CN111525273B - Terahertz super-surface Bessel lens - Google Patents
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- CN111525273B CN111525273B CN202010391879.2A CN202010391879A CN111525273B CN 111525273 B CN111525273 B CN 111525273B CN 202010391879 A CN202010391879 A CN 202010391879A CN 111525273 B CN111525273 B CN 111525273B
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
- H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
- H01Q15/0006—Devices acting selectively as reflecting surface, as diffracting or as refracting device, e.g. frequency filtering or angular spatial filtering devices
- H01Q15/0013—Devices acting selectively as reflecting surface, as diffracting or as refracting device, e.g. frequency filtering or angular spatial filtering devices said selective devices working as frequency-selective reflecting surfaces, e.g. FSS, dichroic plates, surfaces being partly transmissive and reflective
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Abstract
The invention provides a terahertz super-surface Bessel lens, and belongs to the technical field of terahertz. The super surface of the terahertz Bessel lens comprises a plurality of harmonic oscillator array units, the characteristic dimension of each harmonic oscillator is the sub-working wavelength, and the design of the harmonic oscillator array units is as follows: performing multi-stage discretization on the phase of the terahertz Bessel lens to obtain a discretized phase value; simulating by using the phase value after dispersion and the phase distribution relation of the terahertz Bessel lens to obtain the characteristic size of the harmonic oscillator array unit; if the structures and the sizes of the harmonic oscillators in one dimension of the resonance subarrays are the same, the structures and the sizes of the harmonic oscillators in the other dimension of the resonance subarrays are different, or the structures and the sizes of the harmonic oscillators in the two dimensions of the resonance subarrays are different. The terahertz Bessel lens provided by the invention is easy to adjust parameters, simple in preparation process, extremely thin, small in size and easy to realize integration and miniaturization.
Description
Technical Field
The invention relates to the technical field of terahertz, in particular to a terahertz Bessel lens working in a terahertz frequency band and based on a super-surface technology.
Technical Field
Terahertz waves generally refer to waves with frequencies in the range of 0.1THz to 10THz and wave numbers in the range of 3.3cm-1Change to 333.3cm-1Electromagnetic waves having a wavelength of about 30 μm to 3mm and being in the region of the transition from electronics to photonics in the electromagnetic spectrum. In recent years, terahertz waves have unique properties such as low energy, penetrability, absorbability and broadband properties which are not possessed by electromagnetic waves of other frequency bands, so that the terahertz waves have wide application prospects in the fields of nondestructive inspection, safety detection, biochemistry, radar early warning, deep space detection, wireless communication and particularly imaging.
In a terahertz imaging system, an optical element is the most important and indispensable and is widely applied to the fields of scientific research, life, medical treatment, military and the like. Conventional optical elements control the way light propagates by gradually accumulating changes in amplitude, phase and polarization state over the path of light propagation. Generally, the conventional optical element needs a specific material to be prepared, has a specific shape, and has a thickness far exceeding the wavelength, so that the size is relatively large, the processing is not easy, and the integration is difficult to achieve, and the birth of the super-surface technology provides a brand new method for realizing a small-sized planar optical element. The super surface is a metamaterial with a two-dimensional structure, and the amplitude, the phase and the polarization state of near-field electromagnetic waves are changed by utilizing different responses of sub-wavelength resonance structure units with different sizes or shapes to incident electromagnetic waves, so that the regulation and control of far-field electromagnetic waves are realized. As is well known, the phase period of an electromagnetic wave in the propagation process is 2 pi, so that when the phase change of different designed resonance structures reaches 2 pi, the phase of the electromagnetic wave can be regulated and controlled in a full range, and further, a plurality of miniaturized planar optical elements including lenses, wave plates, spiral phase plates, optical filters, gratings and the like can be constructed.
In the terahertz wave band, the traditional lens adopts a high-resistance silicon material or a high polymer material, so that the processing is complex, the size is large, the price is high, and the lens is difficult to be used in a miniaturized terahertz imaging system. Compared with the traditional lens, the super-surface lens can realize the transformation of the appearance of the traditional lens from a curved surface to a plane and eliminate the spherical aberration of the traditional lens, and has the advantages of small size and easiness in integration and processing. The super-surface lens has the advantages of small volume, thinness, lightness and easiness in integration with the existing photoelectronic device, so that the super-surface lens has important application values in the aspects of holography, imaging, spectroscopy, photoetching, laser processing and the like. Compared with the case that the ordinary lens only focuses on one point, the light intensity distribution of the Bezier beam generated by the Bezier lens does not change within a certain distance in the propagation direction, and the propagation distance is called as the maximum transmission distance of the Bezier beam and is also called as the diffraction-free distance. Just because the Bessel beam has a series of unique properties of long diffraction-free distance, small central spot size, high intensity, good directivity, good self-healing property and self-bending property in the transmission process, the Bessel beam is widely applied to the fields of laser drilling, optical collimation and imaging, charged particle acceleration, plasma channel, optical micro-manipulation, nonlinear optics and the like.
Since the discovery of bessel beams by Durnin in 1987, the scientific community has raised the hot tide of research on bessel beams. The traditional methods for generating the Bessel beam comprise a circumferential seam-lens method, a holographic method, a resonant cavity method, a spherical aberration method and the like, and the analysis of the methods for generating the Bessel beam can find that the circumferential seam-lens method and the resonant cavity method have low energy utilization rate on incident light although the structures are simple and easy to realize. The holographic method has high energy utilization rate and simple structure, but has strict requirements on the precision and the manufacturing process of the holographic film. The spherical aberration method has flexible structure and wide application range, but has more parameters, complex processing and difficult realization. Most importantly, the traditional Bessel lens for generating the Bessel beam is large in size, heavy, difficult to integrate and complex to manufacture, and most importantly, is difficult to be compatible with the existing micro-nano processing technology.
Disclosure of Invention
The invention provides a terahertz Bessel lens based on a super-surface technology, wherein a Bessel beam emitted by the terahertz Bessel lens cannot diverge at a certain distance after being focused, so that the terahertz Bessel beam is fully utilized in various scenes.
The technical scheme provided by the invention is as follows:
a terahertz Bessel lens comprises a transmission-type dielectric terahertz Bessel lens or a reflection-type metal terahertz Bessel lens, wherein the super surface of the terahertz Bessel lens comprises a plurality of harmonic oscillator array units, and the terahertz Bessel lens is characterized in that the characteristic dimension of each harmonic oscillator is the sub-working wavelength, and the design of the harmonic oscillator array units is as follows: performing multi-stage discretization on the phase of the terahertz Bessel lens to obtain a discretized phase value; simulating by using the phase value after dispersion and the phase distribution relation of the terahertz Bessel lens to obtain the characteristic size of the harmonic oscillator array unit; if the harmonic oscillator structures and the sizes of the harmonic oscillator sub-arrays in one dimension are the same, and the harmonic oscillator structures and the sizes of the harmonic oscillator sub-arrays in the other dimension are different, the phase of the harmonic oscillator is changed between 0 pi and 2 pi, and a plate-shaped Bessel beam is formed after the terahertz waves are transmitted through the harmonic oscillator sub-arrays; or the harmonic oscillator arrays are different in harmonic oscillator structure and size in two dimensions, so that the phase of the harmonic oscillator is changed between 0 pi and 2 pi in the two dimensions, and a linear Bessel beam is formed after the terahertz wave is transmitted through the harmonic oscillator arrays.
The top view shape of the harmonic oscillator is round, square, cross, rectangle, triangle, split ring, V-shaped, U-shaped or L-shaped.
The medium of the transmission type medium type Bessel lens is made of high-resistance silicon, polymethylpentene, polyethylene or polytetrafluoroethylene materials.
The harmonic oscillator array unit is a composite of one layer, two layers or multiple layers of media.
If the harmonic oscillator structures and the sizes of the harmonic oscillator arrays on two dimensions are different, the phase of the terahertz Bessel lens is calculated according to a formula (1),
if the structures and the sizes of the harmonic oscillators in one dimension of the harmonic oscillator sub-arrays are the same, and the structures and the sizes of the harmonic oscillators in the other dimension of the harmonic oscillator sub-arrays are different, the phase of the terahertz Bessel lens is calculated according to the step (2),
wherein the content of the first and second substances,
the phase position corresponding to the center of the harmonic oscillator, k is the wave vector of incident light, f is the focal length of the terahertz Bessel lens, x is the projection distance between the center of the harmonic oscillator and the center of the terahertz Bessel lens in a preset phase modulation direction, y is the projection distance between the center of the harmonic oscillator and the center of the terahertz Bessel lens in another preset phase modulation direction, and r is the radius of the terahertz Bessel lens.
The harmonic oscillator array unit of the reflective metal terahertz Bessel lens comprises a metal harmonic oscillator, a middle medium layer and a bottom layer metal, wherein the metal is a metal material for highly reflecting terahertz waves, and the medium layer is silicon dioxide, silicon nitride or a polymer.
The invention has the beneficial effects that:
the invention provides a terahertz Bessel lens based on a super-surface technology and working in a terahertz frequency domain. The terahertz Bessel lens has the following advantages:
1) compared with the light beam generated by a common lens, the Bessel light beam generated by the terahertz Bessel lens based on the super-surface technology has the advantages that the central light spot is small, the light intensity is unchanged within a certain distance in the propagation direction, namely, the diffraction-free distance is long, and the light intensity is easy to concentrate in the propagation process. Just because the non-diffraction distance of the terahertz Bessel lens is long, namely, light does not diverge at a certain distance after being focused, so that the terahertz Bessel lens is fully utilized in many scenes.
2) The terahertz Bessel lens is simple in preparation process, small in size, compatible with a micro-nano process and easy to realize integration and miniaturization.
3) The terahertz Bessel lens realizes 2 pi regulation and control of the phase of the terahertz waves by adjusting the size of the harmonic oscillator, 16-level quantization is carried out on the phase distribution of the terahertz Bessel lens by utilizing a phase distribution formula in order to simplify the design, and then 16 basic units are selected to design the terahertz Bessel lens.
4) The harmonic oscillator structure adopted by the terahertz Bessel lens based on the super-surface technology and working in the terahertz frequency domain has the advantages of simple design, easiness in preparation and the like. In addition, the invention provides that the phase of the terahertz Bessel lens is regulated and controlled by changing the size of the harmonic oscillator, and the multistage discretization is carried out on the phase of 0-360 degrees, so that the simplicity of design is ensured.
Drawings
Fig. 1 is a schematic structural diagram of a harmonic oscillator according to an embodiment of the present invention;
FIG. 2 is a two-dimensional phase distribution diagram of a terahertz Bessel lens according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating a calculation of the focusing performance of a terahertz Bessel lens according to an embodiment of the present invention;
FIG. 4 is a layout of a terahertz Bessel lens according to an embodiment of the present invention;
fig. 5 is a photograph of a terahertz bessel lens after the preparation of the embodiment of the present invention is completed.
Detailed Description
The invention will be further described by way of examples of implementation in connection with the accompanying drawings, without in any way limiting the scope of the invention.
The terahertz Bessel lens designed by the invention changes the transmission phase of terahertz waves by changing the structures and the characteristic sizes of the harmonic oscillators forming the resonance subarray, and changes the reflection or transmission mode of the terahertz waves at the interface by introducing the phase distribution with gradient gradual change at the material interface, thereby realizing anomalous refraction or transmission. In order to obtain the phase distribution of the terahertz Bessel lens, the phase of the axicon lens is superposed with the phase of the common lens, and the terahertz Bessel lens can be divided into a conical lens and a conical lens according to the division of dimensions. The phase distribution formula of the conical mirror is shown as formula (1), and the phase distribution formula of the conical mirror is shown as formula (2):
the top view shape of the resonator structure of the terahertz bessel lens designed by the invention is a square (as shown in fig. 1), and the top view shape of the resonator structure can also be a circle, a cross, a rectangle, a triangle, a split ring, a V shape, a U shape, an L shape and the like. Meanwhile, in order to effectively reduce the high-order diffraction, the size of the whole structure needs to satisfy the sub-wavelength size condition.
In order to design harmonic oscillators with different phases, the invention simulates harmonic oscillators of different lengths at the operating frequency, and finds that the amplitude remains greater than 0.7 and the phase changes by nearly 360 ° when the length of the harmonic oscillator varies between 5 μm and 35 μm. Therefore, it can be found that the terahertz wave phase can be regulated and controlled by changing the size of the harmonic oscillator. After the harmonic oscillator size design is completed, harmonic oscillators with different sizes can be arranged according to specific phase distribution according to needs, so that the planar terahertz element with a specific function is realized.
According to the invention, 16 independent phase values with the phase difference of 22.5 degrees are obtained by taking 16-level discretization as an example, and it can be found that the phase distribution of the terahertz Bessel lens designed by utilizing the 16 independent phase values is centrosymmetric, the phase values are in periodic change along the center of the terahertz Bessel lens to the edge direction, and the phase values are changed from the center to the edge more and more quickly.
Because the terahertz Bessel lens designed by the invention contains a large number of sub-wavelength harmonic oscillators, compared with the method for evaluating the focusing effect of the terahertz Bessel lens by adopting time-consuming FDTD full-wave simulation, the method utilizes more effective and more convenient matlab software to theoretically calculate the focusing performance of the terahertz Bessel lens based on the Huygens principle. Here, each harmonic oscillator is considered as a point wave source that emits an electromagnetic wave, the initial amplitude and phase of which are given by 16 harmonic oscillators of different sizes and phases. Therefore, by superimposing the contributions of all point wave sources in the super-surface plane, the electric field at any point on any plane can be calculated. Therefore, the electric field amplitude for any point of the target plane can be calculated using the fresnel-kirchhoff diffraction formula:
wherein:
z is the distance of the super surface from the target plane.
And finally, in order to prepare the terahertz Bessel lens, firstly drawing a layout of the terahertz Bessel lens. When a layout is drawn, grid division is carried out on harmonic oscillator array distribution of the terahertz Bessel lens according to the period of harmonic oscillators, the distance between each grid point and a central point is obtained, the phase is calculated according to a formula (1) or a formula (2), then the phase is mapped to 0-2 pi, discretization is carried out on the phase of 2 pi, a file related to all grid point size information arrangement can be obtained in matlab according to different sizes corresponding to different phases, a blank layout file is generated through L-Edit software, the file related to all grid point size information arrangement is led into the L-Edit software, and therefore the arrangement of the grid points in all grids can be obtained, and the layout is generated.
After the layout is drawn, the terahertz Bessel lens can be prepared by selecting a proper material. The terahertz Bessel lens to be prepared by the invention is based on the principle of a medium super surface (not limited to the medium super surface), the medium super surface is a two-dimensional metamaterial capable of carrying out terahertz wave front regulation and control, and compared with the super surface based on a metal harmonic oscillator, the terahertz Bessel lens has the advantages of simple design, convenience in processing and the like. The super-surface realized by using the dielectric material is based on the Huygens principle, and the energy of an electric field and a magnetic field is constrained in the dielectric material when electromagnetic waves interact with the dielectric material by reasonably designing a sub-wavelength dielectric super-surface unit. Meanwhile, the impedance of the super-surface unit is matched with the impedance of free space, and two resonance modes of electric dipoles and magnetic dipoles simultaneously appear in the medium material. The phase changes caused by the two resonances can be effectively superposed, so that a 2 pi change of the phase of the electromagnetic wave can be realized. Based on the above, the invention designs the dielectric super-surface by using the high-resistance silicon material, because the high-resistance silicon material is a material with higher transmittance in the terahertz waveband. According to the structural relation of the designed terahertz Bessel lens, the terahertz Bessel lens is prepared on a double-polished silicon wafer by utilizing a micromachining process. In the preparation process, the photoresist is used as an etching mask, and the silicon is etched by an anisotropic dry etching method or a wet etching method, so that the corresponding terahertz Bessel lens is finally prepared.
Taking the terahertz bessel lens with the square shape in the top view of the harmonic oscillator structure as an example, the terahertz bessel lens designed by the invention changes the phase by controlling the characteristic size of the harmonic oscillator structure. In order to design resonators with different phases, the present invention simulates resonators with different lengths at an operating frequency of 3.11THz, and sets the period p of the resonator to 40 μm and the thickness h of the resonator to 45 μm. It was found by simulation that when the length l of the harmonic oscillator is varied between 5 μm and 35 μm, the amplitude remains greater than 0.7 at all times, while the phase changes over a range of nearly 360 °. According to the terahertz Bessel lens, the phase distribution of the terahertz Bessel lens can be calculated according to the formula (1), 16-level discretization is carried out on the phase, the two-dimensional phase distribution of the terahertz Bessel lens designed by 16 independent phase values is shown in figure 2, the phase distribution is centrosymmetric, the phase values are periodically changed along the center of the terahertz Bessel lens to the edge direction, and the phase values are changed from the center to the edge more and more quickly. The specific values of the amplitude, phase and length of the 16 harmonic oscillators are shown in the following table.
In order to theoretically evaluate the focusing performance of the terahertz Bessel lens, the focal length of the terahertz Bessel lens is set to be 100mm, the working frequency is set to be 3.11THz, and the radius is set to be 10 mm. The electric field intensity distributions of the x-y focal plane and the x-z plane were calculated according to the fresnel-kirchhoff diffraction formula shown in formula (3), respectively, as shown in fig. 3. It can be seen from figure 3(a) that there is a distinct focused spot at the x-y focal plane. The intensity distribution at the x-z plane is shown in fig. 3(b), and it can be seen that there is a significant diffraction-free long focus in the z direction. Fig. 3(c) and (d) are intensity profiles along the x-axis (y is 0mm) on the x-y focal plane and along the z-axis (x is 0mm) on the x-z focal plane, respectively, from which a full width at half maximum of the spot intensity of 183 μm can be obtained; from (d) the intensity maximum can be found at z 43 mm.
In order to prepare the terahertz bessel lens, firstly, a layout of the terahertz bessel lens needs to be drawn. The harmonic oscillator array distribution of the terahertz bessel lens is subjected to grid division according to the period of the harmonic oscillator, and finally, the layout of the terahertz bessel lens is shown in fig. 4. The terahertz Bessel lens is prepared on a double-polished silicon wafer with the thickness of 381 mu m and the resistivity of 10000 omega cm by utilizing a micromachining process. In the preparation process, the photoresist is used as an etching mask, and the silicon is etched by adopting an anisotropic dry etching method or a wet etching method, so that the prepared terahertz Bessel lens is shown in FIG. 5.
It is noted that the disclosed embodiments are intended to aid in further understanding of the invention, but those skilled in the art will appreciate that: various substitutions and modifications are possible without departing from the spirit and scope of the invention and appended claims. Therefore, the invention should not be limited to the embodiments disclosed, but the scope of the invention is defined by the appended claims.
Claims (7)
1. The terahertz Bessel lens comprises a transmission-type dielectric terahertz Bessel lens or a reflection-type metal terahertz Bessel lens, wherein the terahertz Bessel lens is formed by a super-surface structure, and the super-surface of the terahertz Bessel lens comprises a plurality of resonator array units, and is characterized in that the characteristic dimension of each resonator array unit is a sub-working wavelength, and the design of the resonator array units is as follows: performing multi-stage discretization on the phase of the terahertz Bessel lens to obtain a discretized phase value; simulating by using the phase value after dispersion and the phase distribution relation of the terahertz Bessel lens to obtain the characteristic size of the harmonic oscillator array unit; if the harmonic oscillator structure and the size in one dimension in the harmonic oscillator array unit are the same, and the harmonic oscillator structure and the size in the other dimension are different, the phase of the harmonic oscillator is changed between 0 and 2 pi, and a plate-shaped Bessel beam is formed after the terahertz wave is transmitted through the harmonic oscillator array unit; or the harmonic oscillator structures and the sizes of the harmonic oscillators in the two dimensions in the harmonic oscillator array unit are different, so that the phases of the harmonic oscillators are changed between 0 pi and 2 pi in the two dimensions, and a linear Bessel beam is formed after the terahertz waves are transmitted through the harmonic oscillator array unit, wherein if the harmonic oscillator structures and the sizes of the harmonic oscillators in the two dimensions in the harmonic oscillator array unit are different, the phases of the terahertz Bessel lens are calculated according to a formula (1),
or, if the structures and the sizes of the harmonic oscillators in one dimension in the harmonic oscillator array unit are the same, and the structures and the sizes of the harmonic oscillators in the other dimension are different, the phase of the terahertz bessel lens is calculated according to the formula (2),
wherein the content of the first and second substances,
the phase position corresponding to the center of the harmonic oscillator, k is the wave vector of incident light, f is the focal length of the terahertz Bessel lens, x is the projection distance between the center of the harmonic oscillator and the center of the terahertz Bessel lens in a preset phase modulation direction, y is the projection distance between the center of the harmonic oscillator and the center of the terahertz Bessel lens in another preset phase modulation direction, and r is the radius of the terahertz Bessel lens.
2. The terahertz bessel lens as claimed in claim 1, wherein the top view shape of the harmonic oscillator is a circle, a cross, a rectangle, a triangle, a split ring, a V, a U or an L shape.
3. The terahertz bessel lens as claimed in claim 1, wherein the medium of the transmissive dielectric type terahertz bessel lens is a high-resistance silicon, polymethylpentene, polyethylene or polytetrafluoroethylene material.
4. The terahertz bessel lens as claimed in claim 3, wherein the harmonic oscillator array unit is a composite of one, two or more layers of dielectric.
5. The terahertz bezier lens according to claim 1, wherein the resonator array unit of the reflective metal terahertz bezier lens comprises a metal resonator, an intermediate dielectric layer and a bottom metal.
6. The terahertz bessel lens as claimed in claim 5, wherein the bottom metal is a metal material that is highly reflective of terahertz waves.
7. The terahertz bessel lens as claimed in claim 5, wherein the dielectric layer is silicon dioxide, silicon nitride or a polymer.
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