol directional distribution in the second example is desirably emitted from the liquid crystal optical element 32, a λ/2 wavelength plate can be used as the wavelength plate 31 to make the direction of polarization of the laser light LR prior to incidence on the liquid crystal optical element 32 parallel to the horizontal direction. In the example shown in FIG. 5, the wavelength plate 31 can be omitted as long as the linearly polarized light of the laser light LR emitted from the light source 20 is parallel to the horizontal direction, and the laser light LR emitted from the light source 20 may be directly incident on the liquid crystal optical element 32.

As described above, the polarization conversion part 30 converts the directional distribution of the laser light LR, which is a linearly polarized light beam emitted from the light source 20, into a desired directional distribution, such as the first example of the directional distribution. That is, a conversion plane (modulation plane) 34 on which the liquid crystal is non-uniformly aligned as described above is formed in at least a region of an incident surface 32a of the liquid crystal optical element 32 where the laser light LR is incident. The direction of polarization of the laser light LR, which is a linearly polarized light beam when emitted from the light source 20, is converted into a predetermined directional distribution in a space on the emission side of the liquid crystal optical element 32 when the laser light LR passes through the conversion plane 34. That is, the liquid crystal optical element 32 includes the conversion plane 34 that converts the direction of polarization of the laser light LR into a predetermined directional distribution. When the conversion plane 34 is, for example, composed of liquid crystal molecules designed by controlling the orientation direction as described above, the orientation direction of the liquid crystal molecules is designed such that the incident polarized beam is converted into a polarized beam having a desired polarization distribution (directional distribution) by birefringence of the liquid crystal molecules.

The beam shaping part 40 includes, for example, an axicon lens 41, a convex lens 44, the mirror 50, and the condensing element 60. In the beam shaping part 40, the wavelength plate 31 and the liquid crystal optical element 32 are sequentially disposed, from the side closer to the light source 20, on the optical axis LY frontward of the polarization conversion part 30 in a traveling direction of the laser light LR. In the beam shaping part 40, the mirror 50 and the condensing element 60 are sequentially disposed, from the side closer to the light source 20, on the optical axis LX formed by folding the optical axis LY substantially 90°, frontward of the polarization conversion part 30 in the traveling direction of the laser light LR.

The axicon lens 41 is formed in a conical shape, and has an inclined surface 42 linearly approaching the light source 20 as distance from the optical axis LY increases with the optical axis LY as a vertex, when viewed from a direction orthogonal to the optical axis LY. Since the axicon lens 41 has the inclined surface 42, the axicon lens 41 forms a beam profile (intensity distribution) having an annular shape when viewed along the optical axis LY. A diameter of the annular beam profile of the laser light LR depends on a vertex angle α of the inclined surface 42, and increases as a separation distance between the axicon lens 41 and the convex lens 44 on the optical axis LY becomes increasingly longer than a formation region of a Bessel beam. Further, a width of the annular beam profile of the laser light LR in a radial direction is constant at a predetermined value without dependence on the vertex angle α of the inclined surface 42 and the separation distance between the axicon lens 41 and the convex lens 44. The vertex angle α of the axicon lens 41 is preferably from 120° to 150°, for example, from the viewpoint of forming the laser light LR having a suitable annular shape such that the electron beam ER passes through the central portion when viewed along the optical axis LX, as described below.

The convex lens 44 focuses the laser light LR emitted from the axicon lens 41 to form an image. The laser light LR having a beam profile that is rotationally symmetric with respect to the optical axis LX when viewed along the optical axis LX is formed on an imaging surface. A reflective surface 50r of the mirror 50 is disposed between the imaging surface and the exit surface of the convex lens 44. A material of the axicon lens 41 and the convex lens 44 is, for example, quartz, but may be a material other than quartz, such as sapphire, as long as the material has a desired refractive index and can transmit the laser light LR.

The mirror 50 is formed in a cylindrical shape, for example, and has the reflective surface 50r that forms an angle of substantially 45° with respect to an axial line. A through-hole 52 is formed in the mirror 50 having a cylindrical shape along the axial line, that is, the axis EX of the electron beam ER. The axial line of the mirror 50 is orthogonal to the optical axis LY leading to the light source 20 and overlaps the axis EX. The reflective surface 50r overlaps an intersection point at which the optical axis LY and the axial line of the mirror 50 are orthogonal to each other, and forms an angle of substantially 45° with respect to the optical axis LY and the axis EX. The reflective surface 50r is provided with a metal reflective film made of, for example, gold (Au) or aluminum (Al), or an optical reflective film made of a dielectric multilayer film. To avoid charging, a material of the mirror 50 is, for example, stainless steel (SUS), copper (Cu), or quartz with a metal film made of Au, for example, deposited on a surface thereof. Further, the mirror 50 is appropriately grounded to a housing of the electron microscope. A diameter and a length of the through-hole 52 and a shape of an end portion thereof are appropriately formed such that the quality of the electron beam ER does not deteriorate due to, for example, a mirror image effect by which a positive charge is induced at an inner wall of the through-hole 52 by the charge of the electron beam ER.

The laser light LR, which is a cylindrically symmetric polarized beam shaped into an annular shape, is reflected by the reflective surface 50r of the mirror 50 at substantially 90° toward a side opposite to the electron beam source 200 on the axis EX. Hereinafter, the optical axis of the laser light LR reflected by the reflective surface 50r is referred to as the optical axis LX. That is, the optical axis LY of the laser light LR is refracted by 90° by the reflective surface 50r and becomes the optical axis LX. On the other hand, the electron beam ER is emitted from the electron beam source 200 in an accelerated state, passes through the through-hole 52 without being affected by the mirror 50, and travels straight. The optical axis LX substantially overlaps the axis EX of the electron beam ER.

With the beam shaping part 40, the axicon lens 41 and the convex lens 44 are used to shape the laser light LR into a rotationally symmetric polarized beam. The shaped laser light LR is reflected by the reflective surface 50r of the mirror 50 and travels along the optical axis LX. At this time, when viewed from a direction parallel to the optical axis LX, the laser light LR is shaped into a beam profile in which a region having a high light intensity is formed annularly about the optical axis LX. Further, the convex lens 44 and the condensing element 60 are designed such that an imaging position (focal plane of the convex lens 44) at which an outer diameter of the annular beam profile centered on the optical axis LX is the smallest coincides with a pupil plane 60P of the condensing element 60. A material of the condensing element 60 is, for example, quartz similarly to the convex lens 44, but may be a material other than quartz, such as sapphire, as long as the material has a desired refractive index and can transmit the laser light LR.

The condensing element 60 is at least provided on the optical axis LX frontward of the convex lens 44 in an emission direction of the laser light LR, and is disposed such that the pupil plane 60P of an entrance pupil coincides with the focal plane of the convex lens 44. The condensing element 60 is a lens with a geometric aberration appropriately corrected. Serving as a region through which the electron beam ER passes, a through-hole 62 is formed at a central portion of the condensing element 60 in the radial direction through which the optical axis LX and the axis EX pass. The condensing element 60 is, for example, an objective lens for an optical microscope from which a geometric aberration is appropriately removed. The laser light LR in the pupil plane 60P of the condensing element 60 is shaped into an annular shape by the beam shaping part 40 and has an intensity distribution forming a minimum annular width at the focal plane of the convex lens 44. As shown in FIG. 1, the laser light LR is temporarily condensed at the pupil plane 60P with circular symmetry about the optical axis LX, diffused while maintaining the circular symmetry, and incident on the condensing element 60.

As shown in FIG. 8, when viewed along the optical axis LX, the laser light LR having an annular shape and distributed in the circumferential direction of the optical axis LX is circularly symmetrically incident on the condensing element 60 positioned on an outer periphery of the through-hole 62 and condensed in a focal plane 60F of the condensing element 60. Condensing the laser light LR by the condensing element 60 generates the round light RL having rotational symmetry about the optical axis LX. The round light RL has a predetermined focus length LF substantially centered on the focal plane 60F in the z-direction along the optical axis LX. The focus length LF is determined by an annular width of the laser light LR in the pupil plane 60P, and increases in length as the annular width decreases.

The round light RL includes a trapping potential region NR and a repulsive potential region PR based on the distribution of a ponderomotive potential determined from the optical field of the condensed laser light LR. In the trapping potential region NR, electrons included in the electron beam ER are attracted to a center side in a radial direction (r-direction) about the optical axis LX. On the other hand, in the repulsive potential region PR, electrons included in the electron beam ER are repelled outward in the r-direction. Based on these principles, the electron beam ER that passes through the through-hole 62 formed in the condensing element 60 and is incident on the focal plane 60F is converged or diffused in accordance with the distribution of the trapping potential region NR and the repulsive potential region PR in the round light RL, and modulated in accordance with the distribution.

A magnitude of the potential of the trapping potential region NR and a magnitude of the potential of the repulsive potential region PR depend on a numerical aperture (NA) of the condensing element 60. As the NA of the condensing element 60 increases, the laser light LR is more intensely condensed at a wide angle with respect to the optical axis LX, and thus the magnitudes of the potentials of the trapping potential region NR and the repulsive potential region PR increase. Accordingly, in consideration of factors such as power of the incident laser light LR that can be input and speed of the electron beam ER to be modulated, the NA of the condensing element 60 is set to a suitable NA at which at least the trapping potential region NR and the repulsive potential region PR having magnitudes of potential equal to or greater than those required to modulate the electron beam ER to a desired pattern can be generated. From the viewpoint of suppressing the power of the incident laser light LR and protecting the device from thermal damage and the like, the NA of the condensing element 60 is desirably 0.7 or greater, and preferably as close to 1 as possible.

In the electron beam modulation method according to the present embodiment, for example, the electron beam modulation device 10 described above is used to generate the round light RI, having rotational symmetry about the optical axis LX by condensing, by the condensing element 60, the laser light LR having a direction of polarization modulated to a predetermined directional distribution and an intensity modulated to a predetermined intensity distribution. In the electron beam modulation method according to the present embodiment, the electron beam ER incident on the round light RL is modulated by the trapping potential region NR and the repulsive potential region PR of the round light RL. In the electron beam modulation method according to the present embodiment, the round light RL, which is completely different from an electron lens used in the related art, is used for modulation, such as convergence of the electron beam ER. Further, the electron beam ER is modulated while the electron beam ER travels and while a space 100 in which the electron beam modulation device 10 is disposed is in an electric field-free and magnetic field-free state. The space 100 is, for example, a space in a lens barrel through which the electron beam ER travels in an electron microscope.

Numerical Calculation Example 1 Related to Modulation of Electron Beam

Next, a first numerical calculation example (hereinafter referred to as Numerical Calculation Example 1) related to modulation of the electron beam ER using the electron beam modulation device 10 described above will be described. In Numerical Calculation Example 1, the first example of the directional distribution and the first example of the intensity distribution were adopted as the predetermined directional distribution and the predetermined intensity distribution, respectively. That is, the direction of polarization of the laser light LR passing through the conversion plane 34 of the liquid crystal optical element 32 of the electron beam modulation device 10 was set to be modulated to R-pol such as that shown in FIG. 3. In this case, the intensity of the laser light LR passing through the conversion plane 34 is distributed highly in an annular manner (with rotational symmetry) about the optical axes LY, LX when viewed from the directions along the optical axes LY, LX.

Here, based on the fact that the laser light LR can be regarded as monochromatic light, the electric field of the laser light LR is defined by the following Equation (1).

$Equation 1$

$\begin{matrix} {\vec{E}}^{i n} (\vec{r}; t) = E_{0} Re [{\vec{u}}^{i n} (\vec{r}) e^{- i ω t}] & (1) \end{matrix}$

In Equation (1), E₀represents an amplitude of the electric field, ω represents an angular frequency of the laser light LR, and <>ⁱⁿrepresents a unit vector forming a spatial structure of amplitude, phase, and polarized light when the space 100 is regarded as a field. Note that an arrow above a character in the equation or << >>ⁱⁿthe equation indicates that the variable of the character in the equation or the character surrounded by << >> is a vector. In the pupil plane 60P of the condensing element 60 of the electron beam modulation device 10, the laser light LR can be regarded as parallel light. Therefore, when the condensing element 60 is a convex lens, a wavefront obtained after the laser light LR passes through the pupil plane 60P is converted into a spherical wave that converges about the focal point on the optical axis LX. A field of a focal region FF including the focal plane 60F of the condensing element 60 is obtained by integrating a field of a plane wave converging within a range of a maximum convergence angle α toward the focal point. The maximum convergence angle α is represented by sin⁻¹(NA). (NA) represents the NA of the condensing element 60.

Here, when a cylindrical coordinate system <<r>>=<<r>> (r, φ, z) is introduced, a unit vector <>ⁱⁿof the R-pol laser light LR propagating along the z-axis in the z-direction in FIG. 6 and incident on the condensing element 60 is expressed by the following Equation (2).

$Equation 2$

$\begin{matrix} {\overline{u}}^{in} = (u_{r}^{i n}, 0, 0) & (2) \end{matrix}$

In the cylindrical coordinate system, when the theory of vector diffraction integration is applied, the field of the laser light LR condensed by the condensing element 60 is expressed by the following Equations (3) to (5).

$Equation 3$

$\begin{matrix} u_{r} (r, z) = C \int_{0}^{α} d θ P (θ) \sin 2 θ J_{1} (kr \sin θ) e^{ikz \cos θ} & (3) \end{matrix}$

$\begin{matrix} u_{z} (r, z) = 2 iC \int_{0}^{α} d θ P (θ) \sin^{2} θ J_{0} (kr \sin θ) e^{ikz \cos θ} & (4) \end{matrix}$

$\begin{matrix} u_{ϕ} (r, z) = 2 C \int_{0}^{α} d θ P (θ) \sin θ J_{1} (kr \sin θ) e^{ikz \cos θ} & (5) \end{matrix}$

In Equations (3) to (5), C equals πf/λ, f represents a focal length of the condensing element 60, λ represents a peak wavelength or a center wavelength of the laser light LR, and J_nrepresents an n-th order Bessel function. P(θ) represents an apodizing function determined to satisfy the energy conservation law between the incident side and the exit side of the condensing element 60, and is represented by the following Expression (6) on the basis of Abbe's principle applied to an objective lens or the like.

$Equation 4$

$\begin{matrix} P (θ) = p (f \sin θ) \sqrt{\cos θ} & (6) \end{matrix}$

p(r)=p(f·sin θ) in Equation (6) represents an amplitude of a rotationally-symmetric incident field in the pupil plane 60P. For the field of the incident light on the condensing element 60, to express incident round light having an annular shape, the field of incidence in Equation (7) in which an inner diameter is 0.9 times an outer diameter is defined.

$\begin{matrix} Equation 5 &  \\ ❘ {\vec{u}}^{i n} ❘ = p (r) = {\begin{matrix} 1 & for (0.9 f \sin α \leq r \leq f \sin α) \\ 0 & for (0 \leq r \leq 0.9 f \sin α) \end{matrix} & (7) \end{matrix}$

In this numerical calculation example, λ equals 1 [μm], f equals 4 [mm], NA equals 0.9, P_inequals 100 [W], and E_eequals 1 [keV]. On the basis of the principles described above, the light intensity distribution of the condensed laser light LR is obtained by the sum of a radial component and an axial component of the intensity, |u_r|²+|u_z|², and an azimuth component of the intensity |uΦ|². With the magnetic field dependent on a 0-order Bessel function, the axial component has a maximum value on the optical axis LX while the radial component and the azimuthal component are zero on the optical axis LX.

The ponderomotive forces acting on electrons e in the focal region FF are expressed by the following Equations (8) and (9).

$\begin{matrix} Equation 6 &  \\ \vec{F} (\vec{r}) = - U_{p} \nabla {❘ \vec{u} (\vec{r}) ❘}^{2} & (8) \\ U_{p} = \frac{q^{2} E_{0}^{2}}{4 m ω^{2}} & (9) \end{matrix}$

In Equations (8) and (9), q represents a charge of the electrons e, and m represents a mass of the electrons e. U_prepresents the ponderomotive energy corresponding to the magnitude of the distribution of the ponderomotive potential (simply referred to as “potential” in some cases). At this time, the following Equation (10) is established.

$\begin{matrix} Equation 7 &  \\ \vec{F} = - U_{P} [(\vec{u} \cdot \nabla) \vec{u} + \vec{u} \times (\nabla \times \vec{u}) + cc] & (10) \end{matrix}$

In Equation (10), cc represents a complex conjugate term. Here, when the NA of the condensing element 60 is close to 1, the second term (u×(∇×u*)) in Equation (10) is dominant. In this term, in order to generate a force in the r-direction, it is necessary to orient either <> or (∇×<>*) in the axial direction. In Numerical Calculation Example 1, calculation was performed ignoring the first term ((u·∇)u*), which is relatively smaller than the second term, in Equation (10). With the laser light LR being modulated to R-pol, the normalized electric field is given by <>=(U_r, 0, u_z), and the normalized magnetic field is expressed by the following Equation (11).

$\begin{matrix} Equation 8 &  \\ \nabla \times \vec{u} = (0, \partial_{2} u, - \partial, u_{2}, 0) & (11) \end{matrix}$

The following Equations (12) to (14) are obtained from the Equations (3), (4), and (11) described above.

$\begin{matrix} Equation 9 &  \\ \partial, u, - \partial, u, = {iku}_{ϕ} & (12) \end{matrix}$

$\begin{matrix} {J_{0} (ax)}^{'} = - {aJ}_{1} (ax) & (13) \end{matrix}$

$\begin{matrix} \nabla \times \ddot{u} = ik (0, u_{ϕ}, 0) & (14) \end{matrix}$

Accordingly, in Numerical Calculation Example 1 in which the laser light LR is modulated to R-pol, the ponderomotive force of the round light RL in the focal plane 60F is expressed by the following Equation (15).

$\begin{matrix} Equation 10 &  \\ {\vec{F}}^{u} = - {kU}_{p} [({iu}_{z} \hat{u_{ϕ}}, 0, - {iu}_{p} u_{ϕ}^{*}) + cc] & (15) \end{matrix}$

FIG. 9 shows a result of calculating the light intensity distribution of the round light RL in the focal region FF on the basis of the principles, design parameters, and Equations described above. In FIG. 9 and subsequent drawings, z=0 [μm] represents the focal plane 60F, and r=0 [μm] represents the optical axis LX. As shown in FIG. 9, it can be seen that the light intensity of the round light RL based on the laser light LR modulated to R-pol is highest on the optical axis LX (that is, z=0 [μm]). Further, it can be seen that the light intensity of the round light RL rapidly decreases while fluctuating as a distance from the optical axis LX increases in the r-direction.

FIG. 10 shows a result of calculating the ponderomotive force of the round light RL at z=0 [μm] in the focal region FF on the basis of the principles, design parameters, and Equations described above. The ponderomotive force shows a large value where a gradient of the light intensity shown in FIG. 9 is large. Further, a magnitude of the component of the ponderomotive force in the z-direction is approximately one hundredth a magnitude of the component in the r-direction, and the action on the electrons e in the electron beam ER is dominated by the contribution in the r-direction. Further, a z-direction component of the ponderomotive force has a property in which signs are reversed on the side close to and on the side far from the condensing element 60 with respect to the focal plane 60F. For this reason, the action of accelerating the electrons e included in the incident electron beam ER in the +z-direction (that is, right side of the drawing sheet of FIG. 8) and the action of decelerating the electrons e in the −z-direction (that is, left side of the drawing sheet of FIG. 8) cancel each other out across the focal region FF, and the component of the ponderomotive force in the z-direction has no net effect on the electrons e.

Integrating the ponderomotive force field at z=0 [μm] across the r-direction to zero at infinity resulted in an effective repulsive potential region PR_MAXhaving a maximum value closest to the optical axis LX. Further, as a distance from the optical axis LX increases in the r-direction, the magnitude of the potential decreases, and the trapping potential region NR and the repulsive potential region PR each having a smaller value than the maximum value alternately occur outwardly of the repulsive potential region PR_MAX. In the repulsive potential region PR, a force acts on the electrons e included in the incident electron beam ER in a direction away from a local vertex of the potential shape. On the other hand, in the trapping potential region NR, a force acts on the electrons e in a direction approaching a local bottom of the potential shape. In the distribution shown in FIG. 10, it can be seen that the repulsive potential region PR_MAXcauses the electrons e of the electron beam ER to be subject to a large force in a direction away from the optical axis LX.

FIG. 11 shows a result of calculating an effective potential distribution (effective potential) in the focal plane 60F (that is, z=0 [μm]). As shown in FIG. 11, it is clear that the repulsive potential region PR_MAXappears at z=0 on the optical axis LX, and that the potential values of each of the repulsive potential region PR and the trapping potential region NR rapidly decrease outwardly in the r-direction.

FIG. 12 shows the result of calculating a trajectory of the electron beam ER in the focal region FF. The repulsive potential region PR_MAXoccurs in a region where r is approximately 0.4 or less in the calculation result shown in FIG. 12. As shown in FIG. 12, it was confirmed that the parallel electron beam ER incident from the left side diverges outwardly in the r-direction mainly due to the repulsive potential region PR_MAXwith respect to the round light RL.

Furthermore, FIGS. 13 and 14 show the result of calculating the focal length from the maximum value of the repulsive potential region PR_MAXand the trajectory of the electron beam ER traveling in the z-direction along the vicinity of the optical axis LX in the r-direction when the NA of the lens constituting the condensing element 60 is changed. Even when the power of the laser light LR emitted from the light source 20 is constant, the light intensity on the optical axis LX decreases and generation of the electric field in the z-direction decreases as the condensing angle (that is, the maximum converging angle α) of the condensing element 60 decreases. As shown in FIGS. 13 and 14, as the NA of the condensing element 60 becomes smaller, the repulsive potential region PR_MAXbecomes smaller, the focal length of the electron beam ER becomes longer, and the function of the round light RL to modulate the electron beam ER becomes weaker. That is, conversely, it can be said that the function of the round light RL modulating the electron beam ER intensifies as the NA of the condensing element 60 increases.

Numerical Calculation Example 2 Related to Modulation of Electron Beam

Next, a second numerical calculation example (hereinafter referred to as Numerical Calculation Example 2) related to modulation of the electron beam ER using the electron beam modulation device 10 described above will be described. In Numerical Calculation Example 2, the directional distribution of the second example and the intensity distribution of the second example are adopted as the predetermined directional distribution and the predetermined intensity distribution. That is, the direction of polarization of the laser light LR passing through the conversion plane 34 of the liquid crystal optical element 32 of the electron beam modulation device 10 was set to be modulated to A-pol such as that shown in FIG. 6.

The calculations of the intensity distribution and field of the laser light LR, and the calculations and the like of the repulsive potential region PR and the trapping potential region NR of the round light RL as well as the principles and the like are substantially the same as that described in Numerical Calculation Example 1. However, replacements are as follows.

When the direction of polarization of the laser light LR is A-pol, Equation (2) described above is replaced with the following Equation (16).

$\begin{matrix} Equation 11 &  \\ {\vec{u}}^{(*)} = (0, u_{p}^{i, n}, 0) & (16) \end{matrix}$

According to Equation (16) and the equations described above, Equations (14) and (15) described above are replaced with the following Equations (17) and (18).

$\begin{matrix} Equation 12 &  \\ \nabla \times \vec{u} = - ik (u_{r}, 0, u_{z}) & (18) \end{matrix}$

${\vec{F}}^{A} = - {kU}_{p} [({iu}_{ϕ} u_{z}^{*}, 0, - {iu}_{ϕ} u_{r}^{*}) + cc]$

FIG. 15 shows a result of calculating the light intensity distribution of the round light RL in the focal region FF on the basis of the principles and equations described above and design parameters similar to those of Numerical Calculation Example 1. As shown in FIG. 15, it can be seen that the light intensity of the round light RL based on the laser light LR modulated to A-pol is substantially zero on the optical axis LX (that is, z=0 [μm]), and is distributed annularly and cylindrically with rotational symmetry about the optical axis LX when viewed along the optical axis LX. Further, it can be seen that the light intensity of the round light RL decreases as a distance from the optical axis LX increases in the r-direction.

FIG. 16 shows a result of calculating the ponderomotive force of the round light RL in the focal region FF on the basis of the principles, design parameters, and equations described above. As in Numerical Calculation Example 1, the ponderomotive force shows a large value where the gradient of the light intensity shown in FIG. 15 is large. Further, the magnitude of the component of the ponderomotive force in the z-direction is about one hundredth the magnitude of the component in the r-direction. In Numerical Calculation Example 2, as in Numerical Calculation Example 1, the action on the electrons e included in the electron beam ER is dominated by the contribution in the r-direction, and the components in the z-direction cancel each other out across the focal region FF and do not exert a net action on the electrons e.

In FIG. 16, when the field of the ponderomotive force at z=0 [μm] was integrated across the r-direction to 0 at infinity, a trapping potential region NR_MAXhaving a minimum value closest to the optical axis LX was generated, which was the opposite to Numerical Calculation Example 1. Further, as the distance from the optical axis LX increases in the r-direction, the magnitude of the potential decreases, and the repulsive potential region PR and the trapping potential region NR larger than the minimum value are alternately generated outwardly of the trapping potential region NR_MAX. In the distribution shown in FIG. 16, it can be seen that the trapping potential region NR_MAXcauses the electrons e of the electron beam ER to be subject to a large force in a direction approaching the optical axis LX.

FIG. 17 shows a result of calculating an effective potential based on the ponderomotive force of the round light RL at the focal plane 60F (that is, z=0 [μm]). As shown in FIG. 17, it is clear that the trapping potential region NR_MAXappears at z=0 on the optical axis LX, and that the respective potential values of the repulsive potential region PR and the trapping potential region NR rapidly decrease outwardly in the r-direction.

FIG. 18 shows the result of calculating a trajectory of the electron beam ER in the focal region FF. The trapping potential region NR_MAXoccurs in a region where r is approximately 0.4 or less in the calculation result shown in FIG. 18. As shown in FIG. 18, it was confirmed that the parallel electron beam ER incident from the left side converges toward the optical axis LX in the r-direction mainly due to the trapping potential region NR_MAXwith respect to the round light RL.

The electron beam modulation device 10 according to the present embodiment described above includes at least the light source 20, the polarization conversion part 30, and the condensing element 60. The light source 20 emits the laser light LR. The polarization conversion part 30 has the conversion plane 34 that modulates the direction of polarization and the intensity of the laser light LR emitted from the light source 20 such that the direction of polarization and the intensity of the laser light LR have a predetermined directional distribution and a predetermined intensity distribution, respectively. The condensing element 60 condenses the laser light LR passing through the conversion plane 34. In the focal plane 60F of the condensing element 60, the round light RL is generated in the focal plane 60F by the laser light LR being condensed by the condensing element 60. The round light RL includes the trapping potential region NR in which the electrons e included in the incident electron beam ER are attracted and the repulsive potential region PR in which the electrons e are repelled, and has rotational symmetry about the optical axis LX when viewed along the optical axis LX of the laser light LR.

The electron beam modulation device 10 of the present embodiment can generate the round light RI, using the laser light LR, in place of an electric field lens or a magnetic lens used in the related art for modulating the electron beam ER. The electron beam modulation device 10 according to the present embodiment includes the light source 20, the polarization conversion part 30, and the condensing element 60 as main components, and is easy to construct. In addition, the conditions for generating the round light RL can be easily controlled by the design of the conversion plane 34 and the like. The focal length of the round light RL is directly proportional to the power of the laser light LR and is inversely proportional to the acceleration voltage of the electron beam ER. The conditions of the round light RL and the design parameters of the condensing element 60 can be determined in consideration of such conditions. The electron beam modulation device 10 according to the present embodiment can reduce the power of the laser light LR, and can be applied to, for example, an electron microscope having a low acceleration voltage of 30 kV or less. Further, the electron beam modulation device 10 according to the present embodiment can be applied to an objective lens in a measurement system for a measurement target that requires an electric field-free and magnetic field-free state, and an aberration correction device of a low acceleration STEM or a low acceleration SEM. The electron beam modulation device 10 according to the present embodiment is also useful as a device constituting a phase plate having a rotationally symmetric shape for electronic phase imaging.

In the electron beam modulation device 10 according to the present embodiment, the conversion plane 34 of the liquid crystal optical element 32 constituting the polarization conversion part 30 is designed on the basis of diffraction theory or the like such that the polarization singularity region 36 and the polarization modulation region 38 surrounding the polarization singularity region 36 exist when the laser light LR emitted from the conversion plane 34 is viewed along the optical axes LY, LX. In the polarization singularity region 36, the intensity of the laser light LR is zero. The direction of polarization of the polarization modulation region 38 is distributed with rotational symmetry about the polarization singularity region 36.

According to the electron beam modulation device 10 of the present embodiment, it is possible to easily realize an action similar to that of an electron lens in the related art by shaping a polarized beam that is circularly symmetric about the optical axes LY, LX by the conversion plane 34 and condensing the shaped laser light LR by the condensing element 60.

In the electron beam modulation device 10 according to the present embodiment, the direction of polarization of the laser light LR in the polarization modulation region 38 is in the radial direction about the polarization singularity region 36. In the focal plane 60F of the condensing element 60 of the electron beam modulation device 10 according to the present embodiment, when viewed along the optical axis LX, the repulsive potential region PR_MAX(effective repulsive potential region) having an annular shape is formed about the optical axis LX, and the trapping potential region NR and the repulsive potential region PR are alternately formed outwardly in the r-direction (outwardly in the radial direction) of the repulsive potential region PR_MAXwhile being attenuated. Further, in the focal plane 60F, a high-intensity portion where the light intensity of the laser light LR is higher than that at an outer peripheral portion is formed at a central portion including the optical axis LX, and a low-intensity portion where the light intensity of the laser light LR is substantially zero is formed at the outer peripheral portion.

According to the electron beam modulation device 10 of the present embodiment, the repulsive potential region PR_MAXacts on the electrons e included in the electron beam ER incident on the round light RL in the focal region along the optical axis LX and the axis EX so as to repel the electrons e outwardly in the r-direction from the optical axis LX, making it possible to realize the action of a concave lens and obtain a positive spherical aberration.

In the electron beam modulation device 10 according to the present embodiment, the direction of polarization of the laser light LR in the polarization modulation region 38 is aligned with a tangent in the circumferential direction about the polarization singularity region 36. In the focal plane 60F of the condensing element 60 of the electron beam modulation device 10 according to the present embodiment, when viewed along the optical axis LX, the trapping potential region NR_MAX(effective trapping potential region) having an annular shape is formed about the optical axis LX, and the repulsive potential region PR and the trapping potential region NR are alternately formed outwardly in the r-direction (outwardly in the radial direction) of the trapping potential region NR_MAXwhile being attenuated. Further, in the focal plane 60F, a low-intensity portion where the light intensity of the laser light LR is substantially zero is formed at a central portion including the optical axis LX, and a high-intensity portion where the light intensity of the laser light LR is higher than that at the central portion is formed at an outer peripheral portion outward of the central portion.

According to the electron beam modulation device 10 of the present embodiment, the trapping potential region NR_MAXacts on the electrons e included in the electron beam ER incident on the round light RL in the focal region along the optical axis LX and the axis EX in a direction approaching the optical axis LX in the r-direction, making it possible to realize the action of a convex lens and obtain a negative spherical aberration. In an electron lens in the related art, such as an electric field lens or a magnetic lens, only a positive spherical aberration occurs and a negative spherical aberration cannot be achieved. According to the electron beam modulation device 10 of the present embodiment, the positive spherical aberration that is generated solely by the acceleration of the electron beam ER can be readily canceled by the negative spherical aberration of the round light RL, and spherical aberration can be suppressed.

In the electron beam modulation device 10 according to the present embodiment, the predetermined intensity distribution of the laser light LR is a distribution in which a portion having a high light intensity is annularly formed about the optical axes LY, LX when viewed along the optical axes LY, LX.

According to the electron beam modulation device 10 of the present embodiment, it is possible to obtain the focus length LF in the focal region FF by shaping the polarized beam that is circularly symmetric about the optical axes LY, LX into an annular shape by the conversion plane 34 and condensing the shaped laser light LR by the condensing element 60.

In the electron beam modulation method according to the present embodiment, the direction of polarization and the intensity of the laser light LR emitted from the light source 20 are modulated to a predetermined directional distribution and a predetermined intensity distribution, respectively, and the modulated laser light LR is condensed by the condensing element 60. As a result, the round light RL including the trapping potential region PR in which electrons are attracted and the repulsive potential region NR in which the electrons are repelled and that has rotational symmetry about the optical axis LX when viewed along the optical axis LX is generated. In the electron beam modulation method according to the present embodiment, the electron beam ER incident on the round light RL is modulated in accordance with the relative distribution of the trapping potential region NR and the repulsive potential region PR.

The electron beam modulation method of the present embodiment can generate the round light RL using the laser light LR and modulate the electron beam ER in an electric field-free and magnetic field-free state, and easily control the conditions for generating the round light RL by the design of the conversion plane 34 and the like, in place of an electric field lens or a magnetic lens used in the related art to modulate the electron beam ER.

In Numerical Calculation Examples 1 and 2 described above, calculation was made ignoring the first term ((<>·∇)<>*), which is relatively smaller than the second term, in Equation (10). When the NA of the condensing element 60 is large, the actual result is substantially the same as the result obtained when ignoring the first term ((<>·∇)<>*). When the NA of the condensing element 60 is small, the actual result differs from the result obtained when ignoring the first term ((<>·∇)<>*). In a case in which the direction of polarization of the laser light LR emitted from the conversion plane 34 of the liquid crystal optical element 32 of the electron beam modulation device 10 is modulated to R-pol, when the NA of the condensing element 60 is small and the first term ((<>·∇)<>*) cannot be ignored, the action of the convex lens on the electron beam ER appears.

Numerical Calculation Example 3 Related to Modulation of Electron Beam

Next, a third numerical calculation example (hereinafter referred to as Numerical Calculation Example 3) in which calculations related to modulation of the electron beam ER using the electron beam modulation device 10 described above are performed without ignoring the first term ((<>·∇)<>*) in Equation (10) will be described. In Numerical Calculation Example 3, a light field having a Bessel-Gauss (BG) beam-like intensity distribution on the pupil plane represented by the following Equation (19) is adopted as the field of light incident on the condensing element 60.

$\begin{matrix} Equation 13 &  \\ p (r) = \exp [\frac{{(r - f \sin θ_{0})}^{2}}{w_{0}^{2}}] & (19) \end{matrix}$

In Equation (19), r represents a variable in the radial direction. f represents the focal length of the condensing element 60. θ₀represents a condensing angle of the BG beam and is an angle formed by the optical axis LX and a light beam condensed from an outermost peripheral portion of the condensing element 60 to the focal plane 60F. w₀represents half an annular width of the BG beam. As shown in FIG. 19, the annular width of the BG beam is 2w₀. In Numerical Calculation Example 3, the following conditions were set: wavelength λ of laser light LR=1 [μm], f=2 [mm], w₀=50 [μm], θ₀=60 degrees, P_in=100 [W], and E_e=1 [keV]. In Numerical Calculation Example 3, the NA of the condensing element 60 was set to 1.1 times the condensing angle θ₀of the BG beam, that is, 1.1×θ₀. With this setting, the BG beam having an annular shape is condensed without leakage.

FIG. 20 shows a result of calculating a trajectory of the electron beam ER in the focal region FF when the direction of polarization of the laser light LR emitted from the conversion plane 34 of the liquid crystal optical element 32 was modulated to R-pol. FIG. 21 shows a result of calculating a trajectory of the electron beam ER in the focal region FF when the direction of polarization of the laser light LR emitted from the conversion plane 34 of the liquid crystal optical element 32 was modulated to R-pol. Comparison between the results shown in FIGS. 20 and 21 and comparison between FIGS. 12 and 18 indicates that the trajectory of the electron beam ER when the BG beam of Equation (13) is introduced without ignoring the first term ((<>·∇)<>*) in Equation (10) is similar to the trajectory of the electron beam ER in an approximate case in which the first term ((<>·∇)<>*) in Equation (10) was ignored.

FIG. 22 shows a result of calculating a distance z at which the electron beam ER intersects the optical axis LX when the direction of polarization of the laser light LR emitted from the conversion plane 34 of the liquid crystal optical element 32 is modulated to R-pol, that is, FIG. 22 is a longitudinal spherical aberration diagram. As shown in FIG. 22, it can be seen that a positive spherical aberration appears. FIG. 23 shows a result of calculating the distance z at which the electron beam ER intersects the optical axis LX when the direction of polarization of the laser light LR emitted from the conversion plane 34 of the liquid crystal optical element 32 is modulated to A-pol, that is, FIG. 23 is a longitudinal spherical aberration diagram. As shown in FIG. 23, it can be seen that a negative spherical aberration appears.

FIGS. 24 to 28 show results of calculating light intensity distributions in the optical focal region FF when the condensing angle formed by the laser light LR and the optical axis LX is set to 5 degrees, 15 degrees, 30 degrees, 45 degrees, and 60 degrees, respectively, in a case in which the direction of polarization of the laser light LR emitted from the conversion plane 34 of the liquid crystal optical element 32 is modulated to R-pol. As shown in FIGS. 27 and 28, when the condensing angle formed by the laser light LR and the optical axis LX, that is, the incident angle of the laser light LR on the optical focal region FF was 60 degrees and 45 degrees, a high-intensity portion having a high light intensity was formed at the central portion in the r-direction. As shown in FIGS. 24 to 26, when the condensing angle formed by the laser light LR and the optical axis LX decreased to 30 degrees, 15 degrees, and 5 degrees, the high-intensity portion was formed outwardly in the r-direction, and the low-intensity portion having a light intensity lower than that of the high-intensity portion was formed at the center in the r-direction. That is, when the direction of polarization of the laser light LR is modulated to R-pol, as the condensing angle formed by the laser light LR and the optical axis LX decreases, the light intensity distribution changes from a light intensity distribution having a high-intensity portion at the central portion in the r-direction to a light intensity distribution having a low-intensity portion of substantially zero at the central portion and a high-intensity portion at the outer peripheral portion thereof.

FIG. 29 shows the result of calculating a relationship between the condensing angle formed by the laser light LR and the optical axis LX and the focal length of the lens formed by the laser light LR when the direction of polarization of the laser light LR emitted from the conversion plane 34 of the liquid crystal optical element 32 is modulated to R-pol and A-pol. In the case in which the direction of polarization of the laser light LR is modulated to R-pol, when the condensing angle formed by the laser light LR and the optical axis LX is small, that is, when the NA of the condensing element