CN108682964B - Time domain metamaterial - Google Patents

Time domain metamaterial Download PDF

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CN108682964B
CN108682964B CN201810330542.3A CN201810330542A CN108682964B CN 108682964 B CN108682964 B CN 108682964B CN 201810330542 A CN201810330542 A CN 201810330542A CN 108682964 B CN108682964 B CN 108682964B
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time
metamaterial
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reflection coefficient
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CN108682964A (en
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程强
赵捷
戴俊彦
崔铁军
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Southeast University
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
    • H01Q15/14—Reflecting surfaces; Equivalent structures
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B1/00—Optical elements characterised by the material of which they are made; Optical coatings for optical elements
    • G02B1/002—Optical elements characterised by the material of which they are made; Optical coatings for optical elements made of materials engineered to provide properties not available in nature, e.g. metamaterials
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
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Abstract

The invention discloses a time domain metamaterial, which comprises: n adjustable units with sub-wavelength sizes, wherein the n adjustable units with sub-wavelength sizes are sequentially arranged; the adjustable unit comprises 5 layers from top to bottom in sequence, the first layer comprises two rectangular patches which are connected in series by the variable capacitance diode, the second layer comprises a dielectric substrate, the third layer comprises a feed network layer, the anode and the cathode of the feed network layer are respectively connected with the rectangular patches at the two ends of the variable capacitance diode through metalized through holes in the dielectric substrate, the fourth layer comprises an ultrathin insulating layer, and the fifth layer comprises a metal back plate. The invention can realize the regulation and control of the frequency spectrum of electromagnetic waves, the speed stealth and the communication system for constructing a new framework by carrier modulation.

Description

Time domain metamaterial
Technical Field
The invention relates to the technical field of novel artificial electromagnetic materials, in particular to a time domain metamaterial.
Background
The unit characteristics and spatial arrangement of the traditional metamaterial can be designed, the parameters such as polarization, strength and phase of electromagnetic waves are controlled, the functions of deflection, focusing, wave absorption, energy stray and the like of electromagnetic energy are realized, and the metamaterial can be used in the fields such as antenna, imaging and stealth. However, the traditional metamaterial mainly focuses on the spatial domain characteristics of electromagnetic energy and belongs to a reciprocal and nonlinear device. The regulation and control technology of the spatial domain characteristics of the free space electromagnetic waves is relatively mature, and the research of the time domain characteristics is almost not.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a time domain metamaterial, which can regulate and control the frequency spectrum of electromagnetic waves, realize speed stealth and be used for a communication system for constructing a new framework by carrier modulation.
In order to solve the above technical problem, the present invention provides a time domain metamaterial, including: n adjustable units with sub-wavelength sizes, wherein the n adjustable units with sub-wavelength sizes are sequentially arranged; the adjustable unit comprises 5 layers from top to bottom in sequence, the first layer comprises two rectangular patches 1 connected in series by a variable capacitance diode 2, the second layer comprises a dielectric substrate 3, the third layer comprises a feed network layer 5, the anode and the cathode of the feed network layer 5 are respectively connected with the rectangular patches at the two ends of the variable capacitance diode 2 through metallized through holes 4 in the dielectric substrate 3, the fourth layer comprises an ultrathin insulating layer 6, and the fifth layer comprises a metal back plate 7.
Preferably, the time domain characteristics of the adjustable unit are adjusted to realize the modulation of the spatial wave frequency spectrum, and the adjusting and controlling mode is divided into time domain amplitude modulation, time domain phase modulation and time domain amplitude homodyne.
Preferably, the reflection coefficient gamma of the time domain metamaterial is controlled by an external bias voltage, and a control device is adopted to generate a time-varying signal so as to realize the time-varying reflection coefficient gamma (t); when incident wave Ei(t) upon incidence on the surface, the reflected wave can be denoted as Er(t)＝Ei(t)·Γ(t)；
The reflection coefficient Γ (T) is controlled by using a periodic digital modulation method, and assuming that a period time is T, a sequence length in one period is M, and a time occupied by each symbol is τ T/M, the reflection coefficient in one period can be expressed as:
Figure GDA0001704195150000011
wherein, gamma ismIs the reflection coefficient of the mth symbol; g (t) is a periodic pulse function, which can be expressed as
Figure GDA0001704195150000012
The periodically varying reflection coefficient can be expressed as a fourier series:
Figure GDA0001704195150000021
its fourier transform is:
Figure GDA0001704195150000022
wherein f is01/T, the repetition frequency of the reflection coefficient; delta (f) is a unit impulse function; a iskThe Fourier series for the k-th harmonic can be expressed as:
Figure GDA0001704195150000023
wherein TF is a time factor, and UF is a unit factor;
Figure GDA0001704195150000024
UF characterizes the spectral characteristics of a single pulse g (t); TF and gammamIn relation to, characterizing the effect of time-domain coding on the spectrum;
when incident waves enter the time domain metamaterial, the product of the incident waves and the reflection coefficient obtains reflected waves:
Er(t)＝Ei(t)·Γ(t) (7)
the frequency spectrum can be represented by convolution:
Figure GDA0001704195150000025
can be further expressed as:
Figure GDA0001704195150000026
for conventional devices, the reflection coefficient is time-invariant, so that only a exists0The term, no harmonic term appears; and for the time domain metamaterial, because the reflection coefficient is time-varying, a high-order Fourier series term exists, so that the nonlinear characteristic can be generated, and the frequency spectrum can be adjusted.
Preferably, the time domain metamaterial is divided into different areas, and the different areas are regulated and controlled by adopting different time control sequences, so that the spatial wave frequency spectrum and the far field directional diagram are regulated and controlled simultaneously.
The invention has the beneficial effects that: the invention has novel principle, can adopt a simple mode to control the space electromagnetic wave on the time domain, and can be used for changing the frequency spectrum characteristic of the space electromagnetic wave; compared with the traditional natural material with nonlinear characteristics, the invention is a dynamically adjustable design, can perform multifunctional control on frequency spectrum by selecting different codes, and has extremely high energy conversion efficiency; compared with a mixing device adopted on a traditional circuit, the traditional design is to control guided waves on the circuit, but the invention is to control space waves, realizes the modulation of a reflection coefficient in a complex domain by adjusting a reflection phase, and does not need the traditional IQ multi-path modulation; compared with the traditional reflective array antenna, the frequency selective surface and the metamaterial, the invention can realize time-space coherence, not only can complete the modulation of the traditional directional diagram, but also can carry out the modulation of the frequency spectrum.
Drawings
FIG. 1 is a schematic diagram of a time domain metamaterial model according to the present invention.
Fig. 2(a) is a schematic diagram of time-domain amplitude modulation 1-bit coding according to the present invention.
FIG. 2(b) is a schematic diagram of a time-domain amplitude modulation 1-bit spectrum according to the present invention.
Fig. 2(c) is a schematic diagram of time-domain amplitude modulation 2-bit encoding according to the present invention.
FIG. 2(d) is a schematic diagram of the time domain amplitude modulation 2-bit spectrum of the present invention.
FIG. 3(a) is a schematic diagram of time-domain phase modulation 1-bit encoding according to the present invention.
FIG. 3(b) is a schematic diagram of the time domain phase modulation 1-bit spectrum of the present invention.
FIG. 3(c) is a schematic diagram of the time domain phase modulation 2-bit encoding of the present invention.
FIG. 3(d) is a schematic diagram of the time domain phase modulation 2-bit spectrum of the present invention.
Fig. 4(a) is a schematic diagram of a frequency spectrum generated by the same amplitude and phase modulation in the time domain according to the present invention.
FIG. 4(b) is a schematic diagram of amplitude-phase distribution of time-domain amplitude-phase coherent reflection coefficients according to the present invention.
FIG. 4(c) is a schematic diagram of the distribution of the time domain amplitude coherence spectrum of the present invention.
FIG. 5(a) is a front view of a time domain metamaterial structure of the present invention.
FIG. 5(b) is a left side view of the time domain metamaterial structure of the present invention.
FIG. 5(c) is a schematic structural diagram of the time domain metamaterial according to the present invention.
FIG. 6(a) is a diagram showing simulation results of reflection coefficient reflection amplitudes under different bias voltages.
FIG. 6(b) is a diagram showing the simulation results of reflection phase of reflection coefficient under different bias voltages.
FIG. 7 is a schematic diagram of a time domain metamaterial test according to the present invention.
FIG. 8(a) is a schematic diagram of the test result of the 0-order scattered field of the 1-bit experiment of the present invention.
FIG. 8(b) is a schematic diagram of the +1 order and-1 order fringe field test results of the 1-bit experiment of the present invention.
FIG. 8(c) is a schematic diagram of the results of the scattered field test during + -1 order frequency modulation of the 1-bit experiment of the present invention.
FIG. 9(a) is a schematic diagram of the 2-bit experimental reflection spectrum test result.
FIG. 9(b) is a schematic diagram of the +1 order and-1 order fringe field test results of the 2-bit experiment of the present invention.
FIG. 10(a) is a schematic diagram of the time domain metamaterial of the present invention divided into 4 regions.
FIG. 10(b) is a schematic diagram of the +1 st order fringe field test result of the time domain metamaterial according to the present invention.
Wherein, 1, a rectangular patch; 2. a varactor diode; 3. a dielectric substrate; 4. metallizing the through-hole; 5. a feed network; 6. an ultra-thin insulating layer; 7. a metal back plate.
Detailed Description
The schematic diagram of the time domain metamaterial provided by the invention is shown in fig. 1 and is formed by periodically arranging basic units. The reflection coefficient gamma of the time domain metamaterial can be controlled by an external bias voltage. A control device (such as an FPGA) is adopted to generate a time-varying signal, so that a time-varying reflection coefficient gamma (t) is realized. When incident wave Ei(t) upon incidence on the surface, the reflected wave can be denoted as Er(t)＝Ei(t) · Γ (t). Therefore, the time domain characteristics of the reflected wave can be controlled by the time-varying reflection coefficient.
The invention adopts a periodic digital modulation mode to control the reflection coefficient gamma (t). Assuming that the period time is T, the sequence length in one period is M, and the time occupied by each symbol is τ/M. The reflection coefficient in one period can be expressed as:
Figure GDA0001704195150000041
wherein, gamma ismIs the reflection coefficient of the mth symbol; g (t) is a periodic pulse function, which can be expressed as
Figure GDA0001704195150000042
The periodically varying reflection coefficient can be expressed as a fourier series:
Figure GDA0001704195150000043
its fourier transform is:
Figure GDA0001704195150000044
wherein f is01/T, the repetition frequency of the reflection coefficient; delta (f) is a unit impulse function; a iskThe Fourier series for the k-th harmonic can be expressed as:
Figure GDA0001704195150000045
wherein TF is a time factor and UF is a unit factor.
Figure GDA0001704195150000051
It can be seen that UF characterizes the spectral characteristics of a single pulse g (t); TF andΓmin this regard, the effect of time-domain coding on the spectrum is characterized. Therefore, by selecting a proper coding sequence, the regulation and control of the frequency spectrum can be realized.
When incident waves enter the time domain metamaterial, the product of the incident waves and the reflection coefficient obtains reflected waves:
Er(t)＝Ei(t)·Γ(t) (7)
the frequency spectrum can be represented by convolution:
Figure GDA0001704195150000052
can be further expressed as:
Figure GDA0001704195150000053
for conventional devices, only a exists because the reflection coefficient is time-invariant0And the harmonic terms can not be generated. And for the time domain metamaterial, because the reflection coefficient is time-varying, a high-order Fourier series term exists, so that the nonlinear characteristic can be generated, and the frequency spectrum can be adjusted.
The time domain metamaterial provided by the invention adjusts the time domain characteristics of electromagnetic waves by changing the reflection coefficient. It can be divided into time domain amplitude modulation, time domain phase modulation, and time domain amplitude homodyne.
Time domain amplitude modulation: as shown in fig. 2(a), two states with reflection amplitudes of 0 and 1 are selected as basic symbols to form 1-bit modulation. When modulated with a periodic sequence 01010101.. its frequency spectrum is shown in fig. 2 (b). It can be seen that in addition to the 0 th order component, there are also higher order harmonics. This is the time domain metamaterial property proposed by the present invention. Fig. 2(c) shows 2-bit modulation, that is, four states of 0, 1/3, 2/3 and 1 are selected as basic symbols for encoding, and the encoding sequence is 00-01-10-11-11-10-01-00. Different sequences of symbols are selected to produce different spectral components.
Time domain phase modulation: time domain amplitude modulation has two characteristics: firstly, the 0 th order energy cannot be completely eliminated, and secondly, the frequency spectrum is symmetrical. To suppress its 0 th order energy and to generate a more complex asymmetric spectrum, time domain phase modulation may be employed. Time-domain phase modulation is encoded using symbols that have the same amplitude but different phases. As shown in fig. 3(a), two states with a phase difference of 180 ° are selected to be modulated according to a 01010101. Due to the inverse nature of 0 ° and 180 °, the 0 th harmonic energy is completely cancelled, only odd harmonics are present, and the spectrum is symmetric. When four states with phases of 0 degrees, 90 degrees, 180 degrees and 270 degrees are selected as basic code elements and the simplest 00-01-10-11-. is adopted for 2-bit modulation, asymmetric spectrum modulation can be realized, energy is mainly concentrated on +1 order, and the design can be applied to generating pseudo Doppler frequency, so that echo has a frequency difference, a detection system cannot accurately detect the Doppler frequency of a target, and the real movement speed of the target cannot be accurately detected.
The time domain amplitudes are in the same tone: a more extensive modulation is one in which the amplitude of the time domain is the same. Based on the modulation mode, the invention provides a simple method for randomly controlling harmonic waves, and the method comprises the following two steps: first, the spectrum (as shown in fig. 4(a)) to be generated needs to be transformed, which is expressed in time form and can be expressed as:
Figure GDA0001704195150000061
wherein EkRepresenting the intensity of the k-th order spectral component; then discretizing the continuous gamma (t) to obtain the required reflection sequence gammam. In this example, a reflection sequence Γ with a period sequence length M of 16 is selectedmThe distribution of the web phase of (c) is shown in FIG. 4 (b). The resulting spectrogram based on such a sequence is shown in fig. 4 (c). In contrast, the resulting spectrum is found to be substantially identical to the desired spectrum (fig. 4 (a)).
The theory and modulation method of the time domain metamaterial proposed by the invention have been introduced. In the following, a time domain metamaterial based on time phase modulation is verified from simulation and experiment. The front view and the left view of the basic unit are shown in fig. 5(a) and (b). The whole unit is divided into 5 layers: the first layer is a unit structure and is formed by two rectangular patches 1 connected in series with a variable capacitance diode 2; the second layer is a dielectric substrate 3; the third layer is a feed network 5, the feed network 5 is connected with the upper rectangular patch 1 through a metalized through hole 4 in the dielectric substrate 3, and the feed of the variable capacitance diode 2 is realized; the fourth layer is an ultrathin insulating layer 6; the fifth layer is a metal back plate 7 for preventing transmission of electromagnetic waves. Because the insulating layer 6 is ultra-thin, the feed network 5 and the metal back plate 7 are very close to each other, and the coupling effect of the feed network 5 on the unit is negligible. The entire time domain metamaterial is composed of this basic unit arrangement, as shown in fig. 5 (c).
The simulation results of the reflection coefficients of the units are shown in fig. 6, where (a) is amplitude and (b) is phase, and the operating frequency is 3.6 GHz. From the reflection amplitude results, the cells all have higher reflection coefficients under different reverse biases; from the phase change curve, the unit can obtain larger phase change through voltage control. The unit is suitable for time domain phase modulation time domain metamaterial.
The schematic test diagram of the sample is shown in fig. 7, wherein an electromagnetic wave with a frequency of 3.6GHz is normally incident on the time domain metamaterial sample by using the transmitting antenna, and an echo is detected by using the receiving antenna. The circuit board is controlled through the FPGA, so that different voltage control sequences are applied to the time domain metamaterial, and time phase modulation is achieved.
First, a 1-bit experiment was performed, and reflection coefficients at bias voltages of 0V and-9V, respectively, were selected as symbol 0 and symbol 1, with a phase difference of about 180 ° between the two symbols. When the modulation sequence is 01010101.. the result of the reflected wave spectrum test is shown in fig. 8 (a): the energy is mainly concentrated on the +/-1 order, and the energy of the 0 order and the energy of the rest even orders are lower and are consistent with the theoretical result of a graph 3 (b). When the control circuit board does not work, the reflection coefficient of the sample is time-invariant, and the 0-order scattering directional diagram is shown as a solid line in fig. 8(b), and the 0-order scattering energy is stronger because energy nonlinear conversion does not exist; when the control circuit board works, the 0 th order scattering directional diagram is shown as a dotted line in fig. 8(b), and the 0 th order energy is greatly weakened because the energy is converted to other frequencies. According to fig. 8(a), the energy is now shifted to the ± 1 st order, and the pattern test results of the ± 1 st order are shown in fig. 8 (c).
The 2-bit experiment is carried out next, the reflection coefficients of the bias voltages of 0V, -6V, -9V and-21V are selected as symbols 00, 01, 10 and 11, and the reflection phase states among different symbols are 0 degree, 90 degree, 180 degree and 270 degree. In the case of the control sequence 00-01-10-11-. the spectrum distribution is as shown in fig. 9(a), the spectrum is no longer symmetrical, the energy is mainly concentrated on the +1 order, the energy of the-1 order is very small, and the result is consistent with the theoretical result of fig. 3 (d). In this case, the far field pattern of order + -1 is shown in FIG. 9(b), and the patterns of order +1 and-1 have the same profile and have a difference of about 15dB in amplitude.
Finally, spatiotemporal coherence is discussed. The above test results are only for time domain modulation, and the test results show that the scattering energy is mainly concentrated in the backward direction (theta ═ 0 °). In conventional reflectarray or metamaterial designs, pattern control is achieved by having the phase vary along the surface. By taking the reference of the method, different control signals are adopted to control different regions of the time domain metamaterial, so that the time domain metamaterial not only has time-varying characteristics, but also has space-varying characteristics. As shown in FIG. 10(a), the time domain metamaterial is divided into four distinct regions, two of which are controlled with control signal S1 and the other two of which are controlled with control signal S2. When S1 is (S2) is (00-01-10-11- }, the metamaterial has only temporal characteristics, the + 1-order scattering energy test result is shown as a solid line corresponding to case-I in fig. 10(b), the energy is mainly concentrated in the 0 ° direction, and the result is consistent with that in fig. 9(b), and is only temporal control. When S1 is selected as {00-01-10-11- } and S2 is selected as {10-11-00-01- }, a time difference of a half cycle exists between the two control signals, and the phase difference between adjacent regions is 180 °, so that the reflected energy must be split in the left and right directions. The +1 order scattering energy test result is shown as a dotted line corresponding to case-II in FIG. 10(b), the energy is radiated to two directions of about +/-40 degrees, and the directional diagram has larger change compared with case I, which is time-space coherent. If a more complex control method is adopted, the time domain metamaterial has more enhanced space-time modulation capability. Because of the similar principle, the embodiment will not be described in more detail.
The invention introduces a time domain metamaterial capable of coding and modulating free space waves from the perspective of time domain control, performs experimental verification, combines time domain modulation with traditional space domain modulation, and expands a method of space-time coherence. The characteristics enable the invention to have huge development prospect in the field of radar, and can simultaneously perform target stealth and speed stealth; meanwhile, the method can also be used in communication systems, such as application directions of multi-channel communication, transceiving separation, beam forming, modulation and demodulation and the like.

Claims (4)

1. A time domain metamaterial, comprising: n adjustable units with sub-wavelength sizes, wherein the n adjustable units with sub-wavelength sizes are sequentially arranged; the adjustable unit comprises 5 layers from top to bottom in sequence, the first layer is two rectangular patches (1) connected in series by a variable capacitance diode (2), the second layer is a dielectric substrate (3), the third layer is a feed network layer (5), the positive and negative poles of the feed network layer (5) are respectively connected with the rectangular patches (1) at the two ends of the variable capacitance diode (2) through metallized through holes (4) in the dielectric substrate (3), the fourth layer is an ultrathin insulating layer (6), the fifth layer is a metal back plate (7), the time domain metamaterial controls the reflection coefficient gamma thereof through additional bias voltage, a control device is adopted to generate a time-varying signal, and the time-varying reflection coefficient gamma (t) is realized.
2. The time-domain metamaterial according to claim 1, wherein the modulation of the spatial wave spectrum is achieved by adjusting the time-domain characteristics of the adjustable unit, and the adjustment and control manner is divided into time-domain amplitude modulation, time-domain phase modulation and time-domain amplitude coherence modulation.
3. The time-domain metamaterial according to claim 1, wherein the time-domain metamaterial is partitioned into different regions, and the different regions are controlled by different time control sequences, so that simultaneous control of the spatial wave spectrum and the far-field pattern is achieved.
4. As claimed in claimThe time domain metamaterial of 1, characterized in that when incident wave Ei(t) upon incidence on the surface, the reflected wave can be denoted as Er(t)＝Ei(t)·Γ(t)；
The reflection coefficient Γ (T) is controlled by using a periodic digital modulation method, and assuming that a period time is T, a sequence length in one period is M, and a time occupied by each symbol is τ T/M, the reflection coefficient in one period can be expressed as:
Figure FDA0002399726630000011
wherein, gamma ismIs the reflection coefficient of the mth symbol; g (t) is a periodic pulse function, which can be expressed as
Figure FDA0002399726630000012
The periodically varying reflection coefficient can be expressed as a fourier series:
Figure FDA0002399726630000013
its fourier transform is:
Figure FDA0002399726630000014
wherein f is01/T, the repetition frequency of the reflection coefficient; delta (f) is a unit impulse function; a iskThe Fourier series for the k-th harmonic can be expressed as:
Figure FDA0002399726630000021
wherein TF is a time factor, and UF is a unit factor;
Figure FDA0002399726630000022
UF characterizes the spectral characteristics of a single pulse g (t); TF and gammamIn relation to, characterizing the effect of time-domain coding on the spectrum;
when incident waves enter the time domain metamaterial, the product of the incident waves and the reflection coefficient obtains reflected waves:
Er(t)＝Ei(t)·Γ(t) (7)
the frequency spectrum can be represented by convolution:
Figure FDA0002399726630000023
can be further expressed as:
Figure FDA0002399726630000024
for conventional devices, the reflection coefficient is time-invariant, so that only a exists0The term, no harmonic term appears; and for the time domain metamaterial, because the reflection coefficient is time-varying, a high-order Fourier series term exists, so that the nonlinear characteristic can be generated, and the frequency spectrum can be adjusted.
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