CN113784491B - Plasma electromagnetic parameter measuring method based on defect microwave photonic crystal - Google Patents
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Abstract
The invention discloses a plasma electromagnetic parameter measuring method based on a defective microwave photonic crystal, which comprises the following steps: (1) Constructing a one-dimensional plasma defect microwave photonic crystal structure, and simulating the relationship between the plasma electromagnetic parameters and the frequency offset and peak value of the plasma defect microwave photonic crystal defect transmission peak by using a transmission matrix method; (2) And measuring the transmission spectrum of the microwave photonic crystal with the plasma defects, and inverting the electromagnetic parameters of the measured plasma through the offset and the peak value. The invention obtains the strength and frequency position of the defect transmission peak through a measuring means, and inverts the electromagnetic parameters of the microwave photonic crystal plasma defect to realize the non-contact measurement of the plasma electromagnetic parameters.
Description
Technical Field
The invention relates to a plasma electromagnetic parameter measuring technology, in particular to a plasma electromagnetic parameter measuring method based on a defective microwave photonic crystal.
Background
The plasma is the fourth state of matter, and has very important application prospect in the fields of materials, communication, national defense and the like. The measurement of characteristic parameters of plasma is the basis of the research of plasma technology, and the two promote the development of the plasma technology, so that the diagnosis technology of plasma parameters becomes very important. Through research and study of a plurality of scholars, plasma parameter measurement technologies are mature, and typical methods include a Langmuir probe method, a spectroscopy method and a microwave method.
The Langmuir probe method is the most basic diagnostic method for plasma parameters, and is characterized in that a tiny measuring electrode is inserted into plasma, and plasma parameters are inverted through a volt-ampere characteristic test.
The spectrum method is used for inverting plasma parameters by measuring spectral lines of plasma, and has the defects of complex physical content of spectral data, complex data processing and large parameter inversion error.
The microwave method is to measure the reflection and transmission coefficients of plasma by irradiating the plasma with microwaves to invert plasma parameters, and does not disturb target plasma.
Disclosure of Invention
The purpose of the invention is as follows: in view of the above problems, the present invention aims to provide a method for measuring electromagnetic parameters of plasma based on a defective microwave photonic crystal.
The technical scheme is as follows: the invention discloses a plasma electromagnetic parameter measuring method based on a defective microwave photonic crystal, which comprises the following steps:
(1) Constructing a one-dimensional plasma defect microwave photonic crystal structure, and simulating the relationship between the plasma electromagnetic parameters and the frequency offset and peak value of the plasma defect microwave photonic crystal defect transmission peak by using a transmission matrix method;
(2) And measuring the transmission spectrum of the microwave photonic crystal with the plasma defects, and inverting the electromagnetic parameters of the measured plasma through the offset and the peak value.
Further, the one-dimensional plasma defect microwave photonic crystal is formed by the overlapping growth of a good dielectric material A, a vacuum material B and a defect plasma C, the one-dimensional plasma defect microwave photonic crystal comprises 6 layers of dielectric materials, 4 layers of vacuum and 1 layer of plasma defect layer, and the arrangement structure is represented As (AB) N (ACA)(BA) N And N is the overlapping number of the A dielectric layer and the B dielectric layer, wherein N =2.
Further, the dielectric material A has a dielectric constant of epsilon A (ω)＝9.0ε 0 The dielectric constant of the vacuum material B is epsilon B (ω)＝1.0ε 0 ，ε 0 Is a vacuum dielectric constant; the dielectric constant expression of the defective plasma C is as follows:
in the formula, ω p Is the plasma frequency v c Is the plasma collision frequency, omega is the incident electromagnetic wave frequency, j is the imaginary unit; therefore, the real part ε' (ω) and the imaginary part ε "(ω) of the complex permittivity of the impinging plasma are represented as:
further, under the condition of low-frequency collision, the equivalent refractive index n of the plasma p The approximate expression is:
further, the central working wavelength of the microwave photonic crystal is set to be lambda 0 The optical thickness of the dielectric material layer and the vacuum material layer are both 0.25 lambda 0 And filling the defect layer into a vacuum microwave photonic crystal to serve as a standard sample, and calculating the frequency shift of a transmission peak by comparing the standard sample with a sample to be detected:
a transmission matrix method is adopted to simulate the transmission spectrum of the microwave photonic crystal with plasma defects, and aiming at a one-dimensional multilayer dielectric structure, the transmission matrix of a single-layer dielectric is expressed as follows:
in the formula
d i Is the thickness of the ith layer of material,
respectively the impedance ratio and the admittance ratio of the ith layer material, and the expressions are respectively
ε i (ω) is the complex dielectric constant of the ith layer material, assuming each layer material is nonmagnetic, i.e.
μ 0 Vacuum magnetic conductivity;
the one-dimensional plasma defect microwave photonic crystal multilayer dielectric structure transmission matrix is obtained by multiplying the transmission matrix of each material layer in a cascade mode, and the expression is as follows:
wherein Q represents the number of layers of the multilayer dielectric structure, and X 11 (ω)、X 12 (ω)、X 21 (ω)、X 22 (ω) represents each element of the cascade matrix, respectively;
the transmission coefficient expression of the one-dimensional plasma defect microwave photonic crystal is as follows:
Further, the plasma electromagnetic parameters include a plasma frequency and a plasma collision frequency.
Further, the transmission spectrum of the plasma defect microwave photonic crystal is measured by a free space method.
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages: the intensity and the frequency position of the defect transmission peak are obtained by a measuring means, the electromagnetic parameters of the microwave photonic crystal plasma defect are inverted, the non-contact measurement of the electromagnetic parameters of the plasma is realized, and the defect structure has very high frequency selection characteristic, so that the method has higher sensitivity.
Drawings
FIG. 1 is a schematic view of a one-dimensional defect microwave photonic crystal structure;
FIG. 2 is a schematic structural diagram of a platform for measuring microwave frequency band transmission coefficients in a flat plate dielectric structure;
FIG. 3 is a transmission spectrum at different plasma frequencies: (a) a full band-gap transmission spectrum; (b) partial band gap transmission spectrum.
Detailed Description
The method for measuring the plasma electromagnetic parameters based on the defect microwave photonic crystal comprises the following steps:
(1) A one-dimensional plasma defect microwave photonic crystal structure is constructed, and a transmission matrix method is utilized to simulate the relationship between the plasma electromagnetic parameters and the frequency offset and peak value of the plasma defect microwave photonic crystal defect transmission peak.
The microwave photonic crystal is an artificial periodic structure under the microwave wavelength scale, and the basic characteristics are microwave forbidden band characteristics and microwave local characteristics. When microwave propagates in the microwave photonic crystal, bragg scattering occurs, energy forms an energy band structure, a microwave band gap appears between adjacent energy bands, and the microwave photonic crystal has excellent frequency selectivity. The forbidden band size of the microwave photonic crystal is related to the dielectric constant contrast of the overlapped medium, and the larger the contrast is, the easier the microwave photonic crystal with wider forbidden band can be obtained; the microwave local characteristic is a phenomenon that a certain defect is introduced into the microwave photonic crystal to form a microwave local area in a microwave forbidden band, so that the microwave frequency originally in the forbidden band can tunnel through the microwave photonic crystal structure to form a defect transmission peak.
As shown in FIG. 1, the one-dimensional plasma defect microwave photonic crystal is formed by overlapping and growing a good dielectric material A, a vacuum material B and a defect plasma C, the one-dimensional plasma defect microwave photonic crystal comprises 6 layers of dielectric materials, 4 layers of vacuum and 1 layer of plasma defect layer, and the arrangement structure is shown As (AB) N (ACA)(BA) N And N is the overlapping number of the A dielectric layer and the B dielectric layer, wherein N =2. The dielectric material A has a dielectric constant of epsilon A (ω)＝9.0ε 0 The dielectric constant of the vacuum material B is epsilon B (ω)＝1.0ε 0 ，ε 0 Is a vacuum dielectric constant; the dielectric constant expression of the defect plasma C is as follows:
in the formula, omega p Is the plasma frequency v c Is the plasma collision frequency, omega is the incident electromagnetic wave frequency, j is the imaginary unit; therefore, the real part ε' (ω) and the imaginary part ε "(ω) of the complex permittivity of the impinging plasma are represented as:
from the above two equations, the real part of the complex permittivity of the plasma affects the phase of the electromagnetic wave propagation, and the real part ε' (ω) follows the plasma frequency ω p Gradually decreases in increase; with the same electron density, v is the collision frequency c The real part ε' (ω) increases, gradually approaching the value of the vacuum dielectric constant. When the collision frequency v c Relatively small, v c The effect on the real part of the complex permittivity is negligible. The imaginary part of the complex dielectric constant of the plasma affects the attenuation of the propagation of electromagnetic waves with the plasma frequency omega p The imaginary part epsilon' (omega) is gradually increased, and the propagation loss of the electromagnetic wave is increased; when plasma frequency omega p A timing plasma collision frequency v c The closer to the incident electromagnetic wave frequency ω, the greater the imaginary part and the greater the attenuation loss.
In order to minimize the collision absorption of the plasma to the electromagnetic wave, a small variation range is set for the collision frequency of the plasma in the theoretical calculation process, and the equivalent refractive index n of the plasma is set under the condition of low-frequency collision p The approximate expression is:
setting the central working wavelength of the microwave photonic crystal as lambda 0 =0.15m and a central operating frequency f 0 =2.0GHz, the optical thicknesses of the dielectric material layer and the vacuum material layer being 0.25 lambda 0 Microwave photonic crystal with defect layer filled in vacuum as standard sample, in which omega p =0, and the transmission peak frequency is the forbidden band center frequency f of the microwave photonic crystal 0 =2.0GHz, and the frequency shift of the transmission peak is calculated by comparison with the sample to be measured.
In order to obtain the relationship between the offset and the peak value of the transmission peak frequency of the defect and the plasma parameter of the detected defect, a transmission matrix method is adopted to simulate the transmission spectrum of the microwave photonic crystal with the plasma defect, and aiming at a one-dimensional multilayer dielectric structure, the transmission matrix of a single-layer dielectric is expressed as follows:
in the formula (I), the compound is shown in the specification,
d i is the thickness of the ith layer of material,
respectively the impedance ratio and the admittance ratio of the ith layer material, and the expressions are respectively
ε i (ω) is the complex dielectric constant of the ith layer of material, assuming each layer of material is nonmagnetic, i.e.
μ 0 Is a vacuum magnetic permeability.
The one-dimensional plasma defect microwave photonic crystal multilayer dielectric structure transmission matrix is obtained by multiplying the transmission matrix of each material layer in a cascade mode, and the expression is as follows:
wherein Q represents the number of layers of the multilayer dielectric structure, and X 11 (ω)、X 12 (ω)、X 21 (ω)、X 22 (ω) represents each element of the cascade matrix, respectively;
the transmission coefficient expression of the one-dimensional plasma defect microwave photonic crystal is as follows:
(2) And measuring the transmission spectrum of the microwave photonic crystal with the plasma defects, and inverting the electromagnetic parameters of the measured plasma through the offset and the peak value.
The structure of a commonly used platform for measuring the transmission coefficient of a microwave frequency band with a flat-plate dielectric structure is shown in figure 2, the system measures the transmission spectrum of a defective microwave photonic crystal by adopting a free space method, and main measuring equipment comprises a microwave frequency sweeping source, a microwave network analyzer, a mode converter, a focusing lens transmitting antenna, a focusing lens receiving antenna, a sample to be measured and a standard sample.
The plasma frequency is an important parameter of the plasma, and the density of electrons and ions in the plasma is basically equal, but the activity of the electrons is more active, so that the plasma density can be approximately regarded as the electron density. FIG. 3 (a) shows the collision frequency v c In the case of transmission spectra at different plasma frequencies in the range of 10MHz, it was found that the frequency of the defect transmission peak shifts to a high frequency in the forbidden band and the peak value gradually decreases as the plasma frequency increases. With plasma frequency from ω p =0.0GHz to ω p =6.0GHz, the defect peak frequency of the plasma defect microwave photonic crystal is from f 0 Shift to f by 2.000GHz 0 =2.154GHz, the offset amounts to 0.154GHz; the transmission peak to peak value dropped from 0.99 to 0.91, which was 0.08. The frequency offset changes approximately quadratically in the forbidden band, and the transmission peak attenuates approximately linearly, as shown in fig. 3 (b).
Claims (5)
1. The method for measuring the electromagnetic parameters of the plasma based on the defective microwave photonic crystal is characterized by comprising the following steps of:
(1) Constructing a one-dimensional plasma defect microwave photonic crystal structure, and simulating the relationship between the plasma electromagnetic parameters and the frequency offset and peak value of the plasma defect microwave photonic crystal defect transmission peak by using a transmission matrix method;
the one-dimensional plasma defect microwave photonic crystal is formed by overlapping and growing a good dielectric material A, a vacuum material B and a defect plasma C, the one-dimensional plasma defect microwave photonic crystal comprises 6 layers of dielectric materials, 4 layers of vacuum and 1 layer of plasma defect layer, and the arrangement structure is shown As (AB) N (ACA)(BA) N N is the overlapping number of the dielectric layers A and B, wherein N =2;
(2) Measuring the transmission spectrum of the microwave photonic crystal with the plasma defects, and inverting the electromagnetic parameters of the measured plasma through the offset and the peak value;
setting the central working wavelength of the microwave photonic crystal as lambda 0 The optical thickness of the dielectric material layer and the vacuum material layer are both 0.25 lambda 0 And filling the defect layer into a vacuum microwave photonic crystal as a standard sample, and comparing the standard sample with a sample to be detected to calculate the frequency shift of a transmission peak:
a transmission matrix method is adopted to simulate the transmission spectrum of the microwave photonic crystal with plasma defects, and aiming at a one-dimensional multilayer dielectric structure, the transmission matrix of a single-layer dielectric is expressed as follows:
in the formula (I), the compound is shown in the specification,
d i is the thickness of the ith layer of material,
respectively the impedance ratio and the admittance ratio of the ith layer material, and the expressions are respectively
ε i (ω) is the complex dielectric constant of the ith layer of material, assuming each layer of material is nonmagnetic, i.e.
μ 0 Is a vacuum magnetic conductivity;
the one-dimensional plasma defect microwave photonic crystal multilayer dielectric structure transmission matrix is obtained by multiplying the transmission matrix of each material layer in a cascade mode, and the expression is as follows:
wherein Q represents the number of layers of the multilayer dielectric structure, and X 11 (ω)、X 12 (ω)、X 21 (ω)、X 22 (ω) represents each element of the cascade matrix, respectively;
the transmission coefficient expression of the one-dimensional plasma defect microwave photonic crystal is as follows:
2. A method for measuring electromagnetic parameters of a plasma as defined in claim 1, wherein said dielectric material A has a dielectric constant of ε A (ω)＝9.0ε 0 The dielectric constant of the vacuum material B is epsilon B (ω)＝1.0ε 0 ，ε 0 Is a vacuum dielectric constant; the dielectric constant expression of the defect plasma C is as follows:
in the formula, ω p Is the plasma frequency v c Is the plasma collision frequency, omega is the incident electromagnetic wave frequency, j is the imaginary unit; therefore, the real part ε' (ω) and the imaginary part ε "(ω) of the complex permittivity of the impinging plasma are expressed as:
3. a plasma electromagnetic parameter measurement method according to claim 2, characterized in that, under the condition of low frequency collision, the equivalent refractive index n of the plasma is p The approximate representation is:
4. a plasma electromagnetic parameter measurement method according to claim 1, wherein the plasma electromagnetic parameters include plasma frequency and plasma collision frequency.
5. A plasma electromagnetic parameter measurement method according to claim 1, characterized in that the transmission spectrum of the plasma defect microwave photonic crystal is measured using a free space method.
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