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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 12 — Jun. 7, 2010
  • pp: 12249–12261

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Antireflection coatings for multilayer-type photonic crystals

Yasuo Ohtera, Daniel Kurniatan, and Hirohito Yamada  »View Author Affiliations


Optics Express, Vol. 18, Issue 12, pp. 12249-12261 (2010)
http://dx.doi.org/10.1364/OE.18.012249


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Abstract

The possibility of antireflection (AR) coatings on a dielectric multilayer having sub-wavelength deep structural modification is investigated. We numerically surveyed the effect of reflectivity reduction attained by double-layer AR coatings for a wavy multilayer on a patterned substrate. It was clarified that double-layer AR coatings for wavy multilayer is possible with a similar performance level as conventional flat multilayer. Also, it was demonstrated that a pair of AR layers effectively works for a wide range of the horizontal pitch.

© 2010 OSA

1. Introduction

This work deals with the design of thin film antireflection (AR) coatings on a class of modulated dielectric multilayers. Dielectric multilayer is one of the most common structures as a building block of various interference wavelength filters such as band-pass, edge, and band rejection. Recently, a new trial has been carried out to create novel optical functions by applying proper modification to the layer structure. For example, polarization filtering functions [1

R.-C. Tyan, A. A. Salvekar, H.-P. Chou, C.-C. Cheng, A. Scherer, P.-C. Sun, F. Xu, and Y. Fainman, “Design, fabrication, and characterization of form-birefringent multilayer polarizing beam splitter,” J. Opt. Soc. Am. A 14(7), 1627–1636 (1997). [CrossRef]

,2

M. A. Ahmed, A. Voss, M. M. Vogel, and T. Graf, “Multilayer polarizing grating mirror used for the generation of radial polarization in Yb:YAG thin-disk lasers,” Opt. Lett. 32(22), 3272–3274 (2007). [CrossRef] [PubMed]

], wavelength selective functions [3

N. Destouches, J.-C. Pommier, O. Parriaux, T. Clausnitzer, N. Lyndin, and S. Tonchev, “Narrow band resonant grating of 100% reflection under normal incidence,” Opt. Express 14(26), 12613–12622 (2006). [CrossRef] [PubMed]

,4

R. C. Rumpf, A. Mehta, P. Srinivasan, and E. G. Johnson, “Design and optimization of space-variant photonic crystal filters,” Appl. Opt. 46(23), 5755–5761 (2007). [CrossRef] [PubMed]

] and absolute photonic band-gap properties [5

M. Notomi, T. Tamamura, T. Kawashima, and S. Kawakami, “Drilled alternating-layer three-dimensional photonic crystals having a full photonic band gap,” Appl. Phys. Lett. 77(26), 4256–4258 (2000). [CrossRef]

], etc. On the other hand, a method of fabrication, called autocloning, has been proposed to manufacture multilayers with deep modulation by devising the film deposition technology [6

T. Kawashima, Y. Sasaki, K. Miura, N. Hashimoto, A. Baba, H. Ohkubo, Y. Ohtera, T. Sato, W. Ishikawa, T. Aoyama, and S. Kawakami, ““Development of autocloned photonic crystal devices”, IEICE Trans. Electron,” E 87-C, 283–290 (2004).

]. Reflection type polarization splitters [7

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarisation splitters,” Electron. Lett. 35(15), 1271–1272 (1999). [CrossRef]

], waveplates [8

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34(1/3), 63–70 (2002). [CrossRef]

], arrayed wavelength/polarization filters [9

Y. Ohtera, T. Onuki, Y. Inoue, and S. Kawakami, “Multichannel photonic crystal wavelength filter array for near-infrared wavelengths,” J. Lightwave Technol. 25(2), 499–503 (2007). [CrossRef]

,10

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plate elements,” Appl. Opt. 46(22), 4963–4967 (2007). [CrossRef] [PubMed]

], azimuthal/radial beam formers [11

A. Mehta, J. D. Brown, P. Srinivasan, R. C. Rumpf, and E. G. Johnson, “Spatially polarizing autocloned elements,” Opt. Lett. 32(13), 1935–1937 (2007). [CrossRef] [PubMed]

,12

Y. Kozawa, S. Sato, T. Sato, Y. Inoue, Y. Ohtera, and S. Kawakami, “Cylindrical vector laser beam generated by the use of a photonic crystal mirror,” Appl. Phys. Express 1, 022008 (2008). [CrossRef]

] are some of the examples of the elements that has been produced by the method. As is required for conventional flat layer type devices, optical loss of this class of elements regarding Fresnel reflection has to be suppressed as much as possible with the aid of an AR structure in a specified wavelength range. For bulk materials such as glass substrate, sub-wavelength surface microstructure has been becoming a practical option as an AR [13

Y. Ono, Y. Kimura, Y. Ohta, and N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26(6), 1142–1146 (1987). [CrossRef] [PubMed]

]. On the other hand, for a multilayer, a set of thin films consisting of the same or similar materials as main layers will be advantageous as an AR section [14

J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, “Systematic design of antirefection coating for semi-in nite one-dimensional photonic crystals using Bloch wave expansion,” Appl. Phys. Lett. 82(1), 7–9 (2003). [CrossRef]

] from a viewpoint of the compatibility to the fabrication process, because we need ARs on both its surface and substrate sides.

However, it has not been clear whether or not it is possible to achieve or design multilayer-type AR coatings on such deeply modulated layers with the same design concept as conventional flat or shallowly modulated ones. Also, the effect of reflectivity reduction has not been studied yet.

In this paper, we focus on wavy alternating multilayers as an example and surveyed the possibility of double-layer AR coatings for them through numerical calculation.

2. Structure and reflection spectra

Schematic views of conventional flat type and wavy modulated type alternating multilayers are illustrated in Fig. 1(a) and Fig. 1(b), respectively, In the latter, the interface of layers are modified as triangular wavy curves having a constant slope. The horizontal interval of the modulation, indicated by “Λ”, is shorter than the wavelength in free space. Here the refractive index alters periodically not only to the vertical but also to the horizontal directions with respect to the substrate plane. Therefore it can be classified as a two-dimensional photonic crystal (abbreviated to PhC hereafter) [15

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, 2nd ed. (Princeton University Press, 2008).

]. This wavy type of PhC can be fabricated by an rf bias sputtering process-based method called autocloning [6

T. Kawashima, Y. Sasaki, K. Miura, N. Hashimoto, A. Baba, H. Ohkubo, Y. Ohtera, T. Sato, W. Ishikawa, T. Aoyama, and S. Kawakami, ““Development of autocloned photonic crystal devices”, IEICE Trans. Electron,” E 87-C, 283–290 (2004).

]. A variety of optical elements and devices utilizing autocloned PhC as mentioned before are now commercially available [16

http://www.photonic-lattice.com/en/Products_List.html

]. The angle of the slope is determined by the relative position of the cathode and substrate, and various sputtering parameters such as pressure and bias rf power [6

T. Kawashima, Y. Sasaki, K. Miura, N. Hashimoto, A. Baba, H. Ohkubo, Y. Ohtera, T. Sato, W. Ishikawa, T. Aoyama, and S. Kawakami, ““Development of autocloned photonic crystal devices”, IEICE Trans. Electron,” E 87-C, 283–290 (2004).

].

Fig. 1 Schematic view of the multilayer. (a) flat multilayer, (b) modulated multilayer with triangular wavy modification (two-dimensional photonic crystal).

Schematic of the layer profiles used for the following calculation are sketched in Fig. 2 . Assumed parameters are as follows. Refractive indices of the high (indicated by “H” in the figure) and low (“L”) index layers are n = 2.28 (Nb2O5, etc.) and n = 1.47 (silica), respectively. Thickness of H and L layers are both a/2 with “a” the vertical lattice constant of PhC. Slope angle of the wavy interface: 40 degree, horizontal lattice constant PhC (or a period of grating): Λ = 0.9a. These are typical parameters of practical filter devices at near infrared wavelengths [9

Y. Ohtera, T. Onuki, Y. Inoue, and S. Kawakami, “Multichannel photonic crystal wavelength filter array for near-infrared wavelengths,” J. Lightwave Technol. 25(2), 499–503 (2007). [CrossRef]

]. The unit of the stack of multilayer was set as either (H/2-L-H/2) or (L/2-H-L/2), as is usually employed for the design of ARs using Herpin’s equivalent index [17

H. A. Macleod, in Thin-Film Optical Filters, 3rd ed. (IoP Publishing, 2001), Chap. 6.

,18

C. Ufford and P. Baumeister, “Graphical aids in the use of equivalent index in multilayer-filter design,” J. Opt. Soc. Am. 64(3), 329–334 (1974). [CrossRef]

]. Hereafter we call them LHL-type [Fig. 2(a)] and HLH-type [Fig. 2(b)] for brevity. Also, we only deal with the case of normal incidence. The electromagnetic modes inside the PhC can be classified into two groups depending on their polarization: TE modes (electric field parallel to the layer interface) and TM modes (magnetic field parallel to the interface).

Fig. 2 Multilayer profiles for the calculation of reflectivity. (a) LHL-type, (b) HLH-type. Λ and a are the horizontal and vertical lattice constants of the PhC. k denotes the wavevector.

Note that the body of the multilayer is assumed to have the same wavy interfaces from the first to the last layer, regardless of the shape of the cross section of the initial grating on the substrate. This is because in the autocloning method, prior to the deposition an intermediate SiO2 layer is deposited first on a SiO2 substrate to form triangular surface (the boundary between the substrate and the intermediate layer is shown schematically in Fig. 1 and Fig. 2). The insertion of this layer makes the grating pattern on the substrate invisible from the light, as the refractive indexes of the intermediate layer and the substrate are almost matched. According to our former research [8

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34(1/3), 63–70 (2002). [CrossRef]

], the effect of this insertion has been found to work for a wide range of the period of the grating. Also, the surface of the intermediate layer can be made wavy, even if the pattern of the initial grating is rectangular. Therefore, practically, the final shape of the wavy layer has smaller dependence on the aspect ratio and the shape of the surface grating. Main factors that determine the shape of wavy layer are therefore sputtering parameters for the main multilayer.

Dispersion relation of even symmetric TE modes (electric field distribution being symmetric with respect to the mirror plane normal to the substrate and parallel to the gratings) propagating in an infinitely extending PhC is displayed in Fig. 3 . This relation was calculated by an FDTD (Finite Difference Time Domain)-based method detailed in Ref. 19

Y. Ohtera, “Calculating the complex photonic band structure by the finite-difference time-domain based method,” Jpn. J. Appl. Phys. 47(6), 4827–4834 (2008). [CrossRef]

. Solid lines in black and red correspond to propagation constant of propagating modes and decay constant of evanescent modes, respectively. Doubled lines lying around a/λ~0.35 indicate propagation and decay constants of complex modes. The wavelength (or frequency) regions where no propagating modes exist are so-called stopband while the remainders are passband.

Fig. 3 Complex dispersion relation of even symmetric TE modes in a wavy multilayer PhC. Solid lines in black and red correspond to the propagation constant of propagating modes and the decay constant of evanescent modes, respectively. Doubled lines seen around a/λ~0.35 indicates the propagation and decay constants of the complex modes. “A” and “B” represent the target frequency regions for AR.

In Fig. 3, the dispersion curve of the low frequency mode (e1 ) is quite similar to that of flat multilayer. Although the second mode (e2 ) resembles that of flat layer, its high frequency edge is pressed by obliquely-propagating modes above (e3 and e4 ) and distorted [20

Y. Ohtera and T. Kawashima, “Extremely low optical transmittance in the stopbands of photonic crystals,” Photonics Nanostruct. Fundam. Appl. 7(2), 85–91 (2009). [CrossRef]

]. In frequencies higher than e4 more than two modes can exist at a frequency, causing complicated reflection spectrum. In this study, we deal with two frequency ranges indicated by A (upper edge of e1 ) and B (upper half of e2 ), which are practically important to the application to wavelength and polarization filters and waveplates.

Calculated global feature of the reflection spectra are displayed in Fig. 4 . The film profiles of the left and right figures are: air-(L/2-H-L/2)15-substrate and air-(H/2-L-H/2)15-substrate, respectively. Refractive index of the substrate was assumed to be 1.45. Top, middle, and bottom plots correspond to flat, PhC (TE mode), and PhC (TM mode), respectively. PB and SB mean passband and stopband. All films were assumed to be lossless.

Fig. 4 Reflection spectra of uncoated multilayers. (a) air-(L/2-H-L/2)15-subst., (b) air-(H/2-L-H/2)15-subst. Top, middle, bottom plots correspond to flat, PhC (TE mode), PhC (TM mode), respectively. Arrows indicate the bands having large index mismatch with ambient materials. PB and SB mean passband and stopband, respectively. “A” and “B” are the target wavelength range for AR, and correspond to what shown in Fig. 3.

For the calculation of flat layers we used matrix-based method [21

For example, P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67(4), 423–438 (1977). [CrossRef]

]. For modulated structures, FDTD method [22

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallodielectric photonic crystals,” Phys. Rev. B 54(16), 11245–11251 (1996). [CrossRef]

] was utilized. As can be seen, the reflection spectra of PhC slightly differ from that of flat ones. The degree of discrepancy depends also on the polarization. We can see first and second stopbands around 3.5~4 and ~2 of the horizontal axes. The spectral shape of the passband implies that the equivalent index of PhC, although unavailable via the simple analytical method as flat ones, represents large frequency dispersion as flat layer [23

L. I. Epstein, “The design of optical filters,” J. Opt. Soc. Am. 42(11), 806–810 (1952). [CrossRef]

]. Owing to this nature, in the passbands there exist frequency regions where index of the multilayer is almost matched to surrounding air or substrate [for example, second passband of Fig. 4(a)] and unmatched to them (ex. first passband of Fig. 4(a), indicated by arrows).

In the following we focused on two typical structures or cases, where large index mismatching exist: short-wave edge of the first passband of the LHL-type structure [4<λ/a<8 in Fig. 4(a)], and the shorter half of the second passband of the HLH-type structure [2<λ/a<2.5 in Fig. 4(b)], where the effect of AR may become distinct. Because the first and second passband of TE and TM modes are both single moded (only one propagating mode exists at a frequency), the global feature of the TE and TM example reflection spectra in Fig. 4 resemble each other. The major difference is their spectral position. Therefore it will be reasonable to assume that the mechanism of reflection is similar for both polarizations. For this reason we present the results for TE cases in the following sections.

3. The effect of double-layer AR coatings

3.1. Surface side

3.1.1. LHL-type structure, short-wave edge of the first passband

Relation between the thickness of the AR layers and average power reflectivity in the target wavelength range is calculated using the FDTD method. First, the effect of AR on the surface side, inserted between the air/multilayer boundary, is investigated. Figures 5 shows the reflectivity map for flat multilayer and PhC (TE modes) plotted as a function of the thickness of H and L films, respectively. Grid size of FDTD is Δx = Δz = a/20. The refractive index is volume-averaged in a Yee’s cell and used as a representative index at each grid point. The reflectivity was averaged over the wavelength between the first and 8th valley counting from the edge of the first band in the original refection spectra [see Fig. 4(a)]. Figures 5(a), 5(b) and 5(c), 5(d) correspond to the cases of air-H’-L’-(multilayer)-subst. and air-L’-H’-(multilayer)-subst., respectively.

Fig. 5 Reflectivity map of a surface side AR coatings on the LHL-type flat multilayer. (a) H layer top, flat structure. air-H’-L’-(main multilayer)-subst., (b) H layer top, TE mode of PhC, (c) L layer top, flat structure. air-L’-H’-(main multilayer)-subst., (d) L layer top, TE mode of PhC.

The thinnest optimum configurations of these double-layer coatings were found as follows.

Note that H and L in the above notation mean the thickness in the main multilayer section, and 1.0L = 1.0H = a/2. At minimum reflection points (open circles in Fig. 5) the thickness of the AR films for PhC became quite close to that of flat ones.

From Fig. 5, it was clarified that the reflectivity of the PhC changes with almost the same fashion as that of flat ones, even though their optimum thickness are not exactly coincident. The results also indicate that either air-L’-H’- and air-H’-L’- can reduce reflectivity to a similar level.

3.1.2. HLH-type structure, shorter half of the second passband

Average reflectivity of the HLH-type structure over the wavelength range between the short-wave edge and the center of the second passband is evaluated. This range is most suitable for the application to multichannel edge filters [9

Y. Ohtera, T. Onuki, Y. Inoue, and S. Kawakami, “Multichannel photonic crystal wavelength filter array for near-infrared wavelengths,” J. Lightwave Technol. 25(2), 499–503 (2007). [CrossRef]

] because of its large spectral sensitivity to horizontal lattice constant (Λ). The results are shown in Fig. 6 . Again, Fig. 6(a), 6(b) and 6(c), 6(d) correspond to H layer top and L layer top cases, respectively.

Fig. 6 Reflectivity map of a surface side AR coatings on the HLH-type flat multilayer. (a) H layer top, flat structure. air-H’-L’-(main multilayer)-subst., (b) H layer top, TE mode of PhC, (c) L layer top, flat structure. air-L’-H’-(main multilayer)-subst., (d) L layer top, TE mode of PhC.

The thinnest optimal AR configurations are now as follows.

The discrepancy of the optimum AR thickness is larger than the previous LHL-type case. This will be explained by that at low frequencies they are plane-wave like, whereas at high frequencies the modal fields are distorted from plane wave-like shape and tend to include higher order spatial harmonic components due to the influence of obliquely propagating modes (mode e3 in Fig. 3) [20

Y. Ohtera and T. Kawashima, “Extremely low optical transmittance in the stopbands of photonic crystals,” Photonics Nanostruct. Fundam. Appl. 7(2), 85–91 (2009). [CrossRef]

]. However the global feature of the reflection characteristics resembles to that of the flat multilayer.

3.2. Substrate side

Next, we calculated the reflectivity as a function of the thickness of the AR layersinserted between the main PhC multilayer and the SiO2 substrate. The AR layers on the surface side were kept as the thinnest optimum thickness found in the previous subsection. The results for the first passband of LHL-type and for the second passband of the HLH-type are shown in Fig. 7(a) and 7(b), respectively. As is shown, it was again found that the flat and modulated layers represented the similar dependence on the AR layer thickness.

Fig. 7 Reflectivity map of a substrate side AR coatings. (a) for the LHL-type flat multilayer, (b) for TE modes of LHL-type PhC, (c) for HLH-type flat multilayer, (d) for TE modes of HLH-type PhC.

The configurations giving minimum reflection are summarized as follows.

The reflection spectra of the multilayers with and without the above AR coatings are summarized in Fig. 8 . The upper and lower plots correspond to the flat and modulated (PhC, TE mode) structures, respectively. The intervals indicated by arrows denote the target range of the AR. These results vividly show that the achievable performance of double-layer AR coatings on PhC is almost comparable to flat ones. The quantitative summary of the reflectivity before and after the AR insertion is described in the next section.

Fig. 8 Summary of the reflection spectra with and without AR coatings. (a) Second passband of HLH-type. “B” corresponds to the target region marked in Fig. 3. (b) First passband of LHL- multilayers. Dotted and solid lines denote uncoated and coated structures, respectively. “A” corresponds to another target region and is also indicated in Fig. 3. The upper and lower plots correspond to the result for flat and PhC (TE mode) multilayers.

In the above calculation we first designed the surface side AR, and then proceed to the optimization of the substrate side. In order to precisely refine the design we will need to search an optimum point in four dimensional parameter space (thickness of two layers each at surface and substrate sides). Although such a procedure may require substantial amount of calculation, the results shown here tells us that the optimum point, dependence of the reflectivity on the AR thickness, and the achievable minimum reflectivity to be found by such procedure will be expected to be similar to that of flat multilayer.

3.3. AR performance for various horizontal lattice constant

One of the advantages of the multilayer type PhC is the parallel integration capability. By arranging multiple miniature PhC regions having different periodicity on a single substrate, functional filter elements for imaging application can be created without technological difficulty [9

Y. Ohtera, T. Onuki, Y. Inoue, and S. Kawakami, “Multichannel photonic crystal wavelength filter array for near-infrared wavelengths,” J. Lightwave Technol. 25(2), 499–503 (2007). [CrossRef]

,24

L. Fabre, Y. Inoue, T. Aoki, and S. Kawakami, “Differential interference contrast microscope using photonic crystals for phase imaging and three-dimensional shape reconstruction,” Appl. Opt. 48(7), 1347–1357 (2009). [CrossRef] [PubMed]

]. This is because the horizontal lattice constant of this type of PhC depends only upon the period of the surface grating on the initial substrate, which can be finely controlled by lithography. However, the periodicity perpendicular to the plane ( = layer profile) is forced to be common over the whole structure, as the films are stacked in a common sputtering process. Therefore it is not realistic to tailor the AR design for every PhC regions having different horizontal lattice constant. All the other regions have to tolerate being covered with AR layers which is optimized for a particular PhC region. Considering this circumstance, in this section we investigated the AR tolerance to the horizontal lattice constant of PhC.

Figure 9 shows the calculated reflection spectra of PhC with different Λ, surrounded by the same AR layers. Construction of the AR is the same as found in the Sec. 3-2. Figure 9(a) and 9(b) correspond to HLH-type and LHL-type configurations, respectively. The figures correspond to the shorter half of the second passband of the HLH-type and the first passband of the LHL-type, respectively. Slope angle of the wavy layer interface was kept constant (40 degree) irrespective of the pitch.

Fig. 9 Calculated reflection spectra of PhC (TE wave) with and without double-layer AR coatings. Top, middle, and bottom plots correspond to the horizontal lattice constant of: Λ = 0.7a, 0.9a, and 1.1a, respectively. Film profiles are common for all three cases. (a) HLH-type PhC. air-0.6L-0.21H-(PhC)-0.05L-0.37H-subst. (b) LHL-type PhC. air-2.15L-1.26H-(PhC)-0.42L-0.55H-subst. The regions “A” and “B” correspond to those in Fig. 3.

As is shown, suppression of reflectivity was found to be less sensitive to the pitch Λ as a whole. Figure 10 displays the calculated average reflectivity over the target wavelength ranges with and without the AR coatings. The wavelength range for the evaluation of average reflectivity, plotted by dotted lines, is independently defined for each Λ, as the passband depends on Λ. Refectivities in Fig. 10(a) and 10(b) correspond to Fig. 9(a) and 9(b), respectively. Reflectivity is reduced from 21.3% to 2.5% for Λ/a = 0.9 of HLH-case [Fig. 10(a)] and from 22.8% to 2.0% for Λ/a = 0.9 of LHL-case [Fig. 10(b)]. It is clearly seen that the dependence of the final AR performance upon the horizontal lattice constant is small, and that the reflection can be reduced to 1/5 to 1/10 of bare PhCs. This result implies that in practical applications utilizing multiple horizontal pitches, it is sufficient to explore an AR design for a representative PhC region; i.e., the region having an average horizontal lattice constant.

Fig. 10 Average reflectivity calculated as a function of horizontal lattice constant of PhC. Slope angle of the wavy interface is kept constant as 40 degree. TE mode. (a) HLH-type, shorter half of the second passband, (b) LHL-type, first passband. Dotted lines indicate the lower and upper boundary of the wavelength where average reflectivity is evaluated. Configuration for the surface side and substrate side AR are the same as Fig. 9.

3.4. AR performance for various slope angle

Although the typical slope angle of the wavy layer is around 40 degrees as mentioned, it is informative no investigate the dependence of the AR performance (reflectivity reduction level) upon the slope angle. We calculated the reflectivity for various slope angles for HLH- and LHL-type cases with a specific pitch: Λ = 0.9a. The results are shown in Fig. 11 . Configuration of the AR is the same as described in the Sec. 3-2, optimized for slope angle of 40 degrees. It is clearly seen that the dependence of the final reflectivity upon the angle is still small, and that the reflection can be reduced to 2~5%. To consider the results of previous and this subsections together, it is concluded that in practical applications utilizing multiple horizontal pitches with small divergence of slope angle, it is sufficient to find an AR specification for a representative PhC region; i.e., the region having an average horizontal lattice constant and slope angle.

Fig. 11 Average reflectivity calculated as a function of the local slope angle of the wavy multilayer PhC. Horizontal pitch (L) is kept constant as Λ = 0.9a. TE mode. (a) HLH-type, shorter half of the second passband, (b) LHL-type, first passband. Configuration for the surface side and substrate side AR are the same as Fig. 9.

4. Conclusion

We investigated the possibility of double-layer AR coatings for periodically modulated dielectric multilayers through numerical calculation. In the case of deep wavy layer modification with triangular film interfaces, the AR coating with similar reflectivity suppression was found to be achievable. We mainly investigated index-mismatched wavelength region where original PhC showed large ripples in their reflection spectra. Both (L/2-H-L/2)N and (H/2-L-H/2)N type construction were studied, and double-layer AR design for both between air/PhC and PhC/substrate interfaces are found. We also verified that the optimum AR configuration for a specific PhC dimension (Λ/a) could effectively work for other dimensions. The results shown here will be directly used to improve transmission efficiencies of multilayer type PhC filter devices. As the possibility of double-layer AR coatings on this type of PhC is now verified, in the development of practical devices any efficient optimization method can be used to refine the AR design on request.

Acknowledgments

The authors thank Dr. Takashi Sato, Dr. Takayuki Kawashima and Dr. Yoshihiko Inoue of Photonic Lattice, Inc. for their fruitful discussion. This work has been partly supported by SENTAN project, JST.

References and links

1.

R.-C. Tyan, A. A. Salvekar, H.-P. Chou, C.-C. Cheng, A. Scherer, P.-C. Sun, F. Xu, and Y. Fainman, “Design, fabrication, and characterization of form-birefringent multilayer polarizing beam splitter,” J. Opt. Soc. Am. A 14(7), 1627–1636 (1997). [CrossRef]

2.

M. A. Ahmed, A. Voss, M. M. Vogel, and T. Graf, “Multilayer polarizing grating mirror used for the generation of radial polarization in Yb:YAG thin-disk lasers,” Opt. Lett. 32(22), 3272–3274 (2007). [CrossRef] [PubMed]

3.

N. Destouches, J.-C. Pommier, O. Parriaux, T. Clausnitzer, N. Lyndin, and S. Tonchev, “Narrow band resonant grating of 100% reflection under normal incidence,” Opt. Express 14(26), 12613–12622 (2006). [CrossRef] [PubMed]

4.

R. C. Rumpf, A. Mehta, P. Srinivasan, and E. G. Johnson, “Design and optimization of space-variant photonic crystal filters,” Appl. Opt. 46(23), 5755–5761 (2007). [CrossRef] [PubMed]

5.

M. Notomi, T. Tamamura, T. Kawashima, and S. Kawakami, “Drilled alternating-layer three-dimensional photonic crystals having a full photonic band gap,” Appl. Phys. Lett. 77(26), 4256–4258 (2000). [CrossRef]

6.

T. Kawashima, Y. Sasaki, K. Miura, N. Hashimoto, A. Baba, H. Ohkubo, Y. Ohtera, T. Sato, W. Ishikawa, T. Aoyama, and S. Kawakami, ““Development of autocloned photonic crystal devices”, IEICE Trans. Electron,” E 87-C, 283–290 (2004).

7.

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarisation splitters,” Electron. Lett. 35(15), 1271–1272 (1999). [CrossRef]

8.

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34(1/3), 63–70 (2002). [CrossRef]

9.

Y. Ohtera, T. Onuki, Y. Inoue, and S. Kawakami, “Multichannel photonic crystal wavelength filter array for near-infrared wavelengths,” J. Lightwave Technol. 25(2), 499–503 (2007). [CrossRef]

10.

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plate elements,” Appl. Opt. 46(22), 4963–4967 (2007). [CrossRef] [PubMed]

11.

A. Mehta, J. D. Brown, P. Srinivasan, R. C. Rumpf, and E. G. Johnson, “Spatially polarizing autocloned elements,” Opt. Lett. 32(13), 1935–1937 (2007). [CrossRef] [PubMed]

12.

Y. Kozawa, S. Sato, T. Sato, Y. Inoue, Y. Ohtera, and S. Kawakami, “Cylindrical vector laser beam generated by the use of a photonic crystal mirror,” Appl. Phys. Express 1, 022008 (2008). [CrossRef]

13.

Y. Ono, Y. Kimura, Y. Ohta, and N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26(6), 1142–1146 (1987). [CrossRef] [PubMed]

14.

J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, “Systematic design of antirefection coating for semi-in nite one-dimensional photonic crystals using Bloch wave expansion,” Appl. Phys. Lett. 82(1), 7–9 (2003). [CrossRef]

15.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, 2nd ed. (Princeton University Press, 2008).

16.

http://www.photonic-lattice.com/en/Products_List.html

17.

H. A. Macleod, in Thin-Film Optical Filters, 3rd ed. (IoP Publishing, 2001), Chap. 6.

18.

C. Ufford and P. Baumeister, “Graphical aids in the use of equivalent index in multilayer-filter design,” J. Opt. Soc. Am. 64(3), 329–334 (1974). [CrossRef]

19.

Y. Ohtera, “Calculating the complex photonic band structure by the finite-difference time-domain based method,” Jpn. J. Appl. Phys. 47(6), 4827–4834 (2008). [CrossRef]

20.

Y. Ohtera and T. Kawashima, “Extremely low optical transmittance in the stopbands of photonic crystals,” Photonics Nanostruct. Fundam. Appl. 7(2), 85–91 (2009). [CrossRef]

21.

For example, P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67(4), 423–438 (1977). [CrossRef]

22.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallodielectric photonic crystals,” Phys. Rev. B 54(16), 11245–11251 (1996). [CrossRef]

23.

L. I. Epstein, “The design of optical filters,” J. Opt. Soc. Am. 42(11), 806–810 (1952). [CrossRef]

24.

L. Fabre, Y. Inoue, T. Aoki, and S. Kawakami, “Differential interference contrast microscope using photonic crystals for phase imaging and three-dimensional shape reconstruction,” Appl. Opt. 48(7), 1347–1357 (2009). [CrossRef] [PubMed]

OCIS Codes
(230.4170) Optical devices : Multilayers
(310.1210) Thin films : Antireflection coatings
(350.2460) Other areas of optics : Filters, interference
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Thin Films

History
Original Manuscript: April 13, 2010
Revised Manuscript: May 18, 2010
Manuscript Accepted: May 24, 2010
Published: May 25, 2010

Citation
Yasuo Ohtera, Daniel Kurniatan, and Hirohito Yamada, "Antireflection coatings for multilayer-type photonic crystals," Opt. Express 18, 12249-12261 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-12-12249


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References

  1. R.-C. Tyan, A. A. Salvekar, H.-P. Chou, C.-C. Cheng, A. Scherer, P.-C. Sun, F. Xu, and Y. Fainman, “Design, fabrication, and characterization of form-birefringent multilayer polarizing beam splitter,” J. Opt. Soc. Am. A 14(7), 1627–1636 (1997). [CrossRef]
  2. M. A. Ahmed, A. Voss, M. M. Vogel, and T. Graf, “Multilayer polarizing grating mirror used for the generation of radial polarization in Yb:YAG thin-disk lasers,” Opt. Lett. 32(22), 3272–3274 (2007). [CrossRef] [PubMed]
  3. N. Destouches, J.-C. Pommier, O. Parriaux, T. Clausnitzer, N. Lyndin, and S. Tonchev, “Narrow band resonant grating of 100% reflection under normal incidence,” Opt. Express 14(26), 12613–12622 (2006). [CrossRef] [PubMed]
  4. R. C. Rumpf, A. Mehta, P. Srinivasan, and E. G. Johnson, “Design and optimization of space-variant photonic crystal filters,” Appl. Opt. 46(23), 5755–5761 (2007). [CrossRef] [PubMed]
  5. M. Notomi, T. Tamamura, T. Kawashima, and S. Kawakami, “Drilled alternating-layer three-dimensional photonic crystals having a full photonic band gap,” Appl. Phys. Lett. 77(26), 4256–4258 (2000). [CrossRef]
  6. T. Kawashima, Y. Sasaki, K. Miura, N. Hashimoto, A. Baba, H. Ohkubo, Y. Ohtera, T. Sato, W. Ishikawa, T. Aoyama, and S. Kawakami, ““Development of autocloned photonic crystal devices”, IEICE Trans. Electron,” E 87-C, 283–290 (2004).
  7. Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarisation splitters,” Electron. Lett. 35(15), 1271–1272 (1999). [CrossRef]
  8. T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34(1/3), 63–70 (2002). [CrossRef]
  9. Y. Ohtera, T. Onuki, Y. Inoue, and S. Kawakami, “Multichannel photonic crystal wavelength filter array for near-infrared wavelengths,” J. Lightwave Technol. 25(2), 499–503 (2007). [CrossRef]
  10. T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plate elements,” Appl. Opt. 46(22), 4963–4967 (2007). [CrossRef] [PubMed]
  11. A. Mehta, J. D. Brown, P. Srinivasan, R. C. Rumpf, and E. G. Johnson, “Spatially polarizing autocloned elements,” Opt. Lett. 32(13), 1935–1937 (2007). [CrossRef] [PubMed]
  12. Y. Kozawa, S. Sato, T. Sato, Y. Inoue, Y. Ohtera, and S. Kawakami, “Cylindrical vector laser beam generated by the use of a photonic crystal mirror,” Appl. Phys. Express 1, 022008 (2008). [CrossRef]
  13. Y. Ono, Y. Kimura, Y. Ohta, and N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26(6), 1142–1146 (1987). [CrossRef] [PubMed]
  14. J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, “Systematic design of antirefection coating for semi-in nite one-dimensional photonic crystals using Bloch wave expansion,” Appl. Phys. Lett. 82(1), 7–9 (2003). [CrossRef]
  15. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, 2nd ed. (Princeton University Press, 2008).
  16. http://www.photonic-lattice.com/en/Products_List.html
  17. H. A. Macleod, in Thin-Film Optical Filters, 3rd ed. (IoP Publishing, 2001), Chap. 6.
  18. C. Ufford and P. Baumeister, “Graphical aids in the use of equivalent index in multilayer-filter design,” J. Opt. Soc. Am. 64(3), 329–334 (1974). [CrossRef]
  19. Y. Ohtera, “Calculating the complex photonic band structure by the finite-difference time-domain based method,” Jpn. J. Appl. Phys. 47(6), 4827–4834 (2008). [CrossRef]
  20. Y. Ohtera and T. Kawashima, “Extremely low optical transmittance in the stopbands of photonic crystals,” Photonics Nanostruct. Fundam. Appl. 7(2), 85–91 (2009). [CrossRef]
  21. For example, P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67(4), 423–438 (1977). [CrossRef]
  22. S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallodielectric photonic crystals,” Phys. Rev. B 54(16), 11245–11251 (1996). [CrossRef]
  23. L. I. Epstein, “The design of optical filters,” J. Opt. Soc. Am. 42(11), 806–810 (1952). [CrossRef]
  24. L. Fabre, Y. Inoue, T. Aoki, and S. Kawakami, “Differential interference contrast microscope using photonic crystals for phase imaging and three-dimensional shape reconstruction,” Appl. Opt. 48(7), 1347–1357 (2009). [CrossRef] [PubMed]

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