A time-reversal method for realizing high-pass characteristics in a continuous gradient form

Abstract

The application discloses an anti-time reflection method for realizing high-pass characteristics in a continuous gradient form, and belongs to the technical field of time metamaterials. The method gives total time reflection coefficients from multiple time boundaries, extracts a small reflection theory in the time dimension, and obtains reflection coefficient spectra after interference of infinite time boundaries in any continuous gradient form. The method takes exponential gradient as an example to deduce specific reflection coefficient spectrum analytical expressions, and verifies the correctness of the analytical expressions by electromagnetic full-wave simulation, and obvious super-wideband anti-time reflection phenomena are observed. The continuous gradient form has similar high-pass response characteristics in eliminating time reflection.

Description

Technical Field

[0001] The present invention belongs to the technical field of time metamaterials, and in particular relates to an anti-time reflection method for realizing high-pass characteristics in a continuous gradient form. Background Art

[0002] When the material properties of a medium undergo a sudden change uniformly across space at a specific moment, this temporal discontinuity forms a time boundary. Unlike frequency conservation at spatial boundaries, electromagnetic waves maintain wave number conservation at time boundaries, while frequency transitions occur. Traditional spatial discontinuities introduce spatial reflections, significantly reducing information integrity and energy loss during transmission. By adjusting the electromagnetic properties of the medium in the spatial dimension, anti-spatial reflections are achieved. Correspondingly, by adjusting the electromagnetic properties of the medium in the temporal dimension, anti-temporal reflections can be reduced, achieving maximum transmission of wave-matter interaction.

[0003] The prior art "Antireflection temporal coatings" discloses a time quarter-cycle impedance converter, which is the first to disclose a method for anti-time reflection. This prior art essentially analyzes the matching mechanism of the time quarter-cycle impedance converter: the time Fabry-Perot cavity is restricted by the law of causality, and the total time reflection wave after passing through two time boundaries is only formed by the superposition of two time reflection waves. When the matching conditions are met, the two time reflection waves interfere and cancel each other. Just as a single quarter-wavelength impedance converter in the traditional space field can only achieve narrowband matching, the time quarter-cycle impedance converter also has this shortcoming. The prior art "Ultra-wideband antireflection assistedby a continuously varying temporal medium" adopts time-step multi-section matching to derive the reflection coefficient spectrum of multiple time boundaries, achieving broadband anti-time reflection.

[0004] So far, no anti-time reflection method has been proposed for continuous gradient forms with infinite time boundaries, and the anti-time reflection method system still needs to be improved. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide an anti-time reflection method for realizing high-pass characteristics in a continuous gradient form. Starting from multiple time boundaries and deducing their total time reflection coefficient, the small reflection theory of the time dimension is extracted, and the reflection coefficient spectrum after infinite time boundary interference under any continuous gradient form is obtained. The anti-time reflection effect of the high-pass characteristics is observed by electromagnetic full-wave simulation to verify the correctness of the method.

[0006] The technical problem proposed by the present invention is solved as follows:

[0007] A method for resisting time reflection by realizing high-pass characteristics in a continuous gradient form comprises the following steps:

[0008] Step 1: Calculate the transmittance and reflection coefficient of the time boundary

[0009] Considering an ideal medium that is spatially uniform, unbounded, non-dispersive, and isotropic, the medium's magnetic permeability μ remains constant, but the dielectric constant ε changes in At this moment, the value ε′ suddenly changes to the value ε″, The moment is the time boundary; when the dielectric constant changes suddenly, the following time boundary conditions exist: the electric displacement and magnetic induction intensity are conserved;

[0010] Under the constraints of the time boundary condition, the transmission coefficient R and reflection coefficient T of the time boundary are expressed as:

[0011]

[0012] Among them, Z′ and Z″ are The wave impedance of the front and rear media;

[0013] Step 2: Time Small Reflection Theory

[0014] The change of dielectric constant is step-like, with a total of N+1 time boundaries, where N is a positive integer. At the nth time boundary, i.e., t n-1 The dielectric constant at this moment is given by ε n-1 Mutation to ε n , ε n The duration of the corresponding step is τ n , 1≤n≤N+1;

[0015] When the electromagnetic wave passes through the nth time boundary, the total reflection coefficient and transmission coefficient They are:

[0016]

[0017] in, and are the total reflection coefficient and total transmission coefficient of the n-1th time boundary, respectively, -φ n-1 and φ n-1 They represent the accumulated time phases of the total reflected wave and the total transmitted wave at the n-1th time boundary when propagating between the n-1th time boundary and the nth time boundary, respectively. n and R n are the transmission coefficient and reflection coefficient of the nth time boundary respectively;

[0018] Total reflection coefficient at the N+1th time boundary In , only the case of including the first-order reflection coefficient term is considered. Simplified expression:

[0019]

[0020] in, φ0=0,Z n-1 and Z n are the wave impedances of the media before and after the nth time boundary, 0≤i≤n-1;

[0021] When the frequency f approaches zero, let τ n =0, that is, the dielectric constant ε0 directly jumps to ε f =ε N+1 , at this time the total reflection coefficient Expressed as:

[0022]

[0023] in,

[0024] Since τ n = 0, so φ n =0; have:

[0025]

[0026] From the above formula, the zero-frequency correction term A is expressed as:

[0027]

[0028] Then we get the time minimum reflection theory, the total reflection coefficient when the electromagnetic wave passes through N+1 time boundaries for:

[0029]

[0030] Step 3: Time reflection coefficient spectrum when the dielectric constant changes continuously

[0031] When N tends to infinity, the step mutation transitions to continuous gradual change. At this time, at any time t n Local Γ n and φ n Denoted as dΓ and dφ respectively:

[0032]

[0033] Among them, Z(t) and dZ(t) are t n The wave impedance and its change at time t, dt is n The temporal derivative of a moment;

[0034] According to the time minima reflection theory in step 2, the total time reflection coefficient R(ω) at the total duration τ of the dielectric constant gradient is expressed as:

[0035]

[0036] Where h is the integral variable, h∈[0, t], t∈[0, τ], and the above formula is the time reflection coefficient spectrum corresponding to any continuous time-varying impedance function.

[0037] Furthermore, in step 1, the propagation of electromagnetic waves in the medium follows the following Maxwell differential equations:

[0038]

[0039] in, Indicates partial derivative, t represents time variable, B represents magnetic induction intensity, and D represents electric displacement; represents curl, E represents electric field, H represents magnetic field, and J represents current;

[0040] make in is a positive number, the right side of Maxwell's equation is to The integral of is zero, and the left side of Maxwell's equation satisfies:

[0041]

[0042] Therefore, when the dielectric constant changes suddenly, the following time boundary conditions exist: the electric displacement D and the magnetic induction intensity B are conserved.

[0043] Furthermore, in step 1, the electric field strength E and the magnetic field strength H are The expressions before and after the moment are:

[0044]

[0045] Where j is the sign of the imaginary part, ω and k are the angular frequency and wave number respectively, and z is the distance the electromagnetic field propagates in space; q is the frequency mobility that experiences the time-varying boundary.

[0046] Under the time boundary condition, according to the constitutive relations: D = εE and B = μH, the above equations can be solved to express R and T as follows:

[0047]

[0048] Furthermore, when the dielectric constant changes suddenly, the momentum conservation is satisfied before and after, that is, k remains unchanged. The frequency mobility q is expressed as:

[0049]

[0050] Furthermore, the following exponential gradient is defined: the wave impedance Z(t) starts to change exponentially at time t0 and changes to Z after τ. f , the wave impedance expression is:

[0051]

[0052] Substituting the above formula into the reflection coefficient spectrum expression in step 3, we can obtain the total time reflection coefficient spectrum in the case of exponential gradient:

[0053]

[0054] in,

[0055] Furthermore, the method of the present invention further comprises the following steps:

[0056] Step 4: Verify the correctness of the method using electromagnetic full-wave simulation

[0057] In electromagnetic simulation software, a spatially uniform ideal medium is designed. The dielectric constant varies with time, while electromagnetic waves still propagate through the medium, ensuring that the magnetic permeability remains constant. A Gaussian signal with a set bandwidth is input. When the Gaussian signal completely enters the medium, the dielectric constant begins to vary with time.

[0058] Let the dielectric constant change from ε0 to ε f After a set period of time, the spatial distribution of the reflected and transmitted waves in the medium and the time domain signal at the port are measured to observe the time transmission and reflection phenomenon;

[0059] Let the dielectric constant ε0 be gradually deformed to ε in an exponential form f ,After stabilization, the spatial distribution of reflected and transmitted waves in the medium and the time domain signal at the port are measured to observe the anti-time reflection phenomenon;

[0060] Comparing the spatial distribution of reflected and transmitted waves after the dielectric constant abrupt change and exponential gradient change, if the reflected wave with exponential gradient change is smaller than the reflected wave with a sudden change, it is determined that the exponential gradient change can suppress the temporal reflection generated by the temporal boundary.

[0061] The beneficial effects of the present invention are:

[0062] The method described in this invention achieves ultra-wideband anti-temporal reflection through a continuous gradient, with a high-pass response. The method also derives an analytical solution for the temporal reflection coefficient spectrum corresponding to the continuous gradient, further improving the theoretical system for anti-temporal reflection. This method may open up new avenues for the design of impedance matching devices, enabling greater flexibility and possibilities in controlling wave propagation using temporal metamaterials, and laying the foundation for developments in the space-time domain. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 Schematic diagram of wave propagation under two time boundary conditions in the method of the present invention;

[0064] Figure 2 Schematic diagram of N-level step mutation of dielectric constant in the method of the present invention;

[0065] Figure 3 This is a schematic diagram of the continuous gradual change of the dielectric constant in the method of the present invention;

[0066] Figure 4 A schematic diagram of a time reflection coefficient spectrum corresponding to a gradual change in the dielectric constant exponential in the method of the present invention;

[0067] Figure 5 Schematic diagram of the spatial distribution of time transmission and reflection after a single sudden change and an exponential gradual change of the dielectric constant in the method described in the example;

[0068] Figure 6 Schematic diagram of the reflection spectrum of the dielectric constant single mutation and exponential gradient in the method described in the example;

[0069] Figure 7 Schematic diagram of the theoretical solution and electromagnetic full-wave simulation solution of the time reflection coefficient spectrum in the method described in this example. DETAILED DESCRIPTION

[0070] The present invention will be further described below with reference to the accompanying drawings and examples.

[0071] This embodiment provides a method for achieving anti-time reflection in a continuous and gradual manner, comprising the following steps:

[0072] Step 1: Calculate the transmittance and reflection coefficient of the time boundary

[0073] The temporal transmission and reflection coefficients for a single time boundary are derived. Similar to the derivation of transmission and reflection coefficients for traditional spatial boundaries, starting from the most basic Maxwell equations, the boundary conditions for the temporal boundary are derived. The electric and magnetic field intensities before and after the mutation are combined, and the temporal transmission and reflection coefficients are derived under the constraints of the temporal boundary conditions. The frequency mobility of the transmission and reflection waves is then obtained based on the conservation of momentum.

[0074] Considering an ideal medium that is spatially uniform, unbounded, non-dispersive, and isotropic, the medium's magnetic permeability μ remains constant, but the dielectric constant ε changes in At this moment, the value ε′ suddenly changes to the value ε″, The moment is the time boundary. The electromagnetic wave in the medium follows Maxwell's differential equations during propagation:

[0075]

[0076] in, Indicates partial derivative, t represents time variable, B represents magnetic induction intensity, and D represents electric displacement; represents curl, E represents electric field, H represents magnetic field, and J represents current;

[0077] make in Since the values ​​of the fields and sources are finite, the right-hand side of the above Maxwell equations is to The integral of is zero, so the left side of the equation satisfies:

[0078]

[0079] Therefore, when the constitutive parameters suddenly change, the following time boundary conditions exist: the electric displacement D and the magnetic induction intensity B are conserved.

[0080] The electric field strength E and magnetic field strength H are The expressions before and after the moment are:

[0081]

[0082] Where j is the symbol of the imaginary part, ω and k are the angular frequency and wave number respectively, z is the distance the electromagnetic field propagates in space; Z′ and Z″ are The wave impedance of the front and rear media, q is the frequency mobility that experiences a time-varying boundary; R and T are the temporal reflection and transmission coefficients, respectively.

[0083] Under the time boundary conditions of conservation of electric displacement D and magnetic induction intensity B, according to the constitutive relations: D = εE, B = μH, the above equations can be solved to express R and T as follows:

[0084]

[0085] More specifically, momentum conservation is satisfied before and after the switch, that is, k remains unchanged: Therefore, the frequency mobility q is expressed as:

[0086]

[0087] Step 2: Time Small Reflection Theory

[0088] The total time reflection coefficient of multiple time boundaries is derived, and the theory of time minimum reflection is extracted. Using the transmission and reflection coefficient of a single time boundary, starting from the simplest two time boundaries, it is generalized to the total time reflection coefficient of any number of time boundaries. After simplifying the analytical formula, the theory of time minimum reflection is extracted.

[0089] Due to the law of causality, as many transflection waves as there are time boundaries, they will be superimposed to form the total transflection wave. The wave propagation diagram under two time boundaries is shown in the figure below. Figure 1 As shown in the figure, the dielectric constant ε0 of the medium suddenly changes to ε1 at time t0, forming the first time boundary, generating a group of transflection waves. At time t1, the dielectric constant suddenly changes from ε1 to ε2, forming the second time boundary. The first group of reflection waves and transflection waves respectively generate a group of transflection waves after the second time boundary. The total reflection coefficient after the second time boundary is and the total transmission coefficient They are:

[0090]

[0091] in, and are the total reflection coefficient and total transmission coefficient after the first time boundary, respectively; -φ1 and φ1 represent the time phases accumulated when the first reflected wave and the first transmitted wave propagate between the two time boundaries, respectively; T2 and R2 are the transmission coefficient and reflection coefficient of the second time boundary, respectively;

[0092] In the above formula, the total reflection coefficient Let’s take an example to explain the origin: two time boundaries will only produce two transflections, and the total reflected wave has two waves superimposed: the reflected wave generated by the first time boundary encounters the transmitted wave generated by the second time boundary, and its total reflection coefficient is Where -φ1 means that the wave propagating between the two time boundaries is the reflected wave; the transmitted wave generated by the first time boundary encounters the reflected wave generated by the second time boundary, and its total reflection coefficient is Where φ1 means that the wave propagating between the two time boundaries is the transmitted wave.

[0093] Similarly, when the dielectric constant varies as Figure 2 As shown, the change of dielectric constant is step-like, with a total of N+1 time boundaries, N is a positive integer, and at the nth time boundary, i.e., t n-1 The dielectric constant at this moment is given by ε n-1 Mutation to ε n , each step lasts τ n , 1≤n≤N+1;

[0094] When the electromagnetic wave passes through the nth time boundary, the total reflection coefficient and transmission coefficient They are:

[0095]

[0096] in, and are the total reflection coefficient and total transmission coefficient after the n-1th time boundary, -φ n-1 and φ n-1 They represent the time phase accumulated when the n-1th total reflected wave and the n-1th total transmitted wave propagate between the n-1th time boundary and the nth time boundary, respectively. n and R n are the transmission coefficient and reflection coefficient of the nth time boundary respectively;

[0097] The total reflection coefficient generated by N+1 time boundaries There are 2 N Term, of which N+1 term contains only the first reflection coefficient term, and N-1 term contains only the third reflection coefficient term. When the discontinuity of each order of dielectric constant is very small, T>>R, so We only need to consider the case where the reflection coefficient term is included. Simplified expression:

[0098]

[0099] in,

[0100] When the frequency f approaches zero, the duration of each step τ n It is almost zero relative to the signal period T, that is, the dielectric constant ε0 can be regarded as a direct transition to ε f =ε N+1 , at this time the total reflection coefficient Expressed as:

[0101]

[0102] in,

[0103] Since τ n = 0, so φ n =0; have:

[0104]

[0105] From the above formula, the zero-frequency correction term A is expressed as:

[0106]

[0107] Analogous to the small reflection theory in the traditional space field, the time small reflection theory is obtained. The total reflection coefficient when the electromagnetic wave passes through N+1 time boundaries is for:

[0108]

[0109] Step 3: Time reflection coefficient spectrum when the dielectric constant changes continuously

[0110] The multiple step-change transition is smoothly transformed into a continuous gradient, where a finite number of time boundaries approaches infinity, and the interval between each time boundary approaches infinitesimal. By analogy with the derivation of the reflection coefficient of a traditional spatially gradient transmission line, and utilizing the theory of temporal minima, the total temporal reflection coefficient of a continuous gradient can be calculated by summing all local quasi-space reflections with appropriate phase shifts, multiplying them by a zero-frequency correction term and the total temporal accumulated phase. Using exponential gradients as an example, a specific expression for the temporal reflection spectrum is derived.

[0111] When N tends to infinity, Figure 2 The step-wise transition shown Figure 3 The continuous gradient shown. At any time t n Local Γ n and φ n Denoted as dΓ and dφ respectively:

[0112]

[0113] Among them, Z(t) and dZ(t) are t n The wave impedance and its change at time t, dt is n The temporal derivative of a moment;

[0114] According to the time-small reflection theory in step 2, the total time reflection coefficient R(ω) at the total duration τ of the dielectric constant gradient can be expressed by summing all local quasi-space reflections with a certain phase shift, taking into account the zero-frequency correction term and the total time-accumulated phase, specifically:

[0115]

[0116] Where h is the integral variable, h∈[0, t], t∈[0, τ]. The above formula is the theoretical solution of the time reflection coefficient spectrum corresponding to any continuous time-varying impedance function.

[0117] Take exponential gradient as an example: the impedance Z(t) starts at Z0 and starts to change exponentially at t0, and changes to Z after τ. f , whose expression is:

[0118]

[0119] Substituting it into the above theoretical expression of reflection coefficient spectrum, we can obtain the theoretical time reflection coefficient spectrum under the exponential gradient condition:

[0120]

[0121] in When τ takes a set value, the reflection coefficient spectrum waveform is as follows: Figure 4 shown.

[0122] Step 4: Verify the correctness of the theory using electromagnetic full-wave simulation

[0123] In simulation software, a spatially uniform ideal dielectric is designed. The dielectric's electrical length is long enough to maintain a constant permeability while the wave propagates through the dielectric even when the dielectric constant varies. A Gaussian signal with a certain bandwidth is input. When the Gaussian signal fully enters the dielectric, the dielectric constant begins to vary.

[0124] Let the dielectric constant ε0 suddenly change to ε f After a period of time, the spatial distribution of the time-transmitted reflection wave in the medium and the time domain signal at the port are measured to observe the time-transmitted reflection phenomenon.

[0125] Let the dielectric constant ε0 be gradually deformed to ε in an exponential form f After stabilization, the spatial distribution of the time-transmitted and reflected waves in the medium and the time domain signal at the port are measured to observe the anti-time reflection phenomenon.

[0126] Comparing the spatial distribution of time transmission and reflection after a single mutation and an exponential gradient of the dielectric constant, if we observe that the reflected wave of the exponential gradient is smaller than that of the single mutation, it means that the exponential gradient can suppress the time reflection generated by the time boundary.

[0127] In this embodiment, the dielectric cross section is 1.5 mm × 1.5 mm, the dielectric length is 500 mm, the equivalent magnetic permeability μ is 1, the initial value of the equivalent dielectric constant ε0 is 1, and the final value ε f The value of the dielectric constant is 4, the duration of the exponential gradient is 66 ns, the center frequency of the Gaussian pulse input signal is 30 MHz, the full width at half maximum is 60 MHz, the time domain peak point is located at 120 ns, the moment of dielectric constant mutation and the starting time of the exponential gradient t0 are 900 ns, and the spatial distribution of the transflected wave in the medium is measured at 1500 ns.

[0128] In this embodiment, the spatial distribution diagram of the time transmission and reflection after the single mutation and exponential gradual change of the dielectric constant at a certain moment is as follows: Figure 5 As shown in the figure, the time reflection signal is on the left and the time transmission signal is on the right. Comparing the reflected waves in the two cases, we can see the obvious anti-time reflection effect of the exponential gradient. The Fourier analysis of the time domain reflection signal at the port is performed, and the spectrum diagram is as follows: Figure 6As shown in Figure 2, it can be seen that the exponential gradient anti-reflection effect is ultra-wideband. Dividing the reflection spectrum by the input spectrum before migration, the time reflection coefficient spectrum of the electromagnetic full-wave simulation is extracted and compared with the theory, as shown in Figure 2. Figure 7 As shown in Figure 3, the simulation results are basically consistent with the theoretical solution, verifying the correctness of the theory.

[0129] In summary, the theory described in this invention starts from multiple time boundaries and derives their total time reflection coefficient, extracting the theory of temporal minima, and obtaining the reflection coefficient spectrum after infinite time boundary interference under any continuous gradient form. Using exponential gradient as an example, the theory described in this invention derives a specific analytical formula for the reflection coefficient spectrum, and the correctness of the analytical formula is verified by electromagnetic full-wave simulation, observing the obvious high-pass characteristic anti-temporal reflection phenomenon.

Claims

1. A method for anti-time reflection that realizes high-pass characteristics in a continuous gradient form, characterized in that: The following steps are involved: Step 1: Calculate the transmittance and reflection coefficient of the time boundary Considering an ideal medium that is spatially uniform, unbounded, non-dispersive, and isotropic, the medium's magnetic permeability μ remains constant, but the dielectric constant ε changes in At this moment, the value ε′ suddenly changes to the value ε″, The moment is the time boundary; when the dielectric constant changes suddenly, the following time boundary conditions exist: the electric displacement and magnetic induction intensity are conserved; Under the constraints of the time boundary condition, the transmission coefficient R and reflection coefficient T of the time boundary are expressed as: Among them, Z′ and Z″ are The wave impedance of the front and rear media; Step 2: Time Small Reflection Theory The change of dielectric constant is step-like, with a total of N+1 time boundaries, where N is a positive integer. At the nth time boundary, i.e., t n-1 The dielectric constant at this moment is given by ε n-1 Mutation to ε n , ε n The duration of the corresponding step is τ n , 1≤n≤N+1; When the electromagnetic wave passes through the nth time boundary, the total reflection coefficient and transmission coefficient They are: in, and are the total reflection coefficient and total transmission coefficient of the n-1th time boundary, respectively, -φ n-1 and φ n-1 They represent the accumulated time phases of the total reflected wave and the total transmitted wave at the n-1th time boundary when propagating between the n-1th time boundary and the nth time boundary, respectively. n and R n are the transmission coefficient and reflection coefficient of the nth time boundary respectively; Total reflection coefficient at the N+1th time boundary In , only the case of including the first-order reflection coefficient term is considered. Simplified expression: in, φ0=0,Z n-1 and Z n are the wave impedances of the media before and after the nth time boundary, 0≤i≤n-1; When the frequency f approaches zero, let τ n =0, that is, the dielectric constant ε0 directly jumps to ε f =ε N+1 , at this time the total reflection coefficient Expressed as: in, Since τ n = 0, so φ n =0; have: From the above formula, the zero-frequency correction term A is expressed as: Then we get the time minimum reflection theory, the total reflection coefficient when the electromagnetic wave passes through N+1 time boundaries for: Step 3: Time reflection coefficient spectrum when the dielectric constant changes continuously When N tends to infinity, the step mutation transitions to continuous gradual change. At this time, at any time t n Local Γ n and φ n Expressed as dF and dφ respectively: Among them, Z(t) and dZ(t) are t n The wave impedance and its change at time t, dt is n The temporal derivative of a moment; According to the time minima reflection theory in step 2, the total time reflection coefficient R(ω) at the total duration τ of the dielectric constant gradient is expressed as: Where h is the integral variable, h∈[0, t], t∈[0, τ], and the above formula is the time reflection coefficient spectrum corresponding to any continuous time-varying impedance function.

2. The anti-time reflection method for realizing high-pass characteristics in a continuous gradient form according to claim 1, characterized in that: In step 1, the propagation of electromagnetic waves in the medium follows the following Maxwell differential equations: in, Indicates partial derivative, t represents time variable, B represents magnetic induction intensity, and D represents electric displacement; represents curl, E represents electric field, H represents magnetic field, and J represents current; make in is a positive number, the right side of Maxwell's equation is to The integral of is zero, and the left side of Maxwell's equation satisfies: Therefore, when the dielectric constant changes suddenly, the following time boundary conditions exist: the electric displacement D and the magnetic induction intensity B are conserved.

3. The anti-time reflection method for realizing high-pass characteristics in a continuous gradient form according to claim 1, characterized in that: In step 1, the electric field strength E and magnetic field strength H are The expressions before and after the moment are: Where j is the sign of the imaginary part, ω and k are the angular frequency and wave number respectively, and z is the distance the electromagnetic field propagates in space; q is the frequency mobility that experiences the time-varying boundary; Under the time boundary condition, according to the constitutive relations: D = εE and B = μH, the above equations can be solved to express R and T as follows:

4. The anti-time reflection method for realizing high-pass characteristics in a continuous gradient form according to claim 3, characterized in that: When the dielectric constant suddenly changes, momentum conservation is satisfied before and after, that is, k remains unchanged. The frequency mobility q is expressed as:

5. The anti-time reflection method for realizing high-pass characteristics in a continuous gradient form according to claim 1, characterized in that: The following exponential gradient is defined: the wave impedance Z(t) starts at Z0 and begins to gradient exponentially at time t0, and changes to Zf after τ. The wave impedance expression is: Substituting the above formula into the reflection coefficient spectrum expression in step 3, we can obtain the total time reflection coefficient spectrum in the case of exponential gradient: in, 6. The anti-time reflection method for realizing high-pass characteristics in a continuous gradient form according to claim 1, characterized in that: The method of the present invention further comprises the following steps: Step 4: Verify the correctness of the method using electromagnetic full-wave simulation In electromagnetic simulation software, a spatially uniform ideal medium is designed. The dielectric constant varies with time, while electromagnetic waves still propagate through the medium, ensuring that the magnetic permeability remains constant. A Gaussian signal with a set bandwidth is input. When the Gaussian signal completely enters the medium, the dielectric constant begins to vary with time. Let the dielectric constant change from ε0 to ε f After a set period of time, the spatial distribution of the reflected and transmitted waves in the medium and the time domain signal at the port are measured to observe the time transmission and reflection phenomenon; Let the dielectric constant ε0 be gradually deformed to ε in an exponential form f ,After stabilization, the spatial distribution of reflected and transmitted waves in the medium and the time domain signal at the port are measured to observe the anti-time reflection phenomenon; Comparing the spatial distribution of reflected and transmitted waves after the dielectric constant abrupt change and exponential gradient change, if the reflected wave with exponential gradient change is smaller than the reflected wave with a sudden change, it is determined that the exponential gradient change can suppress the temporal reflection generated by the temporal boundary.

Images