CN115494675B - Phase shifter based on singular points in APT symmetrical Contoll photonic crystal - Google Patents
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Abstract
The inventionThe invention relates to a phase shifter based on singular points in APT symmetrical Controp photonic crystals, which comprises a central symmetrical structure formed by compounding two Controp photonic crystals with the same serial numbers, wherein the whole central symmetrical structure meets the APT symmetry by regulating and controlling the real part and the imaginary part of the refractive index of each dielectric medium, and then the phase shifting effect of pi of the singular point of an APT symmetrical system is utilized to control the frequency of the phase shift of an electric field through dielectric medium loss and an incident angle; the Control photon crystal is composed of several dielectric thin sheets A and several dielectric thin sheets B according to the Nth item S of the Control sequence N ＝S N‑1 (3B) N‑1 S N‑1 Sequentially arranged, wherein S 0 =a, N takes a positive integer. The phase shifter can realize accurate half-wave phase shift, namely, the phase shifter can accurately adjust the phase of a signal wave.
Description
Technical Field
The invention belongs to the technical field of phase shifters, and particularly relates to a phase shifter based on singular points in APT symmetrical Contoll photonic crystals.
Background
In a communication system, it is necessary to perform phase modulation on an analog signal, phase shift keying on a digital signal, and the like, which requires precise manipulation of the phase of a carrier wave. In addition, in optical fiber communication, a half-wave phase shifter is often used. The phase shifter may be used to regulate the phase of the signal wave. In particular, in phase shift keying and phase shifters, half-wave phase shift is a common digital modulation technique, and previous phase modulators have mostly achieved control of the transmission phase of an optical wave by changing the refractive index of a material, but it is difficult to achieve natural and accurate half-wave phase shift keying.
Disclosure of Invention
In order to overcome the defect that the existing phase shift keying and phase shifter are difficult to realize natural and accurate half-wave phase shift, the invention provides a phase shifter based on singular points in an APT (Anti-space-time) symmetrical Controp photonic crystal.
The technical scheme for solving the technical problems is as follows:
the phase shifter based on singular points in the APT symmetrical Contole photonic crystal comprises a central symmetrical structure formed by compounding two Contole photonic crystals with the same serial numbers, and the whole central symmetrical structure can meet the APT symmetry by regulating and controlling the real part and the imaginary part of the refractive index of each dielectric medium layer, namely the refractive index of the material meets the condition: n (z) = -n (-z), wherein z is space position coordinate, and represents complex conjugate operation, then phase shift effect of pi of reflection coefficient phase at optical singular point in APT symmetrical system is utilized to realize half-wave phase shift of electric field, and then electric field frequency of half-wave phase shift is regulated and controlled by dielectric loss and incidence angle;
wherein one Contoll photon crystal is formed by a plurality of dielectric thin sheets A and a plurality of dielectric thin sheets B according to the Nth item of the Contoll sequence, namely S N ＝S N-1 (3B) N-1 S N-1 The other Contole photon crystal is formed by arranging a plurality of dielectric thin sheets A ' and a plurality of dielectric thin sheets B ' in sequence according to the Nth item of the Contole sequence, namely S ' N ＝S' N-1 (3B') N-1 S' N-1 Sequentially arranged, wherein N is more than or equal to 1 and is an integer, and the sequence number is used for representing the sequence, S 0 ＝A，S' 0 =a ', a and B ' are denoted as high refractive index uniform dielectric layers, and a ' and B are denoted as low refractive index uniform dielectric layers.
On the basis of the technical scheme, the invention can be improved as follows.
Further, the sequence number n=2.
Furthermore, the materials of the dielectric thin sheets A and B 'are silicon, the materials of the dielectric thin sheets A' and B are silicon dioxide, and the whole central symmetrical structure meets the APT symmetry through doping, namely the real part and the imaginary part of the refractive index of the material respectively meet the conditions: n is n r (z)＝-n r (-z) and n i (z)＝n i (-z), i.e. the real part of the refractive index n r With respect to the origin odd symmetry, the imaginary part n of the refractive index i Even symmetric about the origin.
Further, the dielectric sheet A has a refractive index n A =3.53+0.01×q, and the refractive index of the dielectric sheet B is n B =1.46+0.01×q, the refractive index of the dielectric sheet a' is n A' =1.46+0.01×q, the refractive index of the dielectric sheet B' is n B' =3.53+0.01×q, where the letter q denotes the loss factor, by doping with iron ions Fe 2+ To achieve optical losses in the dielectric; doping with iron ions Fe 2+ The refractive indices of the subsequent A, B, A 'and B' are n respectively a ＝n A -n 0 ＝1.035+0.01*q、n b ＝n B -n 0 ＝-1.035+0.01*q、n' a' ＝n A' -n 0 -1.035+0.01 q and n' b' ＝n B' -n 0 =1.035+0.01×q, where n 0 =2.495, i.e. the whole structure satisfies APT symmetry.
Further, the loss factor is of a magnitude of Fe 2+ The concentration of ions is regulated.
Further, the dielectric sheets A and A' each have a thickness d a ＝d a' =0.05 μm, the thickness of dielectric sheets B and B' are d b ＝d b' ＝0.1μm。
The beneficial effects of the invention are as follows: the phase shifter can realize accurate half-wave phase shift, namely, the phase shifter can accurately regulate and control the phase of a signal wave. Specifically, two kinds of dielectric thin sheets with different refractive indexes are stacked layer by layer to form two Contoll photonic crystals, and the material loss coefficient in the dielectric thin sheets is regulated and controlled to meet the symmetry of APT (Anti-space-time: anti-space-time): n (z) = -n (-z), where z is the horizontal direction spatial position coordinate. The structure supports the optical fractal effect and thus a plurality of singular points in a parameter space consisting of loss coefficients and normalized frequencies. The reflection coefficient phase has pi phase jump at the singular point, and the propagation phase of the reflected light wave has pi phase shift at the singular point. The position of the singular point and the frequency of the light wave corresponding to the singular point can be flexibly regulated and controlled by the incident angle.
Drawings
Fig. 1 is a schematic diagram of an APT symmetrical cotol photonic crystal structure in a phase shifter according to embodiment 1 of the present invention.
Fig. 2 (a) is the reflectivity of an optical wave in the parameter space of embodiment 2 of the present invention, fig. 2 (b) is the local amplification of the reflectivity near a single singular point in the parameter space of embodiment 2 of the present invention, and fig. 2 (c) is the variation relationship of the reflection coefficient phase corresponding to different loss coefficients q with the normalized frequency in embodiment 2 of the present invention; wherein, the light wave is vertically incident from the left, and the parameter space consists of a loss coefficient and a normalized frequency.
Fig. 3 (a) is the reflectivity of an optical wave in the parameter space of embodiment 3 of the present invention, fig. 3 (b) is the local amplification of the reflectivity near a single singular point in the parameter space of embodiment 3 of the present invention, and fig. 3 (c) is the variation relationship of the reflection coefficient phase corresponding to different loss coefficients q with the normalized frequency in embodiment 3 of the present invention; wherein, the light wave is vertically incident from the right, and the parameter space consists of a loss coefficient and a normalized frequency.
FIG. 4 (a) shows the singular point EP in example 3 of the present invention 13 FIG. 4 (b) shows the relationship between the imaginary part of the eigenvalue of the nearby scattering matrix and the normalized frequency, and the singular point EP in example 3 of the present invention 13 The real part of the eigenvalue of the nearby scattering matrix varies with the normalized frequency.
Fig. 5 (a) shows the relationship between the reflection coefficient phase corresponding to the left incident angle θ=5° and the loss coefficient q=0.41 and the normalized frequency in the embodiment 4 of the present invention, fig. 5 (b) shows the relationship between the reflection coefficient phase corresponding to the left incident angle θ=10° and the loss coefficient q= 0.3075 and the normalized frequency in the embodiment 4 of the present invention, fig. 5 (c) shows the relationship between the reflection coefficient phase corresponding to the left incident angle θ=15° and the loss coefficient q=0.0725 and fig. 5 (d) shows the relationship between the reflection coefficient phase corresponding to the left incident singular point EP in the embodiment 4 of the present invention and the normalized frequency 5 The position in the parameter space varies with the angle of incidence.
Detailed Description
The principles and features of the present invention are described below with examples given for the purpose of illustration only and are not intended to limit the scope of the invention.
Unless otherwise indicated, the raw materials used in the present invention are conventional in the art and are commercially available. In the test methods and the detection methods of the following examples, unless otherwise specified, conventional methods are used, and the apparatus used in the test are commercially available.
The non-periodic photonic crystal has a fractal structure which supports a plurality of defect modes, and the number of the defect modes is divided in geometric progression along with the increase of the sequence number of the photonic crystal. In addition, when there is gain or loss in the material, the system is non-hermite, particularly for one-dimensional structures, when the refractive index of the material satisfies n (z) = -n (-z), where z is the spatial position coordinate, then the non-hermite optical system is said to satisfy APT (Anti-space-time) symmetry. There is a singular point (Exceptional point: EP) in the APT optical system where there is a phase jump of pi in the reflection coefficient phase. Based on the above, the inventor considers combining the aperiodic photonic crystal with the symmetry of the APT, and finds the singular point of the parameter space to realize the half-wave phase shift of the reflection coefficient, and further realize the half-wave phase shift of the propagation phase of the reflected light wave.
The following are examples of the invention
Example 1
Fig. 1 is a schematic structural diagram of an APT symmetrical cotol photonic crystal in a phase shifter according to the present embodiment. Compounding two Control (Cantor) photonic crystals with the same serial numbers to form a central symmetrical structure, and regulating and controlling the real part and the imaginary part of the refractive index of each layer of dielectric medium to ensure that the refractive index of the material of the whole structure meets the symmetry of APT, namely: n (z) = -n (-z), where z is the horizontal direction spatial position coordinate.
Letter I 1 Representing incident light rays, I 2 Representing reflected light rays, I 3 Indicating transmitted light. The device is placed in a horizontal orientation and light waves are incident vertically or obliquely from the left or right, where θ is the angle of incidence. The polarization direction of the light wave may be a transverse wave or a transverse magnetic wave.
The replacement rule of the Cantor sequence in mathematics is: s is S 0 ＝A，S 1 ＝ABA，S 2 ＝ABABBBABA,S 3 ＝S 2 (3B) 2 S 2 ，……，S N ＝S N-1 (3B) N-1 S N-1 … …, where N (n=1, 2,3, … …) is the sequence number of the sequence, S N The nth item of the sequence is represented. In the corresponding Cantor photonic crystal, the letters A, B represent two homogeneous dielectrics, respectively, which differ in refractive index. The composite structure of two Cantor photonic crystals ABABBBABA and a ' B ' a ' with the sequence n=2 is given as fig. 1.
In this embodiment, A is a silicon dielectric sheet having a refractive index n A =3.53+0.01×q; b is a silicon dioxide dielectric sheet having a refractive index n B =1.46+0.01×q; a' is a silicon dioxide dielectric sheet having a refractive index n A' =1.46+0.01×q; b' is a silicon dielectric sheet having a refractive index n B' =3.53+0.01×q. Wherein the letter q represents the gain/loss coefficient of the material, when q>0, loss, and gain when q < 0. In experiments, the loss is easy to realize, so only the loss is taken here, and q is called a loss factor. Optical losses in dielectrics can be reduced by doping with iron ions Fe 2+ To achieve the effect that the loss factor is of the size of Fe 2+ The concentration of ions is regulated.
The thickness of the dielectric sheets A and A' are d a ＝d a' =0.05 μm (micrometers); the thickness of the dielectric sheets B and B' are d b ＝d b' ＝0.1μm。
The whole structure actually meets the APT symmetry condition, namely the refractive index meets the formula: n (z) = -n (-z), where z is the spatial position coordinate, representing the complex conjugate operation. Further, the refractive index is written as a real plus imaginary form n (z) =n r (z)+i*n i (z), the APT symmetry condition is equivalent to two formulas: n is n r (z)＝-n r (-z) and n i (z)＝n i (-z), i.e. the real part is odd symmetric about the origin and the imaginary part is even symmetric about the origin.
Let n be 0 =2.495, the refractive indices of A, B, A 'and B' can be converted to n, respectively a ＝n A -n 0 ＝1.035+0.01*q、n b ＝n B -n 0 ＝-1.035+0.01*q、n' a' ＝n A' -n 0 -1.035+0.01 q and n' b' ＝n B' -n 0 =1.035+0.01×q. It can be seen that the relative refractive index satisfies the APT symmetry condition: n '(z) = -n' (-z).
Example 2
Experiments were performed with the APT symmetric cotol photonic crystal (n=2) obtained in example 1, when a transverse magnetic wave is perpendicularly incident from the left, i.e., the incident angle θ=0°, the frequency of the incident light is changed, and fig. 2 (a) shows the reflection spectrum R of the light wave in the parameter space f . To improve contrast, the reflectivity coefficient is log 10 (R f ). The parameter space is defined by the loss factor q and the normalized angular frequency (omega-omega 0 )/ω gap Composition, wherein ω=2pi c/λ, ω 0 ＝2πc/λ 0 And omega gap ＝4ω 0 arcsin│[Re(n a )-Re(n b )]/[Re(n a )+Re(n b )]| 2 Pi represents the angular frequency of the incident light, the central angular frequency of the incident light and the photonic band gap of the angular frequency, c is the speed of light in vacuum, arcsin is the operation of the arcsin function, and lambda represents the wavelength of the incident light. It can be seen that there are a number of reflectivity minima points in the parameter space, which will later be demonstrated to be optical singularities (Exceptional point: EP), respectively denoted EP, in an APT symmetric system 1 、EP 2 、EP 3 、EP 4 、EP 5 And EP 6 And are marked with circles respectively, and the reflectivity corresponding to the singular points is 0.
For better visualization, FIG. 2 (b) shows the EP 5 A partial enlarged view of the surrounding parameter space. Singular point EP 5 The coordinates in parameter space are [ q=0.4375, (ω - ω) 0 )/ω gap ＝3.7892]The reflectivity of this point is log 10 (R f ) = -4.9266, the reflectivity of this point is practically equal to zero, i.e. R, taking into account the effect of the calculation accuracy f ＝0。
Reflection coefficient r=e o /E i Wherein is E i Input electric field strength E o For the reflected electric field intensities, they are all complex, written in complex exponential form:thereby can be obtainedI.e. propagation phase of the reflected electric field->By controlling the phase of the reflection coefficient ∈ ->To regulate the propagation phase of the reflected electric field>The phase shift effect that the phase of the reflection coefficient at the optical singular point in the APT symmetrical system is pi is utilized to realize the half-wave phase shift of the electric field, and then the electric field frequency of the half-wave phase shift is regulated and controlled through dielectric loss and incidence angle.
FIG. 2 (c) shows EP 5 The corresponding loss coefficient q=0.4375 and the reflection coefficient phase corresponding to the loss coefficient nearby the loss coefficient varies with the normalized frequency. It can be seen that as the normalized frequency increases, the reflection coefficient phase is at (ω - ω) when q=0.4375 0 )/ω gap An upward phase jump occurs at 3.7892, the phase jump variable beingThere is also a 2 pi phase jump elsewhere, which is not significant. When the loss coefficient values corresponding to the points except the singular point are taken, such as q=0.25 and 0.75, no pi phase jump occurs in the reflection coefficient phase no matter how the normalized frequency changes.
Example 3
Experiments were performed with the APT symmetric cotol photonic crystal (n=2) obtained in example 1, when a transverse magnetic wave is perpendicularly incident from the right, i.e., the incident angle θ=0°, the frequency of the incident light is changed, and fig. 3 (a) shows the reflection spectrum R of the light wave in the parameter space b . It can be seen that there are also many points of reflectivity minima in the parameter space, these minimaThe value points are also singular points in the APT symmetrical system and are respectively marked as EP 7 、EP 8 、EP 9 、EP 10 、EP 11 、EP 12 、EP 13 And EP 14 And are marked with circles, respectively, the reflectivity at these point locations is 0.
For better visualization, FIG. 3 (b) shows the EP 13 A partial enlarged view of the surrounding parameter space. Singular point EP 13 The coordinates in parameter space are [ q= 0.7625, (ω - ω) 0 )/ω gap ＝3.868]The reflectivity of this point is log 10 (R b ) = -5.5386, the reflectivity of this point is in fact also equal to zero, i.e. R, taking into account the effect of the calculation accuracy b ＝0。
FIG. 3 (c) shows EP 13 The corresponding loss coefficient q= 0.7625 and the reflection coefficient phase corresponding to the loss coefficient nearby thereof are related to the change of the normalized frequency. It can be seen that as the normalized frequency increases, the reflectance phase is at (ω - ω) when q= 0.7625 0 )/ω gap An upward phase jump occurs at =3.868, the phase jump variable beingThere is also a 2 pi phase jump elsewhere, which is not significant. When the loss coefficient values corresponding to the points other than the singular point, such as q=0.5 and 0.875, no pi phase jump occurs in the reflection coefficient phase no matter how the normalized frequency is changed.
Defining a scattering matrix in the APT Contoler photonic crystal as S= [ t r ] f ；r b t]It is equivalent to Hamiltonian amount in quantum mechanics, where t is the transmission coefficient, r f For the reflection coefficient of light incident from the left, r b The reflection coefficient is the reflection coefficient of light incident from the right. The eigenvector of the scattering matrix is V 1,2 ＝(r f 1/2 ,±r b 1/2 ) Eigenvalue is lambda 1,2 ＝t±(r f r b ) 1/2 . At (r) f r b ) 1/2 The eigenvector is degenerated, which is the origin of the singular point, which is =0With a time reflection coefficient of zero r f =0 or r b ＝0。
FIG. 4 (a) shows the singular point EP 13 The change relation of the eigenvalue imaginary part of the nearby scattering matrix along with the normalized frequency. Scattering matrix eigenvalue imaginary part Im (lambda) 1,2 ) Intersecting at the singular point, the eigenvalue imaginary parts are separated more and more widely as the normalized frequency changes. Overall, the scattering matrix eigenvalue imaginary part Im (λ 1 ) And Im (lambda) 2 ) And presents a crossed state.
FIG. 4 (b) shows the singular point EP 13 The real part of the eigenvalue of the nearby scattering matrix varies with the normalized frequency. Real part of eigenvalue Re (lambda) 1,2 ) Intersecting at the singular point, the eigenvalue real parts gradually diverge as the normalized frequency changes. Overall, the real part Re (λ) of the eigenvalue of the scattering matrix 1 ) And Re (lambda) 2 ) An anti-crossover state is presented.
The intersection and anti-intersection of the imaginary and real parts of the scattering matrix eigenvalues at and near the singular point, respectively, is a typical criterion for determining the singular point in a non-hermite optical system (APT symmetry is a special case of non-hermite).
Example 4
An experiment was performed on the basis of example 2 with APT symmetrical cotol photonic crystals (n=2) obtained in example 1.
Fig. 5 (a) shows the reflection coefficient phase corresponding to the left incident angle θ=5°, and the loss coefficient q=0.41, as a function of the normalized frequency. When light is incident from the left, the incident angle θ=5° is set. Regulating loss coefficient and normalized frequency to obtain singular point EP in parameter space 5 The position of (c) is [ q=0.41, (ω - ω) 0 )/ω gap ＝3.7947]. Therefore, here, the reflection coefficient phase corresponding to q=0.41 is given as a function of the normalized frequency when θ=5°. It can be seen that the reflection coefficient phase varies with the normalized frequency; when (omega-omega) 0 )/ω gap When= 3.7947, the reflection coefficient phase undergoes an upward abrupt jump, the jump being
That is, in (ω - ω) 0 )/ω gap Around the singular point = 3.7947, the frequency (ω - ω 0 )/ω gap Light wave ratio (omega-omega) of ≡ 3.7947 0 )/ω gap <3.7947 the optical wave phase will increase by pi and therefore this effect can be applied to half wave phase shifters.
Fig. 5 (b) shows the reflection coefficient phase corresponding to the left incident angle θ=10°, loss coefficient q= 0.3075, as a function of the normalized frequency. When light is incident from the left, the incident angle θ=10° is set. Regulating loss coefficient and normalized frequency to obtain singular point EP in parameter space 5 The position is [ q= 0.3075, (ω - ω) 0 )/ω gap ＝3.8112]. Therefore, here, the relationship of the reflection coefficient phase corresponding to q= 0.3075 with respect to the normalized frequency is given as θ=10°. It can be seen that the reflection coefficient phase varies with the normalized frequency; when (omega-omega) 0 )/ω gap When= 3.8112, the reflection coefficient phase undergoes an upward abrupt jump, the jump being
Fig. 5 (c) shows the reflection coefficient phase corresponding to the left incident angle θ=15°, and the loss coefficient q=0.0725, as a function of the normalized frequency. When light is incident from the left, the incident angle θ=15° is set. Regulating loss coefficient and normalized frequency to obtain singular point EP in parameter space 5 The position of [ q=0.0725, (ω - ω) 0 )/ω gap ＝3.8373]. Thus, given θ=15°, the phase of the reflection coefficient corresponding to q=0.0725 varies with the normalized frequency. It can be seen that the reflection coefficient phase varies with the normalized frequency; when (omega-omega) 0 )/ω gap When= 3.8373, the reflection coefficient phase undergoes an upward abrupt jump, the jump being
FIG. 5 (d) shows the left incidence singularityPoint EP 5 The position in the parameter space varies with the angle of incidence. The parameter space consists of the loss factor q and the normalized frequency. When the light wave is perpendicularly incident from the left, the position of the singular point also moves in the parameter space in response to changing the incident angle of the light wave. Here in EP 5 For example, increasing the angle of incidence, θ=0° increases to θ=15°, EP 5 The position in the parameter space moves to the right lower side. And then continue to increase the incident angle, EP 5 Will disappear. Therefore, the normalized frequency position point corresponding to pi phase jump of the loss coefficient and the reflection coefficient phase corresponding to the EP point can be regulated and controlled by changing the incident angle.
In a word, two Contoll photonic crystals composed of dielectric thin plates are compounded to form a one-dimensional photonic crystal, and the loss coefficient of the dielectric material is regulated and controlled to meet the APT symmetry. When light is incident from the left or right, there are a plurality of singular points in the parameter space composed of the loss coefficient and the normalized frequency. The phase jump of pi occurs at the singular point of the reflection coefficient phase, so that the half-wave phase shift of the propagation phase of the reflected light wave is realized, and the phase shifter can accurately regulate the phase of the signal wave, namely, the accurate half-wave phase shift is realized. The position of the singular point in the parameter space, namely the position where pi phase shift occurs to the reflection coefficient phase, and the corresponding light wave frequency can be flexibly regulated and controlled by the incident angle.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (6)
1. The phase shifter based on singular points in the APT symmetrical Contoll photonic crystal is characterized by comprising a central symmetrical structure formed by compounding two Contoll photonic crystals with the same serial numbers, and the whole central symmetrical structure can meet APT symmetry by regulating and controlling the real part and the imaginary part of the refractive index of each layer of dielectric medium, namely the refractive index of a material meets the condition: n (z) = -n (-z), wherein z is space position coordinate, and represents complex conjugate operation, then phase shift effect of pi of reflection coefficient phase at optical singular point in APT symmetrical system is utilized to realize half-wave phase shift of electric field, and then electric field frequency of half-wave phase shift is regulated and controlled by dielectric loss and incidence angle;
wherein one Contoll photon crystal is formed by a plurality of dielectric thin sheets A and a plurality of dielectric thin sheets B according to the Nth item of the Contoll sequence, namely S N ＝S N-1 (3B) N-1 S N-1 The other Contole photon crystal is formed by arranging a plurality of dielectric thin sheets A ' and a plurality of dielectric thin sheets B ' in sequence according to the Nth item of the Contole sequence, namely S ' N ＝S' N-1 (3B') N-1 S' N-1 Sequentially arranged, wherein N is more than or equal to 1 and is an integer, and the sequence number is used for representing the sequence, S 0 ＝A，S' 0 =a ', a and B ' are denoted as high refractive index uniform dielectric layers, and a ' and B are denoted as low refractive index uniform dielectric layers.
2. The phase shifter of claim 1, wherein the sequence number N = 2.
3. The phase shifter according to claim 1, wherein the dielectric sheets a and B 'are made of silicon, the dielectric sheets a' and B are made of silicon dioxide, and the whole centrosymmetric structure is doped to satisfy APT symmetry, that is, the real part and the imaginary part of the refractive index of the material satisfy the conditions: n is n r (z)＝-n r (-z) and n i (z)＝n i (-z), i.e. the real part of the refractive index n r With respect to the origin odd symmetry, the imaginary part n of the refractive index i Even symmetric about the origin.
4. A phase shifter according to claim 3, wherein the dielectric sheet a has a refractive index n A =3.53+0.01×q, and the refractive index of the dielectric sheet B is n B =1.46+0.01×q, the refractive index of the dielectric sheet a' is n A' =1.46+0.01×q, the refractive index of the dielectric sheet B' is n B' =3.53+0.01×q, where the letter q denotes the loss factor, by doping with iron ions Fe 2+ To achieve optical losses in the dielectric; doping with iron ions Fe 2+ The refractive indices of the subsequent A, B, A 'and B' are n respectively a ＝n A -n 0 ＝1.035+0.01*q、n b ＝n B -n 0 ＝-1.035+0.01*q、n' a' ＝n A' -n 0 -1.035+0.01 q and n' b' ＝n B' -n 0 =1.035+0.01×q, where n 0 =2.495, i.e. the whole structure satisfies APT symmetry.
5. The phase shifter of claim 4, wherein the loss factor is of a magnitude selected from the group consisting of Fe 2+ The concentration of ions is regulated.
6. The phase shifter of claim 4, wherein the dielectric sheets a and a' each have a thickness d a ＝d a' =0.05 μm, the thickness of dielectric sheets B and B' are d b ＝d b' ＝0.1μm。
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| CN113791463A (en) * | 2021-09-06 | 2021-12-14 | 湖北科技学院 | PT symmetrical Kantol photonic crystal structure capable of realizing coherent absorption of laser spot |
| CN113934072A (en) * | 2021-10-21 | 2022-01-14 | 湖北科技学院 | PT symmetrical Kantol photonic crystal structure capable of realizing optical directional stealth |
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