A tunable plasmonic excitation device and method

Abstract

The application provides a tunable plasmon excitation device, comprising an emission cathode, a composite metal grating, a plasmon output device and a collecting electrode; the emission cathode and the collecting electrode are respectively located on the upper surfaces of two ends of the composite metal grating, and the collecting electrode is used for receiving the electron beam emitted by the emission cathode; the plasmon output device is located between the emission cathode and the collecting electrode, and is connected with one end of the composite metal grating close to the collecting electrode, and is used for guiding the plasmon output of the surface of the metal grating; the composite metal grating comprises a metal substrate and a plurality of rectangular metal plates arranged in cycles, each rectangular metal plate is perpendicular to the metal substrate, and each rectangular metal plate is connected with a metal cover plate at the end away from the metal substrate, one end of the metal cover plate is connected with one end of the rectangular metal plate, and the other end of the metal cover plate is spaced apart from the adjacent rectangular metal plate. The excitation device has the advantages of simple structure, high interaction efficiency, low loss, high coupling strength and tunability.

Description

Technical Field

[0001] This invention relates to the field of terahertz radiation sources and surface plasmons, and particularly to a tunable plasmon excitation device and method. Background Technology

[0002] Artificial surface plasmons (SSPs) are a special type of near-field localized mode in the microwave and terahertz frequency bands, and are generally found on the electromagnetic surfaces of periodic metal, dielectric, or semiconductor waveguide structures.

[0003] In recent years, artificial surface plasmons in periodic metallic structures have been extensively studied and applied in terahertz and microwave integrated waveguides, couplers, power dividers, slow-light systems, and terahertz radiators due to their excellent electromagnetic properties (such as strong near-field coupling, subwavelength localization, and enhanced matter-light interaction). In particular, terahertz waves generated by the interaction of surface plasmons with an external light source or electron beam and a periodic metallic grating have attracted widespread attention. Examples include terahertz Cherenkov lasers with subwavelength periodic metallic gratings, terahertz generators based on infrared lasers with periodic metallic gratings, and terahertz radiation or amplification sources based on electron beam-excited periodic metallic gratings. However, the excitation efficiency in these technologies is limited by the power level of the external excitation source, making further increases difficult. Furthermore, most structures are regular rectangular periodic metallic gratings, resulting in low waveguide Q values, high losses, low interaction efficiency, and poor tunability.

[0004] Therefore, based on the above problems, there is an urgent need to provide a tunable plasmon excitation device and its preparation method. Summary of the Invention

[0005] To address the problems of low excitation efficiency, high loss, and poor tunability of surface plasmons interacting with periodic metal gratings using external light sources or electron beams in related technologies, this invention provides a tunable plasmon excitation device and method.

[0006] In a first aspect, embodiments of the present invention provide a tunable plasmon excitation device, including an emitting cathode, a composite metal grating, a plasmon output device, and a collecting electrode;

[0007] The emitting cathode and the collecting electrode are respectively located on the upper surfaces at both ends of the composite metal grating, and the collecting electrode is used to receive the electron beam emitted by the emitting cathode;

[0008] The plasmon output device is located between the emitting cathode and the collecting electrode, and is connected to the end of the composite metal grating near the collecting electrode, for guiding the plasmon output on the surface of the metal grating;

[0009] The composite metal grating includes a metal substrate and a number of periodically arranged rectangular metal plates. Each rectangular metal plate is perpendicular to the metal substrate. Each rectangular metal plate has a metal cover plate connected to one end away from the metal substrate. One end of the metal cover plate is connected to one end of the rectangular metal plate, and the other end is spaced apart from the adjacent rectangular metal plate.

[0010] Preferably, a magnetic cover plate is also provided above the emitting cathode and the collecting electrode, the magnetic cover plate being used to prevent the electron beam emitted by the emitting cathode from diverging laterally.

[0011] Preferably, the distance between the emitting cathode and the composite metal grating is less than the wavelength at the operating frequency.

[0012] Preferably, the distance a between one end of the metal cover plate and the rectangular metal plate is less than or equal to the distance b between adjacent rectangular metal plates;

[0013] The distance h2 between the upper surface of the metal cover plate and the metal substrate is greater than or equal to the distance h1 between the lower surface of the metal cover plate and the metal substrate.

[0014] Preferably, when the distance a between one end of the metal cover plate and the rectangular metal plate and / or the distance h1 between the lower surface of the metal cover plate and the metal substrate are changed, the plasmon dispersion excited on the surface of the composite metal grating is different.

[0015] Preferably, the metal substrate, the rectangular metal plate, and the metal cover plate are all made of iron or copper.

[0016] In a second aspect, embodiments of the present invention provide a method for preparing the excitation device according to any one of the first aspects above, the method comprising:

[0017] Multiple rectangular metal plates arranged in a periodic manner are disposed on a metal substrate. Each rectangular metal plate is connected to a metal cover plate at the end away from the metal substrate, and the metal cover plate is spaced apart from the adjacent rectangular metal plate to obtain a composite metal grating.

[0018] An emitting cathode and a collecting electrode are respectively disposed on the upper surfaces at both ends of the composite metal grating to transmit an electron beam between the emitting cathode and the collecting electrode;

[0019] An electron beam is emitted from the emitting cathode using a high-temperature heater. The electron beam interacts with the composite metal grating to excite plasmons.

[0020] Preferably, the relationship between the electron beam voltage and the plasmon dispersion satisfies the following formula:

[0021] v e =βc, β = (1-(1+γ))-2 ) 0.5 γ=U / U0

[0022] In the formula, U0 is a constant, U0 = 5.11 × 10 5 V and U are the operating voltages of the electron beam, and c is the speed of light in free space.

[0023] Preferably, the plasmon dispersion characteristics excited on the surface of the composite metal grating can be modulated by changing the interval a between one end of the metal cover plate and the rectangular metal plate and / or the distance h1 between the lower surface of the metal cover plate and the metal substrate.

[0024] Compared with the prior art, the present invention has at least the following beneficial effects:

[0025] This invention provides a tunable plasmon excitation device and method. The plasmon excitation device includes an emitting cathode, a composite metal grating, a plasmon output device, and a collecting electrode. High-efficiency excitation and transmission of surface plasmons are achieved by the interaction between the electron beam emitted by the emitting cathode and the surface of the composite metal grating. Furthermore, by designing the structure and structural parameters of the composite metal grating, a high-Q coupling cavity can be constructed. Flexible control of surface plasmon dispersion is achieved by varying the structural parameters of the composite metal grating. Therefore, the plasmon excitation device of this invention has the advantages of simple structure, high interaction efficiency, low loss, high coupling strength, and tunability. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a schematic diagram of a tunable plasmon excitation device according to an embodiment of the present invention;

[0028] Figure 2 This is a dispersion curve distribution diagram of one end of the metal cover plate and the rectangular metal plate at different intervals in a composite metal grating provided in an embodiment of the present invention;

[0029] Figure 3 This is a distribution diagram of the excited surface plasmon output power as a function of the horizontal width of the periodic metallic waveguide, provided by an embodiment of the present invention.

[0030] Figure 4This is a distribution curve of the interaction frequency of plasmon excitation as a function of different intervals between the metal cover plate and the rectangular metal plate, provided by an embodiment of the present invention.

[0031] In the figure, 100-emitting cathode; 200-magnetic cover plate; 300-electron beam; 400-plasm output device; 500-collector electrode; 600-composite metal grating; 601-metal substrate; 602-rectangular metal plate; 603-metal cover plate. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0033] As mentioned earlier, in the related technologies, the excitation efficiency of plasmons is limited by the power of the external excitation source during the interaction between an external power source or an electron beam and the surface of a periodic metal grating. The excitation efficiency is low. Furthermore, the commonly used periodic metal gratings and other metasurface waveguides based on phase gradients that interact with the external power source or electron beam have low Q values ​​and high losses. At the same time, the interaction frequency between the external power source or electron beam and the periodic metal grating is low, resulting in poor tunability. On the other hand, surface plasmon waveguides made of graphene, liquid crystal materials, etc., can achieve dynamic tuning, but their fabrication is relatively complex and costly.

[0034] To solve the above problems, such as Figure 1 As shown, this embodiment of the invention provides a tunable plasmon excitation device, including an emitting cathode 100, a composite metal grating 600, a plasmon output device 400, and a collecting electrode 500.

[0035] The emitting cathode 100 and the collecting electrode 500 are respectively located on the upper surfaces at both ends of the composite metal grating 600, and the collecting electrode 500 is used to receive the electron beam 300 emitted by the emitting cathode 100.

[0036] The plasmon output device 400 is located between the emitting cathode 100 and the collecting electrode 500, and is connected to the end of the composite metal grating 600 near the collecting electrode 500, for guiding the plasmon output on the surface of the composite metal grating 600.

[0037] The composite metal grating 600 includes a metal substrate 601 and a plurality of rectangular metal plates 602 arranged periodically. Each rectangular metal plate 602 is perpendicular to the metal substrate 601. Each rectangular metal plate 602 has a metal cover plate 603 connected to one end away from the metal substrate. One end of the metal cover plate 603 is connected to one end of the rectangular metal plate 602, and the other end is spaced apart from the adjacent rectangular metal plate 602.

[0038] The plasmon excitation device in this embodiment of the invention includes an emitting cathode 100, a composite metal grating 600, a plasmon output device 400, and a collecting electrode 500. High-efficiency excitation and transmission of surface plasmons are achieved through the interaction between the electron beam emitted by the emitting cathode and the surface of the composite metal grating. Furthermore, by designing the structure and structural parameters of the composite metal grating, a high-Q coupling cavity can be constructed. Flexible control of surface plasmon dispersion can be achieved by varying the structural parameters of the composite metal grating. Therefore, the plasmon excitation device in this invention has the advantages of simple structure, high interaction efficiency, low loss, high coupling strength, and tunability.

[0039] According to some preferred embodiments, a magnet cover plate 200 is also provided above the emitting cathode 100 and the collecting electrode 500, the magnet cover plate 200 being used to prevent the electron beam emitted by the emitting cathode 100 from diverging laterally.

[0040] In this embodiment of the invention, reference continues to be made to... Figure 1 By further providing a magnet cover plate 200 above the emitting cathode and the collecting electrode, the magnet cover plate 200, the emitting cathode 100, the collecting electrode 500 and the composite metal grating 600 form a cavity for the transmission of the electron beam 300. After the electron beam 300 is emitted from the emitting cathode 100, the electron beam 300 interacts with the surface of the composite metal grating 600 to excite plasmons, thereby generating terahertz radiation. The magnet cover plate 200 above the electron beam can prevent the electron beam from diverging laterally during transmission, thereby enabling long-range synchronous interaction with the plasmons on the surface of the composite metal grating 600.

[0041] According to some preferred embodiments, the distance between the emitting cathode 100 and the surface of the composite metal grating 600 is less than the wavelength at the operating frequency.

[0042] In embodiments of the present invention, such as Figure 1As shown, a uniform electron beam is emitted from the emitting cathode at a height g on the surface of the periodic uniform metal grating structure, i.e., the distance g between the emitting cathode and the surface of the composite metal grating is g. Furthermore, by controlling the distance g between the emitting cathode and the surface of the composite metal grating within the aforementioned range, the electron beam emitted from the emitting cathode and the plasmons on the surface of the composite metal grating can achieve high coupling efficiency and strong interaction strength. More specifically, in this embodiment of the invention, the distance between the emitting cathode and the surface of the composite metal grating is 1–9 micrometers.

[0043] According to some preferred embodiments, the distance a between one end of the metal cover plate 603 and the rectangular metal plate 602 is less than or equal to the distance b between adjacent rectangular metal plates 602;

[0044] The distance h2 between the upper surface of the metal cover plate 603 and the metal substrate 601 is greater than or equal to the distance h1 between the lower surface of the metal cover plate 603 and the metal substrate 601.

[0045] In embodiments of the present invention, such as Figure 1 As shown, the distance 'a' between one end of the metal cover plate and the adjacent rectangular metal plate, and the distance 'h2' between the lower surface of the metal cover plate and the metal substrate are not fixed (i.e., the length 'a' and the thickness 'h2' of the metal cover plate are variable). Thus, by changing the length 'a' and the thickness 'h2' of the metal cover plate, cavities of different depths can be constructed, thereby enabling the tunability of the composite metal grating surface plasmon polariton and significantly improving the Q value of the composite metal grating surface plasmon polariton waveguide. Therefore, the transmission loss is lower than that of the traditional metal grating, the interaction strength is greater, the coupling efficiency is higher, and the tunability is better.

[0046] According to some preferred embodiments, when the distance a between one end of the metal cover plate 603 and the rectangular metal plate 602 and / or the distance h1 between the lower surface of the metal cover plate 603 and the metal substrate 601 is changed, the plasmon dispersion excited on the surface of the composite metal grating is different.

[0047] In this embodiment of the invention, a novel terahertz radiation source is used to efficiently excite artificial surface plasmons on a uniform composite metal grating surface using an electron beam. By changing the length a and thickness h2 of the metal cover plate in the periodic metal grating, the dispersion characteristics of the surface plasmons on the composite metal grating can be controlled, and the wave vector matching between the electron beam and the surface plasmons on the composite metal grating can be achieved, thereby achieving highly efficient excitation with tunability.

[0048] For example, when the length *a* of the metal cover plate is the same as the spacing *b* between adjacent rectangular metal plates, or the thickness *h2* of the metal cover plate is the same as the height *h1* of the rectangular metal plates, the composite metal grating includes a metal substrate and several rectangular metal plates arranged perpendicularly to the surface of the metal substrate. When the length *a* of the metal cover plate is less than the spacing *b* between adjacent rectangular metal plates, or the thickness *h2* of the metal cover plate is less than the height *h1* of the rectangular metal plates, the composite metal grating includes a metal substrate and several periodically arranged rectangular metal plates, each rectangular metal plate being perpendicular to the metal substrate, and each rectangular metal plate having a metal cover plate connected to its end away from the metal substrate. Figure 1 As shown, a rectangular metal plate and a metal cover plate form an inverted L-shape on the surface of a metal substrate. Compared with composite metal gratings and other metasurface excitations based on phase gradient in related technologies, the composite metal grating in this embodiment not only enables dispersion modulation and transmission of surface plasmons with greater degrees of freedom, but also has a simpler structure and higher excitation efficiency. It can provide a new tunable means for realizing terahertz radiation sources that efficiently excite surface plasmons with electron beams.

[0049] According to some preferred embodiments, the metal substrate, the rectangular metal plate, and the metal cover plate are all made of iron or copper.

[0050] This invention also provides a method for exciting plasmons using the excitation device described in any one of the above claims, the method comprising:

[0051] Multiple rectangular metal plates arranged in a periodic manner are disposed on a metal substrate. Each rectangular metal plate is connected to a metal cover plate at the end away from the metal substrate, and the metal cover plate is spaced apart from the adjacent rectangular metal plate to obtain a composite metal grating.

[0052] An emitting cathode and a collecting electrode are respectively disposed on the upper surfaces at both ends of the composite metal grating to transmit an electron beam between the emitting cathode and the collecting electrode;

[0053] An electron beam is emitted from the emitting cathode using a high-temperature heater. The electron beam interacts with the composite metal grating to excite plasmons.

[0054] In this embodiment of the invention, the plasmon output coupling device is located between the emitting cathode and the collecting electrode, and is connected to the end of the composite metal grating near the collecting electrode. The plasmon output coupling device guides the surface plasmon output or converts it into spatial radiation wave decoupling through the periodically arranged metal grating structure. The electron beam collecting electrode collects the interacting electron beam. After interacting with the composite metal grating, most of the energy of the electron beam is converted into surface plasmon modes, and the high-energy electron beam can be recovered and reused through the collecting electrode.

[0055] According to some preferred embodiments, the relationship between the electron beam voltage and plasmon dispersion satisfies the following formula:

[0056] v e =βc, β = (1-(1+γ)) -2 ) 0.5 γ=U / U0

[0057] In the formula, U0 is a constant, U0 = 5.11 × 10 5 V and U are the operating voltages of the electron beam, and c is the speed of light in free space.

[0058] In this embodiment of the invention, the dispersion of surface plasmons excited by the interaction between the emitted electron beam and the composite metal grating is determined by the electron beam energy and the structural parameters of the waveguide structure. The excitation frequency f of the surface plasmons can be adjusted by changing the electron beam voltage, and the excitation frequency increases as the electron beam voltage decreases. The surface plasmon dispersion relationship of the periodic composite metal grating is jointly determined by the structural parameters a, b, h1, h2 and the period p, with depth playing a dominant role. The surface plasmon dispersion mode of the periodic metal waveguide decreases as the depth increases. The plasmon excitation device in this invention is achieved by changing the width a of the metal cover plate in the composite metal grating, while the energy of the applied electron beam remains constant. The power of the excitation surface plasmons increases with the increase of a and tends to saturate, and the interaction frequency f also increases linearly with the increase of a.

[0059] According to some preferred embodiments, the plasmon dispersion characteristics excited on the surface of the composite metal grating can be modulated by changing the interval 'a' between one end of the metal cover plate and the rectangular metal plate and / or the distance h1 between the lower surface of the metal cover plate and the metal substrate.

[0060] In this embodiment of the invention, high-efficiency excitation and transmission of surface plasmons are achieved by applying an external electron beam to the surface of a periodic composite metal grating structure. By reasonably setting the electron beam parameters and the composite periodic metal grating structure parameters, the efficient interaction between the electron beam and the plasmons on the surface of the periodic composite metal grating can simultaneously achieve the excitation and transmission of terahertz or microwave artificial surface plasmons. Furthermore, the required emission electron beam energy is relatively small, the near-field coupling is strong, and the excitation efficiency is high. Compared with metal gratings in related technologies, the structural interaction cavity of the composite metal grating in this embodiment has a higher Q value, thus also having advantages such as high efficiency, large interaction strength, large degree of freedom in dispersion control, and good tunability.

[0061] In one specific embodiment, the tunable plasmon excitation device of the present invention, such as Figure 1As shown, it mainly consists of four parts: an electron beam emitting cathode, an interacting periodic composite metal grating, a plasmon output device, and an electron beam collecting electrode. During operation, the electron beam emitting cathode emits a uniform rectangular electron beam at a height g on the surface of the periodic composite metal grating. When passing through the periodic composite metal grating, the excited surface plasmons propagate along the interaction structure. The electron beam is constrained in the plane by a uniform magnetic cover plate to ensure that it does not diverge, thereby achieving high-efficiency excitation. The composite metal grating includes a metal substrate and several periodically arranged (period p = 30 μm) rectangular metal plates. Each rectangular metal plate is perpendicular to the metal substrate. The distance h2 between the upper surface of the metal cover plate and the metal substrate is 66 μm, the distance h2 between the lower surface of the metal cover plate and the metal substrate is 60 μm, and the interval b between adjacent rectangular metal plates is 15 μm. By changing the interval a between the metal cover plate and the rectangular metal plates, the surface plasmon dispersion mode can be changed.

[0062] Figure 2 This is a dispersion distribution diagram of the metal cover plate in a composite metal grating at different lengths 'a', derived from... Figure 2 As can be seen, the surface plasmon modes of the composite metal grating shift downwards as α decreases, and the asymptotic frequency also decreases accordingly. Figure 3 The power distribution of the output surface plasmons obtained by passing a 19.3 kV, 0.5 A electron beam through a 3.8 mm long waveguide under different lengths 'a' of the metal cover plate is presented. Figure 3 As can be seen, when the length 'a' of the metal cover increases, its output power also increases. When the length 'a' of the metal cover further increases, its output power tends to saturate. Figure 4 The interaction frequency increases linearly with the increase of the length a of the metal cover plate.

[0063] In summary, compared with periodic metal grating excitation in related technologies, the composite metal grating structure interaction cavity in this embodiment of the invention has a higher Q value, thus possessing advantages such as high efficiency, large interaction strength, large degree of freedom in dispersion control, and good tunability. Furthermore, by adjusting the parameters of the periodic composite metal grating structure, its independent control and tunable output can be achieved.

[0064] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A tunable plasmon excitation device, characterized in that, It includes an emitting cathode, a composite metal grating, a plasmonic output device, and a collector electrode; The emitting cathode and the collecting electrode are respectively located on the upper surfaces at both ends of the composite metal grating, and the collecting electrode is used to receive the electron beam emitted by the emitting cathode; The plasmon output device is located between the emitting cathode and the collecting electrode, and is connected to the end of the composite metal grating near the collecting electrode, for guiding the plasmon output on the surface of the metal grating; The composite metal grating includes a metal substrate and a number of periodically arranged rectangular metal plates. Each rectangular metal plate is perpendicular to the metal substrate. Each rectangular metal plate has a metal cover plate connected to one end away from the metal substrate. One end of the metal cover plate is connected to one end of the rectangular metal plate, and the other end is spaced apart from the adjacent rectangular metal plate.

2. The excitation device according to claim 1, characterized in that, A magnetic cover plate is also provided above the emitting cathode and the collecting electrode. The magnetic cover plate is used to prevent the electron beam emitted by the emitting cathode from diverging laterally.

3. The excitation device according to claim 1, characterized in that, The distance between the emitting cathode and the composite metal grating is less than the wavelength at the operating frequency.

4. The excitation device according to claim 1, characterized in that, The distance a between one end of the metal cover plate and the rectangular metal plate is less than or equal to the distance b between adjacent rectangular metal plates; The distance h2 between the upper surface of the metal cover plate and the metal substrate is greater than or equal to the distance h1 between the lower surface of the metal cover plate and the metal substrate.

5. The excitation device according to claim 4, characterized in that, When the distance a between one end of the metal cover plate and the rectangular metal plate and / or the distance h1 between the lower surface of the metal cover plate and the metal substrate are changed, the plasmon dispersion excited on the surface of the composite metal grating is different.

6. The excitation device according to claim 1, characterized in that, The metal substrate, the rectangular metal plate, and the metal cover plate are all made of iron or copper.

7. A method for exciting plasmons using an excitation device according to any one of claims 1 to 6, characterized in that, The method includes: Multiple rectangular metal plates arranged periodically are disposed on a metal substrate. Each rectangular metal plate is connected to a metal cover plate at the end away from the metal substrate, and the metal cover plate is spaced apart from the adjacent rectangular metal plate to obtain a composite metal grating. An emitting cathode and a collecting electrode are respectively disposed on the upper surfaces at both ends of the composite metal grating to transmit an electron beam between the emitting cathode and the collecting electrode; An electron beam is emitted from the emitting cathode using a high-temperature heater. The electron beam interacts with the composite metal grating to excite plasmons.

8. The method according to claim 7, characterized in that, The relationship between the electron beam voltage and plasmon dispersion satisfies the following formula: v e =βc,β=(1-(1+γ) -2 ) 0.5 ,γ=U / U0 In the formula, U0 is a constant, U0 = 5.11 × 10 5 V and U are the operating voltages of the electron beam, and c is the speed of light in free space.

9. The method according to claim 7, characterized in that, The plasmon dispersion characteristics excited on the surface of the composite metal grating can be modulated by changing the distance 'a' between one end of the metal cover plate and the rectangular metal plate and / or the distance 'h1' between the lower surface of the metal cover plate and the metal substrate.

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