1 Introduction

Micro/nano structures occurring upon the surfaces of some objects can alter their original surface characteristics. These surface functional characteristics include the surface’s optical response, wettability, and friction. The optical functions generated by surface structures include anti-reflection [1], photonic bandgap [2], and wave plate-like control of polarization [3]. Wettability is related to functions such as super-hydrophobicity [4] and anti-fogging [5]. These controlling surface structures can also contribute to reducing friction at the boundary between two materials [6]. It has been reported that highly effective functional surface structures occur in nature. Significant effort is currently therefore being directed into the study of microfabrication technologies to mimic and produce these micro- and nanostructures. Some naturally occurring functional structures are difficult to fabricate because they are fine and complex structures, for example the anti-reflection function of moths’ eyes, or the super-hydrophobicity of lotus leaves. Additionally, the number of applicable fabrication methods will be lesser if partially different regions which are such fine and complex structures need to be included in the same surface like photonic crystal with artificial defects or micro droplet manipulation devices with an anisotropic structured surface.

Scanning electron microscope (SEM) images of a moth’s eye are shown in Fig. 1 as an example. One typical naturally occurring functional structure is the dual-scale structure, which consists of two different-sized protrusions. In particular, the size of the smaller protrusions in this structure is equal to or less than ~ 200 nm in diameter, which is especially important in order to express optical properties such as antireflection in the visible region without the effect of diffraction and scattering.

Fig. 1
figure 1

Scanning electron microscope (SEM) images of a moth’s eye: a is 1000 (magnification) image, showing the micro-ordered array of hexagonal lenses; b is 20,000 (magnification) image — ~ 200-nm protrusions are arrayed on the lens surface

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A low-cost, high-speed special fabrication technique is needed to synthetically produce such biomimetic relief structures; however, as will be described below, it is difficult to achieve this via the conventional established methods. Combinations of semiconductor processes such as photolithography, electron beam lithography, and etching can produce micro- and nanostructures; however, the associated costs are extremely high, and they are very time-consuming. Although low-cost processes such as nanoimprint lithography and directed self-assembly lithography have been developed, both have low flexibility [7].

To fabricate fine and complex structures, three-dimensional (3D) processes can also be used. The 3D processes can be classified into two types: batch exposure type and scanning type. Batch surface exposure type micro-stereolithography is a rapid prototyping process, which is a batch exposure type of 3D process. It can fabricate 3D complex structures, but the smallest units it is able to process are on the order of several micrometers [8, 9]—much larger than the target. Two-photon micro-stereolithography and focused ion beam additive process are 3D scanning processes of scanning type; the resolution is satisfactory, but its process speed is low.

In addition to the above, methods using a short pulse laser have been proposed recently to produce functional micro-structured surfaces [10]. Two-photon micro-stereolithography as mentioned above is one of the micro fabrication methods using short-pulse lasers. Other than this, an anisotropic superhydrophobic surface, which has rachet-like microstructures, was able to be obtained by the laser ablation using a nano-second laser [11]. Also, laser-induced periodic surface structures (LIPSS) are applied to alter surface wettability [12]. However, the smallest process size of laser ablation is more than 1 μm in practice, and uniformity of each micro structure in LIPSS is low, which causes scattering.

In this paper, we focus on interference lithography (IL) to achieve the target fabrication. IL has been investigated as a potential microfabrication process for micro- and nano-periodic patterns, such as gratings. This process has the advantage of being relatively inexpensive and fast. Various studies have applied IL techniques to the fabrication of surface grating structures, in which surface reliefs such as one-dimensional (1D) lattices, square lattices, and hexagonal lattices have been fabricated [13,14,15]. Although IL is inferior to semiconductor processes in terms of its process flexibility, it is still suitable for fabricating periodic relief structures because it uses more than three beams, and can therefore generate five kinds of patterns (i.e., two-dimensional Bravais lattices) [16]. In terms of dual-scale structure, there is the process through which micrometer-scale dual-scale relief patterns are fabricated by four-beam IL [17]. Micrometer-scale and sub-micrometer-scale relief patterns fabricated by multi-exposure IL process have been reported [18]. The smallest pitch of the latter process is about 300 nm; however, it is slightly insufficient for optical applications. Although IL techniques are superior, as mentioned above, the fabrication of structures with fineness values < 200 nm has still proved to be problematic. The fineness of a structure is determined by the period of an interference fringe pattern that depends on wavelength of a light source, the refractive index, and the incident angle. In the air, the theoretical minimum period of a fabricated pattern is half of the wavelength of the incident light when two beams are in the perfect counter direction, which means incident angles are 90°. In practice, exposure with the perfect counter direction is impossible, and the period is therefore larger than half of the wavelength. Thus, a normal IL technique using a low-cost light source, such as a visible light laser or an ultra-violet (UV) near visible light laser, cannot fabricate the target biomimetic relief structure.

IL using evanescent waves (EWs) has therefore been studied as a way of exceeding this fineness limitation of half of the wavelength. When total internal reflection (TIR) occurs at a boundary between two different mediums, an EW is generated near the boundary surface, on the low refractive index side. This light energy is highly localized because it decays exponentially with increasing distance from the boundary at which TIR occurs, which can make its resolution exceed diffraction limit. Thus, EW is used in the field of observation and measurement such as measuring thickness of a thin film [19, 20]. Furthermore, the wavelength of the EW corresponds to the wavelength of the incident light in the high refractive index medium, and the period of the pattern generated by evanescent wave interference lithography (EWIL) can therefore be made smaller than half of the wavelength of the light source. Some conventional studies on EWIL [21,22,23] have carried out fabrication of a hexagonal lattice and a square lattice by multi-beam IL. Regarding dual-scale structures, there is a study in which four-beam EWIL is applied to dual-scale structures that include fineness < 200 nm [24]. However, these conventional methods have various problems in terms of the flexibility of designing important optical conditions such as variability of the number of beams, the azimuth angles, and polarizations. Therefore, they cannot be applied to more complicated surface structures, for example, a structure including different fine and complex patterns in the same plane for each location or a structure with an artificial defect or an artificial channel for microfluid.

This paper proposes a highly flexible multi-beam EWIL (MBEWIL) system that uses a visible light source to fabricate a sub-half-wavelength complex relief structure with fineness values < 200 nm. Using a mathematical simulation, we theoretically analyze the basic behavior of forms fabricated by EWIL and confirm the potential of the method to fabricate relief patterns with sub-micron plural spatial periods, similar to certain surfaces that occur in nature (Sect. 2). We introduce our developed MBEWIL system using a visible light source and a simple optical assembly, which features a one-shot process and an improved process flexibility (Sect. 3), demonstrate some patterns that can be fabricated using the system, and confirm the validity of the theoretical analyses (first half of Sect. 4). Subsequently, we verify the feasibility of the proposed system by fabricating complex relief patterns, including a sub-half-wavelength periodic structure (latter half of Sect. 4).

2 Theoretical Analysis

2.1 Theoretical Model

In order to theoretically analyze the relationship between the optical condition and the form fabricated by MBEWIL, we visualized the fabricated structures corresponding to their input situations, such as the incident angles, azimuth angles, and polarization conditions of their respective beams. This subsection explains the theoretical model of the simulation, reflecting the practical situation that we assumed. The schematic of this method is shown in Fig. 2a. Photocurable resin was placed on a sheet of glass (which had a higher refractive index than the resin). Beams are incident from the glass side, and they have a larger incident angle than the critical angle, determined by the refractive indices of the resin and the glass. \(\theta_{1}\) and \(\varphi_{1}\) are the incident angle and the azimuth angle of light beam 1, respectively. In this image, three beams are incident, and interference pattern of the EW is generated at the superposed area on the boundary surface. The positive directions of electric field vectors of S and P polarizations are defined as shown in Fig. 2b. Here, \(\theta_{{\text{m}}}\) and \(\theta ^{\prime}_{{\text{m}}}\) are the incident angle and the transmitted angle of the mth beam, respectively. \(n_{{\text{i}}}\) and \(n_{{\text{t}}}\) represent the refractive indices of medium 1, which is assumed to be the glass, and medium 2, which is assumed to be the photocurable resin, respectively.

Fig. 2
figure 2

Coordinate system of a multi-beam evanescent wave interference lithography (MBEWIL). a Schematic image of a three-beam EWIL. b Definition of the electric field vectors of an incident beam and a transmitted beam at the plane of incidence

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The general equation of the electric field distribution, \({\varvec{T}}_{{\text{m}}}\), of the transmitted light of the mth beam in this situation can be expressed as follows:

$${\varvec{T}}_{{\text{m}}} = A_{{\text{m}}} {\varvec{P}}_{{\text{m}}} \exp \left[ { - {\text{i}}\left( { - {\varvec{k}}_{{\text{t,m}}} \cdot {\varvec{r}} + \phi_{{\text{m}}} } \right)} \right]$$
(1)

where \(A_{{\text{m}}}\) is the amplitude of the incident beam, \({\varvec{P}}_{{\text{m}}}\) is the electric field vector (including polarization information), \({\varvec{k}}_{{\text{t,m}}}\) is the propagation vector of the transmitted beam, \({\varvec{r}}\) is the position vector, and \(\phi_{{\text{m}}}\) represents the initial phase shift. In order to consider that the incident angle is larger than the critical angle, \({\varvec{k}}_{{\text{t,m}}}\) is deformed using Snell’s law, as shown in Eq. (2):

$${\varvec{k}}_{{\text{t,m}}} = n_{{\text{t}}} k\left( {\begin{array}{*{20}c} { - \sin \theta ^{\prime}_{{\text{m}}} \cos \varphi_{{\text{m}}} } \\ { - \sin \theta ^{\prime}_{{\text{m}}} \sin \varphi_{{\text{m}}} } \\ {\cos \theta ^{\prime}_{{\text{m}}} } \\ \end{array} } \right) = n_{{\text{i}}} k\left[ {\begin{array}{*{20}c} { - \sin \theta_{{\text{m}}} \cos \varphi_{{\text{m}}} } \\ { - \sin \theta_{{\text{m}}} \sin \varphi_{{\text{m}}} } \\ { \pm {\text{i}}\frac{{n_{{\text{t}}} }}{{n_{{\text{i}}} }}\sqrt {\left( {\frac{{n_{{\text{i}}} }}{{n_{{\text{t}}} }}\sin \theta_{{\text{m}}} } \right)^{2} - 1} } \\ \end{array} } \right]$$
(2)

When Eq. (2) is substituted into Eq. (1), it can be expressed as

$$\begin{gathered} {\varvec{T}}_{{\text{m}}} = A_{{\text{m}}} {\varvec{P}}_{{\text{m}}} \exp \left[ { \mp n_{{\text{t}}} k\sqrt {\left( {\frac{{n_{{\text{i}}} }}{{n_{{\text{t}}} }}\sin \theta_{{\text{m}}} } \right)^{2} - 1} \,z} \right] \\ \,\,\,\exp \left\{ { - {\text{i}}\left[ {\left( {n_{{\text{i}}} k\sin \theta_{{\text{m}}} \left( {\cos \varphi_{{\text{m}}} x + \sin \varphi_{{\text{m}}} y} \right) + \phi_{{\text{m}}} } \right)} \right]} \right\} \\ = A_{{\text{m}}} {\varvec{P}}_{{\text{m}}} \exp \left[ { - n_{{\text{t}}} k\sqrt {\left( {\frac{{n_{{\text{i}}} }}{{n_{{\text{t}}} }}\sin \theta_{{\text{m}}} } \right)^{2} - 1} \,z} \right] \\ \,\,\,\exp \left\{ { - {\text{i}}\left[ {\left( {n_{{\text{i}}} k\sin \theta_{{\text{m}}} \left( {\cos \varphi_{{\text{m}}} x + \sin \varphi_{{\text{m}}} y} \right) + \phi_{{\text{m}}} } \right)} \right]} \right\} \\ \end{gathered}$$
(3)

where \(k = 2{\uppi /}\lambda\) is the propagation constant and \(\lambda\) is the wavelength of the incident beam in a vacuum. Regarding \(\mp n_{{\text{t}}} k\sqrt {\left( {(n_{{\text{i}}} /n_{{\text{t}}} )\sin \theta_{{\text{m}}} } \right)^{2} - 1} z\), we used the negative value because the electric field of EW decays exponentially with increasing distance from the boundary at which total reflection occurs. \({\varvec{P}}_{{\text{m}}}\) is the summation of the electric field vectors of S polarization, \({\varvec{P}}_{{\text{m,S}}}\), and P polarization, \({\varvec{P}}_{{\text{m,P}}}\). These terms are respectively expressed as

$${\varvec{P}}_{{\text{m,S}}} = J_{{\text{m,S}}} \,t_{{\text{m,S}}} \left( {\begin{array}{*{20}c} { - \sin \varphi_{{\text{m}}} } \\ {\cos \varphi_{{\text{m}}} } \\ 0 \\ \end{array} } \right)$$
(4)
$${\varvec{P}}_{{\text{m,P}}} = J_{{\text{m,P}}} \,t_{{\text{m,P}}} \left( {\begin{array}{*{20}c} {\sqrt {1 - \left( {\frac{{n_{{\text{i}}} }}{{n_{{\text{t}}} }}\sin \theta_{{\text{m}}} } \right)^{2} } \cos \varphi_{{\text{m}}} } \\ {\sqrt {1 - \left( {\frac{{n_{{\text{i}}} }}{{n_{{\text{t}}} }}\sin \theta_{{\text{m}}} } \right)^{2} } \sin \varphi_{{\text{m}}} } \\ {\frac{{n_{{\text{i}}} }}{{n_{{\text{t}}} }}\sin \theta_{{\text{m}}} } \\ \end{array} } \right)$$
(5)

where \(J_{{\text{m,S}}} = \cos \alpha_{{\text{m}}}\) and \(J_{{\text{m,P}}} = \sin \alpha_{{\text{m}}} \exp \left( {{\text{i}}\beta_{{\text{m}}} } \right)\) are the S and P polarization components of the Jones vector, respectively. \(\alpha_{{\text{m}}}\) is the angle of the electric field vector from the positive direction of the S polarization component, \(\beta_{{\text{m}}}\) is the phase difference between the S and P polarization components, and \(t_{{\text{m,S}}}\) and \(t_{{\text{m,P}}}\) are the S and P polarization components of the Fresnel transmission coefficients, respectively. \(t_{{\text{m,S}}}\) and \(t_{{\text{m,P}}}\) are expressed as

$$t_{{\text{m,S}}} = \frac{{2n_{{\text{i}}} \cos \theta_{{\text{m}}} }}{{n_{{\text{i}}} \cos \theta_{{\text{m}}} + n_{{\text{t}}} \sqrt {1 - \left( {\frac{{n_{{\text{i}}} }}{{n_{{\text{t}}} }}\sin \theta_{{\text{m}}} } \right)^{2} } }}$$
(6)
$$t_{{\text{m,P}}} = \frac{{2n_{{\text{i}}} \cos \theta_{{\text{m}}} }}{{n_{{\text{t}}} \cos \theta_{{\text{m}}} + n_{{\text{i}}} \sqrt {1 - \left( {\frac{{n_{{\text{i}}} }}{{n_{{\text{t}}} }}\sin \theta_{{\text{m}}} } \right)^{2} } }}$$
(7)

The electric field distribution, composed of EW interference by \(N\) beams, can be described as

$${\varvec{T}} = \sum\limits_{{\text{m = 1}}}^{N} {{\varvec{T}}_{{\text{m}}} }$$
(8)

The intensity distribution, \(I\), that influences curing photocurable resin is expressed as

$$I = \frac{1}{2}{\varvec{T}} \cdot {\varvec{T}}^{ * }$$
(9)

Spaces where \(I\) is larger than the curing threshold, \(I_{{\text{e}}}\), are regarded as being cured resin areas in the simulation.

2.2 Basic Characteristics of Multi-beam Interference Lithography Using Evanescent Wave

The purpose of this section is to show simulation results that describe the basic behavior of MBEWIL, and therefore to demonstrate that our target sub-half-wavelength complex relief structures can theoretically be fabricated. The simulation conditions were determined as follows: the wavelength of the incident beam was 488 nm, the refractive indices of the glass and the photocurable resin were 1.78 and 1.5, respectively, and the incident angle was 65°. In this situation, the critical angle is 57.4°, and the set angle is larger than the critical angle. These constants correspond to the specifications of the MBEWIL system developed and described in the following section. The curing threshold was set at 0.05. When the curing threshold is 0.05 and the other conditions are as mentioned above, the thickness of the cured resin is ~ 200 nm, which is comparable to resin cured by EW in a similar experimental situation [25]. The variables are the number of lights, the azimuth angles, the incident angles, the amplitudes, the initial phases, and the polarization. Of these, the especially dominant variables are the number of incident beams, the azimuth angles, and the polarization. In order to confirm how forms cured by EWIL were changed by the initial conditions, forms fabricated by two-beam EWIL were simulated, with the azimuth angles being changed in two cases, S and P polarization, as shown in Figs. 3 and 4. In these figures, φ(0,30) means that the azimuth angles of beams 1 and 2 are 0° and 30°, respectively.

Fig. 3
figure 3

Two-beam EWIL with S polarization. The azimuth angle of beam 2 was increased by 30° for each simulation, from 30° (a) to 180° (f)

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Fig. 4
figure 4

Two-beam EWIL with P polarization. The azimuth angle of beam 2 was increased by 30° for each simulation, from 30° (a) to 180° (f)

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The difference between the two azimuth angles is defined as the facing angle. The facing angles increase in 30° increments from (a) to (f) in Figs. 3 and 4. One common feature between S polarization IL and P polarization IL is that the period decreased as the facing angle increased. The contrast of the fringe in each facing angle was not consistent, however. Typically, the facing angle was 90°. Although the fringe pattern can be seen in Fig. 4c, the form of Fig. 3c is flat. This is because while interference occurred through the z-direction component of the electric field vectors of the P polarization beams, the electric field vectors of the S polarization beams were orthogonal, and therefore did not interfere with each other. The contrast in the fringe patterns generated by the S polarization beam interferences decreased as the facing angle changed from 0° to 90°, where the form was perfectly flat, and then increased from 90° to 180°. The contrast of the fringe pattern generated by the P polarization beams decreased from 0° to 180°.

When the number of beams was increased to three or more, the relief pattern became more complex. Figure 5 shows example forms fabricated by MBEWIL; specifically, it shows 12 relief patterns of three-beam EWIL with P polarization. The azimuth angles of beams 2 and 3 were changed by 30° in each case. φ(0,30,60) means that the azimuth angles of beams 1, 2, and 3 are 0°, 30°, and 60°, respectively.

Fig. 5
figure 5

Three-beam EWIL with P polarization. The azimuth angles of beams 2 and 3 were increased by 30° in each case. These 12 conditions cover all forms, excluding point symmetric and line symmetric duplication

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As shown in Fig. 5, the surface structures fabricated by MBEWIL were so complex that we had difficulties in supposing the pattern corresponding to a particular optical condition, and therefore in arbitrarily designing the target structure. Now, we focus on the fact that both large and small periodic fringe patterns were superposed in these structures. Each periodic fringe pattern was produced by a certain beam-pair combination. Therefore, \(_{N} C_{2}\) spatial periodic fringes were generated in each structure fabricated by MBEWIL; examples are shown in Fig. 6. Figure 6a shows the surface pattern generated by P polarization three-beam EWIL; it features three spatial periods produced by P polarization interference combinations of φ(0,90), φ(0,180), and φ(90,180). Figure 6b shows the structure generated by P polarization four-beam EWIL; there are six spatial periods produced by the combination of φ(0,30), φ(0,150), φ(0,240), φ(30,150), φ(30,240), and φ(150,240). These observations suggest that it is possible to control the design of a surface’s form to some extent by controlling the direction and the period of each fringe generated by a pair of beams. This can be done by adjusting the number of beams and the azimuth angles.

Fig. 6
figure 6

a Surface patterns generated by a three-beam MBEWIL, consisting of three combinations of 1D patterns. b Surface patterns generated by a four-beam MBEWIL, consisting of six combinations of 1D patterns

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2.3 Designing Optical Conditions for Mimicking Naturally Occurring Surface Relief Structures

As mentioned in Sect. 1, naturally occurring functional surfaces typically exhibit dual-scale relief structures, including structures that are smaller than the sub-half-wavelength of visible light. To replicate such fine and complex structures, in this work we intentionally mixed the optical conditions for both large and small periodic patterns. Regarding the design of the optical conditions required for this purpose, we proposed a three-way incidence of narrow-angle two-beam pairs. Although each narrow-angle two-beam pair generated only a large periodic pattern, three-way incident beams, each separated by 120°, resulted in sub-half-wavelength periodic fringes. Figure 7 shows the simulated results for the proposed optical conditions, i.e., a three-way incidence of narrow-angle two-beam pairs. Figures 7a and b show S polarization beams and P polarization beams, respectively. Two different-sized protrusions, arranged in approximately hexagonal lattice patterns, were observed in the relief structures. These results reveal that the MBEWIL technique and the proposed optical condition have the potential to fabricate the target dual-scale structures, which have sub-half-wavelength fineness.

Fig. 7
figure 7

Simulated sub-half-wavelength fine and complex relief structures generated by the proposed three-way incidence of narrow-angle two-beam pairs, in which two beams with 20° facing angles are incident from three directions (each separated by 120°). a S polarization. b P polarization

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3 Development of Flexible EWIL System

3.1 Concept of the Flexible EWIL System

In the previous section, we analyzed the basic behaviors of MBEWIL, and verified its potential to fabricate fine and complex relief surfaces that occur in nature. However, the theoretical analyses also need to be confirmed through practical experiments accompanied by the exposing and curing of resin. To achieve this, we required a novel EWIL system that was not only able to generate EWs but also had sufficient flexibility to allow adjustment of the dominant variables, such as the number of beams, the azimuth angles, and the polarization. As glass with a high refractive index is needed to generate EW, almost all conventional optical systems for EWIL utilize prisms [21, 23, 24, 26, 27]. Figure 8a shows a typical example of the conventional optical systems using prisms. However, the flexibility of the number of beams in these systems tends to be very low because it is limited by the form of the prism. Furthermore, changing the optical condition is time-consuming because alignment is essential for each setting. To overcome these problems, therefore, we proposed and developed a flexible EWIL system; a conceptual image of the system is shown in Fig. 8b. The system is roughly divided into two units: exposing unit and beam modulating unit. A solid immersion lens is used as the exposing unit, which allows us to generate EW and interference. Further, a changeable mask and a polarization converter constitute the beam modulating unit. The mask produces the required number of light beams; in addition, it can be easily changed to other masks. The polarization converter modulates the polarization of finally incident light beams. We introduce the details of the units in the following subsections.

Fig. 8
figure 8

a Typical conceptual image of the conventional optical systems utilized for EWIL. b Concept of our proposed flexible EWIL system. Expanded light beam is modulated and split by the polarization converter and the changeable mask, respectively, and finally the solid immersion lens generates a standing wave pattern of EW on the exposure plane

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3.2 Exposing Unit

This subsection shows the solid immersion lens we introduced to realize the generation of EW and interference simultaneously. General objective lenses are not suitable for EWIL because their refractive indices are not sufficiently higher than that of resin, and their numerical apertures (NA) are not large enough to ensure that their incident angles are higher than the critical angle. In this work, we therefore utilized a solid immersion lens with a high refractive index and a high NA. Figure 9 shows its exposing unit, which is composed of three components: a cover glass (Apo100xOHR-CG, Olympus Corp.), immersion oil (Apo100xOHR-CG-SP, Olympus Corp.), and an objective lens (Apo100 x OHR, Olympus Corp.). Together, this is regarded as a solid immersion lens with a refractive index of 1.78. We used acrylate resin with a refractive index of 1.5 as a photocurable resin.

Fig. 9
figure 9

Schematic of the solid immersion lens used in this study, consisting of a cover glass, immersion oil, and an objective lens

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The NA of the solid immersion lens is 1.65 when the light beam enters the full range of the objective lens. The lens has a pupil diameter of 5.94 mm, and the diameter at which the incident angle is equal to the critical angle is 5.4 mm. Therefore, the incident angle of the light beam passing through the area where the distance of the optical axis is 2.7 to 2.97 mm is larger than the critical angle, meaning that an EW is generated.

3.3 Beam Modulating Unit

The beam modulating unit consists of a changeable mask and a liquid crystal polarization converter, which converts the polarization and transmits only the required parts of the wavefront of the expanded light beam. By using a mask with multiple pinholes, the wavefront of the light passing through the edge area of the solid immersion lens can be split, as shown in Fig. 10a. As a result, accompanied by the solid immersion lens as mentioned above, the multi-beam interference pattern of EW can be generated. In addition, the mask can be simply substituted with other masks that have differently arranged pinholes to change the optical condition. The masks can easily control the important variables, namely the number of incident light beams and their azimuth angles by their arranged pinholes. Regarding polarization, we used a liquid crystal polarization converter (Radial-Polarization converter, ARCoptix Corp.) to generate radial and azimuth polarizations. Figure 10b shows a schematic image of the polarization converter, which converts the linear polarization of an incident beam to a radial or azimuth polarization. The optical path where the converted wavefront is split by the pinholes on the mask to generate an EW interference pattern is shown in Fig. 10c. The polarizations of the finally incident beams that are immediately before the exposure plane are unified to S polarization or P polarization by the polarization converter.

Fig. 10
figure 10

a Sectional image of the objective lens and the changeable mask. The light beams passing through the mask enter the EW generation region. b Schematic image of the liquid crystal polarization converter. c Schematic showing how polarization is controlled by the polarization converter, and how the wavefront of the incident beam is split by the pinholes on the mask

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3.4 Whole Optical Assembly of the Flexible EWIL System

The whole schematic of the flexible EWIL system that we developed is shown in Fig. 11. The mask cannot be set at the back focal plane of the solid immersion lens (Fig. 9c) because this would require it to be located in the inner body of the objective lens. Hence, the infinity-corrected optical systems were arranged in series with one another. We used an optically pumped semiconductor laser whose wavelength is 488 nm (Sapphire 488 LP, Coherent, Inc.) as a light source. A single-mode optical fiber and lens 1, which has a focal length of 100 mm were used to expand the beam. The expanded light then passed through a polarizer and then the liquid crystal polarization converter. The radially (or azimuthally) converted light beam was then split by the mask with multiple pinholes. This mask can be easily switched with other masks. The mask’s real image was generated at the back focal plane of the solid immersion lens by the infinity-corrected optical system, which was composed of lenses 2 and 3. Both of these lenses had a focal length of 175 mm. The split beams generate EWs and an interference pattern as mentioned above. A nitrogen purge unit was attached to the exposing unit to reduce the influence of dissolved oxygen, which could otherwise inhibit radical polymerization [28]. The exposing unit is set on the XY stage to move the cover glass position between exposures to fabricate multiple structures on a single cover glass. This stage is completely stationary during the exposure processes to stabilize the resin. The light beams reflected at the exposure plane passed through lens 4, which had a focal length of 180 mm, before entering the charge-coupled device (CCD) camera. This camera allows us to observe the exposure plane and make beams overlap on the boundary where TIR occurs by adjusting the working distance between the objective lens and the exposure plane.

Fig. 11
figure 11

Whole schematic of the flexible EWIL system, which consists of two pairs of infinity-corrected optical systems

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The developed system using a visible light source and a simple optical assembly facilitates generation of multi-beam interference patterns with the evanescent wave. The main features of the system are that processing can be performed in one shot and that exposure conditions such as the number of beams, the azimuth angles, and the polarization can be arbitrarily controlled by simply replacing the mask to other masks. We report the experimental results obtained by using the system in the next section.

4 Experimental Demonstrations

4.1 Experiments

This section demonstrates our validation of the simulation results by comparing them to the experimental results obtained by the developed system. Regarding the experiments accompanying the resin curing, the theoretical analyses were confirmed by our experimental results, and the ability of MBEWIL to fabricate sub-micron complex surface structures were verified. We used a photocurable resin, which can react to visible light. The acrylate resin used was a compound of two types of resin materials: initiator (Irgacure 784, BASF Corp.) and prepolymer [UA510-H (Urethane prepolymer), Kyoeisha Chemical Co., Ltd.]. The exposure energy was controlled by the exposure time. We developed the uncured resin by either ethanol or diethyl ether. We observed the cured form via SEM.

Figure 12 shows the cured forms fabricated by two-beam EWIL of S and P polarization, with three types of facing angle conditions: 20°, 30°, and 90°. The theoretical and experimental values of cured fringe periods are summarized in Table 1. The theoretical period, \(L\), was calculated using the following equation:

$$L = \frac{\lambda }{{2n_{{\text{i}}} \sin \theta_{1} \sin \tfrac{\varphi }{2}}}$$
(10)

where the incident angle, \(\theta_{1}\), is equal to \(\theta_{2}\), and \(\varphi\) is the facing angle, which is the difference between azimuth angles \(\varphi_{1}\) and \(\varphi_{2}\). The larger the facing angle is, the smaller the period of the fringe pattern will be. The only case where a fringe pattern was not observed was where the facing angle was 90° and the incident beam was in S polarization. These results correspond to the results mentioned in Sect. 2. There was a slight deviation from the theoretical values at 20°; we infer that this was due to the influence of errors that occurred during processing of the mask. The period was ~ 770 nm at ~ 22.6°. These experimental results validated the theoretical analyses.

Fig. 12
figure 12

SEM images of the cured resin fabricated by two-beam EWIL. Experiments were conducted under both S and P polarization, with azimuth conditions of φ(0,20), φ(0,30), and φ(0,90)

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Table 1 Comparison of simulated period and fabricated period
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In Sect. 2, we suggested that the sub-half-wavelength complex reliefs, like those observed on naturally occurring surface structures, can be fabricated by EWIL, with the three-way incidence of narrow-angle two-beam pairs. An experimental examination was conducted under the same conditions as the simulation mentioned in Sect. 2. Two beams with about 20° facing angles are incident from three directions (each separated by 120°). While conventional optical systems, as shown in Fig. 8a, generally need delicate control of positions and angles in each beam to make spots overlap, the developed system only needs to adjust the working distance once a mask with multiple holes is set appropriately. Figure 13 is the CCD camera images observed while changing the working distance. The fringe patterns generated by narrow-angle two-beam pairs appeared, as shown in Fig. 13a. As the working distance was adjusted, the fringe patterns overlapped at the same position. Figure 14 is the enlarged image of the overlapped area in Fig. 13c. The overlapped three-directional fringe patterns (emphasized with yellow lines) form a hexagonal lattice pattern. Also, each pattern is generated by interference with each narrow-angle beam pair, and its period is ~ 840 nm, which almost matches the calculation in Table 1. The sub-200 nm pitch cannot be observed with this camera due to the lack of optical imaging resolution, but some Moiré fringes can be observed.

Fig. 13
figure 13

The typical observed images of light intensity distribution on the exposure plane when adjusting the working distance

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Fig. 14
figure 14

An enlarged image of Fig. 13c

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The results of the form fabricated by the proposed EWIL condition are shown in Fig. 15. These patterns correspond well with the light intensity distribution in Fig. 14. In addition to ~ 840 nm of the fringe pattern being present, a 190-nm fringe pattern could also be observed in the cured forms fabricated by both S and P polarization (red circles). The theoretical period of the fringe pattern generated by the 120° facing angle was 175 nm; this almost corresponds to the experimental value. In the conventional studies, the fineness of the structures fabricated by IL without EW was insufficient for the sub-200-nm pitch, and when the EWIL was used, almost all of the systems have much limitation in terms of changeability of their optical conditions. In these results, we verified that the proposed system was able to fabricate sub-half-wavelength complex structures such as special surfaces that occur in nature adopting the proposed optical conditions—i.e. a three-way incidence of narrow-angle two-beam pairs.

Fig. 15
figure 15

SEM and simulated images of the sub-half-wavelength complex relief structures formed by EWIL with the three-way incidence of narrow-angle two-beam pairs

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4.2 Discussion

The target fine and complex structures, which had dual scales with sub-half-wavelength fineness, were successfully fabricated. However, periodic structures < 200 nm were observed only in a part of the cured area. In this discussion, we consider why these parts where structures < 200 nm did not occur were formed. We infer that this problem can be attributed to the polymerization and development processes. In the polymerization process, it is possible that the diffusion of free radicals during polymerization filled the valley, or that it inhibited curing owing to small amounts of dissolved oxygen inhibiting the growth of convex parts. Regarding the development process, the developer and the developing time would have influenced the boundaries between the cured and uncured areas. In the future, these processes could be optimized to obtain a more detailed replication of naturally occurring structures.

5 Conclusions

In this study, we developed a flexible EWIL system and verified that MBEWIL using a visible light source could fabricate fine and complex relief structures that have dual-scale fringe patterns and sub-200 nm fineness. To visualize the forms fabricated by MBEWIL and analyze the basic relationships between the optical conditions and the fabricated form, we conducted theoretical simulations. Our results revealed that the solidified forms changed when the number of light beams, the azimuth angles, and the polarization were adjusted, specifically regarding properties such as their contrasts, periods, and directions of fringe patterns. In addition, as the relief pattern fabricated by MBEWIL was the structure generated by superposing multiple two-beam interference fringe patterns, we proposed the following optical conditions: three-way incidence of narrow-angle two-beam pairs. This ensured that the target structures could be theoretically produced. Based on the analyses, we designed and developed a novel MBEWIL system in which the number of beams, the azimuth angles, and the polarization are simply changeable. Our developed system made use of the solid immersion lens, the changeable mask, and the polarization converter. As a result, the system features higher process flexibility and condition changeability than conventional EWIL systems that use prisms. Using this system, we conducted two-beam EWIL experiments with three types of azimuth angle conditions. The results are that the experimental and simulated values were virtually congruent in terms of their fringe periods. We also experimentally verified that the target dual-scale structures with two different periods (840 nm and 190 nm) could be fabricated by MBEWIL using a 488-nm laser. We verified the feasibility and effectiveness of the proposed flexible EWIL system to fabricate fine and complex structures with sub-200-nm-sized patterns, similar to those observed in nature. We expect our method to be applied to the fabrication of some optical elements, wettability-controlled materials, and friction reduction surfaces, and so on.

Although the height of relief structures is also one of the critical parameters to express some functions, we prioritized fabricating laterally fine structures in this paper. In order to get the functionality related to the height, some practical techniques such as a reactive ion etching, a penetration method of EW [27], and a deposition with high refractive index material [29] can be applied to our method.

With the system developed in this study, interference exposure can be performed in one shot at any number of light beams and azimuth angles by replacing the mask. If the mask can be controlled in real time by equipment like a liquid crystal device, it will also be possible to form a relief pattern by changing the conditions for each shot. This suggests the possibility of producing elements with different fine and complex patterns in the same plane for each location, which is expected to be applied to next-generation devices such as components requiring delicate control of wettability and slidability and optical elements for depolarization using structural birefringence.