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The realization of half wave phase retarders based on sub-wavelength periodic gratings typically requires small periods with large aspect ratio features. The required aspect ratio of the grating features can be considerably decreased when high refractive index materials are employed. Because the nano-structuring and processing of such dielectrics is quite difficult, we have designed and developed a half-wave retarder relying on (low index) fused silica (SiO2) gratings that are over-coated by titanium dioxide (TiO2) using atomic layer deposition. The period and depth of the fabricated structures are 400nm and 1700nm, respectively. Half-wave retardation is achieved at 628nm and the total transmission lies above 90%.
© 2014 Optical Society of America
1. Introduction
In recent years, sub-wavelength optical elements have attracted an ever increasing amount of interest. The strong campaign in research of metamaterials has triggered a tremendous effort in the development and improvement of nano-fabrication technologies. Prototypical structures are used, e.g., to achieve asymmetric transmission properties [1] or huge optical activity [2] or to realize perfect absorbers [3, 4]. However, metamaterials are only one example of artificial optical matter where tailoring of sub-wavelength features is used to achieve intended optical properties. Other representatives are blazed gratings [5–7] or computer generated holograms [8–10] composed of effective medium entities. In addition to the possibility to manipulate the phase retardation of light spatially (as it is utilized in the cited examples) a number of optical elements rely on the control of phase retardation with respect to space and polarization. One example is the generation of radially and azimuthally polarized beams by phase masks that are composed of half-wave retarding elements. Several techniques to achieve that aim have already been investigated relying on, e.g., anisotropic crystals [11, 12] or sub-wavelength gratings [13–15]. Although, the application of sub-wavelength gratings offers a high degree of flexibility, their design and fabrication still exhibit severe challenges. A lot of work was attributed to the realization of quarter-wave plates [16–19] but the operation of a half-wave retarder [20–22] especially in the visible regime demands for structures with low periods and large aspect ratio features. One way to tackle this difficulty is to use materials with high refractive indexes, however, their direct patterning [20] is by far not as highly developed as it is the case for silica based materials (the standard material for photo lithography masks).
2. Basic geometry
In this paper we report about the fabrication of half-wave retarding elements in the visible spectrum above 630nm. We rely on low refractive index fused silica gratings (substrate index around 1.46) which are conformally over-coated by a high index layer of titanium dioxide (TiO2; refractive index around 2.35 @632nm) using atomic layer deposition [23] (ALD). A schematic of the structure under consideration is depicted in Fig. 1(a). The element is expected to work for normal incident light in transmission and for a wavelength of 632nm. To guarantee a sub-wavelength configuration the period of the grating is fixed at 400nm. The remaining parameters, i.e. duty cycle (ratio between groove width and period), grating depth and TiO2 film thickness are subject to a dedicated analysis to find a good balance between the expected optical performance and technological feasibilities. For that purpose we have performed rigorous numerical calculations (relying on the Fourier Modal Method [24–26]) evaluating the zeroth order transmission coefficients TTE and TTM depending on the three mentioned parameters [27]. The essence of this analysis is presented in Fig. 1(b). The shown surface defines the parameter’s sub-space such that a phase retardation Δ = −arg(TTM/TTE) of 180° between the two orthogonal polarization states is realized. It has to be mentioned that the irregular features of the iso-phase surface for low duty cycles and large film thicknesses of the TiO2 layer (in the vicinity of the right edge of the presented volume) are caused by the excitation of (leaky) guided modes within the grating layer. Consequentially, this region is unfavorable for the designated element. In addition to the retardation condition of Δ = 180° a perfect half-wave plate must also exhibit an equal intensity transmission ratio, that is |TTM/TTE|2 = 1. Thus, the possible parameter space is further reduced which is eventually represented by the red path (the color shading is a measure for the TM/TE intensity ratio) shown within the iso-phase surface in Fig. 1(b). Here, a phase retardation of 180° and an intensity ratio of 1.0 are achievable simultaneously. It is obvious by inspection of Fig. 1(b) that a perfect half-wave retarder is already realizable even for comparably small grating depth levels starting at approximately 1.1μm. Nevertheless, a more relaxed configuration that is more tolerant with respect to technological aspects (mainly duty cycle and grating depth) appears to be preferable. For that reason, we have decided to realize a series of gratings with a depth around 1.720μm (indicated by the semi-transparent red plane in Fig. 1(b)) and a nominal duty cycle between 0.65 and 0.9. The backbone fused silica gratings were fabricated by electron beam lithography and reactive ion etching (RIE). For that purpose, the blank substrate was coated by chromium and an electron resist layer of 200nm and 400nm thickness, respectively. The resist was then structured using an electron beam writer (Vistec SB350 OS) followed by subsequent development. The structure was then transfered into the chromium layer by RIE and the resist layer was removed. Afterwards, the grating structure was transfered into SiO2 again using RIE (Sentech SI 500) with the chromium masking the developing grating ridges. Eventually, the chromium layer was removed ending up with a monolithic grating in fused silica. In a final step a thin TiO2 layer was deposited onto the backbone grating using plasma enhanced atomic layer deposition. The precursor titanium isopropoxide was oxidized at 100°C substrate temperature. Subsequently, the thickness of the deposited TiO2 layer was determined by ellipsometric measurements at an unstructured area of the substrate and it amounts to 21.6nm. Within the structured region we expect a slightly smaller value because the density of the reactants during the deposition process is affected by the deep grooves of the fused silica grating.
Fig. 1 (a) Schematic of the birefringent grating structure used to achieve high phase retardation in transmission between the two orthogonal polarization states TE and TM. (b) Iso-phase surface corresponding to a phase retardation of Δ = −arg(TTM/TTE) = 180° depending on the grating’s duty cycle, the grating’s depth and the TiO2 layer thickness. The color of the iso-phase surface indicates the intensity ratio |TTE/TTM|2. The contour lines in the bottom plane denote the phase differences (in degree) from the perfect retardation condition for the lowest considered grating depth of 1μm. The semi-transparent red plane indicates a grating depth level of 1.720μm.
We have fabricated four different grating samples with varying duty cycle. The usable size of each sample was 10 × 10mm2. The samples were numbered with decreasing duty cycle and they are denoted as sample #1 to #4. A typical cross section of the fabricated samples is shown in Fig. 2. The shape of the grooves slightly deviates from that of the perfect rectangular one. During the etching process of fused silica also the chromium mask starts to degenerate. This causes the groove width to increase with the advancing etching process, however, the fabricated samples are perfectly applicable as half-wave retarders.
Fig. 2 Cross section of fabricated sample #2. (a) A section ranging throughout the complete depth of the grating structure and (b) shows a zoomed view where only the crowns of the grating lines are visible. The textured shape represents the thin layer of TiO2. All other accumulations of materials were only locally deposited in favor of the cutting process. (c) Schematic view of the more realistic fused silica grating together with the precise geometrical quantities used for numerical simulations of the fabricated samples [28]. The four different values of the trench width W in the box correspond to the four fabricated samples. The lower, trapezoidal section of the trench profile was segmented into 30 individual layers for calculation. The TiO2 layer is not depicted, but it is taken into account during the calculations.
3. Performance of fabricated samples
In order to evaluate the performance of the fabricated samples with respect to phase retardation and TE/TM intensity ratio we have performed ellipsometric measurements (Sentech SE850). The total (polarization sensitive) transmission was additionally measured and the results are summarized in Figs. 3 and 4. The ellipsometric angles Ψ and Δ are linked to the transmission coefficients in the following way: TTM/TTE = tan Ψ · exp(−iΔ). Thus, besides the absolute transmission value they fully characterize the polarization characteristics of the sample. The two graphs of Fig. 3 show measured values of Ψ and Δ and the different symbols are associated to the different samples according to: black stars (#1), blue circles (#2), red crosses (#3), green squares (#4). The corresponding solid lines in case of Δ show the results of numerical calculations relying on the more realistic grating profile as depicted in Fig. 2(c) [28]. Measured and calculated data nicely match to each other, although slight deviations can be identified in the vicinity of resonances [29]. Except sample #1, all samples achieve a half-wave retardation in the non-resonant domain (the bandwidth of Δ being 180° ±10° is about 50nm). Remarkably, sample #2 and #4 simultaneously achieve an intensity ratio |TTM/TTE|2 of nearly 1.0 (Ψ = 45°) at the corresponding wavelengths of 628nm (blue vertical line) and 693nm (green vertical line). In contrast to that, sample #3 is characterized by a value of Ψ = 44.0° at 667nm (red vertical line) which corresponds to an intensity ratio of |TTM/TTE|2 = 0.93.
Fig. 3 Ellipsometric measurement results of the fabricated grating structures. Ψ and Δ are the standard ellipsometric angles (see text). The retardation Δ takes values in the interval |0°, 360°] where a value of 360° corresponds to zero retardation. The different colors (symbols) correspond to four different fabricated samples with varying duty cycle (see text). The solid lines are the results of the numerical simulations. The colored vertical lines indicate the perfect retardation point, i.e. Δ = 180°, of the associated samples.
Fig. 4 Transmission of the fabricated samples #2 and #3. The symbols (solid lines) correspond to measurement (simulations) results. The colored vertical lines indicate the perfect retardation point, i.e. Δ = 180°, of the associated samples. The magenta (grey) curves indicate the measured (calculated) transmission functions of the unstructured substrate with (without) the deposited TiO2 layer on the top side of the substrate.
Figure 4 shows the measured as well as calculated total intensity transmission of sample #2 and #3. The calculation was done once again relying on Fig. 2(c) with Fresnel-losses at the rear side of the substrate already taken into account [30]. In both cases the TE and TM intensity transmission functions undergo Fabry-Perot oscillations that can be attributed to the grating layer acting as an effective medium slab. The intersection points of both curves exactly determine the wavelengths where an intensity ratio |TTM/TTE|2 = 1 can be achieved. Sample #2 shows a total intensity transmission of |TTE|2 = |TTM|2 = 93% at 628nm whereas sample #3 is characterized by |TTE|2 = 92% and |TTM|2 = 86%. Most remarkably, the magenta curve (black line) within Fig. 4 indicates the measured (calculated) transmission functions of the unstructured substrate with (without) the deposited TiO2 layer on the substrate material. Thus, the achieved total transmission of the fabricated half-wave retarders (especially sample #2 and #4) are approximately equal to the intensity transmission through the bare substrate wafer. In particular, it is considerably higher than the intensity transmission through the unstructured but coated substrate wafer. Both aspects cleary emphasize the quality and potential of the chosen design approach.
In conclusion, we have designed and fabricated half-wave phase retarders for the visible to NIR spectral region. The chosen design approach relies on low index sub-wavelength gratings that are over-coated by a high refractive index layer using atomic layer deposition. This approach helps to lower the required aspect ratio for a functional half-wave retarder. An equivalent grating that is simply realized in fused silica (omitting the high index layer of titanium dioxide) would result in a grating depth of at least 3.7μm which doubles the required aspect ratio. Eventually, we have achieved a total intensity transmission of 93% which well corresponds to that of a bare glas sample.
Acknowledgments
We greatly acknowledge F. Fuchs for the development of (and help with) a rigorous Maxwell solver named Moose used to perform the numerical calculations. Parts of the work presented here were supported by the German Ministry of Science and Education in the frame of the projects PhoNa (FZK: 03IS2101D) and NencoS (FZK: 13N12418).
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27. The refractive index of TiO2 was measured by ellipsometry of a thin homogeneous film deposited on an unstructured substrate. The so determined material dispersion was taken into account during the numerical calculations.
28. The exact geometrical parameters as provided by Fig. 2(c) were determined by numerical minimization of the differences between the measured ellipsometric data and the calculated one. Cross-section REM images were only used to produce an educated guess for the minimization problem. A direct usage of the cross-section images was not possible due to insufficient precision.
29. For wavelengths smaller than 585nm the first diffraction orders begin to propagate within the substrate. The sharp resonance peaks between 605nm and 625nm are caused by guided modes excited inside the grating layer. They are more pronounced for the numerical calculation results, although they can also be identified for the measured data at least in case of sample #2 and #3.
30. Essentially, there appears to be a slight offset between the measured and the calculated values which we attribute to some systematic deviation, keeping in mind that the geometrical profile used for numerical calculations is still an approximation.
