CN105607167B - A kind of three-stage surface phasmon lens - Google Patents

Abstract

A three-stage surface plasmon lens relates to surface plasmons. It consists of three layers of rectangular grooves etched on the metal surface. Under the illumination of linear polarized light, it will form a smaller-sized surface plasmon focus that breaks through the diffraction limit. The width of the groove is λ/2. The center of each groove The positions are all distributed on three line segments. For the i-th layer (i=1, 2, 3), the length and center position of each layer of grooves are designed as follows: Satisfying f+(i‑1)d+kλ/3 and f+(i‑1)d+(k+1)λ/3, k is called the order of the groove, so that the k difference between two adjacent grooves on the same layer 3. Each groove corresponds to the Fresnel zone in the traditional zone plate; when the plane wave polarized along the y direction is perpendicular to the metal surface to illuminate the structure, the surface plasmons will be excited in the same phase on each groove and propagate to At the focal point constructive interference forms the focal point.

Description

A three-stage surface plasmon lens

technical field

The invention relates to surface plasmons, in particular to a three-stage surface plasmon lens capable of realizing ultra-small focus.

Background technique

Surface Plasmon Polariton (Surface Plasmon Polariton) is an electromagnetic field surface mode localized on the metal/medium surface, which is characterized by the exponential decay of the electromagnetic field strength in the direction perpendicular to the metal surface; Wavenumbers propagate along the metal surface. Under certain conditions, energy conversion between light and surface plasmons can be achieved. This allows people to use surface plasmons to manipulate light in the range of micrometer and nanoscale. Research on various functional devices based on surface plasmons and related theoretical research has become a hot spot in recent years, attracting the attention of many researchers.

Among the many planar photonic devices of surface plasmons, the research on the lens of surface plasmons has always been a hot spot in the research of surface plasmons, because the realization of focusing is directly related to microscopic imaging, detection, Optical storage, optical tweezers and other application functions currently realize two-dimensional surface plasmon focusing structures mainly include the following schemes: (1) Use the protrusion structure on the metal surface to control the wave front of the surface plasmon in the propagation path. Focusing; (2) Use nanoparticles to form parabola and arc focusing surface plasmons; (3) Prepare circular grating focusing surface plasmons on the metal surface; (4) Use grating segments as the surface of the basic structural unit, etc. excitonic lens, etc. Although the core idea of these schemes is to use the phase coherent enhancement of the electromagnetic field of surface plasmons at the focal point to focus, the specific implementations are slightly different. In schemes (1) and (2), the excitation and phase regulation of surface plasmons are two independent processes: first, the far-field light is first realized through the narrow strip protrusions or nanohole lattices on the metal (as antennas). The conversion coupling to the surface plasmon; secondly, the wavefront is shaped by the micro-nano structure of the metal surface. In schemes (3) and (4), the phase of the surface plasmons has been designed and determined at the same time as the excitation, that is, the excitation coupling and phase control structure of the surface plasmons are combined into one. Among the numerous surface plasmon lens elements mentioned above, the circular lens in solution (3) is the most widely concerned, and its structure is composed of single or multiple concentric annular grooves carved on the metal film. Due to the geometric symmetry of the circle, compared with linearly polarized light illumination, if radially polarized light (Radialy Polarized Light) is used for excitation, the focusing effect will be significantly improved, and a stronger focus and smaller focus half-width will be obtained (G.M.Lerman , A.Yanai, and U.Levy, "Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized light", Nano Lett.9, 2139 (2009); W.Chen, D.C.Abeysinghe, R.L.Nelson, and Q.Zhan, "Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination", Nano Lett. 9, 4320 (2009)). This is because the surface plasmon is a transverse magnetic wave, and only the polarization component perpendicular to the grating structure can be effectively excited. In the case of radially polarized illumination, the light polarization direction is perpendicular to the circular grating everywhere, and each position can excite the surface plasmons propagating along the center of the circle with the same intensity. When linearly polarized light is used as the excitation source, the entire circular grating structure is not fully utilized, especially at the position where the polarization direction is parallel to the arc tangent, and the excitation efficiency of surface plasmons is very low (A.V.Zayatsa, I.I. Smolyaninovb, and A.A. Maradudinc, "Nano-optics of surface plasmon polaritons", Phys. Reports 408, 131 (2005)). However, there are two major problems in the scheme of radially polarized excitation: firstly, linearly polarized light needs to be processed in advance to generate radially polarized light, which brings inconvenience to practical applications; secondly, there is an alignment problem between the light source and the structure in radially polarized illumination , that is, it is necessary to ensure that the center of the excitation spot is on the center of the circular lens. Considering the size of the lens (~ tens of microns in diameter), it is not easy to realize.

Contents of the invention

The purpose of the present invention is to provide a three-segment surface plasmon lens capable of realizing an ultra-small focus.

The invention consists of three layers of rectangular grooves etched on the metal surface. Under the illumination of linearly polarized light incident perpendicular to the metal surface, a smaller-sized surface plasmon focus that breaks through the diffraction limit will be formed. The rectangular grooves The width W of each is λ/2, where λ is the wavelength of the surface plasmon, and the center positions of the grooves in each layer are distributed on three line segments. For the i-th layer (i=1, 2, 3), the trajectory is given by the following piecewise function:

Wherein f is the focal length, d=2λ/3 is the layer spacing of the horizontal line segment, α and β are two parameters that need to be optimized, and the "+" and "-" signs in the formula (1) correspond to x≥[f+( i-1)d]tanα and x≤-[f+(i-1)d]tanα; the length and center position of each layer of grooves are designed as follows: the left and right midpoints of the i-th layer of grooves The distance to the focal point satisfies f+(i-1)d+kλ/3 and f+(i-1)d+(k+1)λ/3 respectively, where the integer k is called the order of the groove, and k is taken as follows value, so that the k difference between two adjacent grooves on the same layer is 3, namely:

Each groove corresponds to a Fresnel zone in a conventional zone plate. When the plane wave polarized along the y direction illuminates the structure perpendicular to the metal surface, the surface plasmons will be excited in phase on each groove, and constructively interfere to form the focus when propagating to the focus.

The present invention can achieve the same performance as that of the radially polarized illumination circular lens only by excitation of linearly polarized light: the focal point has rotational symmetry (rotational symmetry); and the half width of the focal point is the same.

The structure of the present invention can ensure that the orientation and polarization direction of each groove can form a certain angle, effectively avoiding the disadvantage that the surface plasmon is not excited at the position where the polarization direction is parallel to the tangent of the arc when the circular lens is illuminated by linear polarization. The present invention has the following advantages:

1. The grooves arranged on the inclined line segment can provide surface plasmon waves converging at a large angle, which significantly improves the numerical aperture of the lens, so that super-resolution focusing can be realized, that is, the full width at half maximum of the focal spot along the x direction is very small , which cannot be achieved by traditional zone plates.

2. By "dropping" or "retaining" each groove and adjusting the weights of convergent waves at each angle, the size of the focal point can be further optimized.

3. If two identical three-segment surface plasmon lenses are placed up and down (see Figure 3), only under linear polarized light illumination will generate a super-resolution and rotationally symmetric focal point, which is at x The full half-height values in the two directions of λ and y are as small as λ ₀ /3, breaking through the diffraction limit of λ ₀ /2, where λ ₀ is the vacuum wavelength of the incident light. Here, the distance between the two focal points is λ/2 because the surface plasmons excited from the upper and lower lenses have a phase difference of π.

4. The three-stage surface plasmon lens combined with the linearly polarized beam can achieve the focusing effect of the circular lens combined with the radially polarized beam illumination, while avoiding the alignment problem of the beam center and the structure center in the latter, because Only the light needs to be linearly polarized at the same time, reducing the cost of implementation.

Description of drawings

FIG. 1 is a schematic structural view of a three-stage surface plasmon lens of the present invention;

2 is a schematic diagram of the design of the three-stage surface plasmon lens of the present invention;

Fig. 3 is a schematic diagram of relative placement of two identical three-segment surface plasmon lenses of the present invention;

Fig. 4 is a schematic structural diagram of two kinds of three-segment surface plasmon lenses in an embodiment of the present invention;

Fig. 5 is a comparison diagram of focus intensity distribution between a three-stage plasmon lens and a circular lens (single layer, radius = 5 μm) in an embodiment of the present invention;

FIG. 6 shows the one-dimensional intensity distribution in the x and y directions and the full width at half maximum of the focal point of the three-segment surface plasmon lens in the embodiment of the present invention.

detailed description

The following embodiments will further illustrate the present invention in conjunction with the accompanying drawings.

Referring to Fig. 1, the present invention consists of three layers of rectangular grooves 2 etched on the metal surface 4. Under the illumination of the linearly polarized light 1 incident perpendicular to the metal surface 4, a smaller-sized surface plasmon excitation that breaks through the diffraction limit will be formed. Element focal point 3, the width W of described rectangular groove 2 is λ/2, and wherein λ is the wavelength of surface plasmon polaritons (referring to Fig. 2), and the central position of each groove is all distributed on three line segments, for The i-th layer (i=1,2,3), whose trajectory is given by the following piecewise function:

Where f is the focal length, d=2λ/3 is the interlayer spacing of the horizontal line segment, α and β are two parameters that need to be optimized, and their meanings are shown in Figure 2. The signs "+" and "-" in formula (1) correspond to x≥[f+(i-1)d]tanα and x≤-[f+(i-1)d]tanα respectively. The length and center position of each layer of grooves are designed as follows: the distances from the midpoints of the left side and right side of the i-th layer of grooves to the focal point satisfy f+(i-1)d+kλ/3 and f+(i- 1) d+(k+1)λ/3, where the integer k is called the order of the groove, and k is valued as follows, so that the k of two adjacent grooves on the same layer differ by 3, namely:

The structure designed in this way is actually a two-dimensional surface plasmon zone plate, and each groove corresponds to the Fresnel zone in the traditional zone plate. When the plane wave polarized along the y direction illuminates the structure vertically to the surface of the gold film, the surface plasmons will be excited in the same phase on each groove, and constructively interfere to form the focus when propagating to the focus.

Refer to FIG. 3 for a schematic diagram of relative placement of two identical three-segment surface plasmon lenses of the present invention.

Considering a three-segment lens fabricated on a 50nm thick gold film, the depth of the grooves can be 20 to 40nm. For incident light of λ ₀ =830nm, surface plasmon wavelength λ=813.5nm, at this time w=406.75nm, d=542.3nm, design focal length f=5μm-d=4.46μm. α=80 degrees and β=45 degrees, the position and length of each groove are given by formula (2). In order to make the structure compact, the grooves distributed on the inclined line segments on both sides are only reserved to the same height level as the focal point. Under these parameters, the lateral length of the entire device is about 72.6 μm, and the width is about 5 μm. The structure is shown in Figure 4(a). The focus intensity distribution can be obtained by Maxwell’s equations plus boundary conditions or FDTD commercial software or numerical calculation based on the surface plasmon point source model (C. Zhao, J. Zhang, “Plasmonic Demultiplexer and Guiding,” ACS Nano 4,6433 (2010)). Here, the last one, the surface plasmon point source model, is used for calculation. Through calculation, it is found that for the three-segment lens in Figure 4(a), the full width at half maximum of the focal point along the x and y directions are 295 and 762nm respectively, and the full width at half maximum in the x direction is already < λ ₀ /2, breaking through the diffraction limit and achieving ultra-high resolution. Using advantage (2) of this design, after removing the six orders of k=-3,-2,-1,1,2,3, the corresponding structure is shown in Figure 4(b). The full width at half maximum of its focus along the x and y directions are 276 and 760nm respectively, and the former reaches λ ₀ /3. Physically, removing these six orders is equivalent to increasing the weight of the surface plasmon waves converged at a large angle, increasing the equivalent numerical aperture, and thus obtaining a smaller focus. In order to obtain a focus with hand symmetry, it is necessary to compress the full width at half maximum in the y direction to about 1/3λ _0. For this reason, the two structures in Fig. 4(a) are placed opposite to each other according to Fig. (3). The focal intensity distribution map under linear polarized light illumination is shown in Fig. 5(b). For comparison, Fig. 5(a) is a distribution map of the focus of a circular lens with a radius of 5 μm excited by radially polarized light. It can be seen from the figure that the focal spot of the three-segment lens has the same rotational symmetry as that of the circular lens. Further analysis shows that the full width at half maximum of the focus x and y of the circular lens is 289nm, and the full width at half maximum of the focus x and y direction of our structure is about 295nm, see figure (6). Considering that the incident light is 830nm, the half-width of the focus is close to 1/3 wavelength, breaking through the diffraction limit of 1/2 wavelength.

Claims (1)

1. a kind of three-stage surface phasmon lens, it is characterised in that by three layers of rectangular recess group etched in metal surface Into, under the incident linearly polarized light illumination in metal surface, by the more small size surface etc. for the diffraction limit that makes breakthroughs from Excimer focus, the width W of the rectangular recess is λ/2, and wherein λ is the wavelength of surface phasmon, the center of every layer of groove Position is distributed on three line segments, for i-th layer, i=1, and 2,3, its track is provided by following piecewise function：

Wherein f is focal length, and d=2 λ/3 are the interlamellar spacings of horizontal line section part, and α and β are two parameters for needing to optimize, formula (1) In "+" and "-" number respectively correspond to x >=[f+ (i-1) d] tan α and x≤- [f+ (i-1) d] tan α；The length of every layer of groove and Center is according to following design：The left side of i-th layer of groove and right edge midpoint meet f+ (i-1) respectively to the distance of focus D+k λ/3 and f+ (i-1) d+ (k+1) λ/3, wherein integer k are referred to as the level of groove, k values as follows, make same layer phase The k differences 3 of adjacent two grooves, i.e.,：

<mrow> <mi>k</mi> <mo>=</mo> <mfenced open = '{' close = ''> <mtable> <mtr> <mtd> <mrow> <mn>...</mn> <mo>,</mo> <mo>-</mo> <mn>7</mn> <mo>,</mo> <mo>-</mo> <mn>4</mn> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>8</mn> <mo>,</mo> <mn>...</mn> </mrow> </mtd> <mtd> <mrow> <mo>(</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>...</mn> <mo>,</mo> <mo>-</mo> <mn>6</mn> <mo>,</mo> <mo>-</mo> <mn>3</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>6</mn> <mo>,</mo> <mn>9</mn> <mo>,</mo> <mn>...</mn> </mrow> </mtd> <mtd> <mrow> <mo>(</mo> <mi>i</mi> <mo>=</mo> <mn>2</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>...</mn> <mo>,</mo> <mo>-</mo> <mn>8</mn> <mo>,</mo> <mo>-</mo> <mn>5</mn> <mo>,</mo> <mo>-</mo> <mn>2</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>4</mn> <mo>,</mo> <mn>7</mn> <mo>,</mo> <mn>...</mn> </mrow> </mtd> <mtd> <mrow> <mo>(</mo> <mi>i</mi> <mo>=</mo> <mn>3</mn> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>

The Fei Nier bands that each groove corresponds in conventional wave strap；When the plane wave vertical metal surface polarized in the y-direction is shone During bright structure, surface phasmon will mutually be excited together on each groove, and constructive interference forms Jiao when traveling to focal point Point.