CN112433364A - Filter design method based on transmission rate and high-pass filtering of electromagnetic hyperdielectric abnormality - Google Patents
Filter design method based on transmission rate and high-pass filtering of electromagnetic hyperdielectric abnormality Download PDFInfo
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- CN112433364A CN112433364A CN202011279642.1A CN202011279642A CN112433364A CN 112433364 A CN112433364 A CN 112433364A CN 202011279642 A CN202011279642 A CN 202011279642A CN 112433364 A CN112433364 A CN 112433364A
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Abstract
The invention discloses a filter design method based on abnormal transmission rate and high-pass filtering of an electromagnetic hypermedium, which comprises the following steps: the transmission rate varies with the angle of incidence for different optical axis angles: with the angle between the optical axis of the material and the transmission axis
At an angle of incidence thetaIThe value when 0 is decreased when
At normal incidence of electromagnetic wave, i.e. thetaIWhen t is 0, t is 0; following the angle
The value of t in the range around the normal incidence also decreases. Compared with the traditional 4f filter device, the high-pass spatial filter manufactured based on the electromagnetic super medium is greatly reduced firstlyThe size of the spatial filter system is increased because the 4f system adopts a multi-stage image transfer-filter system and a confocal long-focus lens, so that the filter system becomes larger, and secondly, a large amount of vacuum system is not needed to be adopted like the 4f system in order to avoid atmospheric ionization caused by the increase of the focusing power density of the light beam, and only the position and the direction need to be adjusted because the focusing is not needed.
Description
Technical Field
The invention relates to the technical field of filter design, in particular to a filter design method based on transmission rate and high-pass filtering of electromagnetic hyperdielectric abnormality.
Background
When the optical axis of the anisotropic electromagnetic hypermedium and the transmission axis form any included angle, the transmission rate in the condition also has an abnormal phenomenon. In general, when the angle between the optical axis of the material and the transmission axis is 0 degrees, the transmission rate varies with the incident angle, and when the incident angle is small, the transmission rate is large, and when the incident angle is vertical, the transmission rate is maximum. However, we have found that the transmission rate varies with the angle between the optical axis of the material and the transmission axis, but is quite opposite as the angle increases, and is at a minimum at normal incidence and in the vicinity. The transmission rate increases gradually and changes very interestingly with increasing incidence angle, and therefore a filter design method based on anomalous transmission rates of electromagnetic metamaterials and high-pass filtering was devised.
Disclosure of Invention
Based on the technical problems existing in the background technology, the invention provides a filter design method based on the transmission rate and the high-pass filtering of the electromagnetic hyperdielectric abnormality.
The invention provides a filter design method based on transmission rate and high-pass filtering of electromagnetic hyperdielectric abnormality, which comprises the following steps:
s1 variation of transmission rate with incident angle for different included angles of optical axis:
s11 included angle between optical axis of material and transmission axis
At an angle of incidence thetaIThe value when 0 is decreased when
At normal incidence of electromagnetic wave, i.e. thetaIWhen t is 0, t is 0;
s12 following the included angle
The value of t in the vicinity of normal incidence also decreases when
-π/4＜θIWhen the ratio is less than pi/4, t is 0, and total reflection is generated;
s13 when thetaIWhen the angle is close to +/-pi/2, t also drops sharply, and the point of +/-pi/2 is 0, which indicates that the transmission wave cannot be generated at the angle;
s14 when
The transmission rate curve has only one peak when
When the transmission rate is 1, two peak values of the transmission rate appear, and along with the increase of the included angle, two peak value points respectively move leftwards and rightwards, namely the left side moves leftwards and the right side moves rightwards;
s15 following
The range in which the transmission wave can be generated is also becoming narrower and narrower;
when the angle S2 and the dielectric tensor and permeability tensor of the material are both determined, θ can be calculated by the equationCAnd thetaBA specific value of (a);
s3 in conventional right-handed Material when θI＝θBWhen the optical axis and the transmission axis form a certain included angle in the completely anisotropic electromagnetic super medium, the phenomenon generated when the optical axis and the transmission axis are incident at the Brewster angle is obviously different from that of the conventional material;
s4, designing and manufacturing a spatial filter device:
s41 when
Then, an incident range in which t is 0 and the transmission rate is low, that is, in the incident rangeThe incidence angle is 0 degree and in the adjacent interval, the transmission rate is extremely low or 0;
s42 regarding the plane electromagnetic wave with different incident angles as being composed of plane waves with different azimuth angles, i.e. different spatial frequencies
When the electromagnetic wave with the azimuth angle of 0 degree and the adjacent area can not penetrate through the anisotropic electromagnetic super medium, and the anisotropic electromagnetic super medium is equivalent to a high-pass filter;
s5 simulating the spatial filtering made by the electromagnetic hypermedium by using the modulated Gaussian beam with limited bandwidth as an incident beam;
assuming a modulated Gaussian beam is incident from free space into an anisotropic electromagnetic metamaterial
The incident wave vector can be written as k ═ k0+k⊥，k⊥Perpendicular to k0And has ω0＝ck0Assume that the weight of the gaussian beam is:
wherein w0Is the beam waist width of the beam;
get k0Related dielectric tensor ε of anisotropic electromagnetic hypermediay、μx、μzRespectively taking 1, 1 and-1, and respectively enabling the light beams to be incident into the anisotropic electromagnetic hypermedium at angles of-30 degrees, -60 degrees and 60 degrees to respectively generate total reflection and total transmission phenomena.
Preferably, the angle of incidence at which full transmission occurs when t is 1 is referred to as the Brewster's angle (θ)B) (ii) a When t is 0, the incident angle at which total reflection occurs is called the critical angle (θ)C)。
Preferably, when the incident electromagnetic wave is a TE wave, the incident electromagnetic wave is followed by
Increase of thetaBAnd thetaCAre all increasing, and thetaBRatio thetaCTo be large, thetaI＞θCThere is transmission of the refracted wave.
Preferably, when the electromagnetic metamaterial is anisotropic
When the incident angle of the light beam is near the vertical incidence, the total reflection is generated, and the light beam can only penetrate through the material when the incident angle is larger than a certain angle.
Compared with the traditional 4f filter device, the high-pass spatial filter manufactured by the electromagnetic hypermedium firstly greatly reduces the volume of a spatial filter system because the 4f system adopts a multi-stage image transmission-filter system and a confocal long-focus lens, so that the filter system becomes larger, and secondly, a large amount of vacuum systems are not needed to be adopted like the 4f system to avoid atmospheric ionization caused by the increase of the focusing power density of a light beam, and only the position and the direction need to be adjusted because the vacuum systems do not need to be focused.
Drawings
FIG. 1 is a graph showing the variation of transmission rate with incident angle at different included angles of optical axis;
FIG. 2 is a diagram of a simulation of a spatially filtered beam that produces total reflection at an incident angle of minus 30 degrees;
FIG. 3 is a diagram of a simulation of a spatially filtered beam that produces total reflection at an incident angle of 30 degrees;
FIG. 4 is a graph of a simulation of a spatially filtered beam that produces full transmission when the angle of incidence is minus 60 degrees;
fig. 5 is a simulated plot of a spatially filtered beam that yields full transmission when the incident angle is 60 degrees.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
Referring to fig. 1-5, a filter design method based on transmission rate and high pass filtering of electromagnetic hypermedia anomalies includes the steps of:
s1 variation of transmission rate with incident angle for different included angles of optical axis:
s11 included angle between optical axis of material and transmission axis
At an angle of incidence thetaIThe value when 0 is decreased when
At normal incidence of electromagnetic wave, i.e. thetaIWhen t is 0, t is 0;
s12 following the included angle
The value of t in the vicinity of normal incidence also decreases when
-π/4＜θIWhen the ratio is less than pi/4, t is 0, and total reflection is generated;
s13 when thetaIWhen the angle is close to +/-pi/2, t also drops sharply, and the point of +/-pi/2 is 0, which indicates that the transmission wave cannot be generated at the angle;
s14 when
The transmission rate curve has only one peak when
When the transmission rate is 1, two peak values of the transmission rate appear, and along with the increase of the included angle, two peak value points respectively move leftwards and rightwards, namely the left side moves leftwards and the right side moves rightwards;
s15 following
The range in which the transmission wave can be generated is also becoming narrower and narrower;
when the angle S2 and the dielectric tensor and permeability tensor of the material are both determined, θ can be calculated by the equationCAnd thetaBA specific value of (a);
s3 in conventional right-handed Material when θI＝θBWhen the optical axis and the transmission axis form a certain included angle in the completely anisotropic electromagnetic super medium, the phenomenon generated when the optical axis and the transmission axis are incident at the Brewster angle is obviously different from that of the conventional material;
s4, designing and manufacturing a spatial filter device:
s41 when
Then, an incident range in which t is 0 and a low transmission rate is generated, that is, in a range in which the incident angle is 0 degrees and in the vicinity, the transmission rate is extremely low or 0;
s42 regarding the plane electromagnetic wave with different incident angles as being composed of plane waves with different azimuth angles, i.e. different spatial frequencies
When the electromagnetic wave with the azimuth angle of 0 degree and the adjacent area can not penetrate through the anisotropic electromagnetic super medium, and the anisotropic electromagnetic super medium is equivalent to a high-pass filter;
s5 simulating the spatial filtering made by the electromagnetic hypermedium by using the modulated Gaussian beam with limited bandwidth as an incident beam;
assuming that a modulated Gaussian beam is incident from free space into an anisotropic electromagnetic hypermedium
The incident wave vector can be written as k ═ k0+k⊥，k⊥Perpendicular to k0And has ω0＝ck0Assume that the weight of the gaussian beam is:
wherein w0Is the beam waist width of the beam;
get k0Related dielectric tensor ε of anisotropic electromagnetic hypermediay、μx、μzRespectively taking 1, 1 and-1, and respectively enabling the light beams to be incident into the anisotropic electromagnetic hypermedium at angles of-30 degrees, -60 degrees and 60 degrees to respectively generate total reflection and total transmission phenomena.
In the present invention, the incident angle at which full transmission occurs when t is 1 is referred to as the Brewster's angle (θ)B) (ii) a When t is 0, the incident angle at which total reflection occurs is called the critical angle (θ)C)。
In the present invention, when the incident electromagnetic wave is a TE wave, the incident electromagnetic wave is followed by
Increase of thetaBAnd thetaCAre all increasing, and thetaBRatio thetaCTo be large, thetaI＞θCThere is transmission of the refracted wave.
In the present invention, when the anisotropic electromagnetic hypermedium is used
When the incident angle of the light beam is near the vertical incidence, the total reflection is generated, and the light beam can only penetrate through the material when the incident angle is larger than a certain angle.
The invention comprises the following steps: the transmission rate varies with the angle of incidence for different optical axis angles: with the angle between the optical axis of the material and the transmission axis
At an angle of incidence thetaIThe value when 0 is decreased when
At normal incidence of electromagnetic wave, i.e. thetaIWhen t is 0, t is 0; following the angle
The value of t in the vicinity of normal incidence also decreases when
-π/4＜θIWhen the ratio is less than pi/4, t is 0, and total reflection is generated; when theta isIWhen the angle is close to +/-pi/2, t also drops sharply, and the point of +/-pi/2 is 0, which indicates that the transmission wave cannot be generated at the angle; when in use
The transmission rate curve has only one peak when
When the transmission rate is 1, two peak values of the transmission rate appear, and along with the increase of the included angle, two peak value points respectively move leftwards and rightwards, namely the left side moves leftwards and the right side moves rightwards; with following
The range in which the transmission wave can be generated is also becoming narrower and narrower; when the dielectric tensor and the permeability tensor of the included angle and the material are determined, θ can be calculated by the formula and the equation respectivelyCAnd thetaBA specific value of (a); in conventional right-handed materials, when θI＝θBWhen the optical axis and the transmission axis form a certain included angle in the completely anisotropic electromagnetic super medium, the phenomenon generated when the optical axis and the transmission axis are incident at the Brewster angle is obviously different from that of the conventional material; designing and manufacturing a spatial filter device: when in use
Then, an incident range with t equal to 0 and a low transmission rate can be generated, that is, in a region where the incident angle is 0 degrees and in the vicinity thereof, the transmission rate is extremely highLow or 0; the plane electromagnetic waves with different incident angles are regarded as plane waves with different azimuth angles, namely different spatial frequencies
When the electromagnetic wave with the azimuth angle of 0 degree and the adjacent area can not penetrate through the anisotropic electromagnetic super medium, and the anisotropic electromagnetic super medium is equivalent to a high-pass filter; simulating the spatial filtering made by the electromagnetic hypermedium by taking a modulated Gaussian beam with limited bandwidth as an incident beam;
assuming a modulated Gaussian beam is incident from free space into an anisotropic electromagnetic metamaterial
The incident wave vector can be written as k ═ k0+k⊥，k⊥Perpendicular to k0And has ω0＝ck0Assume that the weight of the gaussian beam is:
wherein w0Is the beam waist width of the beam;
get k0Related dielectric tensor ε of anisotropic electromagnetic hypermediay、μx、μzRespectively taking 1, 1 and-1, and respectively enabling the light beams to be incident into the anisotropic electromagnetic hypermedium at angles of-30 degrees, -60 degrees and 60 degrees to respectively generate total reflection and total transmission phenomena.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.
Claims (4)
1. The filter design method based on the abnormal transmission rate and the high-pass filtering of the electromagnetic hypermedium is characterized by comprising the following steps of:
s1 variation of transmission rate with incident angle for different included angles of optical axis:
s11 included angle between optical axis of material and transmission axis
At an angle of incidence thetaIThe value when 0 is decreased when
At normal incidence of electromagnetic wave, i.e. thetaIWhen t is 0, t is 0;
s12 following the included angle
The value of t in the vicinity of normal incidence also decreases when
-π/4＜θIWhen the ratio is less than pi/4, t is 0, and total reflection is generated;
s13 when thetaIWhen the angle is close to +/-pi/2, t also drops sharply, and the point of +/-pi/2 is 0, which indicates that the transmission wave cannot be generated at the angle;
s14 when
The transmission rate curve has only one peak when
When the transmission rate is 1, two peak values of the transmission rate appear, and along with the increase of the included angle, two peak value points respectively move leftwards and rightwards, namely the left side moves leftwards and the right side moves rightwards;
s15 following
The range in which the transmission wave can be generated is also becoming narrower and narrower;
when the angle S2 and the dielectric tensor and permeability tensor of the material are both determined, θ can be calculated by the equationCAnd thetaBA specific value of (a);
s3 in conventional right-handed Material when θI＝θBWhen the optical axis and the transmission axis form a certain included angle in the completely anisotropic electromagnetic super medium, the phenomenon generated when the optical axis and the transmission axis are incident at the Brewster angle is obviously different from that of the conventional material;
s4, designing and manufacturing a spatial filter device:
s41 when
Then, an incident range in which t is 0 and a low transmission rate is generated, that is, in a range in which the incident angle is 0 degrees and in the vicinity, the transmission rate is extremely low or 0;
s42 regarding the plane electromagnetic wave with different incident angles as being composed of plane waves with different azimuth angles, i.e. different spatial frequencies
When the electromagnetic wave with the azimuth angle of 0 degree and the adjacent area can not penetrate through the anisotropic electromagnetic super medium, and the anisotropic electromagnetic super medium is equivalent to a high-pass filter;
s5 simulating the spatial filtering made by the electromagnetic hypermedium by using the modulated Gaussian beam with limited bandwidth as an incident beam;
assuming that a modulated Gaussian beam is incident from free space into an anisotropic electromagnetic hypermedium
The incident wave vector can be written as k ═ k0+k⊥，k⊥Perpendicular to k0And has ω0＝ck0Assume that the weight of the gaussian beam is:
wherein w0Is the beam waist width of the beam;
get k0Related dielectric tensor ε of anisotropic electromagnetic hypermediay、μx、μzRespectively taking 1, 1 and-1, and respectively enabling the light beams to be incident into the anisotropic electromagnetic hypermedium at angles of-30 degrees, -60 degrees and 60 degrees to respectively generate total reflection and total transmission phenomena.
2. The method of claim 1 wherein the angle of incidence at which total transmission occurs when t is 1 is referred to as the Brewster angle (θ)B) (ii) a When t is 0, the incident angle at which total reflection occurs is called the critical angle (θ)C)。
3. The method of claim 1, wherein the incident electromagnetic wave is a TE wave and is followed by a TE wave
Increase of thetaBAnd thetaCAre all increasing, and thetaBRatio thetaCTo be large, thetaI＞θCThere is transmission of the refracted wave.
4. The method of claim 1, wherein the filter design is based on transmission rate and high pass filtering for anisotropic electromagnetic metamaterials
When the incident angle of the light beam is near the vertical incidence, total reflection is generated,the material is only transparent when incident at an angle greater than a certain angle.
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|---|---|---|---|---|
| US20050078372A1 (en) * | 2003-09-01 | 2005-04-14 | Kazuhiko Momoki | Polarization beam splitter and optical system using the same, and image displaying apparatus, using the same |
| WO2006023195A2 (en) * | 2004-07-23 | 2006-03-02 | The Regents Of The University Of California | Metamaterials |
| CN1996096A (en) * | 2006-10-25 | 2007-07-11 | 浙江大学 | Polarization beam splitter based on wave-structured film positive and negative refraction |
| CN103576237A (en) * | 2013-11-18 | 2014-02-12 | 中国科学院大学 | Auto-collimation zero phase shift transmission method based on photonic crystals |
| CN107976733A (en) * | 2017-11-24 | 2018-05-01 | 苏州大学 | A kind of all dielectric polarizes unrelated angular filter |
| CN110568624A (en) * | 2019-08-15 | 2019-12-13 | 复旦大学 | Polarization conversion device based on angular dispersion principle |
-
2020
- 2020-11-16 CN CN202011279642.1A patent/CN112433364A/en not_active Withdrawn
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20050078372A1 (en) * | 2003-09-01 | 2005-04-14 | Kazuhiko Momoki | Polarization beam splitter and optical system using the same, and image displaying apparatus, using the same |
| WO2006023195A2 (en) * | 2004-07-23 | 2006-03-02 | The Regents Of The University Of California | Metamaterials |
| CN1996096A (en) * | 2006-10-25 | 2007-07-11 | 浙江大学 | Polarization beam splitter based on wave-structured film positive and negative refraction |
| CN103576237A (en) * | 2013-11-18 | 2014-02-12 | 中国科学院大学 | Auto-collimation zero phase shift transmission method based on photonic crystals |
| CN107976733A (en) * | 2017-11-24 | 2018-05-01 | 苏州大学 | A kind of all dielectric polarizes unrelated angular filter |
| CN110568624A (en) * | 2019-08-15 | 2019-12-13 | 复旦大学 | Polarization conversion device based on angular dispersion principle |
Non-Patent Citations (1)
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