CN106125165A - A kind of ultra-thin planoconcave lens realizing sub-wavelength focusing - Google Patents

Abstract

A kind of ultra-thin planoconcave lens realizing sub-wavelength focusing, including concave surface ultra-thin medium membrane structure and hyperbolic dispersion planar substrates two large divisions, hyperbolic dispersion planar substrates is made up of with metallized multilayer film medium, ensure tangential dielectric constant and radially dielectric constant contrary sign, concave surface ultra-thin medium film is consistent with the dielectric material of substrate, and concave follows Formula of The Optical Transfer Function.Present invention firstly provides the lens model that " concave curved surface " phase compensation mechanism is combined with hyperbolic dispersion planar substrates, compared with hemispherical Superlens, increase by one layer of concave surface ultra-thin medium film in planar substrates, greatly reduce quality and the size of lens, solving conventional Super lens cannot the problem of far field imaging, it is achieved that the integrated and miniaturization of optical system.

Description

A kind of ultra-thin planoconcave lens realizing sub-wavelength focusing

Technical field

The invention belongs to optical image technology field, relate to middle-infrared band sub-wavelength condenser lens design of Simulation.

Background technology

For a long time, people think that the diffraction limit that Germany scientist Ernst Abbe proposes is lens imaging process always In impassable mountain, in any case the manufacturing process of transformation lens, it is possible to the minimal structure resolved by lens final the most all by The size of the half wavelength that fixes.So-called diffraction pole refer to an ideal point thing when optical system imaging due to the limit of diffraction System, it is impossible to obtain ideal image point but a Fu Lang centered by picture point and fraunhofer-diffraction image.For general optical lens Mirror, its bore is basically round, and the imaging of the most each object point is exactly a disc of confusion, will become after two discs of confusion are close Cannot be distinguished by, this just limits the resolution of conventional optical system, and this disc of confusion is the biggest, and the resolution of system is the lowest.Thing The electromagnetic wave composition of volume scattering not only comprises keying wave composition, the most also comprises the evanescent wave composition of near-field region, Qi Zhongchuan Guided wave composition can completely is transferred to far field by lens arrangement, and the meeting in leaving the distance that object is the shortest of evanescent wave composition Decay rapidly with exponential form, it is impossible to be transferred to far field.But, evanescent wave composition represents the object i.e. thing of the finest information High-frequency components in volume scattering field, these radio-frequency components are along with the propagation of light is with exponential form decay, and this just causes imperfect picture Formation.

The most commonly used Superlens based on metal-dielectric multi-layer film structure realizes the perception to evanescent wave and puts Greatly, it is achieved the sub-wavelength imaging of close objects.Wherein, Superlens based on multilayer film is hemispherical, and curvature is relatively big, and rear end is joined There is microscopic system.At present, there is no the Superlens model for distant objects focal imaging both at home and abroad.And utilize flat ultra-thin Lens focus of the light beam into a minimum hot spot (sub-wavelength dimensions) with the highest light intensity and have important at numerous optical fields Using value, such as fields such as optical storage, photoetching, nanometer laser processing, Confocal laser endomicroscopy and life sciences.

Summary of the invention

Present invention solves the technical problem that and be: overcome the deficiencies in the prior art, it is provided that one can realize far field sub-wavelength and gather Burnt ultra-thin planoconcave lens, solves original Superlens curvature big, and cannot realize the problems such as far field focus.

The technical scheme is that a kind of ultra-thin planoconcave lens realizing sub-wavelength focusing, including metal-dielectric multilamellar Film hyperbolic dispersion planar substrates；Concave surface ultra-thin medium membrane structure is had in planar substrates；Setting of described concave surface ultra-thin medium membrane structure Count and meet equation below:

$n_0{h}_0+n\sqrt{{\mathrm{\ϵ}}_x}f=n_{0}z+n\sqrt{{(h_0-z)}^2+{\[\frac{x(h_0-z)}{L-(h_0-z)}\]}^2}+n\sqrt{{\mathrm{\ϵ}}_x{(f-h_0)}^2-{\mathrm{\ϵ}}_z{\[x+\frac{x(h_0-z)}{L-(h_0-z)}\]}^2};$

Wherein n₀For vacuum refractive index, n is the refractive index of concave surface ultra-thin medium membrane structure material, h₀For concave surface ultra-thin medium The thickness of film, ε_xFor the dielectric constant being perpendicular to plane wave propagation direction of hyperbolic dispersion planar substrates, ε_zFor hyperbolic dispersion flat board The dielectric constant along plane wave propagation direction of substrate, L is object distance, and f is focal length；Concave curved with concave surface ultra-thin medium membrane structure Face upper surface central point is that co-ordinate zero point sets up Descartes's rectangular coordinate system, defines ultra-thin planoconcave lens surface orthogonal two Individual direction is respectively X, Y-axis, is perpendicular to ultra-thin planoconcave lens surface along metal-dielectric multilayer film hyperbolic dispersion planar substrates direction For Z axis, wherein x, y, z is the distance of range coordinate zero point.

Described hyperbolic dispersion planar substrates is made up of metal-dielectric multi-layer film structure, and wherein metal membrane material is doping type Gallium nitride GaN, the material of concave surface ultra-thin medium membrane structure is silicon dioxide SiO₂, the dutycycle of metal film is 0.4998, wherein Alternately arranged totally 200 layers of thickness of metal film 100nm, deielectric-coating thickness 100nm, metal film and deielectric-coating, hyperbolic dispersion each to Opposite sex dielectric constant is respectively ε_x=5.82, ε_z=-0.85；The thickness h of concave surface ultra-thin medium membrane structure₀=15 μm, refractive index is N=3.42；The electromagnetic wavelength of incident ultra-thin planoconcave lens is λ=4 μm.

A diameter of d=100 μm of ultra-thin planoconcave lens, object distance is L=1000 μm, and focal length is f=20 μm.

The present invention compared with prior art provides the benefit that:

(1) present invention is compared with conventional hemispherical shape Superlens, increases by one layer of concave surface ultra-thin medium film in planar substrates, Deielectric-coating and metal-dielectric multilayer film hyperbolic dispersion planar substrates choose same material, and Electro Magnetic Compatibility is good, utilize and more fit The concave curved surface of planar substrates, and select to change the shape of curved surface according to focal length and material, greatly reduce the quality of lens with big Little, it is achieved that the integrated and miniaturization of optical system, it is ensured that high-quality focusing power.

(2) present invention firstly provides the lens mould that " concave curved surface " phase compensation mechanism is combined with hyperbolic dispersion planar substrates Type, under conditions of electromagnetic wavelength is λ=4 μm, it is achieved that sub-wavelength focuses on, a diameter of D=λ/3 of focal beam spot, solves Conventional Super lens cannot the problem of far field imaging.

Accompanying drawing explanation

Fig. 1: ultra-thin planoconcave lens composition schematic diagram.

Fig. 2: " concave curved surface " optical transfer function schematic diagram.

Detailed description of the invention

High frequency evanescent wave cannot be propagated in conventional material, is primarily due to block this physics bottleneck of wave vector, passes through The material system building dielectric constant contrary sign radially and tangentially is that evanescent wave is propagated and the basis of sub-wavelength focal imaging.

As it is shown in figure 1, ultra-thin planoconcave lens includes concave surface ultra-thin medium membrane structure and the big portion of hyperbolic dispersion planar substrates two Point, wherein hyperbolic dispersion planar substrates is made up of with metallized multilayer film medium, it is ensured that tangential dielectric constant and radially dielectric constant Contrary sign." concave curved surface " concrete form such as curve shape is by concave surface ultra-thin medium film and hyperbolic dispersion planar substrates in the model Refractive index, focal length, object distance, dielectric constant and relevant physical dimension limit, and our this curve shape formula is called that optics passes Delivery function.

Solve the optical transfer function of plano-concave thin lens in detail below, with table on the concave curved surface of concave surface ultra-thin medium membrane structure Face central point is that co-ordinate zero point sets up Descartes's rectangular coordinate system, defines the orthogonal both direction in ultra-thin planoconcave lens surface Being respectively X, Y-axis, being perpendicular to ultra-thin planoconcave lens surface along metal-dielectric multilayer film hyperbolic dispersion planar substrates direction is Z axis, Wherein x, y, z is the distance of range coordinate zero point, and as shown in Figure 2, wherein the diameter dimension of lens is at x ∈ [-x_max,x_max] model In enclosing, when a branch of plane wave is irradiated to these lens from the top down, optional two paths calculate light path respectively.

For this paths of OGFM, light path is:

$n_0{h}_0+n\sqrt{{\mathrm{\ϵ}}_x}f---5-1$

For this paths of BCEFM, its light path is divided into three parts to calculate respectively:

BC section light path is:

n₀z 5-2

CE section light path is:

$n\sqrt{{(h_0-z)}^2+{\[\frac{x(h_0-z)}{L-(h_0-z)}\]}^2}---5-3$

EFM section light path is:

$n\sqrt{{\mathrm{\ϵ}}_x{(f-h_0)}^2-{\mathrm{\ϵ}}_z{\[x+\frac{x(h_0-z)}{L-(h_0-z)}\]}^2}---5-4$

Owing to plane wave is converged to FM point by super lens, so the equivalent optical path in any two sections of paths, can obtain as follows Light path equation:

$n_0{h}_0+n\sqrt{{\mathrm{\ϵ}}_x}f=n_{0}z+n\sqrt{{(h_0-z)}^2+{\[\frac{x(h_0-z)}{L-(h_0-z)}\]}^2}+n\sqrt{{\mathrm{\ϵ}}_x{(f-h_0)}^2-{\mathrm{\ϵ}}_z{\[x+\frac{x(h_0-z)}{L-(h_0-z)}\]}^2}---5-5$

Formula 5-5 is the curve equation of phase compensation of the present invention mechanism " concave curved surface ", we term it optical delivery letter Number, this optical transfer function is regulated and controled by five parameters, is h respectively₀,n,f,L,ε_x,ε_z.Adjusted by optical transfer function characteristic Whole parameter, it is possible to obtain preferably phase compensation sag vertical curve, and then determine and realize the concrete of plano-concave thin lens that sub-wavelength focuses on Parameter.

In the present invention, incident electromagnetic wave wavelength is λ=4 μm, a diameter of d=100 μm of thin lens, object distance L=1000 μ M, focal distance f=20 μm.The material of concave surface ultra-thin medium membrane structure is silicon dioxide SiO₂, refractive index n=3.42.Hyperbolic dispersion surpasses Structure material plates substrate is made up of metal-dielectric multi-layer film structure, and wherein metal membrane material is doping type gallium nitride GaN, medium Membrane material is silicon dioxide SiO₂, it is contemplated that the precondition that sub-wavelength focuses on and evanescent wave is propagated, by EFFECTIVE MEDIUM THEORY, Calculating obtains wherein thickness of metal film 100nm, deielectric-coating thickness 100nm, and totally 200 layers, the dutycycle of metal film is 0.4998, is situated between Electric constant is respectively ε_x=5.82, ε_z=-0.85.

In optical transfer function, for the thickness h of concave surface ultra-thin medium membrane structure₀This variable, by utilizing Comosol software carries out emulation experiment, and by relative analysis focused spot size size and intensity, result shows to work as h₀=15 During μm, focal beam spot is minimum and quality is optimal, focused spot diameter dimension D=λ/3.

The content not being described in detail in description of the invention belongs to the known technology of those skilled in the art.

Claims (3)

1. one kind realizes the ultra-thin planoconcave lens that sub-wavelength focuses on, it is characterised in that: include metal-dielectric multilayer film hyperbolic dispersion Planar substrates；Concave surface ultra-thin medium membrane structure is had in planar substrates；The design of described concave surface ultra-thin medium membrane structure meets as follows Formula:

$n_0{h}_0+n\sqrt{{\mathrm{\ϵ}}_x}f=n_{0}z+n\sqrt{{(h_0-z)}^2+{\[\frac{x(h_0-z)}{L-(h_0-z)}\]}^2}+n\sqrt{{\mathrm{\ϵ}}_x{(f-h_0)}^2-{\mathrm{\ϵ}}_z{\[x+\frac{x(h_0-z)}{L-(h_0-z)}\]}^2};$

Wherein n₀For vacuum refractive index, n is the refractive index of concave surface ultra-thin medium membrane structure material, h₀For concave surface ultra-thin medium film Thickness, ε_xFor the dielectric constant being perpendicular to plane wave propagation direction of hyperbolic dispersion planar substrates, ε_zFor hyperbolic dispersion planar substrates The dielectric constant along plane wave propagation direction, L is object distance, and f is focal length；On concave curved surface with concave surface ultra-thin medium membrane structure Centre of surface point is that co-ordinate zero point sets up Descartes's rectangular coordinate system, defines orthogonal two sides, ultra-thin planoconcave lens surface To respectively X, Y-axis, being perpendicular to ultra-thin planoconcave lens surface along metal-dielectric multilayer film hyperbolic dispersion planar substrates direction is Z Axle, wherein x, y, z is the distance of range coordinate zero point.

A kind of ultra-thin planoconcave lens realizing sub-wavelength focusing the most according to claim 1, it is characterised in that: described hyperbolic Dispersion planar substrates is made up of metal-dielectric multi-layer film structure, and wherein metal membrane material is doping type gallium nitride GaN, and concave surface surpasses The material of thin dielectric film structure is silicon dioxide SiO₂, the dutycycle of metal film is 0.4998, wherein thickness of metal film 100nm, Alternately arranged totally 200 layers of deielectric-coating thickness 100nm, metal film and deielectric-coating, the anisotropy dielectric constant of hyperbolic dispersion is respectively For ε_x=5.82, ε_z=-0.85；The thickness h of concave surface ultra-thin medium membrane structure₀=15 μm, refractive index is n=3.42；Incident ultra-thin The electromagnetic wavelength of planoconcave lens is λ=4 μm.

A kind of ultra-thin planoconcave lens realizing sub-wavelength focusing the most according to claim 2, it is characterised in that: ultra-thin plano-concave A diameter of d=100 μm of lens, object distance is L=1000 μm, and focal length is f=20 μm.