1. Introduction

Most commercial instruments that measure transmittance and reflectance use a large beam size which can only give macroscopic information about the material’s properties. To use such instruments for characterization of miniature optical components, special measures must be taken. For blazed diffraction gratings another problem is the fact that the discrete diffraction orders are transmitted at different angles from the sample. Furthermore, internal reflections will be transmitted through the blaze at a different angle compared to that of the incident light. These reflections reduce the effectiveness of the grating since a lower fraction of the transmitted light will be diffracted in the first order.

By adding antireflection (AR) layers it is possible to increase the performance in two ways. Firstly, the total transmittance is increased, and secondly, the internal reflections are reduced. One way to do this is to superimpose a subwavelength grating upon the surface [1]. The structured surface and incident medium form an effective medium, by designing the grating with a correct duty cycle and depth it is possible to obtain an optimal refractive index, removing the reflection completely.

The possibility of superimposing a subwavelength grating on a blazed grating structure [2] in the same manufacturing process is advantageous: it obviates the need for extra processing connected with thin film depositing as well as eliminates problems with thermal expansion or stress associated with thin film layers. Injection molding is a cost-effective process to manufacture blazed gratings with a superimposed subwavelength grating. It is a cheap way to manufacture mass-reproducible optical components for low-cost consumer optics.

In this paper we have produced polycarbonate (PC) injection molded blazed gratings with a superimposed subwavelength AR-grating and applied a sol-gel AR thin film on the back surface to obtain double-sided AR-treated structures.

2. Experiment

2.1. Lithography and injection molding

There are several different techniques for microfabrication. The master used for production of our blazed gratings was prepared using direct-write e-beam lithography. The process starts with a layer of e-beam resist (PMGI SF15) on a quartz substrate. In a first run the e-beam defines the pattern for the blazed grating. The master is partially developed so that the gratings reach a fraction of the projected height [3]. The resist layer is then exposed in a second run with the e-beam to define the pattern for the AR-grating. Again the resist is developed, so that now both the blazed grating and the AR-grating obtain their final shape. A HeNe laser is used to monitor the transmittance during the second development so that the optimum development time is achieved.

The linear blazed grating had a periodicity of 16 μm and a target depth of h = λ/(n-1) = 1.09μm, for a design wavelength λ of 633nm and the refractive index of polycarbonate n which is 1.58 for the given wavelength.

The subwavelength grating consisted of linear grooves with a period of 300nm. The optimised depth should be at least 300 nm for a design wavelength of 633nm. In the case of a binary subwavelength profile the optimum depth is a fixed value, however, in our case the shape is sinusoidal and the optimum depth should be higher [4].

The size of the micro-optical structure used in this study is 0.8×0.8 mm². In principle it is possible to obtain much larger components. However, a stitching error is introduced between writing fields due to the limitation of the area scannable by the e-beam. Every time the sample is moved there is an alignment error of up to 50 nm between two adjacent writing fields. With the lithography equipment used in this study, a JEOL JBX 5D-II, the area covered for one writing field without sample movement is 1.6×1.6 mm² when defining the larger blazed structure and 0.8×0.8 mm² when defining the smaller AR-structure. The size difference between the two writing fields is inherent in the need of higher resolution for definition of the AR-grating. In our case the structures were made to fit into only one writing field, avoiding stitching errors.

Figure 1(a) contains a schematic picture of the principle of the sample structure. The surface of the master has also been studied with AFM measurements which can be seen in Fig. 1(b).

 

Fig. 1. a) The principle for blazed grating with superimposed AR-structure. The backside of the sample is flat without any structure. b) AFM pictograph taken from the master. The peak at the edge of each blaze is for proximity compensation of the rounding at the bottom of the next blaze. The depth as seen as the distance between the two triangle markers is 1 μm.

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Using the e-beam written grating structure we next produced a mold, or cast, by electro forming. The mold material is nickel since it is durable, easy to clean and resistant to a number of solvents.

Polycarbonate (PC) blazed gratings with an AR-structure were then manufactured using injection molding. In the process melted PC is injected into a mold with high pressure and at high temperature. The process is the same used for compact disc manufacturing resulting in a substrate thickness of 1.2 mm. An issue with this replication process is of course how well the small features will be reproduced from the e-beam written original via Ni-mold and into the PC substrate. The fidelity of the replication steps in this process has been studied in both academia and industry [5, 6]. The general conclusion is that going from the master to the Ni-mold there will be an almost 100% replication, except for cases with extreme aspect ratios (which are not present in our case). When going from Ni-mold to a thermoplastic material, such as PC, there will be some shrinkage effects of usually less than one percent volume, which is reproducible.

We emboss the grating features in the molding process but only on one side of the substrate, hence the back surface of the substrate was untreated. It is preferable to create an AR-structure also on the back surface in the molding process but lack of resources made that impossible in this study. To reduce reflections from the back side the sample was dip-coated with a sol-gel normally used for large area AR-coatings. To avoid coating the already AR-treated blazed grating, the structured side was masked so it was possible to coat only one side of the substrate. The process used to dip-coat a substrate with sol-gel has been shown [7] to be a successful AR-treatment. A decrease in reflectance is achieved by applying a thin film with a refractive index which is the square root of that of the substrate. The refractive index of the sol-gel is determined by the effective medium which is formed by the silica particles and the gel. The refractive index of this effective medium is affected by the size, concentration, and size distribution of the silica particles. The concentration of particles in the gel can be controlled by adding more or less solvent, whereas the particle size and size distributions are constant. Even though the method was developed for AR-treatment of glass, Fig. 2 shows that it works in laboratory conditions with PC which has approximately the same, only marginally higher, refractive index as SiO₂ in the studied wavelength region.

It is interesting to note that the sol-gel process gives almost as high transmittance as the subwavelength grating, and even higher for the shorter wavelengths. However, even though the transmittance of the subwavelength grating decreases for shorter wavelengths (for which it is not optimized) that method is preferable for manufacturing reasons since the grating is created in the molding process, and no additional thin film layer material is needed.

 

Fig. 2. The transmittance at normal angle of incidence for the uncoated PC, one-side dip-coated PC, one-side subwavelength grating, and two-side dip-coated PC versus wavelength. The sol-gel reduces the surface reflections, hence increase the transmittance. The wavelength dependence of the AR-coating is not as dominating in the single-side coating as in the double-side coating. The strong decrease in transmittance at lower wavelength for the subwavelength grating is due to scattering into higher orders from the structure, this effect is expected to occur when the wavelength of the illuminating light approaches the grating period.

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2.2. Measurement set-up

A home-built spectrophotometer [8] was used in this study. It was designed for specular measurements at variable angles of incidence. The light source is a 150W halogen lamp which is combined with a scanning monochromator giving a wavelength range from 300 nm to 1100 nm. The detector used is a Si photodiode fitted in a small integrating sphere with a relatively wide entrance port. The sphere is mounted on a movable arm to detect light from different angles from the sample. The instrument is well suited to characterize the blazed gratings. However, the size of the beam spot is larger than the area the grating occupies on the substrate. Measuring without any modification of the set-up would result in a too high intensity when characterizing the undiffracted zeroth order. To reduce the beam size a pinhole was positioned next to the sample. The pinhole was fixed to the mount rather than on the substrate to maintain a constant intensity of the incident light. This is necessary because the intensity of the monochromatic light beam is not necessarily homogeneous over the the beam spot, hence a movement of the pinhole could result in a change of intensity. The intensity decrease is significant and results in a reduction of the usable wavelength region to 350-950 nm.

Due to the large size of the entrance port of the sphere in combination with the distance from the sample to the detector, it was possible to measure the transmittance spectrum for each single order without having to move the detector. It is important to remember that the diffraction angle is wavelength dependent and the range of angles for each diffracted order increases with increasing order number. However, the entrance port of the sphere is large enough to accept the light from adjacent orders when measuring zeroth and first order. To properly characterize the transmitted intensities in the different orders a shield is placed between the sample and the detector. The shield used is basically a stiff plate with holes cut out for each diffraction order. By covering ports in the shield that match the orders not measured, only the measured order is detected. Maintaining a fixed set-up is preferable to moving a single port between the detector and the sample, especially since the lateral spread is different for the different orders.

 

Fig. 3. The measurement set-up for measuring transmittance of the individual diffraction orders. The monochromatic incident light is limited in size by the pinhole. Light is diffracted through the blazed grating. All the ports of the order shield but the 1st order port are covered. The detector is positioned to collect light regardless of the wavelength of the incident light.

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3. Sample characterization

Gratings both with treated and untreated back surface have been characterized using the set-up described. The clear untreated PC has been used as reference to study the increased noise level in the system caused by the low light-intensities due to the pinhole.

The transmittance was only measured for five orders: The first order which has the highest transmittance for the blazed grating; the zeroth order which means no diffraction; of lower intensity was the two first negative orders and the second positive order; the third positive order was measured but found to have a too low transmittance to be significant, i.e., the transmittance was less than the noise.

3.1. Measurement of transmittance of the gratings

Alignment of the grating in front of the pinhole was achieved by measuring, and finding a maximum of, the transmittance at the angle of the first order diffraction at a fixed wavelength. After the sample was fixed in position, measurements for the transmittance in the different orders were carried out. Reference measurements were carried out before and after all five different orders were measured.

3.2. Measurement errors and uncertainties

 

Fig. 4. Transmittance of the untreated PC substrate measured both with and without the pinhole. The measurements are in good agreement, even though the measurement with pinhole shows somewhat more noise towards the shorter wavelengths.

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Since the pinhole drastically lowers the light intensity that reaches the detector it is expected that the ratio between signal and thermal noise should decrease. By measuring the transmittance of the clear PC both with and without the pinhole it is possible to estimate the error introduced due to the low light intensity. In Fig. 4 it is shown that there is no significant shift in transmittance, even though the transmittance measured with pinhole shows more noise towards the shorter wavelengths. The standard deviation of the pinhole measured curve from the macroscopically studied is 0.004.

4. Results

As shown in Fig. 4 the instrument set-up gives acceptable performance for characterization of the samples, even though the signal is reduced due to the use of a pinhole aperture. Not surprisingly the blazed AR-grating with dip-coated back surface gave the best performance. The first order efficiency is shown in Fig. 5 where the transmittance of the first order diffraction is plotted together with the sum of the lowest five orders (first order included). We choose to compare with orders -2 to 2 since the signal in higher orders was expected to be negligible compared to instrument noise. Even though the blaze is designed for 633 nm the first order efficiency and transmittance is almost constant in the range from 600 to 700 nm. The reduction in transmittance for wavelengths longer than 700 nm is not material dependent but an artifact created but the light starting to hit the edge of the order shield.

Figure 6 shows the increase in first order transmittance when the back surface is dip-coated with sol-gel. Not only is an increase in transmittance noted, but also a change in wavelength dependence of the transmittance in such a respect that the transmittance is constant over a much wider range of wavelengths. This wavelength behavior can be attributed to two effects of the anti-reflection treatment. Firstly, the reduction of external surface reflections will increase total throughput, since more light will reach the blazed side. As shown in Fig. 2, the double sided AR-treatment has a maximum at approximately 550 nm, hence improving performance for shorter wavelength than the design optimum 633 nm. Secondly, the reduction of internal reflections will cause less power to be transmitted at other angles than the first order diffraction angle. The slope of the blaze will increase the angle of the internal reflections with increasing number of reflections, causing an angle distribution of the transmitted light. From Fig. 5 it is clear that the first order transmittance is dominant compared to the other orders.

 

Fig. 5. The transmittance of the dip-coated blazed grating for the first order compared to the sum of the transmittances of orders -2, -1, 0, +1, and +2. The effectiveness is high and rather constant around 633 nm.

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In Fig. 2 it was suggested that the total transmittance should be well over 0.9 in the studied region, but the blazed grating shows an absolute transmittance of 0.8 in the five dominating diffraction orders. By using a laser light source it was possible to get some indication to what contributes to this loss in efficiency. Firstly it is possible to see that light is diffracted into much higher orders than +/-3, hence not detected during our measurements. This high order diffraction can be caused by artifacts created in the e-beam writing process. It is also possible to see signs of low-intensity diffuse scattering but the source to this is not clear. We are convinced that the replication process does not create any defects contributing to the efficiency loss. There are also no signs of any effect that would cause a large increase in reflectance; the low angle of the blaze (approximately 4°) is not enough to make a major contribution to the transmittance loss.

 

Fig. 6. Transmittance through the grating in the first diffraction order. The sample with dip-coated back surface shows a higher transmittance and wider wavelength range of effectiveness.

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5. Conclusions and outlook

We have shown that it is possible to characterize blazed diffraction gratings with superimposed subwavelength grating to find first diffraction order efficiency using spectrophotometry. Both the efficiency and the absolute transmittance were experimentally determined.

Double sided AR-treatment has been shown to give not only higher transmittance but also to widen the wavelength region where the first order efficiency is high. However, the sum of the transmittance values of the lowest five orders is lower than that of a flat PC substrate with double-sided AR-treatment. Artifacts created during the e-beam writing process is the most probable cause for the loss in transmittance.

Future work could be to further optimize the process we have demonstrated, in order to achieve even higher diffraction efficiency. Another development would be that of fabricating the subwavelength gratings not only on the side where the blazed gratings are, but also on the unstructured back side. The latter would demand double-sided replication, which so far has been demonstrated merely for low volume replication.