A Metamaterial and Methods for Producing the Same

Background and Field of the Invention

This invention relates to a metamaterial, particularly but not exclusively, which exhibits left-handed passbands in the region 0.5 to 500 THz, and methods for producing such a metamaterial.

Electromagnetic metamaterials exhibit negative values of both dielectric permittivity and magnetic permeability, within a resonance frequency band called left-handed passband. Unusual electromagnetic properties are found in this passband resulting in promising applications for metamaterials such as sub- wavelength resolution imaging.

The electromagnetic response of a metamaterial is due to tiny artificial metallic elements which are densely distributed in space, either embedded in a plastic matrix or deposited on a dielectric substrate. Tiny means that the metallic elements are small compared to the wavelength at which the metamaterial is operated. The metallic elements, such as split-rings, U shapes, rectangles and crosses have been used at THz frequencies while string-like elements like S and ω have been more common in the microwave domain.

However, matrices and substrates may constrain applications due to their electromagnetic, mechanical, thermal, and radiative properties. Interaction of

the electromagnetic waves with the dielectric of either the matrix or substrate may reduce resonance frequency and increase loss. In particular, polymer matrices would show strong absorption bands in the "fingerprint region" (400- 4000 cm ^"1 ) preventing working frequencies from being freely selectable. Electromagnetic metamaterials embedded on substrates may work only in reflection if the substrate is not transparent over the left-handed pass-band. Besides spectral features, commonly used polymer matrices may suffer from ageing and radiation degradation. They may also be limited in operation temperature and may be sensitive to humidity. Finally, the rigidity of substrates may constrain applications further.

It is an object of the present invention to propose a metamaterial and methods of producing such a metamaterial which addresses at least one of the problems of the prior art and/or to provide the public with a useful choice.

Summary of the Invention

In a first aspect of the invention, there is provided a metamaterial comprising an arrangement of resonators supported at selected positions to enable the arrangement of resonators to be suspended in space.

With this arrangement, the resonators are suspended in space and thus, increase the effectiveness and usefulness of the resonators since the spectral characteristics of these resonators are not affected by substrates or matrices on which the resonators are conventionally embedded in.

Preferably, the arrangement of resonators is supported at its ends, by for example, a window frame. Each resonator in the arrangement may be formed by a first structure and a second structure spaced from the first structure by a gap, and the window frame may comprise a first window member for supporting the ends of the first structures of the resonators; and a second window member for supporting the ends of the second structures of the resonators; in which the metamaterial may further comprise spacers carried by the first and/or second window members which define the gap. Preferably, the spacers are carried by the first and second window member.

The gap may be 0.6μm, 1.1 μm or 6.1 μm, which affects the spectral characteristics of the resonators.

In addition or as an alternative to the window frame, the metamaterial may comprise a plurality of interconnecting members arranged to connect selected positions of the resonators in the arrangement.

The arrangement may comprise N rows and each row may comprise a plurality of resonators connected in a string. Each one of the plurality of interconnecting members may be arranged to connect a corresponding end of a resonator in each row wherein the plurality of interconnecting members transverses each string of plurality of resonators.

As an alternative, each one of the plurality of interconnecting members may be

arranged to connect a corresponding end of every other resonator in each row wherein the plurality of interconnecting members transverses each string of plurality of resonators. It should be appreciated that the plurality of interconnecting members may be connected in other ways, for example at three, four or longer periods of the resonators depending on application, provided the decreasing mechanical support does not affect the proper operation of the metamaterial.

Preferably, the resonators comprise an S-shape resonator or are in the form of S-shape resonators, although other types of resonators, such as C, H types of resonators are also envisaged.

Preferably, the resonators are made of gold, and exhibit left handed passband properties at THz frequencies. Possible frequencies may be between 0.5 THz and 500 THz, or more specifically at about 2.2 THz.

In a second aspect of the invention, there is provided a method of producing a metamaterial, the method comprising the steps of: i) forming a first arrangement of structures supported at selected positions; ii) forming a second arrangement of structures supported at selected positions; iii) providing a gap between the first and second arrangements of structures; iv) aligning the first and the second arrangements of structures to form an arrangement of resonators supported at the selected positions to enable the arrangement of resonators to be suspended in space.

Preferably, the first or second arrangements of the structures are produced by UV lithography or X-ray lithography. Using lithography offers control of resonance frequency over a wide range.

The method may further comprise the steps of: depositing a first resist layer over a substrate, patterning the resist layer to form the first or second arrangements of structures, depositing a second resist layer over the first or second arrangements of structures; patterning the second resist layer to form a support structure for supporting the first or second arrangements of structures at the selected positions.

The support structure may comprise a frame member for supporting ends of the first or second arrangements of structures. In the alternative, the support structure may comprise interconnecting members arranged to support the first or second arrangements of structures at the selected positions.

The first resist layer may be about 20 μm thick. Patterning the second resist layer may further comprise forming at least one spacer carried by the frame member.

As an alternative, a spacer foil may be used to define the gap with the separately formed from the first or second arrangements of structures.

The method may further comprise the step of gluing the first and second arrangements of structures and the spacer foil together to form the arrangement

of resonators.

In a third aspect, there is provided a method of producing a metamaterial, the method comprising the steps of: i) embedding a sacrificial layer between two layers of resist to form an intermediate element; ii) patterning the intermediate element to form first and second arrangements of structures; iii) etching the sacrificial layer to create a gap between the first and second arrangements of structures with the first and second arrangements of structures supported at ends of the first and second arrangements. In this way, the gap is defined by the sacrificial layer and thus, may be defined with more certainty.

Step (i) may include the steps of: providing the sacrificial layer between the two layers of resist; and hot pressing the two layers of resist together to form the intermediate element. Step (ii) may include using X-ray lithography to expose top and bottom surfaces of the intermediate element.

Preferably, the sacrificial layer is a metal layer, although other materials are envisaged. Preferably, the resist layer is PMMA.

In a fourth aspect of the invention, there is provided a method of producing a metamaterial having an arrangement of resonators, the method comprising the steps of: i) forming a first arrangement of structures supported at selected positions;

ii) forming a second arrangement of structures. supported at selected positions; iii) forming interconnecting members to support the first and second arrangement of structures at the selected positions and to space the first arrangement of structures from the second arrangement of structures to form the arrangement of resonators supported by the interconnecting members to enable the arrangement of resonators to be suspended in space.

With this process, a self-supporting, locally stiff and globally flexible space grid formed by the interconnecting members and the arrangement of resonators may be achieved.

Step (i) of the fourth aspect may comprise depositing a first resist layer over a substrate; and patterning the resist layer to form portions of the first and second arrangements of structures. Step (iii) may include the steps of depositing a second resist layer over the portions of the first and second arrangements of structures, and patterning the resist layer to form the interconnecting members and further portions of the first and second arrangements of the structures .

Step (ii) may include the steps of depositing a third resist layer over the interconnecting members and the further portions of the first and second arrangements of the structures; and patterning the third resist layer to form the first and second arrangements of structures supported at selected positions by the interconnecting members. Preferably, the metamaterial is produced by UV lithography or X-ray lithography.

It is envisaged that the metamaterial may be produced by injection moulding or hot embossing, especially for mass production. If the metamaterial is produced by injection moulding or hot embossing, the method may further comprise a step of metalising the first and second arrangement of structures. As it can be appreciated, the metamaterial of the present invention is locally stiff due to the interconnecting members , and yet globally flexible. Such a property is similar to a foil and this expands the possible applications of such a metamaterial foil. For example, it is envisaged that such a metamaterial may be used in optics, such as an optical lens having such a metamaterial foil, or a sensor for dielectric materials with the sensor including such a metamaterial foil.

Brief Description of the Drawings

Embodiments of the invention will now be described, by way of example, with reference to the accompanying drawings in which,

Figure 1 shows a metamaterial having strings of S-shape resonators suspended at their ends by a window frame according to a first embodiment of the invention; Figure 2 is a magnified basic structure of one of the S-shape resonator of

Figure 1 , without showing the window frame;

Figure 3 shows an example of an array of the S-shape resonator of Figure 2 freely suspended;

Figure 4 depicts a process flow for manufacturing the metamaterial of Figure 1 by patterning photoresist layers;

Figures 5a, 5b and 5c are photographs of a sample of the metamaterial 100 formed from the process of Figure 4 in various magnifications to show the freely-suspended matrix-free S-string array;

Figures 6a, 6b, 6c and 6d are close-up magnified views of certain portions of the sample of Figure 5a-5c;

Figure 7 depicts another process flow for manufacturing the metamaterial of

Figure 1 by etching a silicon substrate;

Figures 8a and 8b depict a further process for manufacturing the metamaterial of Figure 1 by using a separate spacer foil; Figure 9a, 9b and 9c depict an alternative process to Figures 5, 7 and. 8a and

8b, in which the metamaterial of Figure 1 is formed by hot embossing and double exposure;

Figure 10 shows a variation of the embodiment of the metamaterial of Figure 1 in which the S-shape resonators are also connected by interconnecting studs; Figures 11 a, 11 b and 11 c show a metamaterial having strings of S-shape resonators suspended by interconnecting rods according to a second embodiment of the invention;

Figure 12 are graphs which compare three pairs of measured and simulated transmission spectra of sample metamaterials of Figure 1 , with different gap widths;

Figure 13 shows permittivity and permeability characteristics of a sample metamaterial of Figure 1 ;

Figures 14a to 14d illustrate process steps for producing the metamaterial of

Figure 11a;

Figures 15a and 15b illustrate a mould for producing the metamaterial of Figure

11a using injection moulding;

Figure 16 is a schematic representation of a metamaterial foil produced by the process of Figures 14a to 14d; Figure 17 shows a close-up of part of the metamaterial foil of Figure 16, and also definitions of dimensions of the metamaterial foil;

Figure 18a shows conductors of a first layer of S-structures produced by the process illustrated in Figure 14a;

Figure 18b shows vias and interconnecting members of a second layer produced by the process illustrated in Figure 14b and the first layer of conductors of Figure 18a;

Figure 18c shows conductors of a third layer of S-structures produced by the process illustrated in Figure 14c, and the first and second layer conductors of

Figure 18b; Figure 19a shows a metamaterial foil supported by a window frame, as an alternative to the metamaterial foil of Figure 16; and

Figure 19b shows a number of metamaterial foils of Figure19a arranged one on top of another.

Detailed Description of the Preferred Embodiments

Figure 1 shows a metamaterial 100 according to a first embodiment of the present invention. The metamaterial 100 comprises an arrangement of resonators 102 in the form of an array which has N rows, but for simplicity of

explanation, only two rows are shown in Figure 1. The array of resonators 102 is formed by a bi-layer structure comprising upper S-strings (again, part of the strings are shown) of S-shaped electromagnetic structure 104 and corresponding lower S-strings of S-shaped electromagnetic structure 106 which are symmetrical to the upper S-strings 104. The upper S-strings 104 and each corresponding lower S-strings 106 are placed reversed of each other so that the combination, together with a spacer gap 108, forms the resonator array 102.

Figure 2 shows more clearly the structure of an S-shaped resonator from the array 102 of Figure 1 which comprises two identical S-shape structures 202,204 placed reversed of each other. For practical micromanufacturing, the S-shape resonator 200 is defined by length a and width b of the S structure, top and bottom width of the conductor h and h', its thickness t, and interlayer gap d. The measured values of these parameters for the S-shape resonator 200 in this embodiment are a=104.2 μm, b=34.9 μm, h=15.9 μm, h'=13.4 μm, and t=11.4 μm. The gap d may have values 0.6 μm, 1.1 μm, and 6.1 μm, and in this embodiment, the gap d is 0.6 μm. Figure 2 also shows the incoming wave and incidence angle a as measured with respect to the normal on the mid-plane of the bi-layer structure 200. At the right of Figure 2, schematic cross-sections through bi-layer strings 104,106 in the X-Y plane at a value of Z corresponding to the centre of half an S structure. Basic coupling capacitances are shown. Index doublets (m,n) serve to identify individual strings with a first index denoting the string number in a given layer and the second identifying the layer.

As shown in Figure 1 , the upper S-strings 104 are supported at their ends by an upper frame member 110 and the lower S-strings 106 supported at their ends by a lower frame member 112 (parts of the upper and lower frame members are omitted to show the strings more clearly). In this way, the S-shaped electromagnetic structures 104,106, and thus the resonator array 102, are suspended in space within the upper and lower frame members 110,112, and this is shown more clearly in Figure 3. In this embodiment, the upper and lower frame members 110,112 are made of SU-8 resist, and as can be appreciated from Figure 1 , the upper and lower frame members 110,112 cooperate to form a window frame for the metamaterial 100. The thickness of each window frame member 110,112 is 260 μm, and the outer dimensions are 14.7x12.3 mm ² . The total size of the window is 8.1x6.9 mm ² , resulting in a useful area of about 56 mm ² .

Although two layers of the S-strings as supported by respective window frames are used to produce a bi-layer metamaterial, only one type of layer of the S- string needs to be manufactured for symmetry reasons. However, two distinct photomasks are needed, one containing the S-string pattern, and the other the frame member pattern.

To produce the two photomasks, a 5" soda lime photomask blank (Nanofilm, Wetlake Village, California) with 100 nm-thick chrome and 0.5 μm-thick layer of AZ1518 photoresist is used. A Heidelberg Instruments direct-write laser system DWL 66 is used for patterning the resist. After development of the resist, chromium is etched away where it is not protected by the resist. Then, the no

longer needed resist is dissolved leaving the thin chromium pattern that serves to absorb UV light. Both the photomasks, one containing the S-string array pattern, the other the window-frame pattern, are produced in this way. 4*3 fields with either string or window-frame pattern are inscribed in a circle of 80 mm diameter size photomasks so as to fit onto a standard 100 mm diameter Si wafer which serves as a substrate for the subsequent processing. Both masks have alignment marks for an accurate relative positioning for the two exposures.

These photomasks are used either in a UV lithography process to expose structures in a photoresist or resist layer, or to generate X-ray masks that feature thick (»20 μm) gold structures capable to absorb hard X-rays in case of

X-ray deep lithography. Both lithography are based on the LIGA process

(Lithographie, Galvanoformung and Abformung process) [E. W. Becker, W.

Ehrfeld, P. Hagmann, A. Maner, D. Muenchmeyer, Microelectron. Eng. 4(1986)35-56].

The fabrication of the metamaterial 100 will now be described using the photomasks. Broadly, as one layer of the S-string includes a string layer of about 11.4 μm thick and the frame member that is 260 μm thick, two lithography steps are performed into two different resist depths. The bi-layer is then formed by assembling two complete single layers with their bottom sides facing each other. In this way, the alternating S structure which forms the S-shape resonators that leads to resonance loops is produced. The assembly involves a spacer to define the spacer gap d, and this is achieved by careful relative alignment of upper and lower S-strings, and a final gluing step to fix the parts.

Figures 4 depict a process flow for making the metamaterial 100 of the first embodiment by patterning photoresist/resist layers. At step 300, a Silicon wafer of about 100mm diameter, which acts as a substrate 400 for the subsequent process, is provided and a first AZ1518 resist layer 402 of about 2 μm is formed on the substrate 400 and ultraviolet patterning is carried out with a photomask for patterning cavities 404 for forming spacers later. At step 302, a plating base (not shown) comprising about 100 nm of chromium (Cr) and about 50 nm of gold (Au) is sputtered on the AZ1518 resist layer 402 and the substrate 400. Thereafter, a second resist layer 406 comprising AZ9260 resist is deposited on the metal plating base by spin coating. The second resist layer 406 is about 20μm thick. Next, the substrate 400 coated with the AZ9260 resist layer is soft baked which brings the substrate 400 to 95 ⁰ C for 3 minutes. The S-string pattern photomask is then applied to the substrate 400 and at step 304, the substrate 400 is exposed to UV light through the photomask by using a Karl Suss Mask & Bond Aligner (MA8/BA6) to pattern the S-strings 408 on the AZ9260 resist layer 406.

At step 306, the exposed AZ9260 resist is removed with AZ 400k developer solvent and the remaining patterned AZ9260 resist structures are used as a mould for subsequent gold plating to produce the S-string arrays. A standard Au electroplating process is performed that is based on an Enthone electrolyte formulation and the plating temperature is 50 ⁰ C. After electroplating, the AZ9260 resist is removed by using a proprietary AZ remover (AZ(R) 400T photoresist stripper) to leave the S-string structures 408 which also reveals the

cavities 404. In this way, it is possible to obtain the S-string structures 408 by UV lithography.

All AZ products may be bought from Clariant Corporation, AZ Electronic Materials.

Indeed, it is envisaged that instead of UV lithography, steps 302 and 306 may be performed by X-ray lithography to obtain the S-string structures. To make X- ray masks cost-effectively, a 100 mm diameter graphite wafer of 200 μm thickness is used as a membrane material onto which a 35 μm thick SU-8 resist layer is spin coated. The pattern of the optical mask is transferred to the SU-8 resist layer by UV exposure using a Karl Suss MA8 contact mask aligner. Postexposure bake and development are followed by an electroplating process to deposit 20 μm gold into the SU-8 mould. The graphite membrane with the patterned gold absorber on it is finally glued on an aluminium NIST-standard mask holder.

In the X-ray lithography process, a 100 mm diameter Si wafer is again covered with a plating base of 100 nm thick Cr and 50 nm Au. After forming the cavities 404 just like step 300 in the UV lithography, instead of using an AZ9260 resist layer, a «20 μm thick polymethylmethacrylate (PMMA) resist layer is applied onto the wafer by a multi-spin coating and soft bake process. Five layers are required as each spin process yields approximately 4 μm. The baking temperature is 180 ⁰ C, applied for about 2 min after each spin and 5 min after the final spin. The thus prepared substrate is exposed to synchrotron X-rays

through an X-ray mask with the S-string pattern at the LiMiNT beamline of SSLS. Finally, the exposed PMMA is removed by using the standard GG developer. The PMMA structures formed in this way are used as a mould for a subsequent gold plating process to produce the S-string arrays. Due to the short wavelength of the X-rays used («0.2 nm) and the small local divergence of synchrotron radiation (<1 mrad), sidewalls are smooth and nearly vertical. This is in contrast with sidewalls slanted by about 6° with AZ 9260 resists in the case of the UV lithography.

A standard Au electroplating process is performed that is based on an Enthone electrolyte formulation and the plating temperature is 50 ⁰ C. After electroplating, the PMMA is dissolved by acetone to obtain the freely suspended S-strings and to reveal the cavities 404.

With the S-string structures 408 formed, the next steps are to form frame members 410 of the window frame for holding and stabilizing the freely- suspended matrix-free S-string structures 408 and for easier handling of the final metamaterial. It is important that the frame member 410 must be precisely aligned with the finished gold S-string structures 408. At step 308, SU-8 resist is applied by spin coating to obtain the required thickness of 260 μm on the substrate 400, followed by a soft bake process at 95 ⁰ C for 4 hours. Then, the window frame photomask is applied over the SU-8 resist and the baked substrate is exposed to UV light by using a Karl Suss Mask & Bond Aligner (MA8/BA6) (or to synchrotron X-rays at the LiMiNT beamline of SSLS if X-ray lithography is used). Finally, the unexposed SU-8 resist is removed with SU-8

developer to obtain the frame member 410. In this way, it is possible to obtain an approximately 15 μm thick gold S-string structure array held by 260 μm thick SU-8 window frame member 410 on the silicon substrate 400 to obtain freely suspended S-string structures of any orientation, flat or upright.

To release the single layer structure which consists of 15 μm gold S-string arrays and 260 μm SU-8 window frame member 410 from the substrate 400, the Cr layer of the plating base is used as sacrificial layer that is removed via an etching process. To facilitate this process, etch holes are designed into the frame member 410. First, the sputtered gold of the plating base is removed via an about 30s long gold etching by means of a Kl solution that is custom made (4g Kl (potassium iodide) + 1 g I ₂ (iodine) + 40 ml Dl water). The exposed Cr layer (100nm) is removed by chrome etchant CEP-200 by Microchrome Technology. After this step, the single layer structure is released from the substrate 400, as shown in step 310, and it can be seen that spacers 412 are also formed and attached to the frame members 410.

The assembly of two single-layer structures to form the metamaterial 100 is shown in step 312. Relative alignment of the S-string arrays in both single-layer structures and the control of the gap between two layers are critical issues. The gap is set by the height of the spacers 412 formed from the SU-8 resist along the steps described above. The shape of the spacer corresponds to that of the window-frame. Different thicknesses ranging from 4 μm to 20 μm are fabricated to control mostly capacitance and ensuing pass-band frequency.

The alignment between two S-string structures so that one is an inverted image of the other is done by means of a special optical microscope equipped with micrometric translation and rotation features. When the alignment is satisfactory, the sandwich of two S-string structures with the spacer 412 in between is fixed by gluing to obtain the S-shape resonator array 102 of Figure 1.

Figures 5a, 5b and 5c are photographs of a sample of the metamaterial 100 formed from the process of Figure 4 in various magnifications to show the freely-suspended matrix-free S-string array. The images are taken by a digital camera with Figure 5a being a bird's eye view of about 1.2x 0.9 mm ² . Figures 5b and 5c illustrate the handling and the size of the metamaterial 100.

Figures 6a, 6b, 6c and 6d are close-up magnified views of certain portions of the sample of Figure 5a-5c. Figures 6a and 6b are taken with an optical microscope with Figure 6a focusing on the bottom layer and Figure 6b focusing on the top layer. The magnification is x50 and t he scale bar is 50 μm long.

Figures 6c and 6d are taken with a scanning electron microscope with Figure 6c showing a bird's eye view at a scale bar of 200 μm, and Figure 6d is a close-up view of Figure 6c at a scale bar of 50 μm.

As it can be appreciated, it is possible to use UV lithography or X-ray lithography to build comparatively large areas and quantities of the freely suspended matrix-free metamaterials 100 in which the resonator arrays 102 are

supported at their ends by the window frame. Owing to their size, the metamaterials can be easily handled.

Figure 7 depict another process flow for manufacturing the metamaterial 100 of Figure 1 by etching a silicon substrate 400'. Since the by-product of each step is the same as the by-product of the steps in Figure 5, the same reference numerals are used in Figure 7 with the addition of a prime. Just like step 300 of Figure 5, at step 700, an AZ1518 resist layer 402' of about 2 μm is formed on the substrate 400' and ultraviolet patterning is carried out with a photomask for patterning cavities 404' for forming spacers later. However, unlike the process of Figure 5, at step 702, wet or dry etching of the substrate 400' is carried out to form cavities 404' and the first resist layer 402' is also removed. The subsequent steps 704, 706, 708, 710, 712 are similar to the process steps 302 to 312 of Figure 5, in which the base metal plating is deposited, a second resist layer 406' is formed, patterning the second resist layer 406' to form the S- shaped structures 408', removing the second resist layer 406', forming a SU-8 layer 410' over the S-shaped structure 408' and releasing the single layer structure 408' from the substrate 400'.

The processes of Figures 4 and 7 uses a monolithic spacer method to control and define the thickness of the spacers 412,412' which then defines the spacer gap for the resonator array.

It is envisaged that there are other ways of defining the spacer gap for the resonator array 102 and Figures 8a and 8b illustrate another example.

Figure 8a shows two single layer devices 500, 502, with each single layer device 500,502 including an S-string structure 504 supported at its ends by a frame member 506. Each of these single layer devices 500,502 is manufactured according to the process of Figure 4, except that step 300 is omitted in which the patterning of the cavities is omitted since the spacers are formed separately and step 312 is not necessary. Once the single layer device 500,502 is formed, one is arranged opposite of the other as shown in Figure 8a and a spacer foil 508 is arranged between the devices 500,502. In this example, SU-8 is the material of the spacer foil but other material such as metal or plastic material may be used. For example, aluminium and Kapton may be used, although these may not be preferred.

To produce the spacer foil 508, SU-8 is spin coated on top of a sacrificial layer, X-ray (or UV) exposure, and released by etching the sacrificial layer. The etched SU-8 layer is then cut to size by surgical blade to form the spacer foil

508, laid on top of the frame member of the lower single layer device 502 after which the upper single layer device 500 is placed and aligned under microscope control. To improve on the accuracy of the alignment, the frame member 506 has alignment markers (which may be formed during patterning of the S structures similar to the process at step 704 of Figure 7, and the alignment markers may also be plated with Au) is formed during the formation of the frame member 506 viewable under the microscope to guide the alignment process.

Once assembled, the stack is glued by applying glue 510 to its four outer edges to form the metamaterial 100, as shown in Figure 8b.

As an alternative to the processes depicted in Figures 4, 7 and 8a and 8b, Figures 9a, 9b and 9c depict another process to fabricate the metamaterial 100 monolithically. In this process, two layers of resist 552,554, and in this case PMMA, are arranged to sandwich a metal sacrificial layer 550. The metal sacrificial layer 550 may be any metal such as chromium, aluminium, nickel, silver etc. The thickness of the metal sacrificial layer 550 is chosen according to the spacer gap required between the two S-string layers that are eventually formed. The two resist layers 552,554 are pressed together to form a single sheet 556 as an intermediate element with the metal sacrificial layer therebetween using a hot embossing technique.

The top surface 556a of the single sheet 556 is patterned using a lithography process and the bottom surface 556b is patterned in alignment with the top surface 556a. After development, the top and bottom surfaces 556a, 556b are electroplated to obtain the metal structures 558 followed by deep x-ray lithography (DXRL) exposure at the top and bottom surfaces to define a window 560 for the metal structures and to remove the photoresist in between the metal structures as shown in Figure 9b. After development, the removed resist opens up the window 560 to etch away the metal sacrificial layer 550. Removal of the metal sacrificial layer 550 gives rise to two parallel layers 562,564 of string like structures with a gap 566 between the layers 562,564 and held at both ends by the photoresist frame/sheet 568, as shown in Figure 9c. In this way, two layers of S-string structures 562,564 are fabricated on a single sheet of photoresist

using aligned double exposure and with a gap 566 between the structures defined by the metal sacrificial layer 500.

The metal for the S-string structure may be any metal like gold, nickel etc, provided that the sacrificial layer and the structure are not the same and both types of metals may be selectively etched with suitable chemistry.

In the described embodiment, the S-string resonators are supported at their ends by a window frame. In addition, the S-string resonators may be connected by interconnecting studs 600 of metal or other materials at selected locations such as that shown in Figure 10. The connecting studs are distributed or dispersed across the structure at such distances as to not influence the electromagnetic properties significantly but still provide stabilizing support to the structure of the S-string resonators. The structure shown in Figure 10 featuring interconnecting studs is made by 5-level lithography while the structure shown in Figure 1 1 a only needs 3-level lithography.

Indeed, the interconnecting studs actually form another aspect of the present invention and this is described in a second embodiment in which, instead of a window frame, the S-string resonators are self-supported as an all-metal space grid. Individual S-string structures are connected by transverse Au interconnecting rods creating a space grid which is self-supporting, locally stiff, but globally flexible. It should be appreciated that although it is preferred for the interconnecting rods or studs to be made of metal, it is envisaged, that they may be made of other materials such as an insulating material like resist polymer.

Figure 11a, 11b and 11c show magnified views of the S-strings 798 interconnected by interconnecting rods 800, 802, 804 at selected locations. Figure 11a shows a general arrangement in which the S-strings 798 run from left to right of Figure 11a with interconnecting rods 800 running from top to bottom which transverse the direction of the S-strings 798. Figure 11 b shows that the interconnecting transverse rods 802 repeat every second period of the S-string and Figure 11c shows another variation in which the interconnecting rods 804 repeat with every period of the S-string 798. Of course, it is envisaged that the interconnecting rods 800 may be connected at longer periods, 3, 4 or more, depending on application, provided the decreasing mechanical support does not affect the proper functioning of the metamaterial.

This property is similar to that of a foil and hence the term metamaterial foil or "meta-foil" to describe this embodiment, and a schematic representation of a meta-foil 840. is illustrated in Figure 16. Such a meta-foil may be tailor-made to virtually any shape required by a specific application. It may be bent and wrapped around an object to hide and shield it from electromagnetic radiation.

When the geometric parameters of the S-strings are kept constant across the whole meta-foil, then the optical function is that of a plane-parallel slab. However, if the gepmetrical parameters are spatially varied, then the refractive index is changed as well and the meta-foil can take on almost arbitrary optical functions. For example, a linear variation of the refractive index makes the slab

a prism and a quadratic variation makes a cylinder lens. Quite unusual optical functions may be achieved by this method.

Meta-foils are manufactured by means of 3-level UV/X-ray lithography and related processes from the LIGA process network.

Accordingly, the meta-foil design is divided into three layers, 908,912,914 such as that shown in Figure 17, which shows part of the meta-foil 840 comprising bi- layer S-shape structures 844 suspended in space by interconnecting rods 845, and which also shows definitions of dimensions of the meta-foil 840. The bottom layer 908 contains all conductors of the S-shape structures 844 which are parallel to the y-z plane, the middle layer 912 the "vias" that run along the x- direction and the interconnecting rods 845 that extend along the y-direction, and the top layer 914 also contains all the conductors of the S-shape structures 844 parallel to the y-z plane. The top layer structure is related to the bottom layer structure by a translation along z by (a-h)/2, where "a" and "h" are parameters defined in Figure 17. Accordingly, only two masks are fabricated, one for the bottom and top layer (mask 1 ) and one for the middle layer (mask 2). An exemplary process will now be described to produce the structure shown in Figure 11 a using UV lithography based on parameters shown in Table 1 below to lead to resonance around 3 to 4 THz, although as mentioned earlier, this may also be implemented by X-ray lithography.

Table 1 : Design values of main parameters (all in μm)

The alignment between levels of lithography is obviously very important. In order to keep the resonance frequency within 10 % of the nominal value, the spatial resolution of the alignment must be less than 20% of the gap between adjacent S-strings as this gap determines the capacitance and thus the resonance frequency of the meta-foil.

The exposures start with the bottom layer. Referring to Figure 14a, a substrate 900 is provided and in this embodiment, this is a 4" silicon wafer which is cleaned with acetone, isopropyl alcohol (IPA), de-ionised water and dried. The dried wafer is next cleaned with O ₂ plasma and then a Cr/Au plating base 902 is deposited by sputtering at step 850. Next, at step 852, a first AZ9260 resist layer 904 of 5 μm thickness is deposited by spin coating (about 3500 rpm/35 sec), and soft baked at 95 ⁰ C for three minutes.

At step 854, the baked resist layer is exposed under UV light by using a Karl Suss Mask & Bond Aligner and exposed AZ resist is removed during development with AZ 400k developer, resulting in the resist layer 904 being patterned with all the conductors 846 of the S-shape structures 844 which are parallel to the y-z plane. The end result is shown schematically in Figure 18a

(without showing the substrate 900). At step 856, the conductors 846 of the S- shape structures 844 are electroplated with Au to form the first layer 908 of the three layers of the metamaterial.

Next is the formation of the second layer 912 and this is depicted in Figure 14b. The first layer 908 is next hard baked at 100 ⁰ C for 30 minutes and an Au layer 910 of about 100 nm thickness is sputter deposited as a plating base at step 858 to isolate the first layer 908 from the second layer 912. Next, at step 860, a second AZ9260 resist layer 913 of the same thickness as the first resist layer 904 is spun on at 3500 rpm for 35 seconds and soft baked at 95 ⁰ C for 3 minutes. At step 862, this already structured substrate is now stacked together with the mask 2 and exposed under UV light using Karl Suss Mask & Bond Aligner for the formation of the "vias", which interconnects the first and the third layers 908,914, the interconnecting rods 800 and portions 847 of the S-shape structures at the second layer 912. Here, an accurate alignment of the mask 2 relative to the conductor structure 846 of the bottom layer 908 is required.

After the second exposure, the exposed AZ resist of the second layer 912 is removed using AZ 400k developer and the patterned second layer is used as a mould for gold plating of the second layer 912. A schematic diagram of the patterned second layer which shows the interconnecting rods 800 and portions 847 of the S-shape structures is shown in Figure 18b. Then, at step 864, the vias and interconnecting rod structures 800 are electroplated with Au in the resist voids to complete the second layer 912.

Next is the formation of the third layer 914 and this is depicted in Figure 14c. The intermediate product after step 864 is then hard baked at about 100 ⁰ C for 30 minutes and at step 866, an Au layer 916 of about 100 nm thickness is sputter deposited as a plating base to isolate the second layer 912 from the third layer 914. Next, at step 868, a third AZ9260 resist layer 918 of the same thickness as the first resist layer 904 is spun on (3500 rpm/35 seconds) and soft baked at 95 ⁰ C for 3 minutes. This already doubly structured substrate is now stacked together with the mask 1 again and exposed under UV light by using the Karl Suss Mask & Bond Aligner at step 870 for the formation of top conductor layer 920 i.e. the remaining portions of the S string structures. Here, an accurate alignment of the mask 1 relative to the already existing conductor structure of bottom and middle layers 908,912 is required taking into account the translation along z by (a-h)/2.

The exposed AZ resist from the third layer 914 is removed again with AZ 400k developer and the patterned third layer of AZ resist is used as a mould for the gold plating process. At step 872, Au electroplating is carried out on the top layer S strings 920 to build the third layer 914, and the completed product is shown in Figure 18c

The final steps of the process are illustrated in Figure 14d to release the S- shape structures from the substrate 900 in order to obtain the meta-foil suspended in space. At step 874, a resist remover (such as AZ(R) 400T

photoresist stripper) is used to remove the unwanted AZ resist layers 904,912,918, and the Au film by an Au etchant. Finally, at step 876, the top layer conductors 920 of the S-strings and the lower layer conductors 846 of the S-strings supported by the interconnecting rods 800 are released from the substrate 900 by etching the Cr sacrificial layer 902. It should also be appreciated that the width of the interconnecting rods 800 between bi-layer S- shape structures 844 also defines the gap width between the S-shaped structures 844.

To keep the resonance frequency within 10 % of the nominal value, the spatial resolution of the alignment must be less than 20% of the gap between adjacent S-strings as this gap determines the capacitance and thus the resonance frequency of the meta-foil.

It is noted that the 3-level UV lithography approach may be translated into a plastic moulding process as well so that, in the end, the manufacturing of index- gradient meta-foils may rely on an inexpensive manufacturing method in industry nowadays. This is the way to the mass-production of metamaterials based on the index-gradient meta-foil. Figure 15a shows a first half of a mould insert for injection moulding. A second half that needs to be put on top is configured in the same manner as the first half and is laterally shifted by d+t along the interconnecting rods or lines. The polymer used for injection moulding can be either conducting or non-conducting. In the first case, the final metalisation can be done by electroplating, and in the second case of non-

conducting, by sputter deposition. The manufacture of the mould inserts would also rely on the LIGA process involving three-level lithography.

The spectral response of the metamaterial 100 was characterized by Fourier Transform interferometry (FTIR) in the far infrared around 2 THz. Synchrotron infrared radiation from the edge-effect source of the Helios 2 storage ring at SSLS was used for the experiments. Measured spectra are compared with numerical simulations using commercial software MWS™ and the following summarises the results.

Spectral characterization

For spectral characterization, a bi-layer metamaterial chip produced according to the first embodiment is positioned on a rotational stage in the sample chamber of a Bruker IFS 66 v/S Fourier transform interferometer. The rotation axis is parallel to the string direction as is the electric field vector of the incident radiation. Synchrotron radiation at the ISMI beamline of SSLS is used as a source. The beam spot on sample is about 1 mm wide horizontally and 0.4 mm vertically: A far infrared (FIR) polarizer (gold grid on polyethylene substrate) is introduced before the sample. Transmission spectra are acquired by means of a DTGS detector comparing signals with and without samples. The spectra are taken from nearly 1 THz up to 10 THz with a resolution of 0.12 THz (4 cm ^"1 ). The incidence angle α is varied from normal incidence 0° up to 60°. In this way, the magnitude of the magnetic field component perpendicular to. the inductance loop is varied. Using the transmission of SU-8 in the THz range as measured

[re: B. D. F. Casse, H. O. Moser, J. W. Lee, M. Bahou, S. Inglis, and L K. Jian, Appl. Phys. Lett 90, 254106-1 - 254106-3 (2007)], namely, 0.93 for 25 μm at 1 THz, it is estimated that one leg of the window-frame would have a transmission of 3.9- 10 ^'4 , thus ruling out measurements under 90° incidence angle.

The sample chamber is evacuated to a level of 4 mbar of dry nitrogen gas in order to avoid signal contributions from water vapour and other gases. The geometrical dimensions of the bi-layer chips as built are measured by means of a scanning secondary electron microscope (SEM, FEI Sirion), an optical profiler (WYKO) and an optical microscope (Leica).

Measured and simulated spectral results

Figure 12 compares three pairs of measured and simulated transmission spectra which differ only by the gap width. The geometrical parameters are the same for all three samples as given above, except for the interlayer gap which is 0.6 μm, 1.1 μm, or 6.1 μm wide. For simulation, CST's MWS™ package is used. The basic features of the measured spectra are reproduced by the simulated ones. In particular, in the case of normal incidence (α=0°), there are two prominent pass bands measured at 2.2 THz and between 2.6 to 2.8 THz which can be found as peaks at 2.1-2.4 THz and 2.7-3.6 THz in the simulation. The apparent difference in frequency may be caused by errors in the measured parameters of the bi-layer chips, in particular, the gap.

The dependence of the peak position on incidence angle is also well reproduced for the two smaller values of the gap (0.6 μm, 1.1 μm), whereas it deviates more significantly for the large gap of 6.1 μm. This dependency is related to the fat aspect of the conductors because location and size of a resonance loop as defined by the actual current flow may vary with the incidence angle, thus changing inductance and capacitance.

Finally, the big peak at 90° incidence angle shown by the simulation cannot be observed experimentally due to the complete obstruction by the window-frame. From a robust retrieval algorithm [Re: Xudong Chen, Tomasz M. Grzegorczyk, Bae-lan Wu, Joe Pacheco, Jin Au Kong, Phys. Rev. E 70, 016608-1 - 016608- 7(2004).], values of the effective permittivity ε and permeability μ are obtained which show that the lower frequency pass band around 2.2 THz is left-handed involving a magnetic resonance (Figure 13). This finding was further confirmed by phase tracking that showed backward wave propagation inside the bi-layer. In contrast, the higher frequency pass band between 2.7-3.6 THz is an electric resonance with both ε and μ positive and thus right-handed.

In this normal incidence case, the magnetic field vector is parallel to the x axis. Inductive coupling to the S-strings is possible nonetheless because the inductance loop that is formed by legs b, °, and b in the top and, with opposite

orientation, in the bottom layer lies in a plane inclined by an angle of tan φ = (d -f t) f{b - (7ι — k')/l) which is about 30° with respect to the xz plane

for the gap d=0.6 μm. From one half-S loop to the next, the sign of this inclination angle alternates.

Based on the described processes, it can be appreciated that micro- manufacturing of electromagnetic metamaterials based on precisely aligned freely-suspended matrix free bi-layers of S-string resonators over a comparably large area may be achieved. Further, it can be appreciated that by using UV and/or X-ray lithography, this is restricting the time-consuming primary pattern generation by e-beam or laser beam writing only to the initial mask making. Also, the lithographic approach offers control of the resonance frequency over a wide range. The metamaterial devices built based on the described embodiments exhibit left-handed pass bands around 2.2 THz, and this development opens up applications for large area THz electromagnetic metamaterials in fields including infrared optics and imaging. Still larger areas will be accessible via possible extensions of the process. As micro/nanomanufacturing allows a variation of the geometry of the strings within a broad range, resonance frequencies can be adapted to values as required by applications.

The described embodiments should not be construed as limitative. For example, in the first embodiment, the window frame is made of SU-8, a polymeric material but numerical simulations show that the window frame may well be metallic. Further, although an S-shaped resonator is described but other types of resonators, such as C-shape, U shape resonators having corresponding shaped bi-layer structures may be used. Also, in the case of

Figure 5, it may not be necessary to fabricate two spacers and one spacer supported by a frame member may be used since the devices are symmetrical.

In the second embodiment, the meta-foil produced is supported at selected locations by interconnecting rods. However, it is envisaged that a meta-foil with a window frame may also be produced using the process of the second embodiment. Each of the three layers 908,912,914 are similar produced but instead of forming vias and interconnecting rods at the second layer 912, each of these layers are built with a layer of the window frame and after completing the three layers which complete the S-shape structures, a fourth layer of 15μm thick window frame is formed resulting in a total thickness of the window frame to be about 30μm with the meta-foil to be about 15μm. A simplified view of such a meta-foil 980 is shown in Figure 19a with the window frame 982. It is also envisaged that the meta-foil 980 may be stacked with the window frame 982 being used as a spacer between adjacent meta-foils 980 and this is shown in

Figure 19b. ..

Having now fully described the invention, it should be apparent to one of ordinary skill in the art that many modifications can be made hereto without departing from the scope as claimed.