CN106125165B - A kind of ultra-thin plano-concave lens realized sub-wavelength and focused on - Google Patents

Abstract

An ultra-thin plano-concave lens that realizes sub-wavelength focusing, including two parts: a concave ultra-thin dielectric film structure and a hyperbolic dispersion plate base. The radial dielectric constants have different signs, the concave ultra-thin dielectric film is consistent with the dielectric material of the substrate, and the shape of the concave surface follows the formula of the optical transfer function. The present invention first proposes a lens model combining a "concave surface" phase compensation mechanism with a hyperbolic dispersion flat substrate. Compared with a hemispherical superlens, a layer of concave ultra-thin dielectric film is added on the flat substrate, which greatly reduces the quality and quality of the lens. The size solves the problem that the traditional super lens cannot perform far-field imaging, and realizes the integration and miniaturization of the optical system.

Description

An ultra-thin plano-concave lens for subwavelength focusing

technical field

The invention belongs to the technical field of optical imaging and relates to the simulation design of a mid-infrared band sub-wavelength focusing lens.

Background technique

For a long time, people have always believed that the diffraction limit proposed by the German scientist Ernst Abbe is an insurmountable mountain in the lens imaging process. No matter how the lens manufacturing process is improved, the smallest structure that can be resolved by the lens will eventually be frozen to the size of half a wavelength. The so-called diffraction pole means that when an ideal point is imaged by the optical system, due to the limitation of diffraction, it is impossible to obtain an ideal image point but a Fraunhofer diffraction image centered on the image point. For general optical lenses, the aperture is basically circular, so that the imaging of each object point is a diffuse spot, and the two diffuse spots will become indistinguishable when they are close together, which limits the resolution of conventional optical systems. The larger this speckle, the lower the resolution of the system. The electromagnetic wave components scattered by the object include not only the propagating wave components, but also the evanescent wave components in the near-field region. It will decay exponentially rapidly within a distance and cannot be transmitted to the far field. However, the evanescent wave component represents the most delicate information of the object, that is, the high-frequency component in the object's scattering field. These high-frequency components decay exponentially with the propagation of light, which leads to the formation of imperfect images.

Superlenses based on metal-dielectric multilayer film structures are widely used in the world to realize the perception and amplification of evanescent waves, and realize sub-wavelength imaging of near-field objects. Among them, the superlens based on multilayer film is hemispherical, with a large curvature, and the back end is equipped with a microscopic system. At present, there is no superlens model for focusing imaging of far-field objects at home and abroad. The use of flat ultra-thin lenses to focus the beam to a very small spot (sub-wavelength scale) with high light intensity has important application value in many optical fields, such as optical storage, lithography, nano-laser processing, confocal microscopy and life sciences and other fields.

Contents of the invention

The technical problem solved by the present invention is to overcome the deficiencies of the prior art, provide an ultra-thin plano-concave lens that can realize far-field subwavelength focusing, and solve the problems that the original super lens has a large curvature and cannot realize far-field focusing.

The technical solution of the present invention is: an ultra-thin plano-concave lens for sub-wavelength focusing, comprising a metal-dielectric multilayer film hyperbolic dispersion plate base; a concave ultra-thin dielectric film structure on the plate base; the concave ultra-thin dielectric film The design of the structure satisfies the following formula:

Where n ₀ is the vacuum refractive index, n is the refractive index of the concave ultra-thin dielectric film structure material, h ₀ is the thickness of the concave ultra-thin dielectric film, ε _x is the dielectric constant of the hyperbolic dispersion plate substrate perpendicular to the plane wave propagation direction , ε _z is the dielectric constant of the hyperbolic dispersion plate substrate along the direction of plane wave propagation, L is the object distance, f is the focal length; the Cartesian right angle is established with the center point of the concave surface of the concave ultra-thin dielectric film structure as the coordinate zero point The coordinate system defines the two directions perpendicular to each other on the surface of the ultra-thin plano-concave lens as the X and Y axes, and the direction perpendicular to the surface of the ultra-thin plano-concave lens along the base of the metal-dielectric multilayer hyperbolic dispersion plate is the Z axis, where x and y , z is the distance from the coordinate zero point.

The hyperbolic dispersion plate substrate is composed of a metal-dielectric multilayer film structure, wherein the material of the metal film is doped gallium nitride GaN, the material of the concave ultra-thin dielectric film structure is silicon dioxide SiO ₂ , and the space of the metal film is The ratio is 0.4998, in which the thickness of the metal film is 100nm, the thickness of the dielectric film is 100nm, the metal film and the dielectric film are arranged alternately for a total of 200 layers, and the anisotropic dielectric constants of the hyperbolic dispersion are ε _x = 5.82, ε _z = -0.85; The thickness of the ultra-thin dielectric film structure is h ₀ =15 μm, and the refractive index is n=3.42; the wavelength of electromagnetic waves incident on the ultra-thin plano-concave lens is λ=4 μm.

The diameter of the ultra-thin plano-concave lens is d=100 μm, the object distance is L=1000 μm, and the focal length is f=20 μm.

The beneficial effect of the present invention compared with prior art is:

(1) Compared with the traditional hemispherical superlens, the present invention adds a layer of concave ultra-thin dielectric film on the flat substrate, and the dielectric film and the metal-dielectric multilayer hyperbolic dispersion flat substrate select the same material, and the electromagnetic compatibility is good , using the concave surface that is more suitable for the flat substrate, and changing the shape of the surface according to the focal length and material selection, greatly reducing the quality and size of the lens, realizing the integration and miniaturization of the optical system, and ensuring high-quality focusing ability.

(2) The present invention proposes the lens model that " concave surface " phase compensation mechanism and hyperbolic dispersion plate base combine for the first time, under the condition that electromagnetic wave wavelength is λ=4 μ m, has realized sub-wavelength focusing, and the diameter of focused light spot is D= λ/3, which solves the problem that traditional superlenses cannot perform far-field imaging.

Description of drawings

Figure 1: Schematic diagram of the composition of an ultrathin plano-concave lens.

Figure 2: Schematic of the optical transfer function of a "concave surface".

detailed description

High-frequency evanescent waves cannot propagate in conventional materials, mainly because of the physical bottleneck of truncated wave vectors. By constructing a material system with different signs of radial and tangential dielectric constants, evanescent wave propagation and sub-wavelength focused imaging Foundation.

As shown in Figure 1, the ultra-thin plano-concave lens consists of two parts: a concave ultra-thin dielectric film structure and a hyperbolic dispersion plate base. Different sign to the dielectric constant. In this model, the specific form of "concave surface" such as the shape of the curve is limited by the refractive index, focal length, object distance, dielectric constant and related geometric dimensions of the concave ultra-thin dielectric film and the hyperbolic dispersion plate substrate. We call this curve shape formula is the optical transfer function.

Next, the optical transfer function of the plano-concave thin lens is specifically solved, and the Cartesian rectangular coordinate system is established with the center point of the concave surface of the concave ultra-thin dielectric film structure as the coordinate zero point, and the two directions perpendicular to each other of the ultra-thin plano-concave lens surface are defined as X, Y axis, perpendicular to the surface of the ultra-thin plano-concave lens is the Z axis along the direction of the base of the metal-dielectric multilayer film hyperbolic dispersion plate, where x, y, and z are the distances from the coordinate zero point, as shown in Figure 2, wherein The diameter of the lens is in the range of x∈[-x _max ,x _max ]. When a plane wave irradiates the lens from top to bottom, choose two paths to calculate the optical path respectively.

For the path of OGFM, the optical path is:

For the path of BCEFM, its optical path is divided into three parts to calculate separately:

The optical path length of BC section is:

n ₀ z 5-2

The optical path length of CE segment is:

The optical path of the EFM segment is:

Since the metalens converges the plane wave to the FM point, the optical paths of any two paths are equal, and the following optical path equation can be obtained:

Formula 5-5 is the curve formula of the "concave surface" of the phase compensation mechanism of the present invention, which we call the optical transfer function, which is regulated by five parameters, namely h ₀ , n, f, L, ε _x ,ε _z . By adjusting the parameters of the optical transfer function characteristics, the ideal phase compensation concave curve can be obtained, and then the specific parameters of the plano-concave thin lens for sub-wavelength focusing can be determined.

In the present invention, the wavelength of the incident electromagnetic wave is λ=4 μm, the diameter of the thin lens is d=100 μm, the object distance L=1000 μm, and the focal length f=20 μm. The material of the concave ultra-thin dielectric film structure is silicon dioxide SiO ₂ , and the refractive index n=3.42. The hyperbolic dispersion metamaterial flat substrate is composed of a metal-dielectric multilayer film structure, in which the metal film material is doped gallium nitride GaN, and the dielectric film material is silicon dioxide SiO ₂ . Considering subwavelength focusing and evanescent wave The preconditions for propagation are obtained through equivalent medium theory, where the thickness of the metal film is 100nm, the thickness of the dielectric film is 100nm, a total of 200 layers, the duty ratio of the metal film is 0.4998, and the dielectric constants are ε _x = 5.82, ε _z = -0.85.

In the optical transfer function, aiming at the variable thickness h ₀ of the concave ultra-thin dielectric film structure, the comosol software is used to carry out simulation experiments, and the size and intensity of the focused spot are compared and analyzed. The results show that when h ₀ = 15 μm, the focused spot Smallest and best quality, focal spot diameter size D=λ/3.

The content that is not described in detail in the description of the present invention belongs to the well-known technology of those skilled in the art.

Claims (3)

1. An ultra-thin plano-concave lens that realizes sub-wavelength focusing, comprising a metal-dielectric multilayer film hyperbolic dispersion plate base, is characterized in that: there is a concave ultra-thin dielectric film structure on the plate base; the concave ultra-thin dielectric film structure The design satisfies the following formula: <mrow><msub><mi>n</mi><mn>0</mn></msub><msub><mi>h</mi><mn>0</mn></msub><mo>+</mo><mi>n</mi><msqrt><msub><mi>&amp;epsiv;</mi><mi>x</mi></msub></msqrt><mi>f</mi><mo>=</mo><msub><mi>n</mi><mn>0</mn></msub><mi>z</mi><mo>+</mo><mi>n</mi><msqrt><mrow><msup><mrow><mo>(</mo><msub><mi>h</mi><mn>0</mn></msub><mo>-</mo><mi>z</mi><mo>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo>&amp;lsqb;</mo><mfrac><mrow><mi>x</mi><mrow><mo>(</mo><msub><mi>h</mi><mn>0</mn></msub><mo>-</mo><mi>z</mi><mo>)</mo></mrow></mrow><mrow><mi>L</mi><mo>-</mo><mrow><mo>(</mo><msub><mi>h</mi><mn>0</mn></msub><mo>-</mo><mi>z</mi><mo>)</mo></mrow></mrow></mfrac><mo>&amp;rsqb;</mo></mrow><mn>2</mn></msup></mrow></msqrt><mo>+</mo><mi>n</mi><msqrt><mrow><msub><mi>&amp;epsiv;</mi><mi>x</mi></msub><msup><mrow><mo>(</mo><mi>f</mi><mo>-</mo><msub><mi>h</mi><mn>0</mn></msub><mo>)</mo></mrow><mn>2</mn></msup><mo>-</mo><msub><mi>&amp;epsiv;</mi><mi>z</mi></msub><msup><mrow><mo>&amp;lsqb;</mo><mi>x</mi><mo>+</mo><mfrac><mrow><mi>x</mi><mrow><mo>(</mo><msub><mi>h</mi><mn>0</mn></msub><mo>-</mo><mi>z</mi><mo>)</mo></mrow></mrow><mrow><mi>L</mi><mo>-</mo><mrow><mo>(</mo><msub><mi>h</mi><mn>0</mn></msub><mo>-</mo><mi>z</mi><mo>)</mo></mrow></mrow></mfrac><mo>&amp;rsqb;</mo></mrow><mn>2</mn></msup></mrow></msqrt><mo>;</mo></mrow> Where n ₀ is the vacuum refractive index, n is the refractive index of the concave ultra-thin dielectric film structure material, h ₀ is the thickness of the concave ultra-thin dielectric film, ε _x is the dielectric constant of the hyperbolic dispersion plate substrate perpendicular to the plane wave propagation direction , ε _z is the dielectric constant of the hyperbolic dispersion plate substrate along the direction of plane wave propagation, L is the object distance, f is the focal length; the Cartesian right angle is established with the center point of the concave surface of the concave ultra-thin dielectric film structure as the coordinate zero point The coordinate system defines the two directions perpendicular to each other on the surface of the ultra-thin plano-concave lens as the X and Y axes, and the direction perpendicular to the surface of the ultra-thin plano-concave lens along the base of the metal-dielectric multilayer hyperbolic dispersion plate is the Z axis, where x and y , z is the distance from the coordinate zero point. 2. An ultra-thin plano-concave lens for sub-wavelength focusing according to claim 1, characterized in that: the hyperbolic dispersion plate substrate is composed of a metal-dielectric multilayer film structure, wherein the metal film material is doped Gallium nitride GaN, the material of the concave ultra-thin dielectric film structure is silicon dioxide SiO ₂ , the duty ratio of the metal film is 0.4998, the thickness of the metal film is 100nm, the thickness of the dielectric film is 100nm, and the metal film and the dielectric film are arranged alternately for a total of 200 layers , the anisotropic dielectric constants of hyperbolic dispersion are ε _x = 5.82, ε _z = -0.85; the thickness of the concave ultra-thin dielectric film structure h ₀ = 15 μm, the refractive index n = 3.42; the incident ultra-thin plano-concave lens The wavelength of the electromagnetic wave is λ=4 μm. 3. A kind of ultra-thin plano-concave lens realizing sub-wavelength focusing according to claim 2, characterized in that: the diameter of the ultra-thin plano-concave lens is d=100 μm, the object distance is L=1000 μm, and the focal length is f=20 μm.