JP5521510B2 - Optical deflection element - Google Patents

Description

  The present invention relates to an optical deflection element that changes the traveling direction of light. In particular, the present invention relates to an optical deflection element using a metamaterial.

  Patent Documents 1 to 4 listed below disclose elements that change the traveling direction of light (hereinafter referred to as “deflection”) using a photonic crystal whose refractive index changes periodically. The photonic crystals described in these documents all have a large number of parallel micro-cylinders composed of different parts or spaces of the flat plate and the material in parallel to the thickness direction of the flat plate, and two-dimensionally on the flat plate surface. The refractive index is periodically changed on a two-dimensional surface by arranging them periodically. Then, light is incident from the side surface where the thickness of the flat plate appears in the direction perpendicular to the thickness, that is, the axis of the microcylinder. The light incident at a non-zero incident angle with respect to the normal of the incident side surface propagates through the photonic crystal at a refraction angle corresponding to the relative refractive index and the incident angle of the photonic crystal. The photonic crystal is propagated through the photonic crystal at a refraction angle corresponding to the frequency by utilizing the fact that the refraction angle varies depending on the frequency of incident light due to the dispersion characteristic of the relative refractive index of the photonic crystal.

  In the above photonic crystal, when the incident side surface and the emission side surface are parallel, the propagation direction of light in the photonic crystal can be changed by the frequency, and the light emission position on the emission side surface is changed to the frequency. The emitted light is parallel to the incident light, although it can be varied accordingly. When the outgoing light is not parallel to the incident light, that is, when the traveling direction of the outgoing light is deflected according to the frequency, the outgoing side is made into an arc shape, and the outer side is changed depending on the position on the outgoing side. The refraction angle when the light is emitted into the air can be changed.

  On the other hand, as disclosed in Non-Patent Documents 1 and 2 below, unlike such a structure, a large number of insulating layers and metal layers are laminated to form a large number of columnar holes in the thickness direction on the surface. There is also known a photonic crystal which is a metamaterial having a so-called fishnet structure which is periodically arranged in a two-dimensional manner. Unlike the Patent Documents 1 to 4, the photonic crystal having this structure makes light incident in the thickness direction of the insulating layer and the metal layer, that is, the axial direction of the columnar hole. Further, the light exit surface is not parallel to the entrance surface, but is inclined so as to be a tapered surface that is not 90 degrees with respect to the thickness direction. Thereby, when the light incident perpendicularly to the incident surface reaches the inclined exit surface and is emitted into the air, an incident angle that is not 0 degrees with respect to the air is formed. Then, using this incident angle and the difference between the refractive index of the photonic crystal and the refractive index in the air, the refractive angle into the air, that is, the radiation angle of light into the air, according to the refractive index of the photonic crystal. To change. Further, by utilizing the fact that the refractive index of the photonic crystal varies depending on the frequency, the radiation angle with respect to the exit surface of the photonic crystal is changed according to the frequency of the incident light.

JP2003-279762 JP2003-344678 JP2004-145314 JP2001-13439

Jason Valentine, et al., Three-dimensional optical metamaterial with a negative refractive index, Nature Lett.Vol.455 376-380 (2008) M. Navarro-Cia, et al., Negative refraction in a prism made of stacked subwavelength hole arrays, Vol. 16, No. 2, Optics Express, 560-566 (2008)

However, in both of the above-mentioned patent documents and non-patent documents, in order to deflect the emitted light in a direction that is not parallel to the incident light, the exit surface is curved in an arc shape or is not parallel to the incident surface but is inclined. It needs to be a face. Processing for this purpose is required, and high-precision processing for this purpose is difficult.
In addition, the techniques disclosed in Patent Documents 1 to 4 have a problem that the exit surface has an arc shape and light needs to be incident non-perpendicularly from a thin side surface, which limits the application of the light deflection element. Further, since light is emitted from the side surface having a small area, there is a problem that the opening area is small and the directivity cannot be made steep.
In the technique disclosed in the non-patent document, the light emission angle is determined by the taper angle of the emission surface and the refractive index of the photonic crystal. However, since the taper angle is related to the thickness of the photonic crystal in the light traveling direction, it cannot be increased. For this reason, the variable range of the output angle with respect to the frequency of incident light cannot be enlarged. In addition, the center angle of the variable range of the exit angle is fixed by the taper angle of the exit surface and the refractive index of the photonic crystal at the center frequency, and changing the deflection angle with the exit angle parallel to the incident light as the center angle is not possible. Have difficulty.
The present invention has been made to solve the above-described problems, and an object of the present invention is to make the light emission surface parallel to the incident surface and to expand the variable range of the emission angle.

The main part of the invention for solving the above problems is an optical deflection element in which an insulating layer and a metal layer are periodically stacked in the z-axis direction in the thickness direction, and is perpendicular to the z-axis on the surface of the insulating layer. When the x-axis is in the direction and the y-axis is in the direction perpendicular to the z-axis and the x-axis, the electromagnetic wave propagating in the z-axis direction has a refractive index along the x-axis direction with respect to the first frequency. It consists of a metamaterial element having a characteristic in which the dispersion characteristic of the refractive index is changed along the x-axis direction so as to increase or decrease at a constant change rate in the range .

  The range in which the refractive index is changed at a constant change rate along the x-axis direction may be at least a range in which incident electromagnetic waves exist. Of course, the refractive index may be changed at a constant change rate over the entire x-axis range of the entire element range. In addition to the insulating layer and the metal layer, a layer that functions to reduce the reflectance with respect to the external environment, a protective layer, and the like may be provided on the incident surface and the emission surface of the electromagnetic wave.

  In this invention, the metamaterial element may be configured with a right-handed system having a positive refractive index in the entire range in the x-axis direction, or may be configured with a left-handed system having a negative refractive index in the entire range in the x-axis direction. The right-hand system may be used in a part of the range in the x-axis direction, and the left-hand system may be used in other ranges. Also, it may be a right-handed system or a left-handed system in the entire frequency range of incident light that is planned, and may be a right-handed system in a certain frequency range and a left-handed system in another frequency range. good. In short, it may be configured such that the dispersion characteristic of the refractive index is changed along the x-axis direction so that the refractive index increases or decreases along the x-axis direction with respect to the first frequency. The light incident surface is a surface parallel to the plane formed by the insulating layer and the metal layer. The light incident direction is generally a direction parallel to the normal of the incident surface, but may be a direction inclined with respect to the normal of the incident surface. The insulating layer is composed of an insulator, a dielectric, and a semiconductor. The insulating layer includes an air layer and a vacuum layer. That is, a material in which no material is present is included between adjacent metal layers.

Also, electrodeposition in the presence range of wave, the refractive index along the positive x-axis direction with respect to the first frequency is increased at a constant rate of change, along the positive x-axis direction with respect to a second frequency different from the first frequency The dispersion characteristic of the refractive index may be changed along the positive x-axis direction so that the refractive index decreases at a constant change rate.
With this configuration, when the incident direction of light is parallel to the normal of the incident surface, the light emission angle is set to the positive side at the first frequency with respect to the normal of the outgoing surface, the second The frequency can be changed to the negative side. When the light incident direction is inclined with respect to the normal of the incident surface, the light emission angle is within a range of positive and negative emission angles with respect to the light incident direction with respect to the emission surface. Can be changed.

In the present invention, when the pass frequency band of the electromagnetic wave of the optical deflection element is divided into a high band and a low band with a predetermined intermediate frequency as a boundary, the first frequency is set to the high band frequency, and the second frequency is set to A low-band frequency may be used, and the refractive index dispersion characteristic may be changed along the x-axis direction so that the refractive index does not change along the x-axis direction with respect to the intermediate frequency.
With this configuration, when the incident direction of light is parallel to the normal line of the incident surface, the light emission angle is set to the normal direction of the output surface for light of intermediate frequency, and the high band The frequency can be changed to the positive side with respect to the normal line, and the frequency of the low band can be changed to the negative side with respect to the normal line. When the incident direction of light is inclined with respect to the normal of the incident surface, the light emission angle is the same direction as the incident direction of light for intermediate frequency light, and the high-band frequency. For light of the above, on the positive side with respect to the incident direction with respect to the emission surface, and for light with a low frequency band with respect to the emission surface, negative with respect to the incident direction of light. Can be changed to the side.

Further, the rate of change of refractive Oriritsu is to vary the frequency of the electromagnetic wave, it may be determined in the x-axis direction of the distribution of the dispersion characteristic of refractive index. By comprising in this way, the deflection angle of the emitted electromagnetic wave can be changed according to the frequency of the incident electromagnetic wave.
Also, electric field change rate of the refractive Oriritsu is applied to the metamaterial, the magnetic field, so as to vary the electromagnetic waves including light, it may be determined in the x-axis direction of the distribution of the dispersion characteristic of refractive index. With this configuration, the deflection angle of the emitted electromagnetic wave can be changed depending on the applied electric field, magnetic field, magnitude, direction, polarization direction, and the like of the electromagnetic wave including light.

The metamaterial elements having the above characteristics, in all of the metal layer even without low, the same position, with respect to the same x-coordinate on the x-axis, at equal periods in the y-axis direction, the x-axis direction, z-axis The cross-sectional area perpendicular to can be realized as an element having a hole or slit penetrating in the z-axis direction or an island-like arrangement of conductors, which gradually and changed.
In addition, the cross-sectional shape of the hole or conductor island is arbitrary, such as a circle, an ellipse, a square, a quadrangle, or a polygon. Moreover, the hole and the slit should just be formed in the metal layer, and do not necessarily need to be formed in the insulating layer. However , the holes or slits may be formed so as to penetrate all metal layers and all insulating layers in the z-axis direction. In this case, it becomes easy to manufacture the optical deflection element. Further, the metal layer may have a complementary structure with respect to the arrangement of the holes or slits, that is, a configuration in which the hole or slit portion is an island shape made of a metal conductor and the other portion is a dielectric. Moreover, the hole and the slit may be combined.
As disclosed in Non-Patent Documents 1 and 2, these structures have a structure in which an insulating layer and a metal layer are stacked, and columnar holes in the thickness direction are provided in a two-dimensional periodic structure on the surface. Approximate. The difference from this structure is that the present invention has a predetermined distribution of cross-sectional areas of holes, slits, and islands along the x-axis direction. For example, when a hole or a conductor island is formed, the cross-sectional area of the hole or the island is gradually increased along the x-axis direction. Conversely, in the case of a slit or a slit-shaped island of a conductor, the cross-sectional area gradually decreases in the x-axis direction. In short, in the case of using the configuration of this, the refractive index of the first frequency, the x-axis direction, at a constant rate of change, so as to gradually increasing pore, slits, x-axis direction of the island of the cross section of the conductor It is sufficient to determine the distribution of. Otherwise, when using a configuration of this, the refractive index of the first frequency, the x-axis direction, so that increasing at a constant rate of change, holes, slits, islands of the cross section of the conductor x-axis direction The distribution may be determined, and the distribution in the x-axis direction of the cross section of the hole, slit, and conductor island may be determined so that the refractive index at the second frequency gradually decreases in the x-axis direction at a constant rate of change.

The period of the holes, slits, and conductor islands in the y-axis direction may be constant and unchanged in the x-axis direction. However , the period in the y-axis direction of the hole , slit, or conductor island arrangement may be gradually changed in the x-axis direction. With this configuration, the resonance frequency can be changed along the x-axis direction .

The portion excluding the hole or slit or the island of the conductor may be vacuum or air, but the dielectric constant or permeability of the portion other than the hole or slit or the island of the conductor is an electric field. A substance that changes due to an electromagnetic wave including a magnetic field or light may be filled. According to this configuration, even if the frequency of the incident electromagnetic wave is fixed, the emission angle can be changed by the electromagnetic wave including the applied electric field, magnetic field, and light.

Further, the substance to be filled holes or slits, or a portion excluding the island conductors, by a liquid crystal, by a voltage or a magnetic field to be applied, it is possible to change the dielectric constant.
Moreover, the dispersion characteristics of the refractive index, with respect to the x-coordinate, deformation, as a method of moving, the insulation layer, dielectric constant, magnetic permeability, or thickness, and an electric field, a magnetic field, the substance which changes the electromagnetic waves including light In addition, the insulating layer has state changing means for applying an electric field, a magnetic field, and an electromagnetic wave, and the state changing means changes the dielectric constant, permeability, or thickness of the insulating layer, thereby changing the refractive index dispersion characteristics. You may do it. Further, the distance between the metal layers may be changed by generating an attractive force between the metal layers by an electric field, a magnetic field, or the like.

According to the present invention, the dispersion characteristic of the refractive index is adjusted along the x-axis direction so that the refractive index increases or decreases at a constant change rate along the x-axis direction with respect to the first frequency. Therefore, the wave number and phase velocity of electromagnetic waves are a function of the x coordinate, and when x increases, the phase and phase velocity increase at a constant rate of change. Or it becomes the characteristic which decreases.
As a result, the wave number distribution in the x-axis direction of the plane wave of the incident electromagnetic wave changes at a constant rate of change, so that the electromagnetic wave is emitted from this optical deflection element at a deflection angle corresponding to this rate of change. Become.
Even if the thickness of the structure in which the insulating layer and the metal layer are laminated is constant regardless of the x-coordinate, that is, even if the light incident surface and the light emission surface are parallel to each other, the emitted electromagnetic wave is incident. It can be deflected in a direction different from the direction of electromagnetic light. Moreover, the refractive index of the metamaterial of this structure has a dispersion characteristic. That is, the wave number, refractive index, and phase velocity are functions of nonlinear frequencies that do not pass through the origin. As a result, the rate of change of those values in the x-axis direction can be changed as a function of frequency. As a result, the deflection angle of the emitted electromagnetic wave can be changed by changing the frequency of the incident electromagnetic wave.
Further, by applying an electromagnetic wave including an electric field, a magnetic field, and light to the metamaterial, the dispersion characteristic of the refractive index can be changed, and the change rate of the refractive index in the x-axis direction can be changed. Thus, the deflection angle of the emitted electromagnetic wave can be changed by applying a physical quantity from the outside.

In the present invention, the incident electromagnetic wave having the first frequency in the high band can be deflected to the positive side of the x-axis with respect to the traveling direction, and the incident electromagnetic wave having the second frequency in the low band. In contrast, the outgoing electromagnetic wave can be deflected to the negative side of the x-axis with respect to the traveling direction.
In another invention, even if the frequency of the incident electromagnetic wave does not change, depending on the magnitude, direction, polarization direction, etc. of the electromagnetic field including externally applied electric field, magnetic field, and light, the insulating layer, the metal layer, the hole, and the slit By changing the dielectric constant and permeability of the substance filled in the material, the rate of change in the distribution of the wave number in the x-axis direction can be changed by these physical quantities, and the deflection angle of the outgoing electromagnetic wave can be changed. .

Furthermore, by adopting the configuration of another invention , the dispersion characteristic can be changed in the x-axis direction with respect to the dispersion characteristic of the refractive index for obtaining the above-described change characteristic of the deflection angle. The inclination of the dispersion characteristic of the refractive index can be changed by the size of the hole or slit or the island of the conductor. Further, by changing the period in the y-axis direction, the dispersion characteristic can be translated in the frequency axis direction. This result, holes or slits, or the period in the y-axis direction of the array of islands of the conductor, by changing along the x-axis direction, with respect to the traveling direction of the incident electromagnetic wave can be deflected to both sides .

Sectional drawing perpendicular | vertical to the propagation direction of the electromagnetic waves of the optical deflection | deviation element 100 of this invention. The top view which showed the arrangement | sequence of the hole in the same optical deflection | deviation element. The characteristic view which showed the dispersion characteristic of the wave number for demonstrating operation | movement of this invention. The characteristic view which showed the relationship between the dispersion characteristic of a wave number, and the arrangement period of the y-axis direction of a hole. The characteristic view which showed the dispersion characteristic of the wave number of a right-handed optical deflection | deviation element. The characteristic view which showed distribution of the wave number of the right-handed optical deflection | deviation element in the x-axis direction. Explanatory drawing which showed the mode of deflection | deviation of emitted light. The characteristic view which showed the dispersion characteristic of the wave number regarding one hole. The top view of a deflection | deviation element at the time of changing the parametric period of a y-axis direction regarding an x coordinate in the right-handed optical deflection | deviation element. The characteristic view which showed the dispersion characteristic of the wave number at the time of changing the parametric period of the y-axis direction regarding x coordinate in the right-handed optical deflection element. FIG. 6 is a characteristic diagram showing the distribution of wave numbers in the x-axis direction when the parametric period in the y-axis direction is changed with respect to the x-coordinate in a right-handed optical deflection element. The characteristic view which showed the dispersion characteristic of the wave number in the left-handed optical deflection element. The characteristic view which showed distribution of the wave number of the x-axis direction at the time of changing the parametric period of a y-axis direction regarding x coordinate in the left-handed optical deflection element. The top view of a deflection | deviation element at the time of changing the parametric period of a y-axis direction regarding an x coordinate in the left-handed optical deflection | deviation element. The characteristic view which showed the dispersion characteristic of the wave number at the time of changing the parametric period of a y-axis direction regarding x coordinate in the left-handed optical deflection element. The characteristic view which showed distribution of the wave number of the x-axis direction at the time of changing the parametric period of a y-axis direction regarding x coordinate in the left-handed optical deflection element. The block diagram of the metal layer which has one hole. Explanatory drawing for applying a voltage between metal layers and changing a deflection angle. The top view which showed the other example regarding the hole, a slit, and the island of a conductor.

Hereinafter, specific examples of the present invention will be described with reference to the drawings. However, the present invention is not limited to the examples.
Hereinafter, the principle of the present invention will be described.
The deflection element 100 of this embodiment is shown in FIG. As shown in the sectional view of A, a laminated structure of a dielectric layer 10 and a metal layer 20 is formed. One surface of the deflection element 100 is a rectangular incident surface 30 on which light is incident, and the other surface is a rectangular emission surface 31 on which light is emitted. The entrance surface 30 and the exit surface 31 are parallel. FIG. A, 1. As shown in B, on the incident surface 30, the origin o is taken at one corner of the rectangle of the incident surface, the x-axis is in the long side direction, the y-axis is in the short side direction perpendicular thereto, and the deflection element is perpendicular to both axes. The z-axis is taken in the thickness direction of 100. The deflecting element 100 has a structure shown in FIG. As shown in the plan view of B, a plurality of cylindrical holes 40 having a circular cross section perpendicular to the z-axis and an axis in the z-axis direction are formed in a two-dimensional lattice shape. The radius r of the hole 40 gradually increases in the x-axis direction according to the displacement of the x coordinate. That is, r (x) is a monotonically increasing function. The distance d _{x in the} x-axis direction (arrangement period in the x-axis direction) between the centers of the adjacent holes 40 is constant regardless of the values of the coordinates x and y.

The distance d _{y in} the y-axis direction between the centers of the holes 40 (arrangement period in the y-axis direction) is constant regardless of the coordinate y, but the value of the coordinate x is constant and the value of the coordinate x It may be changed according to the situation. First, the array period d _y in the y-axis direction, will be described a constant regardless of the x coordinate. Further, the arrangement period d _y arrangement period d _x and y-axis direction of the x-axis direction, even equal, or may be a different value.

  Now, it is assumed that incident light (incident electromagnetic wave) is incident on the z-axis direction, that is, perpendicular to the incident surface 30, and the electric field vector is linearly polarized light directed in the y-axis direction. The present optical deflection element 100 can be composed of a right-hand system in which the wave number increases as the frequency increases and a left-hand system in which the wave number decreases as the frequency increases. The hole 40 extending in the z-axis direction is a kind of circular waveguide that blocks electromagnetic waves in a low frequency band. Therefore, a right-handed system is used in a high frequency band where electromagnetic waves propagate through the hole 40, and a left-handed system is used in a low frequency band where electromagnetic waves cannot propagate through the hole 40.

(A) Dispersion characteristics of wave number, refractive index, and phase velocity Dispersion characteristics k (ω) of the wave number k of the electromagnetic wave propagating in the z-axis direction perpendicular to the incident surface 30 in the laminated structure in which the holes 40 are formed are A schematic representation is as shown in FIG. A region where k is positive (first quadrant) indicates a right-handed dispersion characteristic, and a region where k is negative (second quadrant) indicates a left-handed dispersion characteristic. Parameters of each dispersion characteristic is the ratio R = r / d _y for the arrangement period d _y in the y-axis direction of the radius r of the hole 40. As this ratio R is large, i.e., as the cross-sectional area of the holes 40 occupying the arrangement period d _y increases, the same k, or, when compared with the value of the same omega, the rate of change with respect to the frequency omega of the wave number k dk / dω is small.

  Now, ignoring the loss and attenuation of the electromagnetic wave in the optical deflection element 100, only the real part is considered for both the wave number k and the refractive index n. Since the relationship between the refractive index n and the wave number k is k = ωn / c, when viewed at the same frequency, the wave number k gives the refractive index n at that frequency. Where c is the speed of light in vacuum. Further, since the phase velocity v has a relationship of v = c / n, k = ω / v. When viewed at the same frequency, the wave number k gives the phase velocity v at that frequency. Accordingly, the frequency characteristics relating to the refractive index n and the phase velocity v can be similarly obtained from the frequency characteristics of the wave number k.

Next, consider the case of changing the arrangement period d _y in the y-axis direction. Since the metamaterial structure is a periodic structure in both the z-axis direction, the x-axis direction, and the y-axis direction, it has a passband of a predetermined frequency band. When the radius r of the holes 40 is constant and the arrangement period dy in the _y- axis direction is shortened, the resonance frequency is increased. As a result, the dispersion characteristic of FIG. 2 moves in the direction of the frequency axis as shown in FIG. In the present invention, such a property of wave number dispersion characteristics is used.

(B) When the arrangement period dy in the _y- axis direction is constant with respect to the x-axis direction in the right-handed system First, the optical deflection element 100 is configured in the right-handed system, and the arrangement period dy in the _y- axis direction is along the x-axis direction. The case where it is assumed to be constant will be described.
When the radius r of the hole 40 is changed, the wave number dispersion characteristic changes as shown in FIG. These characteristics can be obtained in detail by analyzing Maxwell's equations by the FDTD method. It can be said from the analysis that the rate of change dk / dω with respect to the frequency of the wave number decreases at the same frequency as the radius r of the hole 40 is increased. array period d _y in the y-axis direction, since it is constant irrespective of the x-coordinate, (value at k = 0) lower frequency omega _L of the passband of the optical deflection device 100 is constant regardless of the x-coordinate is there. The wave number k (ω) at an arbitrary frequency ω of the incident electromagnetic wave increases as the radius r of the hole 40 decreases. Therefore, if the radius r of the hole 40 and the frequency ω are given, the wave number k (ω, r) is uniquely determined.

The radius r of the hole 40 is given as a monotonically increasing function r (x) of the x coordinate. Therefore, if the x coordinate and the frequency ω are given, the wave number k (ω, x) is uniquely determined. Accordingly, the wave number k (ω, x) is set so that the rate of change dk / dx of the wave number k with respect to the x coordinate is at least in the range where the electromagnetic wave exists (range of the width L), or the optical deflection element 100, as shown in FIG. The distribution r (x) in the x-axis direction of the radius r of the hole 40 is determined so as to be constant in the entire range that the x coordinate can take in the entire width in the x-axis direction. Further, the x coordinate of the left end of the range L where the electromagnetic wave exists is x ₃ , and the x coordinate of the right end is x ₁ . Since the dispersion characteristic k (ω, r) can be determined in detail by the FDTD method, the derivative dk (ω, r) / dr can be obtained for each frequency ω.

であるので、

により、半径ｒのｘに関する導関数ｄｒ／ｄｘを求めることができる。ｄｒ／ｄｘが求まれば、そのｘに関する積分として、ｒ（ｘ）を求めることができる。
ただし、ａ（ω）は、各周波数ωについて、図５における波数ｋのｘに関する分布特性のｘに対する変化率である。

So

Thus, the derivative dr / dx with respect to x of the radius r can be obtained. If dr / dx is obtained, r (x) can be obtained as an integral with respect to x.
However, a (ω) is the rate of change with respect to x of the distribution characteristic related to x of the wave number k in FIG. 5 for each frequency ω.

  r (x) needs to be a function that does not depend on the frequency ω. For this purpose, dr / dx must also be a function independent of frequency. Therefore, a (ω) / {dk (ω, r) / dr} needs to be a function that does not depend on frequency.

ただし、ｑ( ω−ω_L ）は、ｘ＝０の位置における波数の分散特性である。ｑ( ω−ω_L ）は、ｘ＝０の位置に半径ｒの最小な孔４０が形成されている場合には、その半径ｒの時の波数の分散特性を示し、ｘ＝０の位置では、孔４０が形成されていない場合には、座標ｘ₃ 、ｘ₁ 間の直線を外挿した時のｘ＝０における波数の分散特性である。ｐ（ω−ω_L ）、ｑ（ω−ω_L ）は、パスバンドの下端周波数ω_L において、孔４０の半径ｒに係わらず波数ｋが零となることから、ω−ω_L の関数で表現している。（３）式は、ｘ＝０における基準特性ｑ( ω−ω_L ）に対する、位置の変化量ｘにおける波数の分散特性の変化量がｐ( ω−ω_L ）ｘであることを意味している。もちろん、基準座標ｘ₃ における波数ｋ（ω，ｘ₃ ）＝ｐ( ω−ω_L ）ｘ₃ ＋ｑ( ω−ω_L ）を基準特性として、その基準座標ｘ₃ からの位置の偏差（ｘ−ｘ₃ ）に対する波数の分散特性の変化量がｐ( ω−ω_L ）（ｘ−ｘ₃ ）であることを意味している。 As shown in FIG. 5, in order to make the rate of change dk / dx with respect to x of the wavenumber dispersion characteristic k (ω, x) constant, k (ω, x) needs to be a linear expression with respect to x. is there. Therefore, if the rate of change is p (ω), the wave number k (ω, x) is given by the following equation.

However, q (ω−ω _L ) is a wave number dispersion characteristic at the position of x = 0. q (ω−ω _L ) indicates the dispersion characteristic of the wave number at the radius r when the minimum hole 40 having the radius r is formed at the position of x = 0, and at the position of x = 0. When the hole 40 is not formed, the dispersion characteristic of the wave number at x = 0 when the straight line between the coordinates x ₃ and x ₁ is extrapolated. p (ω−ω _L ) and q (ω−ω _L ) are functions of ω−ω _L because the wave number k becomes zero regardless of the radius r of the hole 40 at the lower end frequency ω _L of the passband. expressing. The expression (3) means that the change amount of the wave number dispersion characteristic at the position change amount x is p (ω−ω _L ) x with respect to the reference characteristic q (ω−ω _L ) at x = 0. Yes. Of course, the wave number k (ω, x ₃₎ in the reference coordinate x ₃ = p the _{(ω-ω L) x 3} + q (ω-ω L) as a reference characteristic, the deviation of the position from the reference coordinates x ₃ (x- This means that the change amount of the wave number dispersion characteristic with respect to x ₃ ) is p (ω−ω _L ) (x−x ₃ ).

In addition, in the wave number dispersion characteristics of FIG. 4, when q (ω−ω _L ) / p (ω−ω _L ) is a constant that does not depend on the frequency, Equation (3) can be expressed as p (ω−ω _L ) (X−x ₀ ). In this case, as shown in FIG. 5, the linear characteristic of wave number k regarding x passes through the positions of x = x ₀ , k = 0 regardless of the frequency ω. When the wave number dispersion characteristic of FIG. 4 is expressed in a similar shape in the k-axis direction, this relationship is obtained. This similarity is naturally satisfied when the wave number dispersion characteristic can be approximated by a straight line in the used frequency band. ,

となり、図５の特性の変化率をｘに関しては一定とし、その変化率は周波数ωの関数とすることができる。 When the relationship of the equation (3) is obtained, the derivative dk (ω, x) / dx with respect to x of k (ω, x) becomes the following equation.

Thus, the rate of change of the characteristic in FIG. 5 is constant with respect to x, and the rate of change can be a function of the frequency ω.

（５）式を（２）式に代入すると、次式が成立する。

ｄｒ／ｄｘがωに依存しないためには、

を満たす必要がある。
すなわち、図５の波数ｋのｘに関する特性の変化率の周波数特性ａ( ω）は、図４における波数ｋの周波数特性から、オフセットｑ( ω−ω_L ）を減算した周波数特性の変化量の基本となっている基本関数ｐ（ω−ω_L ）で決定される。半径ｒをｘに対して、増加するように設定した場合には、ｐ（ω−ω_L ）は負値で、半径ｒのｘに対する変化率が大きい程、ｐの絶対値は大きくなる。 Next, dk / dr is calculated from the equation (3) as follows.

Substituting equation (5) into equation (2), the following equation is established.

In order for dr / dx not to depend on ω,

It is necessary to satisfy.
That is, the frequency characteristic a (ω) of the rate of change of the characteristic relating to x of the wave number k in FIG. 5 is the amount of change in the frequency characteristic obtained by subtracting the offset q (ω−ω _L ) from the frequency characteristic of the wave number k in FIG. It is determined by the basic function p (ω−ω _L ) that is the basis. When the radius r is set to increase with respect to x, p (ω−ω _L ) is a negative value, and the absolute value of p increases as the rate of change of the radius r with respect to x increases.

In the above description, the coordinates of both ends of the width L of the incident electromagnetic wave are x ₃ and x _1, and the radius r of the hole 40 is increased as the x coordinate is increased. As a result, the wave number k (x) and the refractive index n (x) decrease as x increases, and the phase velocity v (x) increases as x increases. The x coordinate where the hole having the radius r ₁ is formed is x ₁ , and the x coordinate where the hole having the radius r ₃ is formed is x ₃ . Therefore, x ₁ > x ₃ . The wave number difference Δk between the positions x ₁ and x ₃ is expressed by the following equation from the equation (3).

ｘ₁ ，ｘ₃ における光偏向素子１００の厚さｈを伝搬するのに要する時間ｔ₁ ，ｔ₃ は、次式で表される。

Times t ₁ and t ₃ required to propagate the thickness h of the light deflection element 100 at x ₁ and x ₃ are expressed by the following equations.

この角α（ω）は、ｚ軸と出射電磁波の進行ベクトルとの成す角で定義され、反時計回転方向を正と定義される偏向角である。この結果から明らかなように、偏向角α（ω）を波数ｋ（ω，ｘ）の特性ｐ（ω−ω_L ）と周波数ωとの比で、変化させることができる。周波数ωをω_L よりも大きくするに連れて、偏向角α（ω）は、大きくなる。 As x is larger, k (ω, x) is smaller, so t ₁ <t ₃ . Therefore, as shown in FIG. 6, the time difference in which the equiphase surface of the electromagnetic wave is emitted from the emission surface 31 at the position x _{3 and} the position x ₁ is t ₃ −t ₁ , and is emitted at the position x _1. that towards the electromagnetic waves, than the electromagnetic waves emitted at the position of x _3, and is emitted to the early space. As a result, at the time when the electromagnetic wave is emitted at the position x ₃ , the electromagnetic wave emitted from the emission surface 31 at x ₁ has already propagated through the space by c (t ₃ −t ₁ ). Therefore, as shown in FIG. 6, when the angle formed by the equiphase surface and the x axis is α (ω), the following equation is established.

Corner of this alpha (omega) is defined by an angle formed between the traveling vector of the outgoing electromagnetic waves and z-axis, a deflection angle defined a counterclockwise direction as positive. As is clear from this result, the deflection angle α (ω) can be changed by the ratio between the characteristic p (ω−ω _L ) of the wave number k (ω, x) and the frequency ω. As the frequency ω is made larger than ω _L , the deflection angle α (ω) increases.

(C) as the radius of the pores is small the arrangement period d _y in the y-axis direction at right-handed, as the radius r of the case is made small hole 40 is small, light deflector of Lowering the array period d _y in the y-axis direction A plan view of 110 is shown in FIG. That, as the x coordinate increases, thereby increasing the arrangement pitch in the y-axis direction d _y (x), the ratio R (x) = r to the sequence period d _y of the radius _{r (x) / d y (} x ) Is enlarged. In other words, than the increase rate d _y / dx arrangement period d _y, it increases the increase rate dr / dx of the radius r.

When the arrangement period d _y (x) in the y-axis direction is increased, the lower end frequency ω _L of the passband is decreased. Therefore, the dispersion characteristics of the wave number k corresponding to Figure 4, with the ratio R holds the relationship that increases in x-axis direction, as the increase the arrangement pitch d _y, translates towards the frequency ω is low . Then, by appropriately setting the array period d _y (x) that is a function of x, as shown in FIG. 9, the dispersion characteristics of the wave number k at all positions in the x-axis direction are made to coincide with each other at the frequency ω _M. In addition, a distribution d _y (x) with respect to x of the array period d _y can be designed.

In FIG. 9, the wave number at the frequency ω _M is k ₀ . Dispersion characteristics of the wave number k changes the ratio arrangement period d _y of the radius r R (x) = r ( x) / d y (x) as a parameter. When the dispersion characteristic of FIG. 9 is used, the distribution characteristic of the wave number k in the x-axis direction is as shown in FIG. When the frequency ω is higher than ω _M and the wave number is larger than k ₀ , the arrangement period d _y (x) is the same as the case of (b) in which x is constant with respect to x, so as the frequency is increased, The deflection angle α (ω) increases in the positive direction. However, the functions p (ω−ω _L ) and q (ω−ω _L ) representing the wave number k (ω, x) in equation (3) are p (ω−ω _M ) and q (ω−ω, respectively. _M ), and ω _L in the equations (4) to (8) and the equation (11) representing the deflection angle is ω _M.

When the frequency ω is equal to ω _M and the wave number is equal to k ₀ , the wave number is constant and unchanged in the x-axis direction, so the deflection angle α (ω _M ) is zero, that is, the electromagnetic wave is in the z-axis direction. Is emitted. On the contrary, when the frequency ω is lower than ω _M and the wave number k is smaller than k ₀ , the wave number k is smaller as the ratio R (x) of the holes 40 is smaller, as is apparent from FIG. The wave number k increases as the ratio R (x) increases. Accordingly, as shown in FIG. 10, the rate of change dk / dx with respect to x of the distribution of wavenumber k with respect to x is positive. As a result, the function p (ω−ω _M ) becomes positive, and the deflection angle α (ω) becomes negative from the equation (11), and a deflection angle inclined in the positive direction of the x axis from the z axis is obtained.

Thus unlike the arrangement period d _y was constant (x) the array period d _y (x) (b), by changing the frequency omega, the z-axis, the positive and negative sides of the deflection angle Can be realized. As the frequency ω is increased from ω _M , the deflection angle α (ω) increases in the positive direction, and as the frequency ω is decreased from ω _M , the absolute value increases in the negative direction. be able to.

When the arrangement period d _y (x) is decreased as the radius r is increased, the dispersion characteristic of the wave number k cannot be crossed in the positive region of the wave number k. Therefore, in this case, the deflection angle cannot be changed in the positive and negative regions of the z axis.

この場合、右手系の（ｂ）場合と異なり、関数ｐ（ω−ω_H ）は正となり、偏向角α（ω）は負となり、ｚ軸からｘ軸の正方向に傾斜した偏向角が得られる。偏向の方向が、右手系とは、異なる方向となる。ただし、左手系の場合には、使用周波数帯域ωは、パスバンドの上端周波数ω_H よりも低い帯域となる。また、周波数ωをω_H から低下させるに連れて、偏向角α（ω）の絶対値は大きくなる。 (D) In the case where the arrangement period dy in the _y- axis direction is constant in the left-hand system in the x-axis direction When the optical deflection element is configured in the left-hand system, the dispersion characteristic of the wave number k (ω) is the wave number in FIG. k is a characteristic indicated by a negative region, which is the characteristic shown in FIG. Actually, one stack has the characteristics as shown in FIG. In this case, as in the case of the right-handed system (b), at the same frequency ω, the larger the radius r of the hole 40, the smaller the absolute value of the wave number k. Accordingly, the distribution of the wave number k in the x-axis direction is as shown in FIG. 12, and as the frequency ω is smaller, the rate of change dk / dx has a positive sign and a larger absolute value. Therefore, the same result as described in the case of the right-handed system (b) can be obtained. However, the functions p (ω−ω _L ) and q (ω−ω _L ) representing the wave number k (ω, x) in equation (3) are p (ω−ω _H ) and q (ω−ω, respectively. _H ), and ω _L in the equations (4) to (8) and the equation (11) representing the deflection angle is ω _H. Expressions (9) and (10) representing the propagation times at the positions x ₁ and x ₃ are also established as they are. However, in the left-handed system, the wave number k is negative and the phase velocity v is also negative. As a result, t ₁ and t ₃ also become negative values, and the expression (11) representing the deflection angle α (ω) is also established as it is and becomes the following expression.

In this case, unlike the right-handed system (b), the function p (ω−ω _H ) is positive, the deflection angle α (ω) is negative, and a deflection angle tilted from the z axis in the positive direction of the x axis is obtained. It is done. The direction of deflection is different from that of the right-handed system. However, in the case of the left-handed system, the use frequency band ω is a band lower than the upper end frequency ω _{H of the} passband. Further, as the frequency ω is decreased from ω _H , the absolute value of the deflection angle α (ω) increases.

(E) as the radius of the hole is large the array period d _y in the y-axis direction in the left-handed, as the radius r of the case is made small hole 40 is large, the light deflecting element of Lowering the array period d _y in the y-axis direction A plan view of 120 is shown in FIG. Also in this case, the array period d _y (x) is set to the x-axis on condition that the ratio R (x) = r (x) / d _y (x) of the holes 40 is increased as x increases. Make it smaller in the direction. When the arrangement period d _y (x) in the y-axis direction is reduced, the upper end frequency ω _H of the passband is increased. Therefore, the dispersion characteristic of the wave number k corresponding to FIG. 11 moves in parallel with the higher frequency ω as the arrangement period _dy is reduced. Then, by appropriately setting the array period d _y (x) that is a function of x, as shown in FIG. 13, the dispersion characteristics of the wave number k at all positions in the x-axis direction are made to coincide with each other at the frequency ω _M. In addition, d _y (x) can be designed.

In FIG. 14, the wave number at the frequency ω _M is set to −k ₀ . When the dispersion characteristic of FIG. 14 is used, the distribution characteristic of the wave number k in the x-axis direction is as shown in FIG. When the frequency ω is lower than ω _M and the absolute value of the wave number is larger than k ₀ , it is the same as in the case of (c) of the left-handed system in which the arrangement period d _y (x) is constant with respect to x. As the value decreases from ω _M , the deflection angle α (ω) increases in the negative direction. However, the functions p (ω−ω _L ) and q (ω−ω _L ) representing the wave number k (ω, x) in equation (3) are p (ω−ω _M ) and q (ω−ω, respectively. _M ), and ω _H in the equations (4) to (8) and the equation (12) representing the deflection angle is ω _M.

When the frequency ω is equal to ω _M and the wave number is equal to k ₀ , the wave number is constant and unchanged in the x-axis direction, so the deflection angle α (ω _M ) is zero, that is, the electromagnetic wave is in the z-axis direction. Is emitted. On the contrary, when the frequency ω is higher than ω _M and the absolute value of the wave number is smaller than k ₀ , as is clear from FIG. 14, at the same frequency, the smaller the ratio R of the holes 40, the smaller the wave number k. The absolute value of the wave number k increases as the ratio R increases. Therefore, as shown in FIG. 15, the rate of change dk / dx with respect to x of the distribution of wavenumber k with respect to x is negative. As a result, the function p (ω−ω _M ) is negative, and from equation (12), the deflection angle α (ω) is positive, and a deflection angle inclined in the negative direction of the x axis from the z axis is obtained. Thus unlike the arrangement period d _y (x) the array period d _y (x) a constant and left-handed in (c), by changing the frequency omega, the z-axis positive and negative sides The deflection angle can be realized.

Thus, as the frequency ω is made smaller than ω _M , the deflection angle α (ω) can be increased in the negative direction, and as the frequency ω is made larger than ω _M , the deflection angle α (ω) becomes positive. In the direction can be larger.

When the arrangement period d _y (x) is increased as the radius r is increased, the dispersion characteristic of the wave number k cannot be crossed in the negative region of the wave number k. Therefore, in this case, the deflection angle cannot be changed in the positive and negative regions of the z axis.
In addition, since the rate of change dk / dω with respect to the frequency ω of the wave number k can be increased in the left-handed system than in the right-handed system, the left-handed system is configured with respect to the frequency ω of the deflection angle α (ω). The rate of change dα (ω) / dω can be increased.

(F) When the right-handed system and the left-handed system are mixed The left-handed area and the right-handed area obtained by dividing the right-handed element in (b) and the left-handed element in (d) into two in the x-axis direction, You may use for. In this case, at a frequency higher than the frequency ω _{L at} which the wave number k becomes zero, the left-handed element cuts off the incident electromagnetic wave, and only the right-handed element functions, and the right-handed element shown in FIG. It becomes the same as the case of. Therefore, as the deflection angle α (ω) is positive and the frequency is increased, the deflection angle α (ω) can be increased. At a frequency lower than the frequency ω _L , the right-handed element cuts off the incident electromagnetic wave, and only the left-handed element functions to be the same as the left-handed element in (d), and the deflection angle α (Ω) can be negative. Of course, even when the arrangement period d _y (x) is changed with respect to x as in the cases (c) and (e), a half area divided into two in the x-axis direction is left-handed. The other half region may be a mixture of a left-handed system and a left-handed system, and conversely, a half divided into two may be a right-handed system, and the other half may be a mixed element of a right-handed system and a left-handed system. In this case, the dispersion characteristic of the wave number k needs to be continuous in the positive region and the negative region of the wave number.

(G) When the dielectric constant inside the hole 40 or the interval between the metal layers is electrically changed In the cases (b) to (e) above, the deflection angle is changed by changing the frequency of the incident electromagnetic wave. I try to let them. Instead of changing the frequency, the hole 40 is filled with a material capable of changing the dielectric constant and permeability by an electromagnetic wave including an electric field, a magnetic field, and light. For example, a liquid crystal whose dielectric constant is changed by an electric field is filled. In this way, by applying the electric field, the dispersion characteristic of the wave number k (ω, x) can be translated in the whole in the range of all x to the higher or lower frequency. it can. The wave number distribution at that time is the same as when the frequency is changed with the characteristics fixed. As a result, the distribution of the wavenumber k in the x-axis direction with respect to the fixed frequency of the incident electromagnetic wave can be changed according to the magnitude of the external electric field. As a result, the deflection angle α can also be changed by an external electric field. Similarly, when the distance between the metal layers is changed by an electrostatic force, by applying an electric field, the dispersion characteristic of the wave number k (ω, x) is generally higher in the range of all x in the range of higher frequency. Or it can be translated in the lower direction. As a result, the deflection angle α can also be changed by an external electric field.

  A structure in which a periodic hole or slit is provided in a metal is called an FSS (Frequency Selective Surface), and is a structure that selectively transmits or shields an electromagnetic wave having a desired frequency by design. FIG. A, 1. In the structure in which the FSS shown in B is laminated (hereinafter referred to as “FSS stack”), the FSS structure and the lamination interval affect the phase velocity v of the electromagnetic wave in the direction penetrating the FSS, that is, the z-axis direction. Further, the phase velocity v has frequency dispersion and varies depending on the frequency. The frequency dispersibility v (ω) of the phase velocity can be controlled by the shape of the holes and slits of the FSS and their period, that is, the structural design, so by gradually changing the FSS structural design in one direction, the FSS stack The phase velocity can be given a distribution v (x), and the frequency dispersion can be given a distribution v (ω, x). In other words, the wave number k (ω, x) in the z direction in the FSS stack is controlled by the position x in the element and the frequency ω.

In this embodiment, an incident electromagnetic wave is a 1.5 μm band infrared laser, and the present invention is used as an optical deflection element for the infrared laser. The element dimensions are considered with reference to the wavelength λg in the medium of the insulating layer 10 used for element preparation. As the insulating layer 10, SiO ₂ was used. Therefore, when the refractive index of SiO ₂ is 1.5, the wavelength in the medium is 1 μm according to the wavelength / refractive index.

1) Configuration of Laminated Structure An SiO ₂ substrate was used as the insulator substrate as the lowermost insulating layer 10. On the SiO ₂ substrate, an Al film as the metal layer 20 and an SiO ₂ film as the insulating layer 10 were laminated. A large number of metal layers 20 and insulating layers 10 are alternately laminated in a range of 5 to 20 layers by using a film forming technique. The thickness of the metal layer 20 is 20 nm which is 1/50 = 0.02 times the wavelength in the medium, and the thickness of the insulating layer 10 is 80 nm which is 4/50 = 0.08 times the wavelength in the medium. .

2) FSS pattern design
2.1) Basic configuration First, the basic FSS pattern is designed. The FSS pattern is basically a half-wavelength hole array. In this case, the array period d _y arrangement period of the x-axis direction of the FSS patterns d _x and y-axis direction was set to 1μm to match the medium wavelength of the incident light. The radius r of the hole 40 was 250 nm, which is ¼ of the wavelength in the medium. As a result, a left-handed FSS stack having a passband upper end wavelength (wavelength in vacuum) of 1.5 μm and an upper end frequency (ω _H / 2π) of 200 THz is formed. Along with the dimensions of the laminated film, FIG. 16 shows a configuration diagram of one cycle of the basic pattern.

2.2) Adjustment of slope of band diagram This embodiment is an embodiment in the case of (d) described above. In order to distribute the fluctuation amount of the wave number in the medium due to the incident wavelength in the x-axis direction in the element, FSS patterns having dispersion characteristics with different slopes dk / dω are designed along the x-axis direction. Since the magnitude of the slope is inversely proportional to the size of the passband bandwidth of the FSS stack, it is sufficient to prepare an FSS stack with a different bandwidth. If the radius r of the hole 40 is reduced with respect to the basic pattern, the band becomes narrower, and the rate of change dk / dω of the wave number in the medium with respect to frequency fluctuation increases. Conversely, if the radius r of the hole 40 is increased, the passband becomes wider. The wave number variation rate dk / dω with respect to the frequency variation becomes small. Therefore, an optical deflection element can be created by creating a pattern in which the radius r of the hole 40 is gradually enlarged in one direction (for example, from left to right). At this time, since the arrangement period d _y in the y axis direction is constant with respect to x, in theory, since passband upper end in all patterns have the same resonance frequency, the lower the frequency of the beam from the passband upper end When swept, the outgoing light can be deflected in the positive direction of the x-axis with respect to the normal of the outgoing surface 31 (z-axis direction, incident light traveling direction). In this embodiment, the center of the incident light is the center of the incident surface 30 of the light deflection element, and the radius r of the hole 40 at that position is 250 nm. is increased from the right end position x ₁ of the beam, and 300 nm, as the x decreases from this value, the left end position x ₃ of the beam, and a 200 nm. During this time, the radius r was varied with an increasing function with respect to x.
3) Processing of hole array The laminated structure is patterned by photolithography, and a hole array is created using anisotropic etching technology.

The present embodiment is an embodiment in the case of (e) described above. The configuration and dimensions of the FSS stack are the same as those in the first embodiment.
1) Adjusting the center of the bus band In the dispersion characteristic of the wave number k in the medium distributed in the x-axis direction, if the point that takes the same frequency at the same wave number is positioned at the center of the pass band, the beam frequency is shifted from the upper end of the pass band. By sweeping to the lower end, the deflection angle of the outgoing light from the deflection in the negative x-axis direction to the positive deflection in the x-axis with respect to the normal line (z-axis) of the emission surface 31 is increased. Can be changed continuously. Therefore, the arrangement pitch d _y in the y-axis direction of the FSS pattern for in all patterns match the frequency of the passband center, along the x-axis direction is adjusted to be constant distribution. When narrowing the arrangement pitch d _y in the y-axis direction of the FSS pattern, the resonant wavelength becomes shorter, the center frequency of the passband is increased, the dispersion characteristic of the wave number, in whole, moves upward in the frequency axis direction. Conversely widening the arrangement pitch d _y in the y-axis direction of the FSS pattern, the resonance wavelength is increased, the frequency of the passband center is decreased, the dispersion characteristics of the wave number, in whole, moves downward in the frequency axis direction .

Therefore, in the present example, the x in the axial distribution of the radius r of the hole 40, as same as in Example 1, was changed only arrangement period d _y in the y-axis direction of the hole 40 in the x-axis direction. Array period d _y is the x-coordinate _{x s = (x 1 + x} 3) / 2 in which the center point of the entrance surface 30 is located, the arrangement period d _y was 1 [mu] m. That is, the dispersion characteristic of the wave number k at the x-coordinate x _s is unchanged as the characteristic of the first embodiment. Therefore, the wavelength of the center frequency of the passband is longer than 1.5 μm. At the position of the left end x ₃ of the beam, the array period d _y (x) is 1.0− (1.0 × 1.5 / λ ₀ ), and at the position of the right end x ₃ of the beam, the array period d _y (x) was set to 1.0+ (1.0 × 1.5 / λ ₀ ). However, λ ₀ is a wavelength in vacuum corresponding to the center frequency of the passband.

ただし、λ_H は、配列周期ｄ_y （ｘ）をｄ_y （ｘ_s ）で一定とした場合のパスバンドの上端の真空中波長である。すなわち、左端ｘ₃ の位置では、配列周期ｄ_y （ｘ）を一定にした場合の波数の分散特性を、（λ₀ −λ_H ）だけ、低周波数側に平行移動させ、右端ｘ₁ の位置では、配列周期ｄ_y （ｘ）を一定にした場合の波数の分散特性を、（λ₀ −λ_H ）だけ、高周波数側に移動させた特性とすればよい。したがって偏向素子のパターンは左から右へ徐々に孔４０の半径ｒ（ｘ）が広がると同時に配列周期ｄ_y （ｘ）が狭くなる構成となる。（１３）式は、近似的な関係式であり、正確には、半径ｒ（ｘ）と周期ｄ_y （ｘ）とから、波数の位置ｘの関数としての分散特性ｋ（ω，ｘ，ｄ_y ）を求めて、全てのｘの位置における分散特性が（ｋ₀ 、ω_M ）の変動範囲の中点を通過するように、ｄ_y （ｘ）が、数値解析により、最適設計される。 That is, the array period _dy was changed in proportion to the wavelength ratio of the upper end wavelength to 1.5 μm.
Therefore, generally, the arrangement period d _y (x) is expressed by the following equation.

However, λ _H is the wavelength in vacuum at the upper end of the passband when the arrangement period d _y (x) is constant at d _y (x _s ). That is, at the position of the left end x ₃ , the dispersion characteristic of the wave number when the arrangement period _dy (x) is constant is translated to the low frequency side by (λ ₀ −λ _H ), and the position of the right end x ₁ Then, the dispersion characteristic of the wave number when the arrangement period d _y (x) is constant may be a characteristic that is moved to the high frequency side by (λ ₀ −λ _H ). Therefore, the pattern of the deflecting element is configured such that the radius r (x) of the holes 40 gradually increases from the left to the right, and at the same time the arrangement period d _y (x) becomes narrow. Expression (13) is an approximate relational expression. To be precise, the dispersion characteristic k (ω, x, d as a function of the wave number position x is calculated from the radius r (x) and the period d _y (x). _y ) is obtained, and d _y (x) is optimally designed by numerical analysis so that the dispersion characteristics at all the x positions pass through the midpoint of the fluctuation range of (k ₀ , ω _M ).

In this embodiment, the deflection angle is changed while the frequency is fixed. The elements created in Examples 1 and 2 can be deflected by controlling the wavelength of incident light. Further, in order to perform fixed frequency scanning, the liquid crystal is impregnated in the hole 40 of the element prepared in the first and second embodiments. If a general nematic liquid crystal is used, the refractive index can be changed from 1.5 to 1.7. This change can shift the passband of the entire device to a lower frequency. Thereby, the same effect as when the frequency of the incident light is scanned from the lower end to the upper end of the passband is obtained. When liquid crystal is impregnated, it is necessary to adjust the refractive index of the liquid crystal portion to 1.6 which is an intermediate value of the change width to determine the FSS arrangement period d _y (x). Although this is a liquid crystal modulation method, since the element is very small, it is possible to apply an external magnetic field uniformly to the entire element.

In this embodiment, the deflecting element of the present invention is applied to a millimeter wave band radar transmitter. 1) FSS pattern design The pattern design method can be performed in the same manner as in the first and second embodiments. If the substrate resin is polyethylene and the dielectric constant is 2.3, the substrate refractive index is 1.5. For a frequency of 60 GHz, the wavelength in vacuum is 5 mm, so the basic array period d _y (x _s ) of the FSS pattern is 3.3 mm, which is 5 mm / 1.5. The basic hole diameter is half that of 1.67 mm.

1) Overall structure FSS pattern is drawn by etching on low-loss resin film substrate, and 5 sheets of 30 sheets are laminated. The thickness of the film is 0.83 mm or less, which is ¼ or less of the wavelength in the medium of the film material. If possible, wideband design is facilitated by using a thin material such as 1/10 or less of the wavelength in the medium.

2) Fixed frequency scanning In order to perform fixed frequency scanning, a porous resin material is used for the resin substrate, and the element prepared in 1) is impregnated with liquid crystal. Alternatively, as in the first and second embodiments, the FSS pattern hole 40 is made a hole together with the substrate, and the liquid crystal is filled in the hole part. Alternatively, as shown in FIG. 17, in the optical deflection elements of Examples 1 and 2, a voltage is applied between adjacent metal layers 20 to change the distance between them. In this case, the dielectric layer 10 may be a space or an elastic body capable of elastic deformation. Or you may comprise the dielectric material layer 10 with the piezoelectric material from which thickness changes with voltage. Even in this case, the emitted light can be deflected by the voltage.

[Modification]
The cross-sectional shape perpendicular to the z-axis of the hole 40 may be square or square. Also, as shown in FIG. 18A, an elliptical shape having a major axis in the y-axis direction may be used as the cross-sectional area increases. Moreover, as shown in (b), a hole and a slit may be formed in a partial region on the x-axis. Further, as shown in (c) and (d), in the metal layer 20, the metal is left only in the portions corresponding to the holes (a) and (b), and otherwise, the dielectric layer 10 may be exposed. good. That is, in the first, second, and third embodiments, the metal layer 10 may have a complementary structure as a pattern.

  The present invention is effective as a deflection element that changes the traveling direction of electromagnetic waves including light.

DESCRIPTION OF SYMBOLS 10 ... Dielectric layer 20 ... Metal layer 30 ... Incident surface 31 ... Outgoing surface 40 ... Hole 100, 110 ... Optical deflection element

Claims (14)

In an optical deflection element in which an insulating layer and a metal layer are periodically stacked in the z-axis direction in the thickness direction,
On the surface of the insulating layer, when the x axis is in the direction perpendicular to the z axis and the y axis is in the direction perpendicular to the z axis and the x axis, the existence range of the electromagnetic wave with respect to the electromagnetic wave propagating in the z axis direction The refractive index increases along the x-axis direction with respect to the first frequency at a constant change rate, and the refractive index changes along the x-axis direction with respect to a second frequency different from the first frequency. An optical deflecting element comprising a metamaterial element having a characteristic in which a dispersion characteristic of the refractive index is changed along the x-axis direction so as to decrease with an index . In an optical deflection element in which an insulating layer and a metal layer are periodically stacked in the z-axis direction in the thickness direction,
On the surface of the insulating layer, when taking the x-axis in the direction perpendicular to the z-axis and the y-axis in the direction perpendicular to the z-axis and the x-axis, the electromagnetic wave propagating in the z-axis direction is a characteristic in which the refractive index dispersion characteristic is changed along the x-axis direction so that the refractive index increases or decreases at a constant change rate in the presence range of the electromagnetic wave along the x-axis direction; Ri from the meta-material element formed,
The distribution in the x-axis direction of the dispersion characteristic of the refractive index is determined so that the rate of change of the refractive index is changed by an electromagnetic field including an electric field, a magnetic field, and light applied to the metamaterial element. An optical deflection element. In an optical deflection element in which an insulating layer and a metal layer are periodically stacked in the z-axis direction in the thickness direction,
On the surface of the insulating layer, when taking the x-axis in the direction perpendicular to the z-axis and the y-axis in the direction perpendicular to the z-axis and the x-axis, the electromagnetic wave propagating in the z-axis direction is a characteristic in which the refractive index dispersion characteristic is changed along the x-axis direction so that the refractive index increases or decreases at a constant change rate in the presence range of the electromagnetic wave along the x-axis direction; Ri from the meta-material element formed,
The metamaterial element has the same position in at least all the metal layers, and the same x coordinate on the x axis has an equal period in the y axis direction, and the period in the y axis direction is the x axis. In the x-axis direction, the cross-sectional area perpendicular to the z-axis gradually changes, and the holes or slits penetrating in the z-axis direction or the island-like arrangement of conductors An optical deflection element comprising: In an optical deflection element in which an insulating layer and a metal layer are periodically stacked in the z-axis direction in the thickness direction,
On the surface of the insulating layer, when taking the x-axis in the direction perpendicular to the z-axis and the y-axis in the direction perpendicular to the z-axis and the x-axis, the electromagnetic wave propagating in the z-axis direction is a characteristic in which the refractive index dispersion characteristic is changed along the x-axis direction so that the refractive index increases or decreases at a constant change rate in the presence range of the electromagnetic wave along the x-axis direction; Made of metamaterial elements ,
The metamaterial element is at the same position in at least all the metal layers, and the same x coordinate on the x axis has an equal period in the y axis direction, and the z axis is in the x axis direction. The cross-sectional area perpendicular to is gradually changed, having holes or slits penetrating in the z-axis direction, or island-like arrangement of conductors,
The hole or slit, or the portion other than the island shape of the conductor, is filled with a substance whose dielectric constant or permeability is changed by an electromagnetic wave including an electric field, a magnetic field, and light.
An optical deflection element characterized by that. In an optical deflection element in which an insulating layer and a metal layer are periodically stacked in the z-axis direction in the thickness direction,
On the surface of the insulating layer, when taking the x-axis in the direction perpendicular to the z-axis and the y-axis in the direction perpendicular to the z-axis and the x-axis, the electromagnetic wave propagating in the z-axis direction is a characteristic in which the refractive index dispersion characteristic is changed along the x-axis direction so that the refractive index increases or decreases at a constant change rate in the presence range of the electromagnetic wave along the x-axis direction; Ri from the meta-material element formed,
The insulating layer is a substance whose dielectric constant, magnetic permeability, or thickness is changed by an electromagnetic wave including an electric field, a magnetic field, and light, and has a state changing unit that applies an electric field, a magnetic field, and an electromagnetic wave to the insulating layer,
An optical deflection element characterized in that the dispersion characteristic of the refractive index is changed by changing the dielectric constant, magnetic permeability or thickness of the insulating layer by the state changing means . When the passing frequency band of the electromagnetic wave of the optical deflection element is divided into a high band and a low band with a predetermined intermediate frequency as a boundary, the first frequency is set as the high band frequency, and the second frequency is set as the frequency The low-band frequency is used, and the refractive index dispersion characteristic is changed along the x-axis direction so that the refractive index does not change along the x-axis direction with respect to the intermediate frequency. The light deflection element according to claim 1 . Wherein as the rate of change of the refractive index is changed by the frequency of the electromagnetic wave, any of claims 1 to 6, wherein the x-axis direction of the distribution of the dispersion characteristic of the refractive index is determined The light deflection element according to claim 1. The distribution in the x-axis direction of the dispersion characteristic of the refractive index is determined so that the rate of change of the refractive index is changed by an electromagnetic field including an electric field, a magnetic field, and light applied to the metamaterial element. The optical deflection element according to any one of claims 1 to 3 and 6 . The metamaterial element is at the same position in at least all of the metal layers, and the same x coordinate on the x axis has an equal period in the y axis direction and is perpendicular to the z axis in the x axis direction. The cross-sectional area has a gradually changing hole or slit penetrating in the z-axis direction, or an island-like arrangement of conductors, or claim 1, claim 2, claim 5, or The light deflection element according to claim 6 . 10. The optical deflection element according to claim 3, wherein the hole or slit penetrates all the metal layers and all the insulating layers in the z-axis direction. 11. . 10. The light according to claim 4 , wherein a period in the y-axis direction of the holes, slits, or island-like arrangement of conductors gradually changes in the x-axis direction. Deflection element. It said holes or slits, or the portion except for the conductor islands of claim permittivity or magnetic permeability, an electric field, a magnetic field, substance which changes the electromagnetic waves including light, characterized in that it is filled 9 The light deflection element described in 1. 13. The light deflection element according to claim 4 , wherein the substance is a liquid crystal. The insulating layer is a substance whose dielectric constant, magnetic permeability, or thickness is changed by an electromagnetic wave including an electric field, a magnetic field, and light, and has a state changing unit that applies an electric field, a magnetic field, and an electromagnetic wave to the insulating layer,
By the state change means, the dielectric constant of the insulating layer, by changing the permeability or thickness, claims 1 to 4, characterized in varying the dispersion characteristic of the refractive index, according to claim 6 The light deflection element according to any one of the preceding claims.

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