1. Introduction

Subwavelength gratings can exhibit resonance effects which can be utilized in many interesting applications such as filters, sensors, pulse-shapers, second-harmonic generation, and field enhancement of fluorescence [1–5]. Typically, these resonance waveguide gratings (RWG) are used as narrow band filters because the resonance effects produce very sharp peaks in the reflection spectrum. However, it has been recently shown theoretically that the RWG structures can also provide very wide bandwidths over which the reflectance is nearly 100% at the IR wavelengths [6–9]. To obtain a wide bandwidth, it is crucial to employ materials which have very high refractive index with negligible absorption. In the IR region there exists suitable materials, such as silicon and germanium, that fulfill these conditions. It has also been experimentally demonstrated by several authors that these materials can be used to fabricate broadband reflectors at the IR wavelengths [10–14].

At the visible wavelengths the lack of high-index materials prevents the realization of very wide bandwidths. Fortunately, there exists a few materials which have rather high refractive index at the visible wavelengths and therefore allow the design of RWG reflectors for which the bandwidth at the visible wavelengths is substantially wider than is achieved by typical resonance structures. In this paper we have designed and fabricated such structures using amorphous atomic layer deposited (ALD) titanium dioxide (TiO₂) as a high-index material. These kind of reflectors may be useful, for example, in filtering or field enhancement applications which make use of LED sources.

2. Design of the RWG structure

Amorphous ALD TiO₂ is a transparent material which has rather high refractive index and almost negligible absorption over the visible spectrum. The refractive index of amorphous ALD TiO₂ is nearly 2.5 at the middle of the visible spectrum [15]. Although this is among the highest refractive indices that can be used at the visible wavelengths, it is still far less than those of the materials that can be used at the IR wavelengths. For example, the refractive indices of silicon and germanium are greater than 3.4 and 4, respectively, at the wavelengths well above their bandgaps. Therefore, it is evident that broadband reflectors, for which the bandwidth is several hundreds of nanometers, cannot be realized at the visible wavelengths in the same manner as in the IR-region.

In this work we designed RWG reflectors employing the properties of ALD TiO₂. Since we also wanted to fabricate the designed RWG structure, we chose a rather simple structure which is also suitable for mass production. The structure contains a binary linear SiO₂ grating with uniform TiO₂ layer deposited on the top of the grating. Therefore, it should be emphasized that it is also possible to obtain notably wider bandwidths at the visible wavelengths than our design provides by using certain multilayer structures or using additional low refractive index materials. However, these structures are problematic from the fabrication point of view and hence we chose to design and fabricate the easiest case.

We designed two similar RWG gratings for the incident angles of 20 and zero degrees where the former gives the reflection peak around the wavelength of 532 nm and the latter around the wavelength of 633 nm. Both structures are designed for TE-polarization, i.e., the polarization of the incident light is parallel to the grooves of the grating. The period of the first grating is d = 378 nm, the height of the grating h_g = 106 nm, and the fill-factor f = 0.26. The thickness of the TiO₂ coating is h_c = 56 nm. The corresponding parameters of the second grating are d = 390 nm, h_g = 120 nm, f = 0.25, and h_c = 68 nm. The schematics of the grating structure is shown in Fig. 1.

 

Fig. 1 Design of the RWG grating where h_c is the thickness of the TiO₂ coating, h_g is the height of the grating, and d is the period of the grating. The substrate material is SiO₂.

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3. Fabrication of the RWG and the optical properties of ALD TiO₂

The RWG gratings were fabricated by patterning the SiO₂ substrate by electron beam lithography and etched by using reactive ion etching. The TiO₂ coating was atomic layer deposited on the SiO₂ grating at 120°C temperature using Beneq TFS 500 reactor with TiCl₄ and H₂O precursor gases. The low temperature of 120°C leads to amorphous TiO₂, which is smooth and has low losses [15]. In ALD process, the film grows equally on all surfaces, which allows the realization of the design shown in Fig. 1. The cycle time in the ALD process was 2.8 s and the growth speed was 0.056 nm per cycle. Although this is quite a slow process, it scales very well and thus makes possible to coat large surface areas at the same time without significantly altering the cycle time.

The optical constants of the amorphous TiO₂ were measured from a 110 nm thick TiO₂ thin film on SiO₂ substrate using variable angle ellipsometer (VASE) supplied by J.A. Woollam Co. The real part of the refractive index is shown in Fig. 2. The extinction coefficient is negligible at the wavelengths above the bandgap and therefore is not included in the figure.

 

Fig. 2 Refractive index of ALD TiO₂ at the visible wavelengths.

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The scanning electron microscope (SEM) image of the RWG structure operating at 20 degrees incident angle is shown in Fig. 3.

 

Fig. 3 SEM image of the RWG grating operating at 20 degrees incidence. The binary SiO₂ grating contains amorphous TiO₂ coating.

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4. Measurements and results

The theoretical reflectance curves of the RWG reflectors were calculated by using Fourier modal method [16] and the optimization was carried out by using MATLAB’s Nelder-Mead Simplex method. The refractive index of amorphous TiO₂ used in the simulations was obtained from the measured data presented in Fig. 2. The measurement of the experimental reflectance curves were carried out by using VASE ellipsometer. The reflectance of the RWG reflector with zero degrees incident angle was determined using transmission measurement because it is not possible to obtain the reflectance at zero degree incidence using VASE ellipsometer. At this point we note that reflectance throughout this paper refers to absolute reflectance.

In Fig. 4 is illustrated the experimental zeroth order reflectance curve and the corresponding theoretical reflectance curve for the RWG reflector with the incidence angle of 20 degrees using the designed parameters. The structure was optimized so that the center of the peak is at the wavelength of 532 nm. It can be seen that the experimental peak has shifted towards the shorter wavelengths. This shift may be caused by a slight deviation in the realized refractive index of TiO₂ or in the thickness of the TiO₂ layer. If either the thickness or the refractive index decreases, the peaks move to the shorter wavelengths.

 

Fig. 4 Reflectance of the RWG grating for the incident angle of 20 degrees in TE- and TM-polarizations. The period of the grating d = 378 nm, the height h_g = 106 nm, the fill-factor f = 0.26, and the thickness of the TiO₂ coating is h_c = 56 nm. TE exp and TM exp denote the measured reflectance curves and TE theory and TM theory are the corresponding calculated reflectances.

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The difference in the theoretical and experimental curves at the shorter wavelengths between 400 nm and 470 nm are caused by the rounding of the rectangular shapes in the fabricated element. The effect of rounding at the shorter wavelengths is treated more extensively shortly in the case of the second RWG reflector.

It should be noted that there exists non-zero diffraction orders in the substrate as well as in the reflection side because the incidence angle is not zero. The theoretical and experimental reflectances are the zeroth orders reflectances although the higher orders also contribute to the total reflectance at the wavelengths below the cut-off wavelength at 510 nm.

Figure 5 illustrates the corresponding experimental and theoretical curves of the RWG reflector at zero degrees incidence angle for which the center of the reflection peak was designed at the wavelength of 633 nm. Also in this case there is a slight deviation from the designed wavelengths in the experimental curves.

 

Fig. 5 Reflectance of the RWG grating for the incident angle of zero degrees in TE- and TM-polarizations. The period of the grating d = 390 nm, the height h_g = 120 nm, the fill-factor f = 0.25, and the thickness of the TiO₂ coating is h_c = 68 nm. TE exp and TM exp denote the measured reflectance curves and TE theory and TM theory are the corresponding calculated reflectances.

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Since the substrate material is SiO₂, it is evident that also non-zero diffraction orders will emerge in the substrate at the wavelengths below the cut-off wavelength at 574 nm. However, in the measurements the higher orders do not propagate after the SiO₂ substrate but they instead undergo a total-internal reflection at the interface between the SiO₂ substrate and air. Thus, it is not possible to measure the non-zero transmitted orders and therefore the experimental results at the wavelengths below the cut-off wavelength are not entirely correct in Fig. 5 if we assume that R = 1 − T. Since we were not able to measure the reflectance at zero degree incidence angle, we resolved this problem as follows: we calculated the theoretical transmittance where we take into account only the zeroth transmitted order (as in the measurements) and determined the reflectance using the relation R = 1 − T. We also used the rounded grating profile in order to obtain the best possible result to match the experimental results shown in Fig. 5. The above mentioned theoretical reflectance curves for the both polarizations are illustrated in Fig. 6 with the black and blue solid lines.

 

Fig. 6 Theoretical reflectance of the RWG grating determined from the transmittance using the relation R = 1 − T. The solid lines represents the case where we take into account only the zeroth transmitted order in the substrate. The dashed lines represents the case where we take into account all the transmitted orders in the substrate. Furthermore, in both cases the grating profile is rounded to match the fabricated profile shown in Fig. 3. Because the cut-off wavelength of the grating is approximately at 574 nm, the solid and dashed lines overlap above this wavelength.

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Now we can easily see in Fig. 6 that the curves with the solid line resemble quite well the experimental results shown in Fig. 5 which is of course as expected because in both cases we use only the zeroth order to determine the reflectance. Thus, we may conclude that the theoretical and experimental results are in rather good agreement with each other also at the shorter wavelengths although this cannot be seen in Fig. 5. Without the rounding of the grating profile the theoretical reflectance of the peak at the wavelength of 525 nm is approximately 50%.

Finally, we also calculated the theoretical reflectance using the rounded grating profile to see how the reflectance would behave if we had the means to measure it. These reflectance curves for the both polarizations are shown in Fig. 5 with the black and blue dashed lines.

5. Conclusions

In this work we have presented RWG reflectors with substantially wide bandwidth compared to typical RWG structures at the visible wavelengths. The reflector is based on amorphous ALD TiO₂ which has very high refraction index at the visible region of the spectrum with negligible absorption. We also fabricated two example reflectors and showed that the theoretical and the experimental reflectance curves are in good agreement with each other. The example reflectors provided approximately 20–30 nm bandwidth with over 90% reflectance. These kind of RWG reflectors can be useful in filtering or field enhancement applications which take advantage of LED sources.

Finally, it should be noted that it is also possible to obtain flattop reflectance curves at the visible wavelengths using similar multilayer structures such as in Ref. [9]. In these cases it is theoretically possible to obtain nearly 100% reflectance over more than a hundred nanometers bandwidth at the visible region of spectrum using ALD TiO₂. However, from the fabrication point of view, these structures are rather difficult to realize because of the adjustment problems with different layers.