Abstract: We present a resonance waveguide grating with relativelywide bandwidth in the visible region of the spectrum compared to typicalresonance structures. The reflective properties of the grating are based onamorphous atomic layer deposited titanium dioxide which has rather highrefractive index at the visible wavelengths. The resonance grating providesapproximately 20–30 nm bandwidth with over 90% reflectance at the visiblewavelengths. The measured reflectances of the fabricated elements showalso very good agreement with the theoretical predictions. These kind ofreflectors may be useful in applications that make use of LED sources.
References and links1. R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).2. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32,
2606-2613 (1993).3. T. Vallius, P. Vahimaa, and J. Turunen, “Pulse deformations at guided-mode resonance filters,” Opt. Express 10,
840–843 (2002).4. M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, and M. Kuittinen, “Strong enhance-
ment of second-harmonic generation in all-dielectric resonant waveguide grating,” Appl. Phys. Lett. 91, 111109(2007).
5. P. Karvinen, T. Nuutinen, O. Hyvarinen, and P. Vahimaa, “Enhancement of laser-induced fluorescence at 473 nmexcitation with subwavelength resonant waveguide gratings,” Opt. Express 16, 16364–16370 (2008).
6. C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband MirrorUsing Low-Index Cladded Subwavelength Grating,” IEEE Photon. Technol. Lett. 16, 518–520 (2004).
7. Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt.Express 12, 5661–5674 (2004).
8. R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16,3456–3462 (2008).
9. M. Shokooh-Saremi and R. Magnusson, “Leaky-mode resonant reflectors with extreme bandwidths,” Opt. Lett.35, 1121–1123 (2010).
10. C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, Y. Suzuki, “Broad-band mirror (1.12-1.62 m)using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
11. L. Chen, M. C. Y. Huang, C. F. R. Mateus, C. J. Chang-Hasnain, and Y. Suzuki, “Fabrication and design of anintegrable subwavelength ultrabroadband dielectric mirror,” Appl. Phys. Lett., 88, 031102 (2006)
12. J. M. Kontio, J. Simonen, K. Leinonen, M. Kuittinen, and T. Niemi, “Broadband infrared mirror using guided-mode resonance in a subwavelength germanium grating,” Opt. Lett., 35, 2564–2566 (2010).
#136467 - $15.00 USD Received 11 Oct 2010; revised 9 Dec 2010; accepted 27 Dec 2010; published 20 Jan 2011(C) 2011 OSA 31 January 2011 / Vol. 19, No. 3 / OPTICS EXPRESS 2126
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14. A. Ricciardi, S. Campopiano, A. Cusano, T. F. Krauss, and L. O’Faolain, “Broadband Mirrors in the Near-InfraredBased on Subwavelength Gratings in SOI,” IEEE Photon. J. 2, 696–702 (2010).
15. T. Alasaarela, T. Saastamoinen, J. Hiltunen, A. Saynatjoki, A. Tervonen, P. Stenberg, M. Kuittinen, and S. Honka-nen, “Atomic layer deposited titanium dioxide and its application in resonant waveguide grating,” Appl. Opt. 49,4321–4325 (2010).
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1. Introduction
Subwavelength gratings can exhibit resonance effects which can be utilized in many interest-ing applications such as filters, sensors, pulse-shapers, second-harmonic generation, and fieldenhancement of fluorescence [1–5]. Typically, these resonance waveguide gratings (RWG) areused as narrow band filters because the resonance effects produce very sharp peaks in the reflec-tion spectrum. However, it has been recently shown theoretically that the RWG structures canalso provide very wide bandwidths over which the reflectance is nearly 100% at the IR wave-lengths [6–9]. To obtain a wide bandwidth, it is crucial to employ materials which have veryhigh refractive index with negligible absorption. In the IR region there exists suitable materials,such as silicon and germanium, that fulfill these conditions. It has also been experimentallydemonstrated by several authors that these materials can be used to fabricate broadband reflec-tors at the IR wavelengths [10–14].
At the visible wavelengths the lack of high-index materials prevents the realization of verywide bandwidths. Fortunately, there exists a few materials which have rather high refractiveindex at the visible wavelengths and therefore allow the design of RWG reflectors for whichthe bandwidth at the visible wavelengths is substantially wider than is achieved by typical reso-nance structures. In this paper we have designed and fabricated such structures using amorphousatomic layer deposited (ALD) titanium dioxide (TiO2) as a high-index material. These kind ofreflectors may be useful, for example, in filtering or field enhancement applications which makeuse of LED sources.
2. Design of the RWG structure
Amorphous ALD TiO2 is a transparent material which has rather high refractive index andalmost negligible absorption over the visible spectrum. The refractive index of amorphous ALDTiO2 is nearly 2.5 at the middle of the visible spectrum [15]. Although this is among the highestrefractive indices that can be used at the visible wavelengths, it is still far less than those of thematerials that can be used at the IR wavelengths. For example, the refractive indices of siliconand germanium are greater than 3.4 and 4, respectively, at the wavelengths well above theirbandgaps. Therefore, it is evident that broadband reflectors, for which the bandwidth is severalhundreds of nanometers, cannot be realized at the visible wavelengths in the same manner as inthe IR-region.
In this work we designed RWG reflectors employing the properties of ALD TiO2. Since wealso wanted to fabricate the designed RWG structure, we chose a rather simple structure whichis also suitable for mass production. The structure contains a binary linear SiO2 grating withuniform TiO2 layer deposited on the top of the grating. Therefore, it should be emphasizedthat it is also possible to obtain notably wider bandwidths at the visible wavelengths than ourdesign provides by using certain multilayer structures or using additional low refractive indexmaterials. However, these structures are problematic from the fabrication point of view andhence we chose to design and fabricate the easiest case.
#136467 - $15.00 USD Received 11 Oct 2010; revised 9 Dec 2010; accepted 27 Dec 2010; published 20 Jan 2011(C) 2011 OSA 31 January 2011 / Vol. 19, No. 3 / OPTICS EXPRESS 2127
We designed two similar RWG gratings for the incident angles of 20 and zero degrees wherethe former gives the reflection peak around the wavelength of 532 nm and the latter around thewavelength of 633 nm. Both structures are designed for TE-polarization, i.e., the polarizationof the incident light is parallel to the grooves of the grating. The period of the first grating isd = 378 nm, the height of the grating hg = 106 nm, and the fill-factor f = 0.26. The thicknessof the TiO2 coating is hc = 56 nm. The corresponding parameters of the second grating ared = 390 nm, hg = 120 nm, f = 0.25, and hc = 68 nm. The schematics of the grating structureis shown in Fig. 1.
hc
hc
hc
hg
TiO2SiO2
d
Fig. 1. Design of the RWG grating where hc is the thickness of the TiO2 coating, hg is theheight of the grating, and d is the period of the grating. The substrate material is SiO2.
3. Fabrication of the RWG and the optical properties of ALD TiO2
The RWG gratings were fabricated by patterning the SiO2 substrate by electron beam lithog-raphy and etched by using reactive ion etching. The TiO2 coating was atomic layer depositedon the SiO2 grating at 120◦C temperature using Beneq TFS 500 reactor with TiCl4 and H2Oprecursor gases. The low temperature of 120◦C leads to amorphous TiO2, which is smooth andhas low losses [15]. In ALD process, the film grows equally on all surfaces, which allows therealization of the design shown in Fig. 1. The cycle time in the ALD process was 2.8 s andthe growth speed was 0.056 nm per cycle. Although this is quite a slow process, it scales verywell and thus makes possible to coat large surface areas at the same time without significantlyaltering the cycle time.
The optical constants of the amorphous TiO2 were measured from a 110 nm thick TiO2 thinfilm on SiO2 substrate using variable angle ellipsometer (VASE) supplied by J.A. Woollam Co.The real part of the refractive index is shown in Fig. 2. The extinction coefficient is negligibleat the wavelengths above the bandgap and therefore is not included in the figure.
The scanning electron microscope (SEM) image of the RWG structure operating at 20 de-grees incident angle is shown in Fig. 3.
4. Measurements and results
The theoretical reflectance curves of the RWG reflectors were calculated by using Fouriermodal method [16] and the optimization was carried out by using MATLAB’s Nelder-MeadSimplex method. The refractive index of amorphous TiO2 used in the simulations was obtainedfrom the measured data presented in Fig. 2. The measurement of the experimental reflectancecurves were carried out by using VASE ellipsometer. The reflectance of the RWG reflector with
#136467 - $15.00 USD Received 11 Oct 2010; revised 9 Dec 2010; accepted 27 Dec 2010; published 20 Jan 2011(C) 2011 OSA 31 January 2011 / Vol. 19, No. 3 / OPTICS EXPRESS 2128
400 450 500 550 600 650 7002.35
2.4
2.45
2.5
2.55
2.6
2.65
2.7
2.75
Wavelength [nm]
Ref
ract
ive
inde
x
Fig. 2. Refractive index of ALD TiO2 at the visible wavelengths.
Fig. 3. SEM image of the RWG grating operating at 20 degrees incidence. The binary SiO2grating contains amorphous TiO2 coating.
zero degrees incident angle was determined using transmission measurement because it is notpossible to obtain the reflectance at zero degree incidence using VASE ellipsometer. At thispoint we note that reflectance throughout this paper refers to absolute reflectance.
In Fig. 4 is illustrated the experimental zeroth order reflectance curve and the correspondingtheoretical reflectance curve for the RWG reflector with the incidence angle of 20 degrees usingthe designed parameters. The structure was optimized so that the center of the peak is at thewavelength of 532 nm. It can be seen that the experimental peak has shifted towards the shorterwavelengths. This shift may be caused by a slight deviation in the realized refractive indexof TiO2 or in the thickness of the TiO2 layer. If either the thickness or the refractive indexdecreases, the peaks move to the shorter wavelengths.
The difference in the theoretical and experimental curves at the shorter wavelengths between400 nm and 470 nm are caused by the rounding of the rectangular shapes in the fabricated
#136467 - $15.00 USD Received 11 Oct 2010; revised 9 Dec 2010; accepted 27 Dec 2010; published 20 Jan 2011(C) 2011 OSA 31 January 2011 / Vol. 19, No. 3 / OPTICS EXPRESS 2129
400 450 500 550 600 650 7000
10
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30
40
50
60
70
80
90
100
TE exp.TM exp.TE theoryTM theory
Wavelength [nm]
Refl
ecta
nce
[%]
Fig. 4. Reflectance of the RWG grating for the incident angle of 20 degrees in TE- andTM-polarizations. The period of the grating d = 378 nm, the height hg = 106 nm, the fill-factor f = 0.26, and the thickness of the TiO2 coating is hc = 56 nm. TE exp and TM expdenote the measured reflectance curves and TE theory and TM theory are the correspondingcalculated reflectances.
400 450 500 550 600 650 7000
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100
TE exp.TM exp.TE theoryTM theory
Wavelength [nm]
Refl
ecta
nce
[%]
Fig. 5. Reflectance of the RWG grating for the incident angle of zero degrees in TE- andTM-polarizations. The period of the grating d = 390 nm, the height hg = 120 nm, the fill-factor f = 0.25, and the thickness of the TiO2 coating is hc = 68 nm. TE exp and TM expdenote the measured reflectance curves and TE theory and TM theory are the correspondingcalculated reflectances.
#136467 - $15.00 USD Received 11 Oct 2010; revised 9 Dec 2010; accepted 27 Dec 2010; published 20 Jan 2011(C) 2011 OSA 31 January 2011 / Vol. 19, No. 3 / OPTICS EXPRESS 2130
element. The effect of rounding at the shorter wavelengths is treated more extensively shortlyin the case of the second RWG reflector.
It should be noted that there exists non-zero diffraction orders in the substrate as well as inthe reflection side because the incidence angle is not zero. The theoretical and experimentalreflectances are the zeroth orders reflectances although the higher orders also contribute to thetotal reflectance at the wavelengths below the cut-off wavelength at 510 nm.
Figure 5 illustrates the corresponding experimental and theoretical curves of the RWG re-flector at zero degrees incidence angle for which the center of the reflection peak was designedat the wavelength of 633 nm. Also in this case there is a slight deviation from the designedwavelengths in the experimental curves.
400 450 500 550 600 650 700
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
TETMTETM
Wavelength [nm]
Refl
ecta
nce
[%]
Fig. 6. Theoretical reflectance of the RWG grating determined from the transmittance usingthe relation R = 1−T . The solid lines represents the case where we take into account onlythe zeroth transmitted order in the substrate. The dashed lines represents the case wherewe take into account all the transmitted orders in the substrate. Furthermore, in both casesthe grating profile is rounded to match the fabricated profile shown in Fig. 3. Because thecut-off wavelength of the grating is approximately at 574 nm, the solid and dashed linesoverlap above this wavelength.
Since the substrate material is SiO2, it is evident that also non-zero diffraction orders willemerge in the substrate at the wavelengths below the cut-off wavelength at 574 nm. However,in the measurements the higher orders do not propagate after the SiO2 substrate but they insteadundergo a total-internal reflection at the interface between the SiO2 substrate and air. Thus, it isnot possible to measure the non-zero transmitted orders and therefore the experimental resultsat the wavelengths below the cut-off wavelength are not entirely correct in Fig. 5 if we assumethat R = 1− T . Since we were not able to measure the reflectance at zero degree incidenceangle, we resolved this problem as follows: we calculated the theoretical transmittance wherewe take into account only the zeroth transmitted order (as in the measurements) and determinedthe reflectance using the relation R = 1−T . We also used the rounded grating profile in orderto obtain the best possible result to match the experimental results shown in Fig. 5. The abovementioned theoretical reflectance curves for the both polarizations are illustrated in Fig. 6 withthe black and blue solid lines.
#136467 - $15.00 USD Received 11 Oct 2010; revised 9 Dec 2010; accepted 27 Dec 2010; published 20 Jan 2011(C) 2011 OSA 31 January 2011 / Vol. 19, No. 3 / OPTICS EXPRESS 2131
Now we can easily see in Fig. 6 that the curves with the solid line resemble quite well theexperimental results shown in Fig. 5 which is of course as expected because in both caseswe use only the zeroth order to determine the reflectance. Thus, we may conclude that thetheoretical and experimental results are in rather good agreement with each other also at theshorter wavelengths although this cannot be seen in Fig. 5. Without the rounding of the gratingprofile the theoretical reflectance of the peak at the wavelength of 525 nm is approximately50%.
Finally, we also calculated the theoretical reflectance using the rounded grating profile to seehow the reflectance would behave if we had the means to measure it. These reflectance curvesfor the both polarizations are shown in Fig. 5 with the black and blue dashed lines.
5. Conclusions
In this work we have presented RWG reflectors with substantially wide bandwidth compared totypical RWG structures at the visible wavelengths. The reflector is based on amorphous ALDTiO2 which has very high refraction index at the visible region of the spectrum with negligibleabsorption. We also fabricated two example reflectors and showed that the theoretical and theexperimental reflectance curves are in good agreement with each other. The example reflectorsprovided approximately 20–30 nm bandwidth with over 90% reflectance. These kind of RWGreflectors can be useful in filtering or field enhancement applications which take advantage ofLED sources.
Finally, it should be noted that it is also possible to obtain flattop reflectance curves at thevisible wavelengths using similar multilayer structures such as in Ref. [9]. In these cases it istheoretically possible to obtain nearly 100% reflectance over more than a hundred nanometersbandwidth at the visible region of spectrum using ALD TiO2. However, from the fabricationpoint of view, these structures are rather difficult to realize because of the adjustment problemswith different layers.
Acknowledgements
The work of T. Alasaarela and A. Lehmuskero was supported by the Finnish Graduate Schoolof Modern Optics and Photonics. T. Alasaarela also acknowledges the Emil Aaltonen Founda-tion. I. Vartiainen acknowledges the Finnish Funding Agency for Technology and Innovation(TEKES).
#136467 - $15.00 USD Received 11 Oct 2010; revised 9 Dec 2010; accepted 27 Dec 2010; published 20 Jan 2011(C) 2011 OSA 31 January 2011 / Vol. 19, No. 3 / OPTICS EXPRESS 2132
