CN103268986A - Ultra-thin electromagnetic wave converging and diverging lens design method based on phase discontinuous surface - Google Patents

Abstract

The invention discloses an ultra-thin electromagnetic wave converging and diverging lens design method based on a phase discontinuous surface and belongs to the field of electromagnetism. The ultra-thin electromagnetic wave converging and diverging lens design method based on the phase discontinuous surface solves the problem that a traditional lens is limited in thickness. The design method includes the following steps that first, the focal distance of a required focus point is set; second, according to the principle of a Pancharatnam-Berry phase device, for vertical incidence electromagnetic waves with the electric field polarized along the X-axis and the Y-axis, the first-stage resonance frequency point of a unit structure with the length of a side equal to 5mm is 9.81GHz, and any dispersed phase shift can be introduced to transmitted electromagnetic waves; third, according to the required phase distribution of the converging and diverging lens, an expression of the relation between the angle theta by which each unit rotates in the positive direction of the X-axis and the distance x from the unit to the original point can be obtained on the first-stage resonance frequency point; fourth, f in the first step is put into the first formula in the third step, and thus design parameters of the lens are obtained, and the ultra-thin electromagnetic wave converging and diverging lens design based on the phase discontinuous surface is completed. The ultra-thin electromagnetic wave converging and diverging lens design method based on the phase discontinuous surface is applicable to the field of designing and machining of electromagnetic wave regulation and control lenses.

Description

Ultra-thin electromagnetic wave based on the phase place noncontinuous surface converges, the method for designing of divergent lens

Technical field

The present invention relates to a kind of method for designing of lens, belong to the electromagnetism field.

Background technology

Lens are widely used in microwave system and the optical system at present as a kind of electromagnetic wave artificial regulatory device commonly used.Because lens can change electromagnetic wave propagation direction and spatial distribution to a certain extent, lens involve at multi-beam antenna, satellite communication, radar surveying calibration, electronic countermeasures, millimeter has important use to be worth in the optical imaging system.The image-forming mechanism of said lens still is based on traditional law of refraction, and namely electromagnetic wave forms phase difference by the accumulation of phase on the propagation path in lens, and then forms specific refraction effect.

Yet, have following defective based on these machine-processed lens: 1, the restriction of lens thickness.At first, for the conventional lenses that is made of the homogeneous refractive index material, when other parameters fixedly the time, the more little corresponding lens thickness of focal length is more big.Can reduce lens thickness to a certain extent though increase index of refraction in lens n, the increase of n also can cause the increase of reflection coefficient.Secondly, introduce phase delay diametrically by tooth-shape structure, can realize comparatively frivolous Fresnel lens.But in order to ensure converging required sphere PHASE DISTRIBUTION, the thickness of Fresnel lens will equal its effective wavelength λ/n at least.The 3rd, for the super lens that is constituted by the artificial electromagnetic medium, often require electric field or magnetic field to pass corresponding artificial electromagnetic media unit, just can inspire its specific galvanomagnetic effect, namely need artificial electromagnetic media unit periodic arrangement on the lens normal direction, formation has certain thickness equivalent medium, just can obtain required phase taper.Therefore, have thickness limit based on the lens of traditional law of refraction, lens thickness can not reduce arbitrarily on the electromagnetic wave direction of propagation.

2, other drawbacks that caused by lens thickness.As mentioned above, lens thickness can not reduce arbitrarily, and the lens weight that causes thus and dielectric loss also are inevitably, and for conventional lenses, and is bigger or during near light source when its thickness, because the temperature difference easily causes bigger internal stress, causes the thick lens breakage.Can avoid curved-surface structure to a certain extent though use the graded index technology, dielectric loss and lens weight are not had greatly improved.And for the Fresnel lens, frivolous planar structure can reduce dielectric loss to a great extent, but the tooth-shape structure of forming these lens is very high to requirement on machining accuracy, and is difficult in manufacturing and the use guarantee its flatness, has distortion easily to cause light to defocus slightly.For artificial electromagnetic medium lens, though there is multiple cellular construction to be suggested and to be applied in the lens design in recent years, and the artificial electromagnetic medium develop ten surplus year in can't overcome its loss characteristic all the time fully, the propagation distance of electromagnetic wave in artificial electromagnetic medium lens is more long, then loss is more big.For these reasons, the present invention is from the principle of phase place noncontinuous surface, designed that microwave band is ultra-thinly compiled, divergent lens.

Summary of the invention

The present invention seeks in order to solve the problem that there is thickness limit in conventional lenses, provide that a kind of ultra-thin electromagnetic wave based on the phase place noncontinuous surface converges, the method for designing of divergent lens.

Ultra-thin electromagnetic wave based on the phase place noncontinuous surface of the present invention converges, the method for designing of divergent lens, and this method for designing is:

Step 1, is at first set the f of lens to be produced, and f is the focal length of focus point;

Step 2, according to the principle of Pancharatnam – Berry phase place device, to the cellular construction of length of side a=5mm, electric field is along the X-axis of this cellular construction and the vertical incidence electromagnetic wave of Y-axis polarization, then the transmission coefficient of this cellular construction is t _xAnd t _y, the first rank resonance frequency is 9.81GHz, at resonance frequency place, first rank, transmission coefficient t _x=1, t _y=0, for the transmitted component of the opposite rotation direction of incident circularly polarised wave, introduce an only phase shift relevant with the individual unit anglec of rotation;

Wherein, the X-axis of cellular construction and Y-axis are that the central point with this cellular construction plane is two reference axis of two rectangular coordinate systems of the origin of coordinates, and wherein X-axis is parallel with the limit of the horizontal direction of this cellular construction;

Step 3, for the wavelength X of the incident electromagnetic wave of single order resonance frequency correspondence, when the initial condition of cellular construction, θ=0, wherein θ is the anglec of rotation of the cellular construction at certain position place, along the angle θ of each cellular construction of X-axis positive direction rotation and its apart from initial point apart from x=na (n=0, ± 1, ± 2 ...) relational expression as follows:

$\mathrm{\&theta;}=\&PlusMinus;0.5\&CenterDot;\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(\sqrt{{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00003181958800022.png,HDA00003181958800031.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+x^2}-|f\left|\right)$ Formula one;

Symbolic representation cellular construction wherein is according to clockwise or be rotated counterclockwise, and symbol "+" expression rotates clockwise, and symbol "-" expression is along being rotated counterclockwise; The phase difference that cellular construction is introduced becomes parabolic distribution along X-axis, and the equivalent phase difference that makes any position arrive focus point equates, and incident electromagnetic wave is collected in focal spot;

Step 4, the f in the step 1 is brought in the formula one of step 3, thereby obtain that ultra-thin electromagnetic wave based on the phase place noncontinuous surface compiles, the angle θ along each cellular construction rotation of X-axis positive direction of divergent lens, thereby obtain the angle that any position cellular construction need rotate on the lens surface, finish namely that ultra-thin electromagnetic wave based on the phase place noncontinuous surface compiles, the design of divergent lens.

Advantage of the present invention: the present invention proposes that a kind of novel ultra-thin electromagnetic wave converges, divergent lens.Utilize the phase place parabolic distribution on the interface, realized electromagnetic artificial regulatory, cellular construction size of the present invention is little, thin thickness, transmissivity height.And it is only relevant with the rotation direction of incident circularly polarised wave that it converges, disperses performance, and same lens can realize that electromagnetic wave converges and disperses effect by the rotation direction of regulating incident electromagnetic wave.

The electromagnetic wave of realizing according to this method converges divergent lens, thickness on the electromagnetic transmission direction is compared very little in wavelength, propose a kind of ultra-thin lens based on PCB processing among the design, the metal layer thickness that is used for the required PHASE DISTRIBUTION of realization has only 0.035mm, and electric size has only 0.0011 λ.Suitable with wavelength than the desired lens thickness of conventional lenses, and thickness h ≈ λ, lens proposed by the invention have the ultra-thin characteristics of thickness.

Description of drawings

Fig. 1 is cellular construction schematic diagram of the present invention, and the length of side a of cellular construction is 5mm among the figure, and b is 0.6a, and c is 0.25a, and d is 0.05a;

Fig. 2 is that the cellular construction that has changeed after the θ angle of the present invention revolves schematic diagram;

Fig. 3 is the level that obtains of cellular construction emulation of the present invention, the in-field transmission coefficient of perpendicular polarization;

The transmitted field that Fig. 4 records when being right-handed circular polarization ripple vertical incidence converges the design sketch of effect;

The design sketch of the transmitted field effect weakening that Fig. 5 records when being left-hand circular polarization ripple vertical incidence.

Embodiment

Embodiment one: below in conjunction with Fig. 1 present embodiment is described, the described ultra-thin electromagnetic wave based on the phase place noncontinuous surface of present embodiment converges, the method for designing of divergent lens, and this method for designing is:

Step 1, is at first set the f of lens to be produced, and f is the focal length of focus point;

Step 2, according to the principle of Pancharatnam – Berry phase place device, to the cellular construction of length of side a=5mm, electric field is along the X-axis of this cellular construction and the vertical incidence electromagnetic wave of Y-axis polarization, then the transmission coefficient of this cellular construction is t _xAnd t _y, the first rank resonance frequency is 9.81GHz, at resonance frequency place, first rank, transmission coefficient t _x=1, t _y=0, for the transmitted component of the opposite rotation direction of incident circularly polarised wave, introduce an only phase shift relevant with the individual unit anglec of rotation;

Wherein, the X-axis of cellular construction and Y-axis are that the central point with this cellular construction plane is two reference axis of two rectangular coordinate systems of the origin of coordinates, and wherein X-axis is parallel with the limit of the horizontal direction of this cellular construction;

Step 3, for the wavelength X of the incident electromagnetic wave of single order resonance frequency correspondence, when the initial condition of cellular construction, θ=0, wherein θ is the anglec of rotation of the cellular construction at certain position place, along the angle θ of each cellular construction of X-axis positive direction rotation and its apart from initial point apart from x=na (n=0, ± 1, ± 2 ...) relational expression as follows:

$\mathrm{\&theta;}=\&PlusMinus;0.5\&CenterDot;\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(\sqrt{{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00003181958800022.png,HDA00003181958800031.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+x^2}-|f\left|\right)$ Formula one;

Symbolic representation cellular construction wherein is according to clockwise or be rotated counterclockwise, and symbol "+" expression rotates clockwise, and symbol "-" expression is along being rotated counterclockwise; The phase difference that cellular construction is introduced becomes parabolic distribution along X-axis, and the equivalent phase difference that makes any position arrive focus point equates, and incident electromagnetic wave is collected in focal spot;

Step 4, the f in the step 1 is brought in the formula one of step 3, thereby obtain that ultra-thin electromagnetic wave based on the phase place noncontinuous surface compiles, the angle θ along each cellular construction rotation of X-axis positive direction of divergent lens, thereby obtain the angle that any position cellular construction need rotate on the lens surface, finish namely that ultra-thin electromagnetic wave based on the phase place noncontinuous surface compiles, the design of divergent lens.

Embodiment two: present embodiment is described below in conjunction with Fig. 1, present embodiment is described further execution mode one, the principle of the Pancharatnam – Berry phase place device described in the present embodiment step 2 refers to: the opposite rotation direction transmitted component to the incident circularly polarised wave is introduced an arbitrary phase sudden change amount, circular polarization vertical incidence ripple for left-handed or dextrorotation, each cellular construction is behind its axle rotation θ, and its transmitted field is expressed as:

Wherein ${\mathrm{\&eta;}}_E={\left|\frac{1}{2}(t_x+t_y{e}^{\mathrm{i\&phi;}})\right|}^2,$ ${\mathrm{\&eta;}}_R={|\frac{1}{2}(t_x-t_y{e}^{\mathrm{i\&phi;}})<{\stackrel{\&RightArrow;}{E}}_{\mathrm{in}}|\stackrel{\&RightArrow;}{L}>|}^2;$ ${\mathrm{\&eta;}}_L={|\frac{1}{2}(t_x-t_y{e}^{\mathrm{i\&phi;}})<{\stackrel{\&RightArrow;}{E}}_{\mathrm{in}}|\stackrel{\&RightArrow;}{R}>|}^2$ Be each component transmission coefficient, t _x, t _yFor cellular construction for the electromagnetic transmission coefficient of vertical incidence along the polarization of X-axis and Y-axis,＜α | β the expression inner product; Wherein, there are two components in the transmitted field, first rotation direction that keeps former incident wave, the rotation direction of second component is opposite with the rotation direction of incident wave, if incident wave is left-handed, then this component is dextrorotation, vice versa; Wherein introduced phase change amount ± 2 θs relevant with the angle θ of cellular construction rotation in second component, its symbol is determined by the direction of rotation of incident wave rotation direction and unit.

Operation principle: the ultra-thin electromagnetic wave based on the phase place noncontinuous surface of the present invention converges, the method for designing of divergent lens, be based on the concept of phase place noncontinuous surface, constructed the artificial surface that phase place becomes parabolic distribution in microwave band, realized a kind of ultra-thin novel artificial electromagnetic wave regulation and control device, the performance of device does not rely on its thickness, can realize ultra-thin lens.The structure of novel unit and size, cellular construction have only 0.16 wavelength.Resonant element is operated in resonance frequency place, first rank, and this moment, Electromgnetically-transparent efficient was very high.Converge and disperse only relevantly with the rotation direction of incident circular polarization electromagnetic, same lens can realize that electromagnetic wave converges and disperses effect by the rotation direction of regulating incident electromagnetic wave.

Claims (2)

1. Ultra-thin electromagnetic wave based on the phase place noncontinuous surface converge, the method for designing of divergent lens, it is characterized in that this method for designing is:

   Step 1, is at first set the f of lens to be produced, and f is the focal length of focus point;

   Step 2, according to the principle of Pancharatnam – Berry phase place device, to the cellular construction of length of side a=5mm, electric field is along the X-axis of this cellular construction and the vertical incidence electromagnetic wave of Y-axis polarization, then the transmission coefficient of this cellular construction is t _xAnd t _y, the first rank resonance frequency is 9.81GHz, at resonance frequency place, first rank, transmission coefficient t _x=1, t _y=0, for the transmitted component of the opposite rotation direction of incident circularly polarised wave, introduce an only phase shift relevant with the individual unit anglec of rotation;

   Wherein, the X-axis of cellular construction and Y-axis are that the central point with this cellular construction plane is two reference axis of two rectangular coordinate systems of the origin of coordinates, and wherein X-axis is parallel with the limit of the horizontal direction of this cellular construction;

   Step 3, for the wavelength X of the incident electromagnetic wave of single order resonance frequency correspondence, when the initial condition of cellular construction, θ=0, wherein θ is the anglec of rotation of the cellular construction at certain position place, along the angle θ of each cellular construction of X-axis positive direction rotation and its apart from initial point apart from x=na (n=0, ± 1, ± 2 ...) relational expression as follows:

   $\mathrm{\&theta;}=\&PlusMinus;0.5\&CenterDot;\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(\sqrt{f^2+x^2}-|f\left|\right)$ Formula one;

   Symbolic representation cellular construction wherein is according to clockwise or be rotated counterclockwise, and symbol "+" expression rotates clockwise, and symbol "-" expression is along being rotated counterclockwise; The phase difference that cellular construction is introduced becomes parabolic distribution along X-axis, and the equivalent phase difference that makes any position arrive focus point equates, and incident electromagnetic wave is collected in focal spot;

   Step 4, the f in the step 1 is brought in the formula one of step 3, thereby obtain that ultra-thin electromagnetic wave based on the phase place noncontinuous surface compiles, the angle θ along each cellular construction rotation of X-axis positive direction of divergent lens, thereby obtain the angle that any position cellular construction need rotate on the lens surface, finish namely that ultra-thin electromagnetic wave based on the phase place noncontinuous surface compiles, the design of divergent lens.
2. According to the described ultra-thin electromagnetic wave based on the phase place noncontinuous surface of claim 1 converge, the method for designing of divergent lens, it is characterized in that, the principle of the Pancharatnam – Berry phase place device described in the step 2 refers to: the opposite rotation direction transmitted component to the incident circularly polarised wave is introduced an arbitrary phase sudden change amount, circular polarization vertical incidence ripple for left-handed or dextrorotation, each cellular construction is behind its axle rotation θ, and its transmitted field is expressed as:

   

   Wherein ${\mathrm{\&eta;}}_E={\left|\frac{1}{2}(t_x+t_y{e}^{\mathrm{i\&phi;}})\right|}^2,$ ${\mathrm{\&eta;}}_R={|\frac{1}{2}(t_x-t_y{e}^{\mathrm{i\&phi;}})<{\stackrel{\&RightArrow;}{E}}_{\mathrm{in}}|\stackrel{\&RightArrow;}{L}>|}^2;$ ${\mathrm{\&eta;}}_L={|\frac{1}{2}(t_x-t_y{e}^{\mathrm{i\&phi;}})<{\stackrel{\&RightArrow;}{E}}_{\mathrm{in}}|\stackrel{\&RightArrow;}{R}>|}^2$ Be each component transmission coefficient, t _x, t _yFor cellular construction for the electromagnetic transmission coefficient of vertical incidence along the polarization of X-axis and Y-axis; Wherein, there are two components in the transmitted field, first rotation direction that keeps former incident wave, the rotation direction of second component is opposite with the rotation direction of incident wave, if incident wave is left-handed, then this component is dextrorotation, vice versa; Wherein introduced phase change amount ± 2 θs relevant with the angle θ of cellular construction rotation in second component, its symbol is determined by the direction of rotation of incident wave rotation direction and unit.

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