1. Introduction

Recently, there has been significant interest in the fabrication and application of quasi-periodic structures [1–13] and metallic structures [14–22]. The quasi-periodic structures consist of higher rotation symmetries than conventional photonic crystals, affecting their optical properties. And the excitation of surface plasmon (SP) resonances introduces a variety of unusual optical phenomena in metallic structures. In this paper, a combination of metallic structures and quasi-periodic structures is used to exploit the optical properties of metallic quasi-periodic structures.

A variety of fabrication method, including holography lithography [2,3,5,6,9,12], direct laser writing[7], optical induction technique[8], phase-mask lithography[12], have been used to fabricate different quasi-periodic structures. Multi-beam interference lithography is a very flexible and inexpensive technique to fabricate large-area intriguing interference patterns. The metallic structures can be generated in association with usual evaporation and lift-off process [23].

Here, a robust multi-beam interference lithography setup is employed to generate the intriguing quasi-periodic patterns. In association with thermal evaporation and lift-off process, the prepared templates are used to create metallic quasi-periodic structures. The optical properties of two-dimensional (2D) metallic quasi-periodic structures are demonstrated in the transmission experiments.

2. Experiments

In this work, a He-Cd laser (325nm and 442nm, Kimmon Electric Co.) is used as a light source for multi-beam laser interference lithography. In the robust experimental setup employed here, the laser beam is focused by a plano-convex lens onto a pinhole with a diameter of 10µm. The laser beam is expanded and re-collimated behind the pinhole, and subsequently separated into three peripheral beams (arranged symmetrically at an angle of 120° to one another in the plane normal to the propagation direction) and one central beam, as shown in Fig. 1. An interference pattern in the sample plane is generated using these four beams by means of three mirrors. Each of the side beams forms an angle θ with the central beam. The three side beams are represented by wave vectors:

Here, n=1, 2, 3. k=2π/λ, λ is the wavelength of the laser light inside the photoresist. β is the incident angle inside the photoresist between the three side beams with the central beams, and β is defined by the angle θ for a given exposure wavelength and photoresist. And the central beam is given by

The spatial distribution of light intensity can be expressed by

Here the reciprocal lattice vectors G_nm=k_n-k_m are determined by the differences of the wave vectors k_n of the incident plane waves and the form factors a_nm=E ⁰ _n·E ⁰*_m, resulting from the relative amplitudes of the incident laser beams. The interference pattern of multi-exposure is given by the following intensity distribution:

T is the exposure times, φ is the rotation angle.

 

Fig. 1. A schematic of experimental mirror setup for the multi-beam interference lithography. (a) the specially designed reflection mirror setup; (b) a schematic illustration of the four-beam geometry.

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To fabricate metallic quasi-periodic structures, a positive photoresist (AZ 1505) with a thickness of 200nm is spin-coated onto a glass wafer. After multiple exposures, the exposed areas of the photoresist are dissolved during development. A variety of intriguing interference patterns are generated in the photoresisit as a template. Subsequently, the metal films are thermally evaporated onto the template. A lift-off process is followed to remove the remaining photoresist, forming the metallic quasi-periodic structures. The overall sample size is around ~5mm², depending on the angle used during the exposure process.

3. Experimental results

The fabricated metallic periodic-quasi structures are characterized by scanning electron microscope (SEM, DSM 962 Carl Zeiss). Figure 2(a) shows SEM image of the fabricated 2D metallic structures in the interference area of the three side beams. The exposure wavelength is 442nm, and the angle θ is 22°. The metallic quasi-periodic structures are originated from the fundamental 2D structures (the period is approximately 775nm). For the 2D metallic quasi-periodic structures, the interference patterns are generated with multiple exposures. Figure 2(b) shows the fabricated metallic quasi-periodic structures with three exposures (at φ=0°, and then at φ=40°, finally at φ=80°). The interference patterns with rotation angle are not overlapped but reoriented to another direction with respect to the previous ones. Figure 2(c) shows the fabricated metallic quasi-periodic structures with four exposures (at φ=0°, and then at φ=30°, φ=60°, finally at φ=90°). A twelve-fold symmetry structure can be clearly observed on its top surface. The mismatch is caused by the fact that the rotation angle is not exact 30°. In the robust experimental setup employed here changing the angle θ and mutual alignment of interference beams is very easy, Figure 2(d) shows the fabricated metallic quasi-periodic structures with three exposures at the angle θ of 35° (at φ=0°, and then at φ=40°, finally at φ=80°). Compared with Fig. 2(b), the structures with smaller period can be generated by increasing the angle θ.

 

Fig. 2. SEM micrographs of fabricated metallic structures using the exposure wavelength at 442nm, (a),(b)&(c) the angle θ is 22°. (a) the fundamental 2D structures; (b) the quasi-periodic structures with three exposures at a rotation angle of 40°; (c) the quasi-periodic structures with four exposures at a rotation angle of 30°; (d) the quasi-periodic structures with three exposures at a rotation angle of 40° (the angle θ is 35°).

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4. Optical transmission with refractive-index sensitivity

The SP resonances, originating from the strong coupling between light and surface charges bound to the metal surface, are excited in the metallic structures with distinct frequencies. The SP resonances match the momentum conditions [15, 16]:

Where k_sp is the surface plasmon wave vector, k_x=(2π/λ)sinα is the component of the wave vector of the incident light that lies in the plane, α is the incident angle and α=0 for normal incidence, G_x and G_y are the reciprocal lattice vectors, depending on the periodicity a of the periodic metallic structures, and i and j are integers determining the SP propagation direction. Eq.(5) indicates that the SP resonances are determined by the geometry of metallic structures and the incident angle α. The metallic structures can fulfill the matching-momentum conservation to excite SP resonances. On the other hand, the SP resonances can be excited only if a metal surface supports them [15, 16, 24]:

Where ω is the optical frequency, c is the speed of light, and ε_d is the dielectric constant of the medium in contact with the metal and ε_m(ω) is that of the metal. From Eq.(6) it follows that the dielectric medium influence the excitation of the SP resonances.

An association of the momentum-matching conditions and the dispersion relationship can give a rough expression of the maxima transmission position:

Where n_d is the refractive index of the dielectric medium, where $n_d=\sqrt{{\epsilon }_d}$ , P is a geometry parameter depending on the metallic structures, for 2D square structure p=a(i ²+j ²)^-1/2 and 2D triangular array p=a[(4/3)(i ²+ij+j ²)]^-1/2 [16]. In the case of quasi-periodic structures, it’s difficult to give an accurate expression of the geometry parameter P, which is influenced by the intriguing structures and the period of the 2D metallic structures. It’s still in underway to obtain the detailed comparison with theory.

The transmission minima can also be observed as the result of Wood’s anomaly (light wave diffracted to pararell to the surface plane) [15,16, 25], which occurs when light waves are diffracted to move in the plane of the surface. The positions of Wood’s anomaly minima are approximately expressed by

The optical transmission is measured to characterize the SP resonances in metallic quasi-periodic structures for normal incidence. The excitation of a SP resonance will show up as a maximum in the transmitted light. The measurements are performed using a AQ-4303B white light source in conjunction with a AQ-6315A optical spectrum analyzer, and collimated microlenses with anti-reflection coating (ARC, 600~1050nm) are used for collecting light. Figure 3(a) demonstrates the measured transmission spectra of the metallic quasi-periodic structures (Cr/Au-3nm/30nm) as shown in Fig. 2(d). The same glass wafer coated with Cr/Au-3nm/30nm is used as the background spectrum. As the air/Au interface, the enhanced transmission peak is not very clear, and a small peak can be observed at 658nm. To demonstrate the sensitivity to the dielectric environment in contact with the metal surface, water (refractive index n:1.33) and immersion oil (refractive index n:1.515~1.517) are coated onto the top surface, altering the dielectric environment. When the interface is altered into water/Au interface, a clear transmission peak appears around 720nm due to an increase of refractive index n_d. When the immersion oil is applied to the water/Au interface, the transmission peak shifts to the long-wavelength 763nm, with a shift of 231nm RIU^-1(per refractive index unit). Moreover, a transmission minimum is seen around 678nm, which can mostly be attributed to the Wood’s anomaly.

Figure 3(b) illustrates the transmission spectra of the metallic quasi-periodic structures (Cr/Au-3nm/30nm) as shown in Fig. 2(c). As the light is incident from the air/Au interface, a clear transmission peak is observed around 732nm, and one transmission minimum is seen approximately 658nm. Compared with the spectra in Fig. 3(a), the differences are caused by the change of the period. When the immersion oil (refractive index n:1.29) is used to vary the dielectric environment, the transmission peak shifts to 982nm, accompanying with 862nm RIU^-1. ε_m is the wavelength-dependent, and influences the position of the enhanced transmission peak.

 

Fig. 3. The transmission spectra of the fabricated metallic quasi-periodic structures. (a) the quasi-periodic structures with three exposures at a rotation angle of 40° (the angle θ is 35°);(b)the quasi-periodic structures with four exposures at a rotation angle of 30° (the angle θ is 22°).

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These results exhibit the unusual optical properties of metallic quasi-periodic structures. The optical transmission is also influenced by the incident angle, and the optical transmission exhibits direction dependence for oblique incidence, which is beyond the scope of this paper. It’s the first step to investigate the intriguing optical properties of metallic quasi-periodic structures. The metallic quasi-periodic structures can be used as a template to create refractive index sensors.

5. Conclusions

In summary, the fabrication and characterization of 2D metallic quasi-periodic structures are described in this paper. In association with thermal evaporation and lift-off process, the 2D metallic quasi-periodic structures are generated using the robust multi-beam interference lithography setup. A twelve-fold symmetry structure can be clearly observed in fabricated structures with four exposures. The excitation of SP resonances, which are determined by the geometry of metallic structures, and the refractive index n_d of the adjacent dielectric medium, are demonstrated in the optical transmission experiments. The optical transmission of metallic quasi-periodic structures can be tuned by varying the refractive index n_d and changing the period a.