1. Introduction

Artificial metamaterials are attracting increasing interests due to their distinguishing electromagnetic properties from naturally occurring materials such as negative magnetic permeability and negative refractive index [1–3], which make the materials potential applications in various technological realms such as invisibility cloaking [4], negative refraction [5], super-resolution imaging [6], and planar slab lensing [7]. So far, considerable progress has been made in fabricating diverse structures of metamaterials including double split-ring resonator (SRR) arrays [1,5,8-10], double-split rings [11,12], single SRR structures [13], U-shaped structures [14,15], pairs of nanorods/cut-wire pairs [16,17] and circular/ellipsoidal voids [18,19] etc. have been demonstrated theoretically and experimentally to have negative permeability or negative refractive index in the ranges of from microwave to optical frequency. These new materials are generally fabricated step-by-step by conventional lithography [14, 15], which is relatively slow and an expensive process at the limit of current technology for operating at optical frequency. A high throughput fabrication method for optical metamaterials with a combination of advantages such as fast fabricating time, low cost, easy operation process, well reproducible precision for large-scale production remains a considerable challenge at the moment. Here, we show a single-beam holographic lithography to generate diverse metamaterial structures by using an optical prism to arrange the interference beams [20–24]. Cylindrical nanoshells, U-shaped resonator arrays, and double-split ring arrays are obtained respectively by real time modulating the phase relation of the interference beams. This easy-to-use method can resolve the above challenge and overcomes the constraints of multi-beam interference technique requiring very stable optical devices and precise and complicated adjustment systems [24].

2. Theoretical design and experimental procedures

We design a symmetrically top-cut hexagonal prism (TCHP, made of BK7 glass with refractive index n =1.52 ) to split a collimated laser beam into seven interference beams by the top- and six side-surfaces of the TCHP firstly and then to automatically reassemble the seven beams together under the bottom of the TCHP to form the interference patterns. Figure 1 shows the schematic for the TCHP (left) and the beam arrangement (right) formed under its bottom. The TCHP has symmetric equilateral hexagonal bottom and top surfaces with side lengths L = 24mm and l = 5.39mm , respectively, and height h = 22mm . The angle between the side- and bottom-surfaces of the TCHP is γ = 53.77° [Fig. 1, left], which makes the side surface refracted beams κ ₁ - κ ₆ symmetrically surrounded the z axis with δ = 34.23° in free space under the bottom of the TCHP [Fig. 1, right]. The wave vectors of beams K ₁ - K ₆ can be read as K _m=k [sin mϕ sin (δ)i + cos(mϕ) sin(δ)j + cos(δ)k], where m=1,2,…6, i , j , and k are the unitary vectors in the x, y, and z directions, respectively, ϕ=π/3 is the azimuth angle of the six beams. Figure 2(a) shows the simulated interference patterns under the bottom of the TCHP. In the simulation, the polarization direction of laser beam and the phases of beams K ₁ - K ₆ are assumed to be the same as that in our experiment.

 

Fig. 1. Structure of TCHP (left) and the wavevectors of K ₀ -K ₆ (right) under the bottom of the TCHP.

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As a positive photoresist film (photolysis will take place in the exposed resist) is used to record the resultant interference pattern as shown in Fig. 2(a), we can obtain cylindrical nanoshells (black interference rings in the figure) in the resist films in principle since the exposed positive resist (around points A and B of Figs. 2(a), 3(a), and 4 (a)) will be removed completely in the developing process. From Fig. 2(a) we see that the exposed areas around point B do not show high enough intensity contrast comparing with unexposed areas (dimmest areas surrounding point A) where the resist will be maintained (similar case appears in Figs. 3(a) and 4(a)). To improve the intensity contrast of exposed and unexposed portions in the resist films for facilitating the experimental realization of requested structures, we introduce an auxiliary beam K ₀ by modulating its phase to ψ ₀ = ψ+(2q++1)π (π is the initial phase of the incident laser beam at the top surface of TCHP, q is an integer) into the interference beams. K 0 is resulted from the light beam directly passing through the top-bottom surface of the TCHP. Figure 2(a) shown is the simulated interference pattern as the auxiliary beam K 0 is involved into the interference, in which a single cell is denoted by dot curve (same in Figs.3 and 4). Obviously, the intensity contrast between the exposed and unexposed areas is greatly enhanced comparing with Fig. 2(a). On the other hand, as a 3D interference pattern, the intensity contrast is also dependent on the sampling location in the z direction. Therefore, in our experiments we chose the position of the recording films placed by a scanning charge coupled device (CCD) along the z direction to look for a higher intensity contrast to record the interference patterns. The phase relation among the interference beams is achieved by dropping a drip of index matching oil on the corresponding surfaces of the TCHP and pressing the oil film with a glass bar to modulate the thickness of the oil film. With different thickness of the oil film, we can get a required phase relation of the interference beams due to the variation of the optical paths of light beams. This process is accomplished by using a CCD to real time monitor the interference patterns in different interference regions under the bottom of the TCHP. When the requested interference patterns such as that shown in Figs. 2(b), 3(b), and 4(b) appear on CCD screen, the phase modulation process is accomplished.

Notice that when K 0 is interfered with beams K 1 - K 6 , a three-dimensional interference pattern will be formed [20–22]. The periodicity of the interference pattern in the z direction is d_z = λ / [sin(δ)tan(δ/2)] = 2542nm (λ=442 nm in our experiment), which is much larger than the thickness of the photoresist films obtained in our experiment (see below). Figure 2(c) shown is the pattern of Fig. 2(b) transferring into the positive photoresist films with 1000 nm thickness. We see that the resultant structures obtained can in fact be regarded as a two-dimensional lattice (see Figs. 2(d) and 2(e)). By further thinning the thickness of the photoresist films (for example, we can get a thinner than 150 nm thick photoresist film by diluting the resist solution), we can get a perfect 2D structures.

Optical setup for recording the interference patterns is from Refs.20–21. The positive photoresist (from S9918M PHOTO RESIST, Shipley Company) is diluted with deionized water (1:1 ) and then spun onto biological cover slides with spinning speed at 1000 rpm for 10 seconds firstly and then to 4000 rpm or 6000 rpm for 60 seconds (KW-4A Spin Coater, Type CG Vacuum Chucks, CHEMAT TECHNOLOGY INC.). After baking the coated slides at 90°C for about 15min to evaporating the solvent, we get 400 –1000nm thick resist films. The resist coated slide substrate is index-matched to the bottom surface of TCHP with a refractive index oil to reduce the effects of backward-reflected laser light. The recording light is a λ = 442nmlight beam irradiated from a He-Cd laser ( 70mW ) with a linear polarization direction perpendicular to the plane of recording platform. Exposure does in recording process is adjusted in the range of 60 – 90mJcm^-2 so that the required structures can be created in the photoresist films in the experiments. The developer is an alkaline Tetramethylammonium hydroxide (TMAH, (CH₃)4N(OH)∙5H₂O) aqueous solution (10% ). In order to effectively control over this etching rate in practice, we dilute the developer with distilled water at ratio1: 3–5 . In this case, developing process can be accomplished in 2–10 seconds. After rinsing the developed samples with deionized water and then hard baking them at 120°C for about 20min , the patterned samples were obtained.

3. Experimental results

 

Fig. 2. Simulated interference pattern under the bottom of TCHP by beams (a) K 1-K ₆ and (b)K₁-K ₆ plus the auxiliary K ₀. (c) Conversion of (b) into the positive photoresist films. d is the lattice constant. (d) SEM image of nanoshells with oblique view. Bar, 1μm . Inset: Normal view. Bar, 4μm (e) Magnified view of a portion of (d). Bar, 500nm .

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Figure 2(d) is a scanning electron microscopy (SEM) image (SIRION 200 TMP, FEI COMPANY with 40 deg oblique angle, same in Figs. 3(d) and 4 (d)) of the recorded microstructures in the positive resist film under the bottom of TCHP, confirming the formation of calculated cylindrical nanoshell contours as shown in Fig. 2(c). The cylindrical shells have 380nm core diameter and 100nm shell thickness. The inset shown is the normal view of the structures. We can see that a perfect circular void array is formed. Figure 2 (e) is a magnified view of a portion of Fig.2 (d), showing a perfect cylindrical nanoshell structure.

Following the demonstration that single SRR arrays can provide both electric and magnetic responses simultaneously at the same frequency range [13], U-shaped resonator arrays can push the magnetic response to telecom wavelength because U-shaped structures can effectively decrease the capacitance of capacitors [14,15]. To get U-shaped structure arrays, focused-ion-beam [14] and electron-beam lithography [15] are the crucial techniques at the moment. Here we use the TCHP to create such structures by real time changing the phase ψ ₆ of K ₆ from ψ to π + (2q+1/2)π but keeping that of K ₁ -K ₅ directly produced by the prism. In this case, the interference fringes formed by K ₁ -K ₅ interfering with K ₆ will respectively shift 1/4 period along the -K ₆ direction. As a result, each cylindrical shell as shown in Fig. 2(c) will be split to form U-shaped structures.

 

Fig. 3. Simulated interference patterns under the bottom of TCHP by beams (a)K ₁ -K 6 and (b) K ₁ -K ₆ plus the auxiliary K ₀. (c) Conversion of (b) into the positive photoresist films. d is the lattice constant. (d) SEM image of U-shaped arrays with oblique view. Bar, 1μm . Inset: Normal view. Bar, 4μm (e) Magnified view of a portion of (d). Bar, 500nm .

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Figure 3(a) shows the simulated interference pattern of beams K ₁ - K ₆ with the above phase relation. Similarly, the auxiliary beam K ₀ with phase ψ ₀=ψ+(2q+4/5)π is also introduced for producing the interference pattern a better intensity contrast [Fig. 3(b)]. Figure 3(c) is the conversion of Fig. 3(b) into the positive photoresist films. One can see that a U-shaped array is formed. By exposing the resist films to the interference pattern and then post processing the recorded samples, we get the resultant interference structure. Figure 3(d) is an oblique SEM view of the recorded microstructures in the positive resist film under the bottom of TCHP, and the inset shown is the normal view of the SEM images. Figure 3 (e) is a magnified view of a portion of Fig. 3 (c). We can see that the experimental result clearly shows a regular U-shaped nanoshell array, confirming the formation of predicted structures as shown in Fig.3(c).

In addition to Pendry’s double SRRs, which can mimic electronic circuits consisted of inductive and capacitive elements to produce a negative permeability [1, 5, 8, 9], planar metal double-split ring arrays can also produce a magnetic response [11,12]. By real time modulating the phase relation of beams K ₁ -K ₄ to ψ + 2qπ but that of K₅ -K ₆ to ψ + (2q +1/2)π , we can get such double-split rings. Figure 4(a) shows the simulated interference pattern of the six beams with the above phase relation. The auxiliary beam K ₀ with ψ ₀ = ψ(2q+3/2)π is also introduced for improving the intensity contrast of the interference pattern (Fig. 4(b)). Figure 4(c) shows the conversion of Fig. 4(b) into the positive photoresist films, displaying the formation of a double-split ring arrays. After exposure and post processing according to the procedure described in Section 2, we get the resultant interference structure. Figure 4(d) shown is an oblique SEM view of the recorded structures and the inset is a normal view. Figure 4(e) is the magnified image of a portion of Fig. 4(d). The figures demonstrate that the experimental results are well agreement with the calculated structures of double-split ring arrays (Fig. 4(c)).

 

Fig. 4. Simulated interference patterns under the bottom of TCHP by (a) beams K ₁ -K ₆ and (b) K ₁ -K ₆ plus the auxiliary K ₀ . (c) Conversion of (b) into the positive photoresist films. d is the lattice constant. (d) SEM image of U-shaped arrays with oblique view. Bar, 1μm . Inset: Normal view. Bar, 4μm (e) Magnified view of a portion of (d). Bar, 500nm .

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It should be pointed out that we focus our attention on the holographic realization of structures of the metamaterials that have been widely demonstrated both theoretically and experimentally (obtained by other lithographic techniques) to have interesting electromagnetic response [11–14, 18, 19]. To achieve the realistic metamaterials, we have to transfer the interference patterns into metal materials. This work is currently on going in our group and will be reported in an oncoming paper.

4. Conclusion

In conclusion, we have demonstrated a robust holographic lithography to generate diverse structures for optical metamaterials, including cylindrical nanoshells arrays, U-shaped resonator arrays, and double-split ring arrays just by real time modulating the phase of different interference beams produced by an optical prism. This easy-to-use technique may provide a roadway for the design and fabrication of future metamaterials requiring diverse structures for effectively manipulating electromagnetic properties at optical frequency.