1. INTRODUCTION

A polarization converter transforms an optical input beam of polarization state ${\mathcal{P}}_1$ into an output beam of polarization state ${\mathcal{P}}_2$. Any polarization converter is based on an anisotropy of the propagation parameters for the two transverse components of the electric field. In natural materials, such as calcite (${\mathrm{CaCO}}_3$), the molecular structure leads to two different refractive indices and thus birefringence. In recent years, synthetic designs based on micro- and nano-structuring have been used to mimic natural birefringence (see, for example, [1,2]). In contrast to natural materials, the optical properties of these elements are determined by the geometry rather than the material properties. Anisotropy is achieved by two different propagation constants that lead to a phase shift between orthogonal modes [3]. Well-known examples for artificial polarization converting elements are based on dielectric subwavelength gratings [4–6] and metamaterials [7,8]. In dielectric subwavelength gratings, the effective index is different for the two transverse directions and can be varied by the fill factor of the grating. For this, gratings with subwavelength periods and high aspect ratios are required. By varying the fill factor of the grating across the element, however, a space-variant polarization converter can also be realized. Due to optical cross-coupling between different ribs of the grating, the resolution, however, is limited to a few periods of the grating.

Here, we follow a different approach by using the concept of a hollow waveguide to implement anisotropic propagation [9]. A hollow waveguide consists of a dielectric medium surrounded by a metallic wall. Anisotropy is achieved by using rectangular waveguides. Lateral dimensions of such waveguides are on a subwavelength scale. The sidewalls are metallic, e.g., Au or Ag, and the waveguide itself is made of a dielectric material, which in the simplest case can be air. In an array, all waveguides may be identical, however, variations are possible with respect to width and orientation. Compared to, e.g., dielectric gratings, the fields in the single waveguides are strongly confined and do not extend into the neighboring guides. With this feature, local polarization rotation shall be achieved, which might be utilized in high-resolution devices. It should be emphasized that the fabrication of such devices is technologically very demanding. Therefore, we concentrate on the design, fabrication, characterization, and optical testing of a hollow waveguide array (HWA) in this article.

Fabrication can be accomplished by various techniques: direct writing by electron beam lithography (EBL), deep mask-based lithography [10], and two-photon polymerization (TPP). For all these approaches, the technological challenge is to fabricate waveguides with submicron cross-sections, rectangular shapes, and micrometer-scale depths. Structuring of the waveguides is followed by electrochemical deposition of gold. Here, we present a study on the suitability of the TPP process to build an HWA. In contrast to other techniques, for example, EBL, two-photon polymerization has advantages like shorter fabrication time, larger maximum size of the entire array while achieving a comparable minimum structure size as with EBL, and an extended depth range [11,12].

This paper is organized as follows. In Section 2, we start with a brief description of the principle and geometry of hollow waveguide arrays, followed by a detailed description of the fabrication process in Section 3. In Section 4, we characterize the hollow waveguide array by polarization measurements.

2. HOLLOW WAVEGUIDE ARRAY AS A POLARIZATION CONVERTER

The overall objective of this work is to achieve a space-variant polarization conversion. An application that has already been described previously is the conversion of linearly polarized into circularly polarized beams [9]. Here, we will focus on a second application, the design of high-resolution devices. In this section, we will briefly repeat the principle of polarization conversion and show how this can be achieved with hollow waveguides. After that we present the idea of designing such high-resolution devices.

A. Principle of Polarization Rotation

The principle of the polarization rotation is shortly explained with the help of Fig. 1. A birefringent material is illuminated with a linearly polarized plane wave. Then the arbitrarily oriented electric field is divided into the components parallel to the axes of the material (here $x$ and $y$). Due to birefringence, these two components travel with different phase velocity, i.e., they have different propagation constants ${\beta }_{x,y}$. For a given material with thickness $h$, the phase difference is given by

 

Fig. 1. Polarization rotation in a birefringent material. Left, field components of input beam; center, field components of output beam; right, resulting polarization rotation for total fields.

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B. Basic Theory of a Hollow Waveguide

In our work, we use a metallic film with a subwavelength structure as the polarization converting component. The idea is based on the physics of a hollow waveguide (HW) that is known from microwave theory [9,10,13].

The cross-section of such a hollow waveguide is shown in Fig. 2. An incident field propagates in the air region, and the gold sidewalls act as mirrors to guide the incident field through the structure. For using such a device as the polarization converting element, it is important that the two lowest order modes (labeled ${\mathrm{TE}}_{10}$ and ${\mathrm{TE}}_{01}$) are purely vertically or horizontally polarized in the case of ideal metal. This is illustrated in Fig. 2, where the electric field of these modes is presented.

 

Fig. 2. Electric field distribution of the lowest order modes in a rectangular hollow waveguide.

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Further, as common for waveguides, the eigenmodes possess different propagation constants. For ideal metal, the effective index of these modes (which is related to the propagation constant $\beta =k_0{n}_{\mathrm{eff}}$, $k_0=2\pi /{\lambda }_0$) is determined as

C. Structure of a Hollow Waveguide Array

For controlling the polarization of a laser beam, the spot size being much larger than the dimension of a single HW has to be considered. As a consequence, hollow waveguides are arranged into an array (HWA) as illustrated in Fig. 3. Typically, such an HWA consists of hundreds of HWs in both directions.

 

Fig. 3. Schematic drawing of the HWA with dimensions in the top view and the side view. The yellow-colored structure is the surrounding gold sidewalls. The spacing in between is air.

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D. Space-Variant Polarization Conversion

It is of particular importance that the polarization conversion in hollow waveguide arrays can be varied locally. By variation of the waveguide parameters, polarization can be varied from one cell to the next. The principle is shown graphically in Figs. 4 and 5. Here, a small array of $1\times 3$ cells in the center is selected to generate a different polarization rotation than the surrounding cells. Figure 4 shows the input to the HWA, and Fig. 5 shows the output. By the suitable choice of cell parameters, polarization is changed for the modes traveling through the tilted cells, whereas polarization is preserved in the other ones.

 

Fig. 4. Hollow waveguide array illuminated with a vertically polarized plane wave. The arrows indicate the direction of the electric field.

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Fig. 5. Principle of a local polarization rotation. At the output of an HWA a polarization rotation occurs in the tilted cells. The arrows indicate the direction of the electric field.

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We would like to remind the reader that polarization conversion can also be achieved using other principles, e.g., with an interferometrically fabricated subwavelength dielectric grating (DG) a phase difference of $\pi /2$ was achieved. The birefringence in this DG was realized by different fill factors in the two lateral directions [14]. Space variance can be introduced by using a local variation of the period, orientation, and/or fill factor as demonstrated by [15] with very good contrast. Here, we focus our attention on the higher resolution that can be achieved and compare HWA and DG. For the comparison, it is useful to note that the DG may also be viewed as a waveguide array as suggested earlier by [16]. In our calculations, we used the parameters shown in Tables 1 and 2.

Table 1. Hollow Waveguide Array

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Table 2. Dielectric Grating

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For a qualitative comparison, a modal analysis was performed. For this purpose, the eigenmodes of a dielectric waveguide and of a hollow waveguide with the dimensions given in the tables above were determined. For the computations, in-house software is used where the method of lines was applied. Details about this algorithm can be found in Ref. [10] and references therein. Of particular importance is the lateral shape of the electric fields for HW and DG. In Figs. 6 and 7, calculated field distributions for the fundamental eigenmodes are shown. While for the HWA the field is essentially confined to one cell (Fig. 6), the field in the DG extends over several periods (Fig. 7). We concede that this comparison is qualitative, yet the curves show that the HWA is able to provide a higher resolution in the lateral direction than the DG. This may be of interest for specific applications, for example, in imaging where polarization may be useful to highlight certain areas.

 

Fig. 6. Electric field of the fundamental mode in a hollow waveguide. The field is essentially confined to the width of the waveguide. Calculation is done with the paramaters of Table 1.

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Fig. 7. Dielectric subwavelength grating: the electric field distribution of the fundamental mode is shown. In comparison to Fig. 6, one recognizes that the field extends over several lateral periods. Calculation is done with the paramaters of Table 2.

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3. FABRICATION

A. Two-Photon Polymerization with Femtosecond Pulses

In comparison to other lithography processes, with two-photon polymerization (TPP) a complete three-dimensional (3D) fabrication in a photoresist is possible. Using TPP, a beam of a femtosecond laser is tightly focused into the volume of a transparent photosensitive material (photoresist). The cross-linking process can be initiated by nonlinear absorption within the tightly confined focal volume, a so called voxel (volume pixel). By moving the beam focus three-dimensionally inside the material, 3D structures can be fabricated in a pinpoint writing process [17–19]. The two-photon polymerization technology is unique in the sense that it allows the fabrication of fully 3D structures with resolution beyond the diffraction limit.

Here, a TTP setup with a second-harmonic erbium-doped femtosecond oscillator is used (Nanoscribe GmbH, Germany). This TPP setup provides 100 fs pulses at 780 nm with a repetition rate of 80 MHz and an average output power of 120 mW. An acousto-optic modulator regulates the laser power, and with a beam delivering system the laser beam is circularly polarized and expanded before it is focused with a microscope objective into the sample. For achieving a minimum linewidth, a ZEISS Plan-Apochromat $63\times$ oil immersion objective with a NA of 1.4 is used. The laser beam is deflected by a galvometric scanner system, and a writing area of $150\mathrm{\mu m}\times 150\mathrm{\mu m}$ is exposed line by line within one writing field. The writing fields are stitched together to get the entire writing area.

B. Fabrication of the Negative Structure

The HWA structure shown in Fig. 3 is fabricated on a quartz glass substrate coated with indium tin oxide (Zeiss AG, Germany). The indium tin oxide (ITO) layer is used for its electrical conductivity. As will be described below in more detail, the HWA is fabricated by a negative process. For this, first a grid pattern is written into a photoresist. Here, AZ3027 photoresist (Microresist GmbH, Germany) is used, which provides good mechanical contact with the ITO-coated substrate. The substrate surface is prepared by applying TiPrime adhesion promotor (Microchemicals GmbH, Germany). Following, the grid pattern, i.e., the inverted structure, is fabricated using a TPP process.

The process chain is depicted in Fig. 8. To improve adhesion, initially an adhesion promoter is spin coated onto the cleaned ITO-coated glass substrate with a rotational speed of 3000 rpm and activated in a subsequent baking step at 120°C for 2 min. Subsequently, the substrate is cooled to room temperature, and the photoresist is applied (spin coating, 2800 rpm). In combination with the ITO-coated glass substrate and the photoresist, a layer thickness of 3 μm is obtained. For mechanical and chemical stabilization of the spin-coated layer, the sample is baked on a hotplate at 100°C for 1 min to further reduce the solvent content in the photoresist. Following, the photoresist is exposed with the TPP setup described in subsection A. The average laser power behind the microscope objective is 12.5 mW and the writing speed 15 mm/s. The writing fields are stitched together to get the entire array with a total area of about $4\mathrm{mm}\times 4\mathrm{mm}$. Immediately after exposure, the resist film is baked at110°C for 1 min and after cooling to room temperature the sample is developed in a ready-to-use developer AZ726MIF (Microchemicals GmbH, Germany). The developed photoresist layer is thoroughly rinsed with deionized water. As a result of this process chain, a negative structure of the hollow waveguide array is fabricated. The freestanding photoresist pillars are shown in Fig. 9.

 

Fig. 8. Process chain for the fabrication of the negative structure using two-photon polymerization.

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Fig. 9. Scanning electron microscope image of freestanding photoresist pillars after the two-photon polymerization process and development.

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C. Electrochemical Deposition of the Gold Structure

Figure 10 explains the process used for the electrochemical deposition. After developing the resist film, a thin inhibition layer is formed on the ITO layer. This thin layer prevents contact between the ITO and the electrolyte and must therefore be removed. In order to maintain the structure of the negative as much as possible, anisotropic reactive ion etching is used to first remove the thin inhibition layer. The electrochemical deposition chamber is placed on a heating plate at 60°C. As the anode, a platinum mesh is used and serves as a redox electrode because platinum is inert in this ready-to-use electrolyte solution. The glass substrate with the deposited ITO layer acts as the cathode. To achieve a smooth cladding surface and a good mechanical stability, the electrochemical deposition is performed by alternating pulsed and constant current. In the pulsed mode, the current is varied between 0 μA and $-175\mathrm{\mu A}$ with a duration of 1 s and an interval of 3 s between each of a total of 30 pulses. The current in the constant mode is $-150\mathrm{\mu A}$ applied for 190 s. Starting with pulsed current, the electrochemical deposition repeats alternately three times with constant and pulsed current. The total time for electrochemical deposition is 17.5 min, resulting in a total gold height of 2 μm. In order to enhance the adhesion of the gold layer on the ITO layer, a EpoCore5 photoresist layer (Microresist GmbH, Germany) is spin coated over the entire structure and softbaked at 90°C for 5 min. Subsequently, the resist is exposed by UV light of a mask aligner at a dose of $220\mathrm{mJ}/{\mathrm{cm}}^2$ (broadband illumination, no bandpass filter is used). Immediately after exposure, the resist film is baked at 85°C for 5 min and after cooling to room temperature the sample is developed in a ready-to-use mr-Dev 600 developer (Microresist GmbH, Germany) and thoroughly rinsed with isopropanol. With this last developing step, the second resist layer is opened in a circular area of 1.5 mm in diameter and within this area, also the freestanding pillars are completely removed. The final hollow waveguide array is shown in Fig. 11.

 

Fig. 10. Process chain for the electrochemical deposition of the gold structure.

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Fig. 11. Scanning electron microscope image of a hollow waveguide array.

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4. EXPERIMENTS

First, the topographical structure of the hollow waveguide array is characterized by a scanning electron microscopy (SEM) and a tactile surface profiler, respectively. The SEM image in Fig. 11 highlights the geometrical uniformity of the openings of the hollow waveguide array. For a quarter-wave plate, openings of $w_x=1150\mathrm{nm}$ and $w_y=930\mathrm{nm}$ and a total height of 2 μm are necessary. For the realized HWA shown in Fig. 11, these dimensions are determined as $w_x=1140.4\mathrm{nm}$ with a standard deviation of 35.1 nm for twenty measured waveguides and $w_y=938.3\mathrm{nm}$ with a standard deviation of 27.6 nm, proving excellent agreement. It is also worth stressing that by using the combination of TPP and electrochemical deposition we achieve a width of the gold sidewalls of only 415 nm. This is only half of the width previously reported in Ref. [20] where the same technological approach was used and is comparable to the values in Ref. [10] using electron beam lithography. The reduced width of the gold sidewalls increases the optical transmission. Here, a transmission of 61.2% can be achieved. This value is in a good agreement with the value obtained from simulations of 67% [21]. Small differences between the actual transmitted value and the transmission value obtained from simulations can be explained by slightly wider gold structures ($\pm 15\mathrm{nm}$) and a larger distance between the element and the photodetector.

Figure 12 depicts the surface profile across the entire HWA at two positions (black and red curves), and the inset shows the profile in the active area of the HWA. We measure a mean height over the total length of the HWA of $h=1.854\mathrm{\mu m}$ with a standard deviation of 0.096 μm, which is in accordance to the calculated height of 2 μm. This corresponds to an aspect ratio of 5∶1 (height∶width). The surface roughness $R_a$ is determined to 0.056 μm, i.e., about $\lambda /27$ highlighting the quality of the gold deposition process.

 

Fig. 12. Height profile of the entire hollow waveguide array at two positions.

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The experimental setup to characterize the hollow waveguide array consists of a laser diode (LD), a beam shaper (BS), the HWA, a linear polarizer, and a detector (see Fig. 13; LD and BS are not shown in the figure). The HWA sample is mounted on a micrometer stage and illuminated by a plane wave from a laser diode ($\lambda =1550\mathrm{nm}$, $\text{average power}=4.5\mathrm{mW}$). The BS is used to reduce the beam diameter from 3 mm to 1 mm. Finally, with a linear polarizer the polarization state of the laser transmitted through the HWA is analyzed and the transmitted laser power is measured with an optical detector at the end of the experimental setup.

 

Fig. 13. Experimental setup: a linearly polarized laser diode illuminates the HWA. The HWA is placed in a rotatable holder for changing the rotation angle $\alpha$. The angle $\alpha$ denotes the angle between the orientation of the electromagnetic field ($x$) and of the HWA ($x^{\prime }$). To measure the maximum and minimum transmitted power a linear polarizer (analyzer) and a detector are used.

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Results of the measured variable polarization degree versus rotation angle of the hollow waveguide array are shown in Fig. 14. Here, the angle $\alpha$ is stepwise changed from 0° to 360° in steps of 10°. The margin of error in this measurement is $\pm 2.5\%$ at maximum. Generally, the field at the output of the HWA is elliptically polarized. Hence, the fields rotate along an ellipse with a major and a minor axis. These axes are detected by the polarizer and the corresponding maximum and minimum power ($P_{\max }$ and $P_{\min }$) are measured with the optical detector. From these values, the degree of polarization $\mathrm{PG}$ is defined as [see, e.g., [3], pp. 46–47]

 

Fig. 14. Measurement for degree of polarization as a function of rotation angle $\alpha$ with margin of error (shaded in gray).

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With the dimensions of the fabricated waveguide mentioned earlier, the structure characterized here should work as a quarter-wave plate, i.e., PG should decrease to $\mathrm{PG}=0$. This, however, is not observed in the measurements. This discrepancy can be explained by the deviation of the generated cross-section of the HWA from a rectangular shape. As Fig. 11 reveals, the waveguides do not possess a perfect rectangular shape, but the corners are slightly rounded. This rounding occurs during the exposure process, in which all lines are exposed in the $x$ direction first and second in the $y$ direction, i.e., the crossings of the lines are exposed twice and these areas become slightly wider than those exposed only once. Therefore, the values initially calculated for these locations do not agree with the actual dimensions of the fabricated structure and the phase shift differs from the calculated value $\pi /2$. As a consequence, the polarization degree does not reach its minimum value $\mathrm{PG}=0$ (corresponding to a circular polarization) but an elliptical polarization state remains. Taking the slightly rounded corners into account, the dimension of the air-filled waveguides $w_{x/y}$ or the height $h$ of the HWA must be adjusted to approach the ideal value $\mathrm{PG}=0$.

5. CONCLUSION

We report on the fabrication of a hollow waveguide array and demonstrate its use as a space-variant polarization converter. Using two-photon polymerization and electrochemical deposition of gold, feature sizes of 415 nm and an aspect ratio of 5∶1 were demonstrated. These results are comparable to what might also be realized by electron beam lithography, yet with the advantage of higher writing speed, large writing area, and extended depth range. Hence, in comparison, the concept demonstrated here, if further optimized, may prove to be a competitive approach.