DESIGN A WIDE-ANGULARINCIDENCE BROADBAND VISIBLE ANTIREFLECTION COATING USING TUNING SEARCH METHOD

Yeuh-Yeong Liou1 and Shau-Kuei Wang2

1Institute of Electronic Engineering, ChienkuoTechnologyUniversity

No. 1, Jieh Shou N.Road, Chang-Hua 500, Taiwan, Republic of China

2Institute of Mechatronoptic Systems, ChienkuoTechnologyUniversity

Tel.:04-7111111Ext.3366, Fax:04-7111111Ext.3304, E-Mail:

(NSC 96-2221-E-270-005-)

Abstract --- A tuning search method is applied to design a wide-angularincidence visible antireflection (AR) coating with an incident angle up to 45o from the normal. The AR performances for the maximum visible reflectivity and the average wide-angular visible spectral reflectivity can be reduced to less than0.74%and 0.40%, respectively.

Keywords: antireflection coating, wide angular, broadband, tuning search

INTRODUCTION

Most broadband visible AR coatings are designed for the normal incidence [1-4]. However, it is difficult to design a low-loss broadband visible AR coating over a wide range of incident angles since the reflectance of dielectric thin film at large oblique incident angle has a strong polarization effect, in which the design should simultaneously suit for two differenteffective substrate indices of the s- and p-polarization over a wideband spectral region of 400-750 nm.Generally the AR performance for an unpolarized light departs from a low reflectivity as the incident angle increases, and degrades dramatic when the incident angle is beyond than 20o [5].

Premoli and Rastello utilizedthe minimax refining method [6] to refine wide-angular incidence wideband AR coatings using some known solutions as the starting designs. The reflectivity of unpolarized light over 0.4-0.9 m was refined to less than 1% for incident angles ranging from 0 to 30o. We used a jumping search technique [7] to design a wide-angler-incidence broadband visible AR coating for incident angles ranging from 0 to 45o. The maximum value of the wide-angler visible spectral reflectivity is decreased to below than 0.87%.

In this study, a tuning search technique, consisted of layer-thickness tuning and layer exchanging operations, is applied to design a wide-angler broadband visible AR coating forincident angles range from 0 to 45o. The wide-angular incidence visible AR coating design, obtained by the tuning search method for a 50-layer system using only two materials, is decreased to 28-30layered structure, that the maximum visible reflectivity can be reduced to less than0.74% and the average wide-angular visible spectral reflectivity (AWAVSR) can be reduced to less than0.40%, respectively.

DESIGN ALGORITHM OF TUNING SEARCH

The design algorithm of the tuning search for obtaining a wide-angular incidence AR coating design is given as follows:

A) Select a total physical thickness of D for a two-material system, and divide it into N-layer with all layers set initially at an equal physical thickness.

B)Tune the thickness of multilayer one by one from the substrate to the incident medium to decrease the mean visible reflectivityMF. Here, the MFdefined the AWAVSR of 71 equal spectral points over the 400-750 nm regions for the incident angles of 0 and 45o given as

, (1)

where the normal reflectivity and the reflectivity at the incident angle 45o of p- and s-polarized light

, (2) are calculated on the basis of characteristic matrix theory [8].The tuning search is operated according by tuning the thickness of layer 1 firstly; follow by next layer; and so forth all layers are tuned, where the layer 1 denotes the layer that next to the substrate. If a pass of all layers is tuned and MF is refined, the tuning of next pass is then carried out. Once the MF stabilizes in a pass in all layers, and then finishes the tuning operation.

C) To further simplify the design structure and refine the wide-angular visible AR performance, an operation of layer exchanging is afterward applied. This layer exchanging search can be carried out by following different manners.

(a) Exchanges the layers from the incident medium to the substrate.

(b) Exchanges the layers from the thick layer to the thin layer.

As a pair of layers is exchanged, the layer-thickness tuning operation in step (B) is restarted to refine the MF. Ifthe MF stabilizes in a pass in all layers, then the layer exchanging operation is terminated and the solution is obtained.

D) Generally, the reflectance at a large incident angle becomes larger at the tail of long-wavelength spectral region, which degrades the wide-angular visible AR performance. To suppress this tail effect, an additional operation of tuning search with a modified merit function MF' is used to obtain a better performance, in which the weighting of wavelengths greater than 730 nm is replaced with (>1), and MF'is defined as follows,

, (3)

Restart the tuning search of the design obtained in step (C), and the desired design is considered to be achieved if MF'is no further refined in this additional tuning search in all layers.

RESULTS AND DISCUSSION

We applied the tuning search technique to design a wide-angular incidence visible AR coating for a two-material 50-layer system starting with a total physical thickness of 870 nm and with the refractive indices coded asnH-nL-nH-nL-..., in which the film materials were TiO2 and MgF2with the high and low refractive indices, nHand nL, respectively. Dispersive values of optical constants of the film materials and the glass substrate were taken into account in the calculations [9]. The tuning thickness was 0.1 nm. After 228 passes of layer-thickness tuning operation,8-9 passes of different types of layer exchanging operation, and with a w=4 in the additional tuning search, the results were obtained and are shown in Figs. 1-2.

Final designs shown in Figs. 1(a) and 2(a), obtained by exchanging the layers from the incident medium to the substrate and exchanging the layers form the thick layer to the thin layer, are decreased to 28- and 30-layered structures with the total physical thickness of 1047.1 and 1061.0 nm. The maximum visible spectral reflectivity shown in Figs. 1(b) and 2(b), occurred at the angle of 45o, are reduced to less than 0.72 and 0.74%, respectively, and that the AWAVSR for incident angles lying in the range of 0-45o, are reduced to below than 0.39 and 0.40%.These wide-angular visible AR performances are quite acceptable.

It is shown that the polarization effect causes a serious increase in reflectivity for the largest incident angle at the long wavelength of the visible region, which the tail reflectivity may greater than 1.30 %. We use a modified merit function with an additional tuning search to effective suppress the maximum reflectivity to lower than 0.75%. Here, the operation of layer exchanging can also be carried out in other different types to obtain similar resultsby exchanging layers from the substrate to the incident medium or from the thin layer to the thick layer. It is found that the starting points are the same, but different types of layer exchanging operation may lead to different final designs; however, their wide-angular visible AR performances are comparable to each other. The tuning search algorithm used in this study is quite simple and can be applicable for the coating materials and substrate that with dispersion of their refractive indices and absorbent. Besides, it is easily to generate its own starting design, and adjust the construction parameters afterward to refine the mean wide-angular visible spectral reflectivity to obtain the desired solution.

CONCLUSIONS

A tuning search method is applied to achieve a wide angular visible AR coating design for the incident angle ranges from 0 to 45o. It is shown that the wide angular visible AR coating designs obtained by different types of tuning search for a two-material 50-layer system are reduced to 28-30layered structures and their wide angular visible AR performances are highly comparable to each other. The maximum visible spectral reflectance and the AWAVSR for the incident angles lying in the range of 0-45o are reduced to 0.72-0.74% and 0.39-0.40%, respectively.

REFERENCES

[1] J. A. Dobrowolski and R. A. Kemp, “Refinement of Optical Multilayer Systems with Different Optimization Procedures,” Appl. Opt., 29, pp. 2876-2893 (1990).

[2] A. Premoli and M. L. Rastello, “Minimax Refining of Optical Multilayer Systems,” Appl. Opt., 31, pp. 1597-1602 (1992).

[3] W. H. Southwell, “Coating Design Using Very Thin High- and Low-Index Layers,” Appl. Opt., 24, pp. 457-460 (1985).

[4] Y. Y. Liou, “Designing a Broadband Visible Antireflection Coating by Jumping Search Method,” Jpn. J. Appl. Phys., 44, pp. 8462-8466 (2005).

[5] A. Thelen, Design of Optical Interference Coatings, McGraw-Hill, New York, pp. 23 (1989).

[6] A. Premoli and M. L. Rastello,“Minimax Refining of Wideband Antireflection Coatings for Wide Angular Incidence,”Appl. Opt., 33, pp. 2018-2021 (1994).

[7] Y. Y. Liou, “Design a Wide Angular-Incidence Antireflection Coating over the Visible Spectral Region,” Jpn. J. Appl. Phys., 45, pp. 4051-4057 (2006).

[8] H. A. Macleod,Thin-Film Optical Filters, Macmillan, New York, 2nd ed., Chap. 2, pp. 43 (1986).

[9] Data obtained from the Optical Coating Design Software, Essential Macleod, ThinFilmCenter (2006).

Fig. 1 (a) Refractive index profile and (b) wide-angular visible spectral reflectivity of the tuning search AR coating design for a two-material 50-layer system with exchanging layers from the incident medium to the substrate. The final design is a 28-layered structure with a total physical thickness of 1047.1 nm, and the maximum visible reflectivity and the AWAVSR are reduced to less than 0.72 and 0.39%, respectively.

Fig. 2 (a) Refractive index profile and (b) wide-angular visible spectral reflectivity of the tuning search AR coating design for a two-material 50-layer system with exchanging layers from thethick layer to the thin layer. The final design is a 30-layered structure with a total physical thickness of 1061.0 nm, and the maximum visible reflectivity and the AWAVSR are reduced to less than 0.74 and 0.40%, respectively.