1. Introduction

Waveplates are common optical devices for changing the polarization of light by introducing a phase shift between the two polarization components of an incoming light wave. The two most common types are the half-wave plate (HWP) and the quarter-wave plate (QWP). As the names imply, these introduce a phase shift of half a wave and a quarter wave respectively. HWPs are used to rotate the polarization direction of linearly polarized light and QWPs can be used to convert between linearly and elliptically or circularly polarized light. Waveplates are commonly made from birefringent crystals such as quartz. Gratings with a period smaller than the wavelength of interest can also display birefringence [1,2], so called form birefringence, which can be used for making waveplates [3,4]. In this paper we demonstrate two designs of QWPs made out of diamond sub-wavelength gratings (SWGs). Using the form birefringence of a SWG comes with certain advantages compared to birefringent crystals: Waveplates can be made from materials that are not otherwise birefringent, they can be made more achromatic [3,4], the direction of the optical axis can be controlled locally [5,6], and the waveplate can be made very thin. The last is demonstrated in this work by making a waveplate grating without a substrate. Even deep in the infrared, such a free-hanging grating QWP is just a few microns thick. Grating waveplates are a particularly good choice for use at longer wavelengths, where suitable optical materials can be hard to find and manufacturing of SWGs get easier. The waveplates presented here are designed for use with a CO₂ laser emitting at 10.6 µm wavelength. We have chosen diamond as the grating material because of its good optical transmission for almost any wavelength above the near ultraviolet. The refractive index of diamond, while extremely high compared to other materials transparent in the visible range, is actually quite modest when compared to some materials used in mid-infrared optics such as germanium or gallium arsenide. This middle ground refractive index turns out to be favorable for the design of grating waveplates. The refractive index has to be high enough for the grating to be reasonably shallow to facilitate the etching process, but not too high or the design will be too sensitive to small variations in grating dimensions or it may not be possible to find a good overlap between the right phase shift and high transmission. There are certainly other materials with a similar refractive index to diamond, such as zinc selenide, but diamond has unmatched hardness and thermal conductivity, as well as high chemical stability which allow less gentle handling and processing. Diamond also has very low thermal expansion and thermo-optic coefficients [7], reducing temperature dependence in waveplate performance, which in other materials can be significant [8]. In the following we will first, in section 2, briefly discuss the birefringence of SWGs and how this is used to design waveplates. In section 3 we will describe the fabrication of our SWGs, followed by the optical characterization in section 4. Finally some conclusions and outlook will be discussed in section 5.

2. Theory and design

We talk about SWGs when the wavelengths of light (λ) of interest are longer than the period of the grating (Λ) in the incident and transmitting media (n_i, n_t) (Fig. 1(a)). In the case of normal incidence this can be written as Λ < λ/max(n_i, n_t). If this is fulfilled, light incident on the grating will not be diffracted as by a classical grating, but will be transmitted or reflected in the zeroth order only. Light passes through the grating as if it was a film of some continuous medium with optical properties determined by the grating materials as well as its shape. If the grating is one-dimensional it will typically be birefringent: the refractive index is different between light polarized perpendicular and parallel to the grating lines. In the case of a simple binary grating, the phase difference in degrees introduced by the grating can be expressed as ∆Φ = 360 × ∆n (h / λ); where ∆n is the difference in refractive index between polarizations and h is the height of the grating. Even in this simplest case, ∆n is not easily calculated. Also, a binary grating is not a very good approximation of the gratings we can produce in diamond. Plasma etching of diamond does not produce perfectly vertical walls, an angle of a few degrees is typical and should be taken into account when designing the grating [9].

 

Fig. 1 (a) Schematic cross section of a grating. (b) Cross-section of a trapezoidal grating line showing some relevant parameters, and a stepped discretization as used in the RCWA calculations.

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To find optimal grating parameters for our diamond QWPs, we turned to Rigorous Coupled Wave Analysis (RCWA). This method is suitable for periodic dielectric structures and its implementation is particularly straight-forward for 1-D gratings such as the ones we are interested in here. The structure is divided into layers (uniform in Z) and the problem is solved by finding the electromagnetic modes in each layer and matching the boundary conditions between layers [10]. A trapezoidal grating is thus approximated by a stepped structure (Fig. 1(b)). Relatively few layers were required for good convergence (6 were used to find potential solutions and up to 15 to study candidates in more detail).

The relative phase difference (∆Φ) and transmission at 10.6 µm wavelength were calculated for wide ranges of the grating parameters (line width w, height h and period Λ, see Fig. 1). The side-wall angle (α) was kept fixed at 2° and 3° for the surface and free-hanging gratings respectively. We looked for solutions with ∆Φ = 90° as well as high and equal transmission of both polarizations. As the grating can act as an antireflective structure, with light reflected from the back of the grating interfering destructively with light reflected from the front, very low reflection losses are possible. A good solution should also be robust, especially with respect to variations in h and w. A precise period is easier to achieve in the fabrication and a solution stable with respect to w tends not to be very sensitive to α either. In the case of the free-hanging gratings longer periods can satisfy the SWG criterion Λ< λ/max(n_i, n_t), since n_i = n_t = 1. It should be noted that with a lower index both above and below the grating, there exist resonant modes that should be avoided [11].

The solution we settled on for the surface grating was Λ = 4 µm, w = 1.45 µm and h = 5 µm; and for the free-hanging grating Λ = 7 µm, w = 1.8 µm and h = 3.45 µm. In the case of the free-hanging grating in particular this solution gives both the correct phase shift and excellent transmission (over 99%). The surface grating has lower transmission (around 91.5%), but still close to equal transmission for both polarizations. This is for the grating itself, without AR-treatment of the opposite side of the substrate the transmission through the component as a whole is 77%. The free-hanging grating, not having a substrate, avoids the issue of reflection from the backside. Figure 2 shows maps of relative phase shift and transmission around the optimized grating solutions. The phase shift in both cases is less sensitive to errors in w than h. This is an advantage for the free-hanging grating, since h is set by the thickness of the diamond film; which can be etched to a suitable thickness with great precision (see section 3). An issue for the free-hanging grating is that some residual stress is expected from the growth of the diamond film. This may cause the grating lines to buckle as they are released from the substrate. To ensure that all the lines bend in the same direction, designs with 5 µm wide crossbars perpendicular to the grating were prepared. Designs without crossbars, a single crossbar in the center of the grating and crossbars every 0.5 mm were tested.

 

Fig. 2 Maps showing the deviation from quarter wave (90°) phase shift as well as transmission around the optimized designs. The period is 4 µm for the surface grating on the left and 7 µm for the free-hanging grating on the right.

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3. Fabrication

Two types of diamond samples were used for this study: a 300 µm thick polished polycrystalline diamond substrate, 1 cm in diameter, for the surface grating, and a (nominally) 4 µm thick polished polycrystalline diamond film on 500 µm thick silicon, diced in 1x1 cm² pieces, for the free-hanging grating (both from Diamond Materials GmbH). The masking and etching processes used were largely similar to what we have previously described [12,13], particularly for the surface grating, so the description here will be kept brief.

3.1 Surface grating

A stack of three masking layers, 1 µm Al, 450 nm Si and 100 nm Al, was deposited on the diamond by sputtering. The grating pattern was written in 530 nm thick photoresist on a glass photomask (MB Whitaker & Associates) by direct laser writing (Heidelberg Instruments DWL 200). This pattern was then moulded in PDMS and transferred to the metal coated diamond substrate by solvent assisted microimprint moulding (SAMIM): S1813 photoresist (Shipley) and AZ EBR 70/30 solvent (MicroChemicals) were mixed (1:2, vol) and spin coated on the samples (6000 rpm, 30 s). After baking (115° C, 60 s), the PDMS pattern was placed against the photoresist. The samples were then left in ethanol vapour to allow the photoresist to soften and fill the pattern. Due to the larger grating periods, a longer imprint time (over night) than in [13] was used. The sample was then baked (60° C, 10 min) to remove remaining ethanol and harden the photoresist before the PDMS was removed. To improve the photoresist stability during etching, the samples were hard baked at 115° C for 5 minutes. The SAMIM process was chosen because it is well suited for patterning fine gratings on small samples.

All etching was carried out in a PlasmaTherm SLR ICP etcher. The top Al layer was etched using Cl₂/BCl₃ plasma. The silicon layer was then etched with SF₆/C₄F₈/Ar plasma and the thick Al layer was etched by cycling Cl₂/BCl₃ and O₂/Ar plasmas in a process developed to produce vertical sidewalls in aluminum [12]. All etching parameters for the mask layers were the same as those in reference [13]. With the thick Al mask complete, the diamond was etched in an O₂ plasma at 5 mTorr with 850 W inductively coupled power and 320 W capacitively coupled power. To reach the correct depth despite fluctuations in etch rate of up to a few percent, a reference sample was patterned and etched in parallel with the grating until the estimated depth was slightly less than the target depth. The reference was then cracked and the cross section studied by scanning electron microscopy (SEM) to determine the etched depth. Based on this, a short remaining etch time could be determined for the QWP sample. After etching, remaining mask material was removed in hot piranha solution (H₂SO₄/H₂O₂) followed by a mixture of HF/HNO₃ and rinsing in water and isopropanol.

3.2 Free-hanging grating

The thickness of the initial diamond film should ideally be the same as the thickness of the designed grating, however we could not source a polished film with high enough precision in thickness. Instead we started with a thicker film and etched it to the appropriate thickness in a Cl₂/Ar plasma (5 mTorr, 40 sccm Cl₂, 25 sccm Ar, 600 W inductively coupled power, 90 W capacitively coupled power). The Cl₂ plasma helps keep the surface free from contaminants during etching, preserving the surface smoothness [14]. Cl₂ plasma etches diamond slower than O₂ and together with the low bias gives low etch rate (~40 nm/min). By iterating etching and thickness measurement (K-MAC ST 4000 interferometer) several times, high precision in film thickness could be reached. The precision was limited not by the etching or measurement, but by thickness variations in the initial film (~70 nm within the grating area).

The masking and diamond etching was the same as for the surface grating, with the addition of an aperture fastened on top of the sample during the first Al etch step. The aperture was a 4 mm diameter hole etched in a piece of 300 µm thick silicon and held in place on the sample with Crystalbond 509. After etching the top Al film, the silicon aperture was removed by heating the sample to 90° C to melt the Crystalbond. The remaining mask layers and diamond film were then etched as for the surface grating, but with no reference sample to check the etch rate in diamond After etching the diamond, the silicon substrate was etched using a Bosch process that was deliberately made less anisotropic by shortening the polymer deposition step and lengthening the silicon etch step. By the time the silicon substrate was etched through, the grating was left hanging free with no silicon left underneath, but with a frame of silicon around it. Remaining mask material was removed with piranha solution. A final rinse in acetone was used before drying to reduce capillary forces which otherwise cause the diamond lines to stick together. Crossbars were found to be necessary to ensure that the grating lines buckled in the same direction. With a single crossbar across the middle of the grating, the lines still buckled unpredictably up or down, ruining the grating (this could be seen with the naked eye). With crossbars every 0.5 mm however, the grating bulged as a whole, causing minimal distortion.

SEM was used to study the geometry of the finished gratings. To measure the depth of the surface grating, several micrographs were taken at different angles and the depth was calculated from the parallax. The parameters for the surface grating agreed well with the design. There was some trenching along the walls due to ions deflecting off the walls during etching (see Fig. 3), but the depth appears to be 5 µm in the middle of the grooves and 5.1-5.2 µm close to the walls. In the case of the free-hanging grating, the line width at the top was narrower (~1.6 µm) and the wall angle in the upper part of the grating was much greater than expected (around 20°). Together these resulted in a wider effective line width than in the optimized design. This was likely due to sputtered mask material re-depositing lower in the wider grooves in combination with a longer than necessary etch time. As noted in section 2, the design is fairly robust to variations in line width, at least in terms of ∆Φ. The free-hanging grating also had a larger number of small defects than the surface grating, possibly due to the SAMIM and mask etching process not being as well optimized for the larger grating period.

 

Fig. 3 SEM micrographs of etched diamond gratings. (a) Cross section of a surface grating with aluminum mask remaining on top. (b) Surface grating. (c) Free-hanging grating where it meets a crossbar (top). (d) Free-hanging grating with crossbar.

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4. Optical Testing

The experimental setup is depicted on the right in Fig. 4. Light from a vertically polarized (~20 dB extinction ratio) CO₂ laser (Universal Laser Systems, ULR-25) emitting at 10.6 µm wavelength was first sent through an aperture to ensure that the beam was smaller than the aperture of the QWPs. Then the light (~300 mW) was sent through the QWP and the transmission and polarization state was measured. The transmission of the free-hanging grating and the surface grating were measured to 93% and 75% respectively. This was slightly lower than the optimal values of 99% and 77%. As expected, the discrepancy is greater in the case of the free-hanging grating as it deviates more from the optimized design.

 

Fig. 4 Normalized transmission of the mid-IR polarizer as function of the rotation angle for the free-hanging and surface grating diamond QWP. The curves are displaced in angle for visual clarity. On the right: a diagram of the experimental setup.

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By adjusting the angle of the QWP relative to the polarization of the CO₂ laser, the polarization could be rotated from linear to circular. The power passing an interrogating mid-IR polarizer (with 1:300 polarization extinction ratio at 10.6 µm wavelength) was measured as a function of the rotation angle of the QWP. This transmitted power was then normalized and a least-square fit of the data was performed. The data for the two QWP is plotted in Fig. 4 together with its corresponding fitting. The curves follow the expected cosine with a period of 90° and are displaced in angle relative to each other for visual clarity.

5. Conclusions and outlook

We have demonstrated the fabrication and optical performance of two types of quarter-wave plates consisting of sub-wavelength gratings in diamond: A grating on the surface of a solid diamond substrate and a free-hanging diamond grating on a silicon frame. Both were produced by plasma etching after a single masking step. The free-hanging grating, while more fragile, has some advantages: Without a high index substrate, a larger grating period can be used while retaining sub-wavelength grating characteristics. The lack of substrate also means there is no need for an anti-reflective treatment of the backside to improve transmission and avoid stray signals in sensitive systems. In the case presented here (a diamond QWP grating for 10.6 µm wavelength), the free-hanging grating could also be designed to give a higher transmission than the surface grating. However, this will not necessarily be the case for other wavelengths, materials or types of waveplate. The free-hanging grating also has a better potential for batch processing, as a large area diamond thin film on silicon is much cheaper than a large diamond substrate (not to mention easier to dice). This would require an optical quality diamond film polished to a uniform thickness (within ~2%) across the wafer. An alternative may be to use a nanocrystalline diamond film, which can be grown to a more uniform thickness but with more uncertain optical characteristics, or a different material like ZnSe or ZnS. The performance of the fabricated free-hanging grating could definitely be improved by optimizing the fabrication process for the larger grating period (the process used here was optimized for 4 µm). The crossbars could likely be made narrower and possibly spaced wider apart without affecting the stability of the grating.