This paper presents a noble diffractive grating so as to achieve high diffraction order. A v-shaped groove transmission grating with reflective and refractive surfaces (VGRRS) is proposed. Design, fabrication, and optical testing of the VGRRS are described. This grating is simulated by Rigorous coupled-Wave analysis (RCWA) for TE mode and fabricated by thermal evaporation on the replica which is obtained through a hot-embossing process using a v-shaped groove mold. The most important property of VGRRS is to conduct a high diffraction order at visible wavelengths. When used at the wavelength of 406nm, the VGRRS can strongly have two high diffracted lights in terms of -4th and -10th transmission diffraction orders.
© 2008 Optical Society of America
Diffractive optics elements (DOEs) such as a diffractive lens, a diffraction grating, and beam shaping have been the subject of wide interest in the field of industrial and commercial applications because they have advantages as compact, lightweight structures. Among these DOEs, a diffraction grating defined as an optical component with a regular pattern has been researched on the basis of the Huygens-Fresnel principle, and categorized in terms of its surface profiles such as simple grating slits, a blazed grating, binary grating, and a v-shaped groove grating .
Especially, since this grating has the property of high diffraction order compared to other gratings, a v-shaped groove grating can be used in a broad variety of applications, such as optical dividing elements, wavelength division multiplexing, and spectrometer. Among these applications, a grating as a dispersive element can play an important role in a spectrometer [2–4].
Two factors of a period of a grating and diffraction order are important keys in order to separate the incident light in a spectrometer, based on the principle of the grating equation given by
in which n is the refractive index, m is the diffraction order, θi is the angle of incident light, θm is the angle of diffraction light, and λ is the wavelength . If the incident angle θi is 0° in Eq.(1), the diffraction angle θm of the incident light increases with the decreasing grating period and increasing diffraction order. Therefore, it is possible for a grating with a smaller period and a higher diffraction order to function as a spectrometer with high performance. For this reason, v-shaped groove gratings including a property of high diffraction order have recently been reported. In additional, various researchers have focused on the decrease of the grating period to increase the performance in a spectrometer [5–9].
In this paper, we propose and demonstrate another method to increase the diffraction order using a v-shaped groove transmission grating with reflective and refractive surfaces (VGRRS), resulting in high performance in a spectrometer. Our approach has the advantage that the diffraction order is higher with the VGRRS presented in this paper than with a traditional v-shaped groove grating. The proposed VGRRS is composed of a reflective surface of metal and a refractive surface of plastic, while the traditional v-shaped groove grating consists of refractive surfaces at both sides as shown schematically in Fig. 1. It would therefore be of great interest to investigate the proposed grating called VGRRS.
The diffraction orders and efficiencies of VGRRS were analyzed by Rigorous Couple- Wave Analysis (RCWA) which is an exact solution of Maxwell’s equations for the electromagnetic diffraction in a grating [10–13]. In fabrication of VGRRS in (100) crystalline silicon, the mold can be easily fabricated by the traditional method in Micro-Electro- Mechanical Systems (MEMS) using lithography and wet anisotropy etching, and the replica is obtained using a hot-embossing process. However, the important key to completely fabricate VGRRS is to use a shadowing effect in thermal evaporation, which is one of the oldest of the thin film deposition techniques [14–15].
2. Design and numerical results
The VGRRS is similar to a traditional v-shaped groove transmission grating, but is different because it consists of refractive and reflective surfaces, whereas the traditional grating consists only of refractive surfaces. In simulation of VGRRS, our prototype was designed to have a period of 3µm and a thickness of 2.199µm with a material PMMA and to cover the entire visible wavelength from 400 to 700nm. The grating thickness was determined by the grating period owing to the property of wet anisotropy etching in (100) crystalline silicon.
In order to simulate the VGRRS with RCWA in this paper, it was necessary to divide the grating into a large number of thin slabs as shown in Fig. 2. In order to prevent the antireflection from each slab during simulation, the number of layers and the thickness of each slab were defined as 26 layers and 81.5nm, and the materials considered for reflective and refractive surface are aluminum and PMMA, respectively. Additionally, the refractive index of PMMA for the wavelength of 406nm is 1.50529, and the angle of incident light is 0°.
The simulated performance of the VGRRS for the visible wavelength is shown in Fig. 3. As a result, there are some dominant transmission diffraction orders, while all of reflection diffraction efficiencies are small compared to other transmission diffraction efficiencies. Figure 3(a) is the graph of the numerical results for a traditional v-shaped groove transmission grating without reflective surfaces. It can be easily seen that -4th and +4th transmission diffraction orders are dominant with the same efficiencies around wavelengths from 400nm to 450nm, and a -3rd and +3rd transmission diffraction orders are dominant with the same efficiencies near wavelengths from 500nm to 650nm. The reason -3rd and +3rd transmission diffraction orders have the same efficiency is that the structure of a traditional v-shaped groove transmission grating consists of a bilateral symmetry of PMMA. Here, it is obvious that the other transmission and reflection diffraction orders have low diffraction efficiencies, below 5%.
Figure 3(b) shows the numerical results of the VGRRS made with reflective and refractive surfaces. There are higher diffraction orders in the VGRRS than in a traditional v-shaped groove transmission grating. In case of the wavelength of 406nm, there are two dominant transmission diffraction orders: the -4th diffraction order with a percent of 36.8 and the -10th diffraction order with a percent of 28.6, not the +4th diffraction order as shown in Fig. 3(c). Here, the sign convection for the sign of the diffraction order can be defined as following: the diffraction order is positive if the diffracted light travels to the right of grating, and negative if the diffraction light travels to the left of grating.
Figure 4 explains schematically the reason that the -4th and -10th transmission diffraction orders occur in the proposed VGRRS. If an incident light enters into the refractive surfaces, the path difference for constructive interference between adjacent lights is four times as large as the wavelength of the incident light. In case of the light entering into the reflective surfaces, the path difference for constructive interference between adjacent lights is ten times as large as the wavelength of the incident light. The incident light can therefore travel with higher diffraction order in VGRRS than in a traditional v-shaped groove transmission grating. As a result of calculating diffraction angles using Eq. (1), the -4th and -10th transmission diffraction orders have the diffraction angles of -21.1° and 64.0°, respectively. As mentioned above, the merit of the VGRRS grating is to enable the light to be diffracted with a higher diffraction order.
3. Fabrication and results
Figure 5 illustrates the fabrication processes of the VGRRS, which consists mainly of the fabrication of the mold of the VGRRS and the replica. The mold of VGRRS has been fabricated through thermal oxidation to TMAH etching process. For the mold fabrication of VGRRS, all of the experiment conditions should be considered under an anisotropy etching process by TMAH, such as the etching ratio for (100) and (111), and misalignment. In the first step, the substrate of SiO2 with a thickness of 70nm was coated with the EB resist (ZEP-520A) for a resist thickness of 500nm. After electron beam lithography (JBX-5000LS) with above substrate, SiO2 was etched using FAB plasma etching (60 ML, ABARA Co., Ltd). In the second step, v-shaped grooves designed as the mold of VGRRS can finally be formed through TMAH anisotropy etching with an etching rate of 500nm/min for (100) surface at an etching temperature of 80°. In the third step, the replica of the VGRRS with PMMA can be fabricated by hot embossing process whose conditions include a temperature of 180°, pressure of 4MPa, and PMMA of 0.5g. Here, before the hot embossing process, the mold should be coated with two chemicals of EGC-1720 and JFE-7100 in order to make it easy to exfoliate the replication form the mold.
To completely fabricate the VGRRS as proposed, there is only one process for fabrication of reflective surfaces: thermal evaporation using the shadowing effect . In this paper, the shadowing effect can be recognized as the important key to complete the proposed VGRRS, whereas it has usually been recognized as a demerit due to its non-uniform deposition according to structure. This process of using the shadowing effect ensured that Al was only deposited on the reflective surfaces, without deposition on the refractive surfaces if the replica is tilted with satisfaction at the angle of 90° between the vector of the material source and the normal vector of the refractive surface, as shown in Fig. 6. Considering the experiment conditions in thermal evaporation, such as the distance and position between the material source and the mold, the angle for the radial vector of the material source can be calculated as 26.6°. Thus, the tilted angle of α=28.1° can be geometrically found by satisfying β=90°, the angle between the radial vector of material source and the normal vector of the refractive surface.
As a result, the VGRRS as proposed was successfully fabricated through the above processes. Figure 7 shows the fabrication results for the mold of VGRRS, which is measured with a period of 3µm and a thickness of 2.113µm. Compared to the design parameters such as period and thickness, the fabrication error is insignificant.
4. Optical measurements
Optical observations of the VGRRS were made using the optical system, which is schematically shown in Fig. 8. For our experiment, a wavelength of 406nm as light source was chosen. The diffraction order in this experiment was measured outside of PMMA while the diffraction orders were calculated on PMMA material in the analysis of VGRRS. In optical evaluation of VGRRS, the light propagation through the grating to screen has to be considered. Figure 8(b), which is the magnified schematic from VGRRS to screen in Fig. 8(a), shows the light propagation in this optical evaluation. The principle of light propagation is that the collimated light entering to the VGRRS is first diffracted, and then the diffracted light is refracted at the interface between PMMA and air. These diffraction and refraction angles were calculated using the grating equation and Snell’s law according to the diffraction orders, as shown in table 1. The angles of diffracted light from the 0th order to the -7th order are smaller than the critical angle of 41.7° between PMMA and air, while the angles from the -8th order to the -10th order are larger than the critical angle. Thus, the diffracted lights above -8th order in this evaluation travel with the property of total internal reflection (TIR) in PMMA.
Figure 9 shows the results of the optical observations for the proposed and fabricated VGRRS through the experiment set-up with the light source of 406nm. Figure 9(a) shows the diffracted light with a smaller diffraction angle than the critical angle through VGRRS, and Fig. 9(b) shows the diffracted light with a larger diffraction angle than the critical angle. Thus, it is obviously seen that the two dominant transmission diffraction orders were measured in this experiment: a -4th order and a -10th order as designed. As a result of measuring the diffraction efficiencies for the -4th order and the -10th order, the diffraction efficiencies in both orders were measured to be 33.1% and 25.5%, respectively, compared to designed diffraction efficiencies of 36.8% for the -4th order and 28.6% for the -10th order.
In conclusion, the v-shaped groove grating with reflective and refractive surfaces proposed in this paper has the potential for unique characteristics of high diffraction order. Using this grating with a period of 3µm and a thickness of 2.119µm at a wavelength of 406nm, -4th and -10th transmission diffraction orders strongly occur. The diffraction efficiencies for the -4th and -10th transmission diffraction orders based on RCWA theory are found to be 36.8% and 28.6%, respectively. The experimentally measured diffraction efficiencies are close to calculation results using RCWA. In order to successfully fabricate the gratings, the shadowing effect in thermal evaporation on the replication of v-shaped groove gratings had to be carried out. Considering the definition of the resolving power of a grating, the grating proposed in this paper should be suitable for use as a spectrometer because it can make the light more separated with a high diffraction order.
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