Optical reflectionless potentials for broadband, omnidirectional antireflection L. V. Thekkekara,1 Venu Gopal Achanta,1* and S. Dutta Gupta2 1
Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005 India School of Physics, University of Hyderabad, Gachibowli, Hyderabad 500 046 India * [email protected]
2
Abstract: Reflectionless potentials (RPs) represent a class of potentials that offer total transmission in the context of one dimensional scattering. An optical realization of RP can exhibit a truly broadband omni-directional antireflection. We report our experimental observations confirming the reflectionless behavior. Stratified media conforming to RP's are designed and fabricated using Al2O3 and TiO2 heterolayers. They showed < 0.5% reflection over the broad wavelength range of 350 nm to 2500 nm for angles of incidence 0 - 50 degrees. These RPs can be designed on substrates and are thus interesting for optical instrumentation as broadband, omnidirectional antireflection coatings. ©2014 Optical Society of America OCIS codes: (160.1245) Artificially engineered materials; (160.4760) Optical properties; (310.1210) Antireflection coatings.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
I. Kay and H. E. Moses, “Reflectionless transmission through dielectrics and scattering potentials,” J. Appl. Phys. 27(12), 1503–1508 (1956). S. Flügge, Practical Quantum Mechanics (Springer, 1994) pp. 244–247. N. Kiriuscheva and S. Kuzmin, “Scattering of a Gaussian wave packet by a reflectionless potential,” Am. J. Phys. 66(10), 867–872 (1998). J. Lekner, “Reflectionless eigenstates of the sech2 potential,” Am. J. Phys. 75, 1151–1157 (2007). S. Dutta Gupta and G. S. Agarwal, “A new approach for broad-band omnidirectional antireflection coatings,” Opt. Express 15(15), 9614–9624 (2007). L. Rayleigh, “On the reflection of vibrations at the confines of two media between which the transition is gradual,” Proc. Lond. Math. Soc. 11, 51–56 (1880). R. W. Wood, “Some experiments on artificial mirages and tornadoes,” Philos. Mag. 47, 349–353 (1899). U. B. Schallenberg, “Nanostructures versus thin films in the design of antireflection coatings,” Proc. SPIE 8168, 81681N (2011). D. Poitras and J. A. Dobrowolski, “Toward perfect antireflection coatings. 2. Theory,” Appl. Opt. 43(6), 1286– 1295 (2004). Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, “Improved broadband and quasi-omnidirectional antireflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007). J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, “Optical thinfilm materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176– 179 (2007). C.-H. Sun, P. Jiang, and B. Jiang, “Broadband moth-eye antireflection coatings on silicon,” Appl. Phys. Lett. 92(6), 061112 (2008). S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett. 93(25), 251108 (2008). S. L. Diedenhofen, G. Vecchi, R. E. Algra, A. Hartsuiker, O. L. Muskens, G. Immink, E. P. A. M. Bakkers, W. L. Vos, and J. G. Rivas, “Broad-band and omnidirectional antireflection coatings based on semiconductor nanorod,” Adv. Mater. 21(9), 973–978 (2009). C. H. Chang, P. Yu, and C. S. Yang, “Broadband and omnidirectional antireflection from conductive indium-tinoxide nanocolumns prepared by glancing-angle deposition with nitrogen,” Appl. Phys. Lett. 94(5), 051114 (2009).
#213638 - $15.00 USD (C) 2014 OSA
Received 9 Jun 2014; accepted 27 Jun 2014; published 9 Jul 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.017382 | OPTICS EXPRESS 17382
16. M. F. Schubert, D. J. Poxson, F. W. Mont, J. K. Kim, and E. F. Schubert, “Performance of antireflection coatings consisting of multiple discrete layers and comparison with continuously graded antireflection coatings,” Appl. Phys. Express 3(8), 082502 (2010). 17. P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692–696 (2012). 18. C. L. Tan, S. J. Jang, and Y. T. Lee, “Localized surface plasmon resonance with broadband ultralow reflectivity from metal nanoparticles on glass and silicon subwavelength structures,” Opt. Express 20(16), 17448–17455 (2012). 19. T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Non-polarizing broadband multilayer reflectors in fish,” Nat. Photonics 6(11), 759–763 (2012). 20. A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. A. Sukhorukov, “Realization of reflectionless potentials in photonic lattices,” Phys. Rev. Lett. 106(19), 193903 (2011).
1. Introduction Achieving null reflection in a stratified medium at a specific angle of incidence or at a specified wavelength is easy. The real challenge lies in having antireflection at any wavelength or for any angle. In this context reflectionless potentials (RP's) were introduced and thoroughly discussed by Kay and Moses [1]. A great deal of theoretical work has been carried out on one specific example of the RP, namely, the Poschl-Teller potential having the sech2 dependence [2–4]. Some properties of the RP's were revealed in these studies. It was shown that the group delay associated with the passage of a Gaussian pulse can be negative and such superluminal transit is associated with pulse narrowing. In this report we exploit the recent results on a generalized optical RP [5] to design the heterolayer. We demonstrate broadband omnidirectional antireflection with < 0.5% reflection over the broad wavelength range of 500 – 2500 nm. Conventional AR coatings are, in general, interference based that work on the principle of cancellation of reflections by destructive interference over narrow regions of wavelength and angles of incidence. Graded index AR coating works over larger ranges of wavelength and angles due to the gradual change in the refractive index [6]. However, even the graded index profiles offer reflection at oblique angles [7]. Recently there have been several proposals and demonstrations of anti-reflection coatings based on graded index profiles, surface Mie resonators, bio-inspired guanine crystals, and localized plasmon resonances in metal nanoparticles [8–19]. Inspite of considerable research, true broadband, omni-directional, polarization independent antireflection coatings are not available. Optical realization of RP's through a stratified medium can offer the true solution [5,8]. Note that a discrete model system conforming to reflectionless Ablowitz-Ladik soliton potential has been recently reported [20]. However, the latter cannot be implemented in optical instrumentation to improve the optical throughput. 2. Methods 2.1 Design methodology Let a plane monochromatic wave be incident at an angle θ on a stratified medium with dielectric function profile ε(z).The problem is effectively one dimensional by virtue of the fact that dependence on x (transverse coordinate) is given by eik x x , with k x = k0 ε s sin θ , εs is the dielectric constant far away from the profile ε(z). Note that kx is the same for each layer (follows from the continuity of tangential fields) leading to a propagation equation in z [5]. The propagation equation for TE-waves for electric field when compared with the Schrödinger equation gives the relation between the energy, potential and the refractive index profile as, E = k 02ε s cos2 θ , V ( z ) = k 02ε s − k 02ε ( z ) , k o = ω / c,
(1)
V(z) is reflectionless if any wave with positive energy passes through the potential. We stress the fact that the potential is reflectionless for arbitrary E > 0 in the quantum problem. #213638 - $15.00 USD (C) 2014 OSA
Received 9 Jun 2014; accepted 27 Jun 2014; published 9 Jul 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.017382 | OPTICS EXPRESS 17383
Translated to the optics problem, arbitrary E implies arbitrary kx, see Eq. (1) satisfying the following,
k02ε s − k x2 > 0
(2)
For a given wavelength, it further means arbitrary θ (0 ≤ θ < π/2). Thus a reflectionless profile for TE waves would mean null reflection over the whole possible range of θ, namely, (0 ≤ θ < π/2). Equation (2) also implies propagating waves in the medium. Truncation of infinite profile leads to deviation from the perfect antireflection feature. It has been shown that such a reflectionless potential for TE polarized light is almost reflectionless for TM as well [5]. In addition, the reflection at shorter wavelengths is shown to be not too different from the longer wavelengths thus resulting in broad wavelength range anti-reflection coatings. Design flow for such anti-reflection coating starts by considering a set of linear equations given by, N
M j =1
ij
Fij ( z ) = − Ai eκ i z
(3)
Ai and κi being positive arbitrary constants for i = 1, N. The reflectionless potential V(z) is given in terms of the determinant (D) of the matrix Mij as [5], V ( z ) = −2
d2 [log( D )] dz 2
(4)
From this the refractive index profile is given by, n 2 ( z ) = ns2 +
2 d2 [log( D)] k02 dz 2
(5)
Fig. 1. Schematic of the reflectionless potential realized by heterolayers (black vertical lines) with blue shaded region indicating the refractive index profile between two quartz substrates (white regions) is shown. Reflectionless refractive index profile that is calculated (red line) and the mean position of each period in the deposited heterolayers (circles) between two quartz substrates are also shown.
The value of D depends on the matrix Mij and thus on the choice of parameters Ai and κi. For one parameter family with A1 = 2κ1, V(z) conforms to the Poschl-Teller potential. It may be seen that with increasing N (dimension of the parameter set) we can get more and more complex profiles that can result in infinitely many reflectionless potential profiles. The choice of the parameters thus can be chosen so that the reflectionless potential can be achieved with the available materials.
#213638 - $15.00 USD (C) 2014 OSA
Received 9 Jun 2014; accepted 27 Jun 2014; published 9 Jul 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.017382 | OPTICS EXPRESS 17384
We use 4-parameter family in designing the reflectionless potential. Solid line in Fig. 1 shows the calculated profile for (A1,A2,A3,A4) = (5.8,0.7,1.0,0.1) and (κ1,κ2,κ3,κ4) = (2.9,0.6,0.6,0.1). In addition, we consider the role of substrate and finite potential profile thickness. Considering that we have A1 = 2κ1 and the values of nmax (2.25) and nmin (1.67) from the potential profile, we get the design wavelength to be 2.3 µm. The parameters and thus the calculated refractive index profile are chosen such that it can be realized by a heterolayer consisting of pairs of Al2O3 and TiO2 layers. 2.2 Stratified medium preparation The designed profile was realized with 43 periods of 24 nm thick each deposited by electron beam evaporation or radio frequency (rf)-magnetron sputtering. Each period has a pair of layers whose relative thickness is varied from one period to other to achieve the required refractive index profile. Schematic of the layer structure along with the calculated and realized refractive index profile are shown in Fig. 1. In the electron beam evaporation method, at a base chamber pressure of 8x10−7 mbar, 99.99% pure Al2O3 or TiO2 was melted in separate graphite crucibles by electron beam heating. Deposition rate for Al2O3 and TiO2 is 9 ± 0.5 nm/min and 4.2 ± 0.5 nm/min, respectively. The other method employed is rf magnetron sputtering deposition where with a base pressure of 5x10−6 mbar, Argon was introduced to 2x10−2 mbar pressure. Al2O3 and TiO2 targets with 99.99% purity were sputtered in Argon plasma with rf-power of 100W. Uniform films are obtained by rotating the substrate. The deposition rate obtained was 0.81 ± 0.5 nm/min of Al2O3 and 0.51 ± 0.5 nm/min for TiO2. Deposition rate was determined by profilometer and surface quality by AFM. Surface roughness of the deposited film on ITO coated glass is 6 ± 0.5 nm for Al2O3 and 0.6 ± 0.5 nm for TiO2. Spectroscopic ellipsometer was used for measuring the refractive index of the individual layers. These values are used in calculating the reflectionless potential.
Fig. 2. Measured normal incidence (a) transmission spectra of RP is shown (red line) and calculated (black line) and (b) reflection spectra in air (red line) corrected for air-quartz interface reflection and that measured in index matching liquid (blue line). Insets show the angle dependence of measured % T and % R as a function of wavelength.
2.3 Optical measurements White light angle resolved transmission and reflection measurements were performed using commercial spectrometers or home built setups with collimated white light having a beam divergence of
Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005 India School of Physics, University of Hyderabad, Gachibowli, Hyderabad 500 046 India * [email protected]
2
Abstract: Reflectionless potentials (RPs) represent a class of potentials that offer total transmission in the context of one dimensional scattering. An optical realization of RP can exhibit a truly broadband omni-directional antireflection. We report our experimental observations confirming the reflectionless behavior. Stratified media conforming to RP's are designed and fabricated using Al2O3 and TiO2 heterolayers. They showed < 0.5% reflection over the broad wavelength range of 350 nm to 2500 nm for angles of incidence 0 - 50 degrees. These RPs can be designed on substrates and are thus interesting for optical instrumentation as broadband, omnidirectional antireflection coatings. ©2014 Optical Society of America OCIS codes: (160.1245) Artificially engineered materials; (160.4760) Optical properties; (310.1210) Antireflection coatings.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
I. Kay and H. E. Moses, “Reflectionless transmission through dielectrics and scattering potentials,” J. Appl. Phys. 27(12), 1503–1508 (1956). S. Flügge, Practical Quantum Mechanics (Springer, 1994) pp. 244–247. N. Kiriuscheva and S. Kuzmin, “Scattering of a Gaussian wave packet by a reflectionless potential,” Am. J. Phys. 66(10), 867–872 (1998). J. Lekner, “Reflectionless eigenstates of the sech2 potential,” Am. J. Phys. 75, 1151–1157 (2007). S. Dutta Gupta and G. S. Agarwal, “A new approach for broad-band omnidirectional antireflection coatings,” Opt. Express 15(15), 9614–9624 (2007). L. Rayleigh, “On the reflection of vibrations at the confines of two media between which the transition is gradual,” Proc. Lond. Math. Soc. 11, 51–56 (1880). R. W. Wood, “Some experiments on artificial mirages and tornadoes,” Philos. Mag. 47, 349–353 (1899). U. B. Schallenberg, “Nanostructures versus thin films in the design of antireflection coatings,” Proc. SPIE 8168, 81681N (2011). D. Poitras and J. A. Dobrowolski, “Toward perfect antireflection coatings. 2. Theory,” Appl. Opt. 43(6), 1286– 1295 (2004). Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, “Improved broadband and quasi-omnidirectional antireflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007). J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, “Optical thinfilm materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176– 179 (2007). C.-H. Sun, P. Jiang, and B. Jiang, “Broadband moth-eye antireflection coatings on silicon,” Appl. Phys. Lett. 92(6), 061112 (2008). S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett. 93(25), 251108 (2008). S. L. Diedenhofen, G. Vecchi, R. E. Algra, A. Hartsuiker, O. L. Muskens, G. Immink, E. P. A. M. Bakkers, W. L. Vos, and J. G. Rivas, “Broad-band and omnidirectional antireflection coatings based on semiconductor nanorod,” Adv. Mater. 21(9), 973–978 (2009). C. H. Chang, P. Yu, and C. S. Yang, “Broadband and omnidirectional antireflection from conductive indium-tinoxide nanocolumns prepared by glancing-angle deposition with nitrogen,” Appl. Phys. Lett. 94(5), 051114 (2009).
#213638 - $15.00 USD (C) 2014 OSA
Received 9 Jun 2014; accepted 27 Jun 2014; published 9 Jul 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.017382 | OPTICS EXPRESS 17382
16. M. F. Schubert, D. J. Poxson, F. W. Mont, J. K. Kim, and E. F. Schubert, “Performance of antireflection coatings consisting of multiple discrete layers and comparison with continuously graded antireflection coatings,” Appl. Phys. Express 3(8), 082502 (2010). 17. P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692–696 (2012). 18. C. L. Tan, S. J. Jang, and Y. T. Lee, “Localized surface plasmon resonance with broadband ultralow reflectivity from metal nanoparticles on glass and silicon subwavelength structures,” Opt. Express 20(16), 17448–17455 (2012). 19. T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Non-polarizing broadband multilayer reflectors in fish,” Nat. Photonics 6(11), 759–763 (2012). 20. A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. A. Sukhorukov, “Realization of reflectionless potentials in photonic lattices,” Phys. Rev. Lett. 106(19), 193903 (2011).
1. Introduction Achieving null reflection in a stratified medium at a specific angle of incidence or at a specified wavelength is easy. The real challenge lies in having antireflection at any wavelength or for any angle. In this context reflectionless potentials (RP's) were introduced and thoroughly discussed by Kay and Moses [1]. A great deal of theoretical work has been carried out on one specific example of the RP, namely, the Poschl-Teller potential having the sech2 dependence [2–4]. Some properties of the RP's were revealed in these studies. It was shown that the group delay associated with the passage of a Gaussian pulse can be negative and such superluminal transit is associated with pulse narrowing. In this report we exploit the recent results on a generalized optical RP [5] to design the heterolayer. We demonstrate broadband omnidirectional antireflection with < 0.5% reflection over the broad wavelength range of 500 – 2500 nm. Conventional AR coatings are, in general, interference based that work on the principle of cancellation of reflections by destructive interference over narrow regions of wavelength and angles of incidence. Graded index AR coating works over larger ranges of wavelength and angles due to the gradual change in the refractive index [6]. However, even the graded index profiles offer reflection at oblique angles [7]. Recently there have been several proposals and demonstrations of anti-reflection coatings based on graded index profiles, surface Mie resonators, bio-inspired guanine crystals, and localized plasmon resonances in metal nanoparticles [8–19]. Inspite of considerable research, true broadband, omni-directional, polarization independent antireflection coatings are not available. Optical realization of RP's through a stratified medium can offer the true solution [5,8]. Note that a discrete model system conforming to reflectionless Ablowitz-Ladik soliton potential has been recently reported [20]. However, the latter cannot be implemented in optical instrumentation to improve the optical throughput. 2. Methods 2.1 Design methodology Let a plane monochromatic wave be incident at an angle θ on a stratified medium with dielectric function profile ε(z).The problem is effectively one dimensional by virtue of the fact that dependence on x (transverse coordinate) is given by eik x x , with k x = k0 ε s sin θ , εs is the dielectric constant far away from the profile ε(z). Note that kx is the same for each layer (follows from the continuity of tangential fields) leading to a propagation equation in z [5]. The propagation equation for TE-waves for electric field when compared with the Schrödinger equation gives the relation between the energy, potential and the refractive index profile as, E = k 02ε s cos2 θ , V ( z ) = k 02ε s − k 02ε ( z ) , k o = ω / c,
(1)
V(z) is reflectionless if any wave with positive energy passes through the potential. We stress the fact that the potential is reflectionless for arbitrary E > 0 in the quantum problem. #213638 - $15.00 USD (C) 2014 OSA
Received 9 Jun 2014; accepted 27 Jun 2014; published 9 Jul 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.017382 | OPTICS EXPRESS 17383
Translated to the optics problem, arbitrary E implies arbitrary kx, see Eq. (1) satisfying the following,
k02ε s − k x2 > 0
(2)
For a given wavelength, it further means arbitrary θ (0 ≤ θ < π/2). Thus a reflectionless profile for TE waves would mean null reflection over the whole possible range of θ, namely, (0 ≤ θ < π/2). Equation (2) also implies propagating waves in the medium. Truncation of infinite profile leads to deviation from the perfect antireflection feature. It has been shown that such a reflectionless potential for TE polarized light is almost reflectionless for TM as well [5]. In addition, the reflection at shorter wavelengths is shown to be not too different from the longer wavelengths thus resulting in broad wavelength range anti-reflection coatings. Design flow for such anti-reflection coating starts by considering a set of linear equations given by, N
M j =1
ij
Fij ( z ) = − Ai eκ i z
(3)
Ai and κi being positive arbitrary constants for i = 1, N. The reflectionless potential V(z) is given in terms of the determinant (D) of the matrix Mij as [5], V ( z ) = −2
d2 [log( D )] dz 2
(4)
From this the refractive index profile is given by, n 2 ( z ) = ns2 +
2 d2 [log( D)] k02 dz 2
(5)
Fig. 1. Schematic of the reflectionless potential realized by heterolayers (black vertical lines) with blue shaded region indicating the refractive index profile between two quartz substrates (white regions) is shown. Reflectionless refractive index profile that is calculated (red line) and the mean position of each period in the deposited heterolayers (circles) between two quartz substrates are also shown.
The value of D depends on the matrix Mij and thus on the choice of parameters Ai and κi. For one parameter family with A1 = 2κ1, V(z) conforms to the Poschl-Teller potential. It may be seen that with increasing N (dimension of the parameter set) we can get more and more complex profiles that can result in infinitely many reflectionless potential profiles. The choice of the parameters thus can be chosen so that the reflectionless potential can be achieved with the available materials.
#213638 - $15.00 USD (C) 2014 OSA
Received 9 Jun 2014; accepted 27 Jun 2014; published 9 Jul 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.017382 | OPTICS EXPRESS 17384
We use 4-parameter family in designing the reflectionless potential. Solid line in Fig. 1 shows the calculated profile for (A1,A2,A3,A4) = (5.8,0.7,1.0,0.1) and (κ1,κ2,κ3,κ4) = (2.9,0.6,0.6,0.1). In addition, we consider the role of substrate and finite potential profile thickness. Considering that we have A1 = 2κ1 and the values of nmax (2.25) and nmin (1.67) from the potential profile, we get the design wavelength to be 2.3 µm. The parameters and thus the calculated refractive index profile are chosen such that it can be realized by a heterolayer consisting of pairs of Al2O3 and TiO2 layers. 2.2 Stratified medium preparation The designed profile was realized with 43 periods of 24 nm thick each deposited by electron beam evaporation or radio frequency (rf)-magnetron sputtering. Each period has a pair of layers whose relative thickness is varied from one period to other to achieve the required refractive index profile. Schematic of the layer structure along with the calculated and realized refractive index profile are shown in Fig. 1. In the electron beam evaporation method, at a base chamber pressure of 8x10−7 mbar, 99.99% pure Al2O3 or TiO2 was melted in separate graphite crucibles by electron beam heating. Deposition rate for Al2O3 and TiO2 is 9 ± 0.5 nm/min and 4.2 ± 0.5 nm/min, respectively. The other method employed is rf magnetron sputtering deposition where with a base pressure of 5x10−6 mbar, Argon was introduced to 2x10−2 mbar pressure. Al2O3 and TiO2 targets with 99.99% purity were sputtered in Argon plasma with rf-power of 100W. Uniform films are obtained by rotating the substrate. The deposition rate obtained was 0.81 ± 0.5 nm/min of Al2O3 and 0.51 ± 0.5 nm/min for TiO2. Deposition rate was determined by profilometer and surface quality by AFM. Surface roughness of the deposited film on ITO coated glass is 6 ± 0.5 nm for Al2O3 and 0.6 ± 0.5 nm for TiO2. Spectroscopic ellipsometer was used for measuring the refractive index of the individual layers. These values are used in calculating the reflectionless potential.
Fig. 2. Measured normal incidence (a) transmission spectra of RP is shown (red line) and calculated (black line) and (b) reflection spectra in air (red line) corrected for air-quartz interface reflection and that measured in index matching liquid (blue line). Insets show the angle dependence of measured % T and % R as a function of wavelength.
2.3 Optical measurements White light angle resolved transmission and reflection measurements were performed using commercial spectrometers or home built setups with collimated white light having a beam divergence of
