Abstract: Diffractive slanted gratings are manufactured onto plastic light guides using a high refractive index material and UV replication technology. We show that the manufacturing of such components is possible in large quantities. The applications of the slanted gratings are a high efficiency light in- and outcoupling with plastic light guides. We also show that it is possible to control which outcoupling diffraction order, reflective or transmissive, is dominating and hence to maximize the light power to one direction.
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1. Introduction
Diffractive incoupling of light into light guides is very important for several mobile optical applications such as backlights [1] and virtual displays [2] and also for integrated optical components [3,4]. By using binary gratings only a very limited efficiency into one pre-defined
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direction inside of the light guide can be achieved and in many applications this is a show stopper. Asymmetric gratings are more desirable, especially blazed gratings, but in the case of the grating period in the range of the visible wavelengths, the manufacturing of blazed gratings is very sensitive to manufacturing errors [5-7]. A much better choice is to produce a binary mask and then to etch binary slanted surface relief gratings since they are well known to couple monochromatic light into a light guide with ~97% efficiency [8].
Previously it was shown that the manufacturing of small area slanted gratings is possible with a normal RIE etcher using a Faraday cage setup [9]. Much bigger areas can be manufactured with ion beam etching (IBE) of with reactive ion beam etching (RIBE) technology. The major limitation of these methods is the very complicated and expensive equipment which leads to a very high production price and hence there is a big difficulty to obtain the price level that is accepted in the consumer product market. Therefore, the development of replication methods for the slanted gratings is very important and our task here was to establish a method that can produce slanted gratings with mass quantities having a pre-defined optical performance.
Typical plastic materials have "low" refractive indices in the range of n=1.49 (PMMA) - 1.59 (PC) which is typically a big limitation for the grating design. The increase of the refractive index also increases the phase shift of the grating and this leads to shallower grating profiles which are then easier to manufacture by lithographic techniques. Furthermore, the higher refractive index makes efficient grating designs easier for a wider optical spectrum. Nowadays, there exist some optical high refractive index materials in the market and it is shown that in some of them the grating manufacturing is possible [2, 10]. We chose a high refractive index optical resin ("episulfide") from Mitsubishi Gas Chemical Inc. for the base of the numerical simulations and to experimental testing for this article [11].
In this article, we maximized the light incoupling with the transmitted first diffraction order with slanted gratings using a rigorous diffraction theory [12,13]. For the light outcoupling we had an interest to find a solution in which the contrast between the transmitted and reflected outcoupled beams is maximized. This is especially important with the diffractive virtual displays and also for several backlighting systems.
This article contains the following sections. In section 2 we introduce the optical geometry and give the numerical simulation results for light in and outcoupling with high contrast outcoupling values. In section 3 we show that mass manufacturing of slanted gratings is possible with the UV replication technology and give the experimental results of the optical measurements. Finally the conclusions are made in section 4.
2. Numerical simulation
Let us consider a case where light is coupled into a light guide using diffraction of light from surface relief gratings on the light guide surface. The necessary condition is that the angles of the propagation of light in the light guide are such that the light is trapped inside the light guide due to total internal reflection (TIR). We also limit our discussion to the cases where only the first order diffractions in the incoupling are allowed. This means that the grating period will be in the range of λ/2 to λ. The maximum value of the period depends on the angular distribution of the light that is needed in the light guide and typically the period is about 80% of the wavelength. It is beneficial to use a high refractive index material, because generally the diffraction efficiencies are higher and the angular spread of the beams inside the light guide is smaller. In this article, the chosen high refractive index episulfide material is typically used in eyeglasses and has a refractive index of nD = 1.716@532 nm.
2.1 Light incoupling
The overall amount of light coupled into a light guide depends not only on the coupling efficiency of the grating but also on the grating area. If the width of the grating is too large, a significant part of the incoupled light is coupled out because the light returns back on the
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grating and is diffracted back to the original direction as depicted in Fig. 1 for a binary incoupling grating.
Fig. 1. Incoupling (ηT1) and back-coupling (2 x ηT1) of the light in a wide grating area with a binary incoupling grating.
Now, the efficiency of the incoupling and the back-coupling is exactly the same
according to the reciprocity theorem [13]. The maximum width of the grating area is thus Wmax=2Dtanθ, where D is the thickness of the light guide and θ is the angle of the light beam with respect to the normal of the plate, and ηT1 is the efficiency of the first incoupled diffraction order. Furthermore, with binary gratings the light incoupling geometry is symmetrical and this may cause a significant loss of the light going to wrong direction depending of the application.
The situation changes dramatically if the grating type is highly slanted (the parameters of the binary slanted grating are defined in Fig. 2). In the incoupling the other diffraction order (ηT-1 or ηT1) dominates and practically the light is diffracted into one direction with the light incidence to the normal of the grating. In all the grating calculations we did use a generalized coordinate transformation method [12], which is very convenient in calculating the efficiencies of practical shaped slanted gratings. In our example, where the slanting angle is ϕ = 35º, wavelength λ = 532 nm, and period d = 405 nm (leading to θ = 49.06º), the other component almost vanishes, while the other approaches unity.
Fig. 2. Definitions of the parameters of slanted binary grating. The width c of the groove is measured at the half height and the ratio c/d is called the filling ratio. The grating period is d and the grating vertical depth is h. The slanted angle is defined as ϕ = (ϕ1+ϕ2)/2. Generally the angle ϕ1 must be bigger than the angle ϕ2 (i.e. causing a positive slope for the grating line).
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Fig. 3. The incoupling of the light in a splitted grating area.
The incoupling area can be now divided in two parts, where the slanting directions are opposite, as depicted in Fig. 3. The first observation is that the coupling towards the right side is dominating and the weak coupling towards left side can be neglected, because the calculated efficiencies at optimum height h = 330 nm and at optimum filling ratio c/d = 55% (material) are ηT- 1= 0.920 and ηT1 = 0.005 (with the TE-polarization). Therefore, the coupling area Wmax can be two times larger than in the case of incoupling using symmetrical groove profiles. Actually, the coupling area could be even larger, because the back-coupling (ηT1) is weak, but there is also the second order diffraction (ηR2) when the beam meets the grating again. This second order diffraction turns the light backwards and the beam will eventually meet the grating again, and will be strongly diffracted out from the light guide back to the incoming direction which actually limits to expand Wmax.
2.2 Light outcoupling
The outcoupling grating systems can be categorized in the reflection type and transmission type as depicted in Fig. 4 based on which diffraction order is the strongest. The slanting angle direction is the parameter that affects mostly in the diffraction order selection. The Fig. 4 shows a typical slanting orientation in both cases with respect to the incoming light beam.
Fig. 4. Reflection (left) and transmission (right) type outcoupling of slanted gratings. The gratings can be optimized for given wavelength and angular parameters by adjusting
the slanting angle ϕ, grating vertical depth h, and filling ratio c/d. In Fig. 5 are shown the calculated efficiencies of slanted binary gratings in two different outcoupling configurations. As can be seen, the transmissive one is more favorable, because the first diffraction order is very efficient and all the other orders are very weak at h = 330 nm (actually this is the same depth that was the optimum for the incoupling).
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Fig. 5. Calculated outcoupling efficiencies of slanted binary gratings as a function of grating vertical depth. The left graphs correspond to the reflection type outcoupling and right hand side the transmissive type outcoupling. The parametrers are λ = 532 nm, d = 405 nm, ϕ = 35 º, and c/d = 55% (episulfide material).
3. Experimental results
3.1 Grating mould manufacturing
We manufactured the gratings by using a 5" x 5" x 0.09" SiO2 plate as a base substrate. The substrate was commercially coated with 80 nm chrome layer (Cr) added with 20 nm thick low reflective chrome layer (LRC) for the antireflection. The substrate was then coated with a diluted Shipley S1800 series resist with the resist thickness of 200 nm (spinning with 3000 rpm for 60 seconds) and the substrate was then baked on a hotplate at 110ºC for 120 seconds. Then the resist layer was patterned with a well known holographic recording (LIL technology) with an Argon-ion laser operating at the wavelength of λAr = 363.8 nm [14]. Our target was to produce the grating period of d = 405 nm which yields the exposure angle of 26.69º in the holographic setup. The exposure distance between the objective lenses and the substrate was ~105 cm and we had uniform exposure area of ~3 cm x 3 cm on the substrate holder. After 30 mJ/cm2 exposure (within 40 seconds) the substrate was baked on hotplate at 90ºC for 120 seconds in order to stabilize the resist and to improve the resist line roughness. The resist was then developed at 21ºC in Shipley MF-351 developer (NaOH) and distilled water solution (1:5) for 60 seconds. During the development the substrate was upside down and gently shaken. After the development, the resist profile shown in Fig. 6 (left) was obtained having a good resist line roughness and a slight positive slope.
Fig. 6. Left: A developed photoresist mask on 100 nm thick Cr layer (80 nm Cr + 20 nm LRC). The grating period is d = 405 nm. Right: An example of the 100 nm thick Cr mask profile after the chlorine dry etching process.
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The resist pattern was then transferred into the Cr layer by a chlorine dry etching process. We used Oxford Instruments Plasmalab 100 with ICP380 source (but etched only in the RIE mode). The used process parameters were: Power (RIE) = 75 W, Cl2 = 60 sccm, O2 = 8 sccm, p = 98 mTorr, etching time t = 420 seconds, no Helium backside cooling applied, and the substrate was clamped with 4" round clamping ring. The Cr-etch rate was ~15 nm/min and the etching selectivity of 1.5:1 (Cr : photoresist) was obtained within the grating area of 30 cm2
(several grating apertures were exposed on the same substrate). After the etching process the remaining photoresist was stripped with an oxygen plasma process. The obtained Cr profile is shown in Fig. 6 (right) having an excellent vertical profile shape for the following reactive ion beam etching (RIBE) with freon based chemistry. In the RIBE etching process an ionized Argon beam is directed to the substrate with an oblique angle of incidence. The selectivity between SiO2 and Cr is increased by adding reactive gas (freon) to the etching chamber (like in a normal reactive ion etching). As a result a slanted grating is etched into SiO2. The RIBE etching was subcontracted and the exact process parameters are not known. However, we found out that 100 nm thick Cr hard mask was well enough to etch up to hmax = 400 nm deep slanted gratings. The etching was performed with ϕ = 35º and ϕ = −35º slanted angles to the vertical etching depth of h = 330 nm (the etching was done in two phases by protecting half of grating areas). It is worth stressing that the RIBE etching with an oblique angle makes almost automatically a positive slope (i.e. not totally a binary slanted grating) in the grating sidewalls due the Cr mask erosion. After the RIBE etching the Cr mask was removed by a standard wet etching process and a cross section of the mould is shown in Fig. 7 (left).
3.2 Slanted grating UV- replication
The SiO2 master mould for the UV replication process was anti adhesion treated with a standard process by immersing the sample in a 0.2% solution of tridecafluoro-1,1,2,2-tetrahydro-octyl-trichlorosilane by using methyl-nonafluoro-butylether as the solvent for 10 minutes and then immersed in pure methyl-nonafluoro-butylether for 10 minutes followed by drying in nitrogen atmosphere. The chemical formula of tridecafluoro-1,1,2,2-tetrahydro-octyl-trichlorosilane is CF3(CF2)5(CH2)2SiCl3 and methyl-nonafluoro-butylether was commercially available under the trade name "HFE-1700" by the company "3M Minnesota Mining & Manufacturing Co".
After the anti adhesion treatment we tested the possibility to replicate the slanted gratings from the SiO2 mould [15]. We had two 4 mm wide grating areas side by side with ϕ = 35º slanting angles at opposite directions (ϕ = +35º on the right side and ϕ = -35º on the left side) and the cross section of the grating is shown in Fig. 3. The grating line height was 15 mm (i.e. we had a 8 mm x 15 mm grating). As a replication plastic substrate we used ~2 cm x 3 cm x 1.3 mm parts of thermally cured episulfide material. The master mould was then placed on a metallic plate having uniform temperature of 60 ºC, we dispensed a small drop of UV curable episulfide with an injection needle on the grating, then placed the plastic substrate without applying any pressure, and cured the whole package with UV energy of 120 mJ/cm2 (the UV lamp spectrum had the maximum at λUV=360 nm). The replica was separated by peeling off with a knife from the plastic substrate edge and no separation problems were observed although the gratings had slanting angles to the opposite directions. This was a very surprising result and we decided to do a test the lifetime of the mould and continued the replication. After the 120 replications we had to clean the master in a heated vacuum oven by heating the mould to >500 ºC which evaporates the plastic from the surface. Then we did the anti adhesion treatment again. After that 400 more replicas were made without any problems. A SEM picture of the 520th replica is shown in Fig. 7 (right) and no damages either on the replica or the master grating were observed. The replica is almost a perfect copy from the mould. This is for our known the first time when slanted gratings are successfully replicated in mass quantities. Based on our experience, we think that the mould lifetime will be very long and therefore we decided not to continue the lifetime testing since it would be a very long lasting task.
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Fig. 7. Left: A cross section of the manufactured SiO2 mould (grating period is d = 405 nm and vertical depth is h = 330 nm). Right: UV-replica number 520 showing almost an exact copy of the master mould. The corners are sharp that indicates a good replication degree. The grating lines have a small positive slope (few degrees) caused by the RIBE etching process which is one key factor for the replica separation.
The heating, well done anti adhesion treatment, material properties, and positive slope in
the grating lines are the key factors that makes the replica opening from the mould very easy (the process is still harder than with normal binary grating with the same depth). However, if some of them fail, the replication process is a hard one and will easily cause a mold breakage (as will also do the negative slope with higher grating depths). We also tested the replica separation without heating and with a long time used anti adhesion treatment, and then the replica was separated only with a high force and that caused a terrible sound (like sliding glass plates face-to-face). However, even in this case the master mould survived without any damages, which further indicates a long lasting mould.
We also studied how much the grating can be slanted so that the replication still can be performed with d = 405 nm grating period. This depends of course on the vertical depth of the grating, which we now limited to h = 300 nm for our test. We observed that the gratings can be replicated up to ϕ = 50º slanting angle before the grating line bottom starts to be ripped off in plastic. This is sufficiently far away from the practical slanting angles that are between ϕ = 25-40º for most of the applications.
3.3 Experimental in and outcoupling efficiencies
Our target was to manufacture a very efficient diffraction grating for the light incoupling. Furthermore, we wanted to have an outcoupling grating that provides a very high contrast between ηT1 and ηR1. For these reasons we tested the grating profile that is illustrated in Fig. 7. Generally the incoupling efficiency depends on the filling ratio of the grating and we can expect that there is some variation from sample to sample in the maximum efficiency. Calculations indicate that 1% change in the filling ratio changes the incoupling efficiency by 3%. The highest measured incoupling efficiency from our samples was 89% for one incoupled diffraction order. The measurements where done using a prism attached on the plastic plate with index matching fluid and the reflection losses on the interfaces were taken into account. The light source was a laser producing 0.2 mW light having the wavelength of λ = 532 nm. The results of experiments with a typical sample are shown in Table 1. The experiment and calculations are generally very close to each other, although some deviations are in the low efficient diffraction orders. These differences can be attributed to the experimental setup errors and the small deviations of the experimental groove shape from the modeled one. For the outcoupling we were able to have experimentally a contrast value of ηT1/ηR1=0.8/0.08=10 which is a very high ratio for the first results. We expect to improve the contrast value in the future by improving the manufacturing precision of the moulds. Furthermore, we had experimentally a light incoupling efficiency of 80% into one direction which is a sufficiently high number for the applications.
#78620 - $15.00 USD Received 2 January 2007; revised 14 February 2007; accepted 14 February 2007
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Table 1. The measured and calculated efficiencies from a replicated slanted grating structure.
Incoupling Transmission type outcoupling
Reflection type outcoupling
Diffraction order
Experiment Theory Experiment Theory Experiment Theory
T-1 0.80 0.83 - - - -
T1 0.03 0.00 0.80 0.83 0.03 0.01
T0 0.10 0.12 - - - -
R0 0.06 0.07 0.06 0.11 0.10 0.11
R1 - - 0.08 0.01 0.57 0.50
R2 - - 0.07 0.05 0.30 0.38
4. Conclusions
The results shown here provide high potential to manufacture slanted diffractive gratings by a simple replication technology. The slanted gratings can be used efficiently in the light incoupling and also light outcoupling into one direction from the light guide. We expect that by the process introduced here the mass replicated slanted gratings can be used also in many commercial consumer market products due to the low end price of the high efficiency components. Furthermore, the usage of the high refractive index materials is feasible and this makes it possible to produce more complicated diffraction gratings due to their lower depth.
Acknowledgments
The authors wish their best acknowledgements to Nokia Research Center and University of Joensuu, Department of Physics and Mathematics for running "HoloLito" and "Vapola" projects funded by the National Technology Agency of Finland (TEKES). The funding from TEKES and the Academy of Finland (project number SA 201008) are gratefully appreciated. We thank Dr. Hemmo Tuovinen for performing the holographic exposures, Dr. Victor Prokofiew for the dry etching, and Dr. Jari Lautanen for the SEM analysis. We thank Mrs. Viljakaisa Aaltonen, Mr. Jyrki Kimmel, Mr. Peter Eskolin, and Dr. Pekka Äyräs for performing the lifetime test of the mould. The authors acknowledge the Network of Excellence on Micro-Optics (NEMO), http://www.micro-optics.org.
#78620 - $15.00 USD Received 2 January 2007; revised 14 February 2007; accepted 14 February 2007
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