Abstract

Obliquely deposited thin films with helical microstructures exhibit circular Bragg effects. In this study, the effect of film porosity on the circular birefringence of helical thin films is investigated in TiO2 films deposited at angles ranging from 30° to 87° in order to determine the various mechanisms responsible for the circular Bragg effects. Specular transmittance and diffuse scattering measurements indicate two film growth regimes of enhanced circular Bragg effects: The first regime is due to a maximum in form birefringence while the second regime is caused by strong anisotropic scattering.

©2006 Optical Society of America

1. Introduction

Optical activity was observed in obliquely deposited thin films as early as 1959 when Young and Kowal used physical vapour deposition (PVD) to fabricate obliquely deposited thin films (<70°) on continuously rotating substrates [1]. Thirty years later, Motohiro and Taga used oblique angle deposition to create thin films with simple chevron microstructures. By abruptly rotating the substrate 180° halfway through each deposition [2], Motohiro and Taga were able to fabricate inorganic thin film waveplates with reduced positional homogeneity and film retardation anisotropy. In the years immediately after this milestone, theoretical studies on obliquely deposited films were performed by Azzam [3] as well as Lakhtakia and Weiglhofer [4]4. Following these studies, Robbie et. al. developed the glancing angle deposition (GLAD) technique [5–8] which incorporates substrate motion to achieve nano-scale control over thin film porosity and morphology.

The optical properties of an obliquely deposited thin film can be tailored by dynamically varying the orientation of the substrate during fabrication. This high degree of control can be utilized to engineer thin films for specific applications such as three-dimensional photonic crystals [9–11], gradient index optical filters [12, 13], broadband antireflection coatings [14], and linear polarizers [15]. Helical films are of interest due to their ability to differentiate states of circularly polarized light and are excellent candidates for circular polarization elements including sources, reflectors, filters, and detectors [16]. Porous helical films can be infiltrated with liquid crystals to enable switching behaviour [17] and have been proposed as a possible 3-D photonic crystal structure [18]. The circular Bragg behaviour exhibited in highly porous helical films can be harnessed to create humidity sensors, which have been experimentally shown [19]. We report on the use of porosity, as controlled by deposition angle, to alter the optical response to circularly polarized light in helical TiO2 thin films and identify the mechanisms which are responsible in determining this response. Throughout the studies cited in this section, it is apparent that a wide range of film structures can be grown with oblique deposition. This study differs from these others in that it looks at determining the mechanisms responsible for the circular Bragg behaviour and hopes to provide insight as to which helical film structures will perform the most favourably in applications where film porosity is an issue, such as the ones stated above.

2. Glancing angle deposition

GLAD is a thin film PVD technique that utilizes substrate shadowing to produce highly porous thin films with engineered morphology. Substrate shadowing occurs when the deposition angle α (measured from the substrate normal) is large enough (> 80°) for nuclei that form in the initial stages of film growth to prevent vapour flux from reaching portions of the substrate. This results in the film preferentially growing from the nucleation sites, which evolve into isolated columnar structures that are inclined towards the vapour source. At lower deposition angles (< 80°) substrate shadowing is minimized and the films obtain a tightly-packed structure. In this film growth regime, the deposition process is most commonly referred to as oblique angle deposition. By incorporating substrate rotation about an axis normal to the substrate surface (ϕ), the azimuthal column growth direction can be dynamically varied, which allows for control of the column shape over the entire film thickness. The helical films fabricated for this study were grown by holding α constant while continuously rotating ϕ at a constant speed, relative to the film growth rate. A crystal thickness monitor (CTM) was used to track the deposition rate and to provide feedback to the computer software responsible for governing substrate motion.

The helical films grown for this study were deposited by electron beam evaporation from 99.9% titanium dioxide source material (Cerac Inc.) to obtain a high refractive index and transparency in the optical wavelength regime, and were deposited onto glass substrates (Corning 7059). Fourteen helical films were grown, each at a unique deposition angle ranging from 30° to 87°. Selected scanning electron microscopy (SEM) images of these helical films are shown in Fig. 1. Helical films were fabricated with three right-handed helical turns and a helical pitch of 330 nm by applying three full clockwise substrate revolutions (as seen from the vapour source) over the duration of the 1 μm deposition. The deposition pressure was kept constant at 7×10-3 Pa by adding O2(g) to the vacuum chamber.

The normal incidence deposition rate ranged from 1.0-1.5 nm/s as measured by the CTM.

 figure: Fig. 1.

Fig. 1. SEM images of helical obliquely deposited films deposited at (a) 30°, (b) 65°, (c) 80° and (d) 87° illustrate the wide range of attainable film porosities. Side views are shown in the left column, top-down views are shown in the right column.

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3. Optical characterization

Helically structured films exhibit circular Bragg effects and tend to reflect circularly polarized light of same handedness while transmitting circularly polarized light of opposite handedness. The right-handed helical films fabricated for this study should preferentially transmit left circularly polarized (LCP) and reflect right circularly polarized light (RCP), whereas a left-handed film would behave in a reverse manner. The wavelength at which maximum circular Bragg reflectance occurs is proportional to both the average film index n and film pitch p (λ~np).

Optical measurements were taken in the visible to near infrared wavelength range. Highly porous films deposited at glancing angles tend to diffusely scatter a significant amount of light. Both specular and diffuse optical measurements were made to characterize the relationship between film porosity and the selective response to circular polarized light.

A variable angle spectroscopic ellipsometer (VASE) (model V-VASE from J. A. Woolam Co. Inc.) was used to measure selective specular transmittance, which is the difference in transmittance between LCP and RCP light that propagates through the sample and re-emerges at the same trajectory as the incident light. The specular response was measured by performing a spectroscopic scan to obtain the m 14 (1st row 4th column) Mueller matrix coefficient. The Mueller matrix is a 4×4 matrix that operates on Stokes vectors to determine polarization changes upon propagation through an optical medium for light of a given angle of incidence and wavelength. A Stokes vector defines the polarization state and intensity of the light represented with a basis containing linear and circular polarization states [20]. Having obtained the transmittance Mueller matrix, the selective specular transmittance of circularly polarized light is calculated with Eq. (1):

T(LCP)sT(RCP)s=2m14(λ).

Specular transmittance measurements were repeated using a Perkin Elmer Lambda 900 UV/VIS/NIR spectrophotometer. LCP and RCP light were generated by passing unpolarized light through a linear polarizer followed by an Oriel achromatic quarter wave plate with its fast axis oriented ±45° relative to the transmission axis of the linear polarizer. The resulting circularly polarized light then propagated through the sample and into a detector, positioned far behind the sample to collect only the specular-transmitted light. Due to thin film interference effects, the data obtained with the spectrophotometer was found to be highly dependent on the orientation of the substrate. To alleviate this issue, multiple data sets were obtained in the spectrophotometer with different in-plane substrate rotations and averaged. The resulting data was then found to be in close agreement with the data obtained through ellipsometry.

Helical films deposited at glancing deposition angles (α > 80°) appear hazy to the naked eye, suggesting significant diffuse scattering. To measure the contributions of diffusely scattered light to the circular Bragg response, the aforementioned spectrophotometer apparatus was refitted with a broadband integrating sphere to capture the diffusely scattered light as it left the sample. To measure diffuse transmittance, the sample was mounted on the integrating sphere’s front port. With the exit port covered, this arrangement captures both the specular and diffusely transmitted light. To separate the two contributions, the previously obtained specular transmittance result was subtracted:

T(LCP)DT(RCP)D=T(LCP)T(RCP)[T(LCP)ST(RCP)S].

Diffuse reflectance was measured by mounting the sample against the exit port of the integrating sphere. In this arrangement, light that undergoes specular reflection escapes through the front port and only the diffusely reflected contribution is collected. A small portion of the scattered light that escapes through the front port of the integrating sphere and light that is scattered laterally in the plane of the substrate was unaccounted for.

4. Results

A characteristic transmittance spectrum taken with the spectrophotometer is shown in Fig. 2(a). The selective transmittance is obtained by subtracting the LCP and RCP transmittance spectra from each other, the result of which is shown in Fig. 2(b). The two features of the response that are of interest are the magnitude and wavelength position of the peak circular Bragg response.

 figure: Fig. 2.

Fig. 2. (a). Transmittance and (b) selective transmittance spectra of a helical film deposited at α = 65°.

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The magnitude of the response can be controlled by the number of turns in the film. In general, the magnitude of the circular response can be increased with additional turns. However, at highly oblique deposition angles, column competition during film growth results in column extinction, leading to broadening in the remaining columns so that constant film porosity can be maintained, which tends to cause TiO2 helical films with more turns to lose structural definition [12]. Since scattering is more prominent in thick films, the usefulness of adding turns to helical films to increase their response is limited at glancing deposition angles. In this study, three helical turns were used for each sample to obtain appreciable circular Bragg effects while avoiding excessive scattering losses.

The dependence of the Bragg wavelength on the film deposition angle is shown in Fig. 3. The peak wavelength blue-shifts with increasing deposition angle, which is due to the increasing porosity in the films. The film porosity can be derived from Eq. (3), which is an approximation of the film density [21]:

ρρo=2cos(α)1+cos(α).
 figure: Fig. 3.

Fig. 3. Peak selective transmittance wavelength vs. deposition angle α.

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Here ρo is the density of a film deposited at normal incidence and the film porosity is (1 - ρρb1), where ρb is the bulk density. The dependence of film porosity on the deposition angle, as well as porosity measurements of obliquely deposited films have been previously reported [22–25]. Obliquely deposited films can be treated as an effective air/film medium, with an average refractive index that is a combination of the film material index and the refractive index of air. As the film becomes more porous, the contribution of the air filled pores to the effective index of refraction increases, causing the average refractive index to decrease. At this point, it should be noted that the term effective index refers to the case for normally incident light and is a combination of the three primary indices of refraction [26].

The dependence of the maximum selective specular transmittance of circularly polarized light on the film deposition angle, obtained through spectroscopic ellipsometry, is reported in Fig. 4. Due to the unreliability of fabricating films at deposition angles >87°, the maximum film deposition angle that was studied was 87°. This causes the data to appear to have a maximum at 87°, but it is uncertain as to whether or not the selective behaviour will continue to increase in films grown at higher deposition angles. The data in Fig. 4 shows two regimes where the response is maximized. The first local maximum in the circular Bragg response occurs at a deposition angle of 65°. In this regime, the deposition angle is not large enough to promote significant substrate shadowing and the resulting films are comprised of closely packed helical columns. Because atomic-shadowing only occurs in the deposition plane, obliquely deposited thin films tend to consist of inclined columns which fan out and chain together perpendicular to the deposition plane [27]. The anisotropic nature of the growth mechanism produces substantial form birefringence, which is amplified as the deposition angle is increased. However, the form birefringence also scales with the refractive index of the film, which decreases as the deposition angle is increased. Furthermore, the column tilt angle, measured from the substrate normal, increases from approximately 25 deg. to 45 deg. as alpha increases from 50° to 87°, which also lowers the in-plane form birefringence. These competing effects result in a maximum form birefringence that occurs at deposition angles ranging between 55° and 65° for most materials [26, 28–29]. A helical film can be interpreted as a material in which the orientation of a local linear-birefringence rotates through the thickness of the film to produce a circular Bragg grating. The maximum form birefringence produces a maximum circular birefringence, which is responsible for the stronger Bragg reflectance observed in chiral TiO2 films deposited near 65°.

 figure: Fig. 4.

Fig. 4. Maximum selective specular transmittance of circularly polarized light in helical TiO2 thin films

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The second local maximum in the selective response to circularly polarized light occurs at glancing deposition angles where substrate shadowing is significant and the films are highly porous [Fig. 1(d)]. In this regime, the films are comprised of individual isolated helical structures as opposed to tightly packed columns. The isolated helices provide a large number of air/film interfaces for light to scatter off of. Due to the chiral film structure, if the scattering that occurs is anisotropic, it can be expected that scattering will contribute to the selective circular Bragg response.

Diffuse transmittance and reflectance data are shown in Fig. 5(a) and 5(b) respectively. As the deposition angle is increased beyond 80°, amplified substrate shadowing causes column separation. This produces films with higher surface area which exhibit increased anisotropic scattering. The contribution of anisotropic diffuse scattering was subtracted from the response shown in Fig. 4 and re-plotted in Fig. 6. The SEM images in Fig. 1 suggest that the onset of scattering occurs when the helical structures transition from densely packed to separated structures. As expected, the first local maximum, where the film is comprised of tightly packed columns, remains relatively unchanged. This indicates a minimal contribution from scattering in this regime. However, the second maximum, where the film is comprised of isolated columns, is reduced substantially when the diffusely scattered components are removed, suggesting the anisotropic scattering, not form birefringence, is the dominant mechanism contributing to the selective response to circularly polarized light witnessed in these helical films. It is for this reason that helical films grown at higher deposition angles have lower absolute transmittance, making them less suitable than helical films grown at lower deposition angles in most applications. Since the regions in which the selective behaviour reaches its maximum depend on the dominant film growth mechanisms and that the magnitude of the response is dependent on the bulk refractive index of the evaporant used to grow the film, it is expected that other thin film oxides would overall have similar selective behaviour as TiO2 in their respective regions of transparency, but would be scaled based on their bulk refractive index relative to that of TiO2.

 figure: Fig. 5.

Fig. 5. (a). Maximum selective diffuse transmittance of circularly polarized light in helical TiO2 thin films; (b) Maximum selective diffuse reflectance of circularly polarized light in helical TiO2 thin films.

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 figure: Fig. 6.

Fig. 6. Maximum selective specular transmittance of circularly polarized light in helical TiO2 films (○ diffuse components included, ● diffuse components removed).

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5. Conclusion

Helical films exhibit a circular Bragg response, preferentially transmitting light with circular polarization that is opposite to the helical film handedness, an effect that is strongly affected by film porosity. By varying the deposition angle, a set of TiO2 helical films was fabricated, each with a different porosity. SEM analysis revealed a transition in structural morphology that occurs at a deposition angle of 80°. Below 80° helical films are comprised of closely packed helical columns, and the circular Bragg reflectance is dominated by a maximum in form birefringence. Beyond 80° substrate shadowing becomes sufficient to cause the helical columns to separate into isolated structures, resulting in the proliferation of air/film interfaces. At glancing deposition angles, diffuse scattering measurements made with an integrating sphere reveal that the selective transmittance of circularly polarized light, for films deposited at glancing angles, is due to strong anisotropic diffuse scattering.

Acknowledgments

The authors acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC), the Alberta Informatics Circle of Research Excellence (iCORE), Micralyne Inc., and the Alberta Heritage Scholarship Fund. The authors would also like to thank George Braybrook for the exceptional SEM images.

References and links

1. N. O. Young and J. Kowal, “Optically active fluorite films,” Nature 183, 104–105 (1959). [CrossRef]  

2. T. Motohiro and Y. Taga, “Thin film retardation plate by oblique deposition,” Appl. Opt. 28, 2466–2482 (1989). [CrossRef]   [PubMed]  

3. R. Azzam, “Chiral thin solid films: method of deposition and applications,” Appl. Phys. Lett. 61, 3118–3120 (1992). [CrossRef]  

4. A. Lakhtakia and W. S. Weiglhofer, “On light propagation in helicoidal bianisotropic mediums,” Proceedings of the Royal Society of London A 448, 419–437 (1995). [CrossRef]  

5. K. Robbie and M. J. Brett, “Sculptured thin films and glancing angle deposition: Growth mechanics and applications,” J. Vac. Sci. Technol. A 15, 1460–1465 (1997). [CrossRef]  

6. K. J. Robbie and M. J. Brett, “Method of depositing shadow sculpted thin films,” U S patent 5,866,204 (2 February 1999).

7. K. J. Robbie and M. J. Brett, “Shadow sculpted thin films,” U S patent 6,248,422 (19 June 2001).

8. K. J. Robbie and M. J. Brett, “Glancing angle deposition of thin films,” U S patent 6,206,065 (27 March 2001).

9. S. R. Kennedy, M. J. Brett, O. Toader, and S. John, “Fabrication of Tetragonal Square Spiral Photonic Crystals,” Nano Lett. 2, 59–62 (2002). [CrossRef]  

10. S. R. Kennedy, M. J. Brett, H. Miguez, O. Toader, and S. John, “Optical properties of a three-dimensional silicon square spiral photonic crystal,” Photon. Nanostruct. 1, 37–42 (2003). [CrossRef]  

11. Y. P. Zhao, D. X. Ye, P. I. Wang, G. C. Wang, and T. M. Lu, “Fabrication of Si nanocolumns and Si square spirals of self-assembled monolayer colloid substrates,” Int. J. Nanosci. 1, 87–97 (2002). [CrossRef]  

12. A. C. van Popta, M. H. Hawkeye, J. C. Sit, and M. J. Brett, “Gradient-index narrow bandpass filters fabricated with glancing-angle deposition,” Opt. Lett. 29, 2545–2547 (2004). [CrossRef]   [PubMed]  

13. K. Kaminska, T. Brown, G. Beydaghyan, and K. Robbie, “Vacuum evaporated porous silicon photonic interference filters,” Appl. Opt. 42, 4212–4219 (2003). [CrossRef]   [PubMed]  

14. S. R. Kennedy and M. J. Brett, “Porous broadband antireflection coating by glancing angle deposition,” Appl. Opt. 42, 4573–4579 (2003). [CrossRef]   [PubMed]  

15. Q. H. Wu, L. De Silva, M. Arnold, I. J. Hodgkinson, and E. Takeuchi, “All-silicon polarizing filters for near-infrared wavelengths,” J. Appl. Phys. 95, 402–404 (2004). [CrossRef]  

16. I. Hodgkinson and Q. Wu, “Inorganic chiral optical materials,” Adv. Mater. 13, 889–897 (2001). [CrossRef]  

17. S. R. Kennedy, J. C. Sit, D. J. Broer, and M. J. Brett, “Optical activity of Chiral Thin Film and Liquid Crystal Hybrids,” Liq. Cryst. 28, 1799–1803 (2001). [CrossRef]  

18. A. Chutinan and S. Noda, “Spiral three-dimensional photonic-band-gap structure,” Phys. Rev. B 57, 2006–2008 (1998). [CrossRef]  

19. A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculpted-thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33–46 (2001). [CrossRef]  

20. C. F. Borhen and D. R. Huffman, Absorption and scattering of light by small particles, (Wiley, New York, 1983), pp. 44–56.

21. R. N. Tait, T. Smy, and M. J. Brett, “Modelling and characterization of columnar growth in evaporated films,” Thin Solid Films 226, 196–201 (1993). [CrossRef]  

22. K. D. Harris, D. Vick, E. J. Gonzalez, T. Smy, K. Robbie, and M. J. Brett, “Porous thin films for thermal barrier coatings,” Surf. Coat. Technol. 138, 185–191 (2001). [CrossRef]  

23. J. J. Steele, K. D. Harris, and M. J. Brett, “Nanostructured oxide films for high-speed humidity sensors,” Mat. Res. Soc. Symp. Proc. 788, 473–478 (2004).

24. J. N. Broughton and M. J. Brett, “Electrochem. Solid-State Lett.5, A279–A282 (2002).

25. K. Robbie and Ph.D. Thesis, University of Alberta, Edmonton, AB, (1998).

26. I. Hodgkinson, Q. Wu, and S. Collett, “Dispersion equations for vacuum-deposited tilted-columnar biaxial media,” Appl. Opt. 40, 452–457 (2001). [CrossRef]  

27. R. N. Tait, T. Smy, and M. J. Brett, “Structural anisotropy in oblique-incidence thin metal-films,” J. Vac. Sci. Technol. A 10, 1518–1521 (1992). [CrossRef]  

28. G. Beydaghyan, K. Kaminska, T. Brown, and K. Robbie, “Enhaced birefringence in vacuum evaporated silicon thin films,” Appl. Opt. 43, 5343–5349 (2004). [CrossRef]   [PubMed]  

29. A. C. van Popta, J. C. Sit, and M. J. Brett, “Optical properties of porous helical thin films,” Appl. Opt. 43, 3632–3639 (2004). [CrossRef]   [PubMed]  

References

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  • |

  1. N. O. Young and J. Kowal, “Optically active fluorite films,” Nature 183, 104–105 (1959).
    [Crossref]
  2. T. Motohiro and Y. Taga, “Thin film retardation plate by oblique deposition,” Appl. Opt. 28, 2466–2482 (1989).
    [Crossref] [PubMed]
  3. R. Azzam, “Chiral thin solid films: method of deposition and applications,” Appl. Phys. Lett. 61, 3118–3120 (1992).
    [Crossref]
  4. A. Lakhtakia and W. S. Weiglhofer, “On light propagation in helicoidal bianisotropic mediums,” Proceedings of the Royal Society of London A 448, 419–437 (1995).
    [Crossref]
  5. K. Robbie and M. J. Brett, “Sculptured thin films and glancing angle deposition: Growth mechanics and applications,” J. Vac. Sci. Technol. A 15, 1460–1465 (1997).
    [Crossref]
  6. K. J. Robbie and M. J. Brett, “Method of depositing shadow sculpted thin films,” U S patent 5,866,204 (2 February 1999).
  7. K. J. Robbie and M. J. Brett, “Shadow sculpted thin films,” U S patent 6,248,422 (19 June 2001).
  8. K. J. Robbie and M. J. Brett, “Glancing angle deposition of thin films,” U S patent 6,206,065 (27 March 2001).
  9. S. R. Kennedy, M. J. Brett, O. Toader, and S. John, “Fabrication of Tetragonal Square Spiral Photonic Crystals,” Nano Lett. 2, 59–62 (2002).
    [Crossref]
  10. S. R. Kennedy, M. J. Brett, H. Miguez, O. Toader, and S. John, “Optical properties of a three-dimensional silicon square spiral photonic crystal,” Photon. Nanostruct. 1, 37–42 (2003).
    [Crossref]
  11. Y. P. Zhao, D. X. Ye, P. I. Wang, G. C. Wang, and T. M. Lu, “Fabrication of Si nanocolumns and Si square spirals of self-assembled monolayer colloid substrates,” Int. J. Nanosci. 1, 87–97 (2002).
    [Crossref]
  12. A. C. van Popta, M. H. Hawkeye, J. C. Sit, and M. J. Brett, “Gradient-index narrow bandpass filters fabricated with glancing-angle deposition,” Opt. Lett. 29, 2545–2547 (2004).
    [Crossref] [PubMed]
  13. K. Kaminska, T. Brown, G. Beydaghyan, and K. Robbie, “Vacuum evaporated porous silicon photonic interference filters,” Appl. Opt. 42, 4212–4219 (2003).
    [Crossref] [PubMed]
  14. S. R. Kennedy and M. J. Brett, “Porous broadband antireflection coating by glancing angle deposition,” Appl. Opt. 42, 4573–4579 (2003).
    [Crossref] [PubMed]
  15. Q. H. Wu, L. De Silva, M. Arnold, I. J. Hodgkinson, and E. Takeuchi, “All-silicon polarizing filters for near-infrared wavelengths,” J. Appl. Phys. 95, 402–404 (2004).
    [Crossref]
  16. I. Hodgkinson and Q. Wu, “Inorganic chiral optical materials,” Adv. Mater. 13, 889–897 (2001).
    [Crossref]
  17. S. R. Kennedy, J. C. Sit, D. J. Broer, and M. J. Brett, “Optical activity of Chiral Thin Film and Liquid Crystal Hybrids,” Liq. Cryst. 28, 1799–1803 (2001).
    [Crossref]
  18. A. Chutinan and S. Noda, “Spiral three-dimensional photonic-band-gap structure,” Phys. Rev. B 57, 2006–2008 (1998).
    [Crossref]
  19. A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculpted-thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33–46 (2001).
    [Crossref]
  20. C. F. Borhen and D. R. Huffman, Absorption and scattering of light by small particles, (Wiley, New York, 1983), pp. 44–56.
  21. R. N. Tait, T. Smy, and M. J. Brett, “Modelling and characterization of columnar growth in evaporated films,” Thin Solid Films 226, 196–201 (1993).
    [Crossref]
  22. K. D. Harris, D. Vick, E. J. Gonzalez, T. Smy, K. Robbie, and M. J. Brett, “Porous thin films for thermal barrier coatings,” Surf. Coat. Technol. 138, 185–191 (2001).
    [Crossref]
  23. J. J. Steele, K. D. Harris, and M. J. Brett, “Nanostructured oxide films for high-speed humidity sensors,” Mat. Res. Soc. Symp. Proc. 788, 473–478 (2004).
  24. J. N. Broughton and M. J. Brett, “Electrochem. Solid-State Lett. 5, A279–A282 (2002).
  25. K. Robbie and Ph.D. Thesis, University of Alberta, Edmonton, AB, (1998).
  26. I. Hodgkinson, Q. Wu, and S. Collett, “Dispersion equations for vacuum-deposited tilted-columnar biaxial media,” Appl. Opt. 40, 452–457 (2001).
    [Crossref]
  27. R. N. Tait, T. Smy, and M. J. Brett, “Structural anisotropy in oblique-incidence thin metal-films,” J. Vac. Sci. Technol. A 10, 1518–1521 (1992).
    [Crossref]
  28. G. Beydaghyan, K. Kaminska, T. Brown, and K. Robbie, “Enhaced birefringence in vacuum evaporated silicon thin films,” Appl. Opt. 43, 5343–5349 (2004).
    [Crossref] [PubMed]
  29. A. C. van Popta, J. C. Sit, and M. J. Brett, “Optical properties of porous helical thin films,” Appl. Opt. 43, 3632–3639 (2004).
    [Crossref] [PubMed]

2004 (5)

2003 (3)

2002 (3)

Y. P. Zhao, D. X. Ye, P. I. Wang, G. C. Wang, and T. M. Lu, “Fabrication of Si nanocolumns and Si square spirals of self-assembled monolayer colloid substrates,” Int. J. Nanosci. 1, 87–97 (2002).
[Crossref]

S. R. Kennedy, M. J. Brett, O. Toader, and S. John, “Fabrication of Tetragonal Square Spiral Photonic Crystals,” Nano Lett. 2, 59–62 (2002).
[Crossref]

J. N. Broughton and M. J. Brett, “Electrochem. Solid-State Lett. 5, A279–A282 (2002).

2001 (5)

I. Hodgkinson, Q. Wu, and S. Collett, “Dispersion equations for vacuum-deposited tilted-columnar biaxial media,” Appl. Opt. 40, 452–457 (2001).
[Crossref]

K. D. Harris, D. Vick, E. J. Gonzalez, T. Smy, K. Robbie, and M. J. Brett, “Porous thin films for thermal barrier coatings,” Surf. Coat. Technol. 138, 185–191 (2001).
[Crossref]

A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculpted-thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33–46 (2001).
[Crossref]

I. Hodgkinson and Q. Wu, “Inorganic chiral optical materials,” Adv. Mater. 13, 889–897 (2001).
[Crossref]

S. R. Kennedy, J. C. Sit, D. J. Broer, and M. J. Brett, “Optical activity of Chiral Thin Film and Liquid Crystal Hybrids,” Liq. Cryst. 28, 1799–1803 (2001).
[Crossref]

1998 (1)

A. Chutinan and S. Noda, “Spiral three-dimensional photonic-band-gap structure,” Phys. Rev. B 57, 2006–2008 (1998).
[Crossref]

1997 (1)

K. Robbie and M. J. Brett, “Sculptured thin films and glancing angle deposition: Growth mechanics and applications,” J. Vac. Sci. Technol. A 15, 1460–1465 (1997).
[Crossref]

1995 (1)

A. Lakhtakia and W. S. Weiglhofer, “On light propagation in helicoidal bianisotropic mediums,” Proceedings of the Royal Society of London A 448, 419–437 (1995).
[Crossref]

1993 (1)

R. N. Tait, T. Smy, and M. J. Brett, “Modelling and characterization of columnar growth in evaporated films,” Thin Solid Films 226, 196–201 (1993).
[Crossref]

1992 (2)

R. N. Tait, T. Smy, and M. J. Brett, “Structural anisotropy in oblique-incidence thin metal-films,” J. Vac. Sci. Technol. A 10, 1518–1521 (1992).
[Crossref]

R. Azzam, “Chiral thin solid films: method of deposition and applications,” Appl. Phys. Lett. 61, 3118–3120 (1992).
[Crossref]

1989 (1)

1983 (1)

C. F. Borhen and D. R. Huffman, Absorption and scattering of light by small particles, (Wiley, New York, 1983), pp. 44–56.

1959 (1)

N. O. Young and J. Kowal, “Optically active fluorite films,” Nature 183, 104–105 (1959).
[Crossref]

Arnold, M.

Q. H. Wu, L. De Silva, M. Arnold, I. J. Hodgkinson, and E. Takeuchi, “All-silicon polarizing filters for near-infrared wavelengths,” J. Appl. Phys. 95, 402–404 (2004).
[Crossref]

Azzam, R.

R. Azzam, “Chiral thin solid films: method of deposition and applications,” Appl. Phys. Lett. 61, 3118–3120 (1992).
[Crossref]

Beydaghyan, G.

Borhen, C. F.

C. F. Borhen and D. R. Huffman, Absorption and scattering of light by small particles, (Wiley, New York, 1983), pp. 44–56.

Brett, M. J.

J. J. Steele, K. D. Harris, and M. J. Brett, “Nanostructured oxide films for high-speed humidity sensors,” Mat. Res. Soc. Symp. Proc. 788, 473–478 (2004).

A. C. van Popta, M. H. Hawkeye, J. C. Sit, and M. J. Brett, “Gradient-index narrow bandpass filters fabricated with glancing-angle deposition,” Opt. Lett. 29, 2545–2547 (2004).
[Crossref] [PubMed]

A. C. van Popta, J. C. Sit, and M. J. Brett, “Optical properties of porous helical thin films,” Appl. Opt. 43, 3632–3639 (2004).
[Crossref] [PubMed]

S. R. Kennedy, M. J. Brett, H. Miguez, O. Toader, and S. John, “Optical properties of a three-dimensional silicon square spiral photonic crystal,” Photon. Nanostruct. 1, 37–42 (2003).
[Crossref]

S. R. Kennedy and M. J. Brett, “Porous broadband antireflection coating by glancing angle deposition,” Appl. Opt. 42, 4573–4579 (2003).
[Crossref] [PubMed]

S. R. Kennedy, M. J. Brett, O. Toader, and S. John, “Fabrication of Tetragonal Square Spiral Photonic Crystals,” Nano Lett. 2, 59–62 (2002).
[Crossref]

J. N. Broughton and M. J. Brett, “Electrochem. Solid-State Lett. 5, A279–A282 (2002).

K. D. Harris, D. Vick, E. J. Gonzalez, T. Smy, K. Robbie, and M. J. Brett, “Porous thin films for thermal barrier coatings,” Surf. Coat. Technol. 138, 185–191 (2001).
[Crossref]

S. R. Kennedy, J. C. Sit, D. J. Broer, and M. J. Brett, “Optical activity of Chiral Thin Film and Liquid Crystal Hybrids,” Liq. Cryst. 28, 1799–1803 (2001).
[Crossref]

K. Robbie and M. J. Brett, “Sculptured thin films and glancing angle deposition: Growth mechanics and applications,” J. Vac. Sci. Technol. A 15, 1460–1465 (1997).
[Crossref]

R. N. Tait, T. Smy, and M. J. Brett, “Modelling and characterization of columnar growth in evaporated films,” Thin Solid Films 226, 196–201 (1993).
[Crossref]

R. N. Tait, T. Smy, and M. J. Brett, “Structural anisotropy in oblique-incidence thin metal-films,” J. Vac. Sci. Technol. A 10, 1518–1521 (1992).
[Crossref]

K. J. Robbie and M. J. Brett, “Glancing angle deposition of thin films,” U S patent 6,206,065 (27 March 2001).

K. J. Robbie and M. J. Brett, “Method of depositing shadow sculpted thin films,” U S patent 5,866,204 (2 February 1999).

K. J. Robbie and M. J. Brett, “Shadow sculpted thin films,” U S patent 6,248,422 (19 June 2001).

Broer, D. J.

S. R. Kennedy, J. C. Sit, D. J. Broer, and M. J. Brett, “Optical activity of Chiral Thin Film and Liquid Crystal Hybrids,” Liq. Cryst. 28, 1799–1803 (2001).
[Crossref]

Broughton, J. N.

J. N. Broughton and M. J. Brett, “Electrochem. Solid-State Lett. 5, A279–A282 (2002).

Brown, T.

Chutinan, A.

A. Chutinan and S. Noda, “Spiral three-dimensional photonic-band-gap structure,” Phys. Rev. B 57, 2006–2008 (1998).
[Crossref]

Collett, S.

De Silva, L.

Q. H. Wu, L. De Silva, M. Arnold, I. J. Hodgkinson, and E. Takeuchi, “All-silicon polarizing filters for near-infrared wavelengths,” J. Appl. Phys. 95, 402–404 (2004).
[Crossref]

Gonzalez, E. J.

K. D. Harris, D. Vick, E. J. Gonzalez, T. Smy, K. Robbie, and M. J. Brett, “Porous thin films for thermal barrier coatings,” Surf. Coat. Technol. 138, 185–191 (2001).
[Crossref]

Harris, K. D.

J. J. Steele, K. D. Harris, and M. J. Brett, “Nanostructured oxide films for high-speed humidity sensors,” Mat. Res. Soc. Symp. Proc. 788, 473–478 (2004).

K. D. Harris, D. Vick, E. J. Gonzalez, T. Smy, K. Robbie, and M. J. Brett, “Porous thin films for thermal barrier coatings,” Surf. Coat. Technol. 138, 185–191 (2001).
[Crossref]

Hawkeye, M. H.

Hodgkinson, I.

Hodgkinson, I. J.

Q. H. Wu, L. De Silva, M. Arnold, I. J. Hodgkinson, and E. Takeuchi, “All-silicon polarizing filters for near-infrared wavelengths,” J. Appl. Phys. 95, 402–404 (2004).
[Crossref]

A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculpted-thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33–46 (2001).
[Crossref]

Huffman, D. R.

C. F. Borhen and D. R. Huffman, Absorption and scattering of light by small particles, (Wiley, New York, 1983), pp. 44–56.

John, S.

S. R. Kennedy, M. J. Brett, H. Miguez, O. Toader, and S. John, “Optical properties of a three-dimensional silicon square spiral photonic crystal,” Photon. Nanostruct. 1, 37–42 (2003).
[Crossref]

S. R. Kennedy, M. J. Brett, O. Toader, and S. John, “Fabrication of Tetragonal Square Spiral Photonic Crystals,” Nano Lett. 2, 59–62 (2002).
[Crossref]

Kaminska, K.

Kennedy, S. R.

S. R. Kennedy, M. J. Brett, H. Miguez, O. Toader, and S. John, “Optical properties of a three-dimensional silicon square spiral photonic crystal,” Photon. Nanostruct. 1, 37–42 (2003).
[Crossref]

S. R. Kennedy and M. J. Brett, “Porous broadband antireflection coating by glancing angle deposition,” Appl. Opt. 42, 4573–4579 (2003).
[Crossref] [PubMed]

S. R. Kennedy, M. J. Brett, O. Toader, and S. John, “Fabrication of Tetragonal Square Spiral Photonic Crystals,” Nano Lett. 2, 59–62 (2002).
[Crossref]

S. R. Kennedy, J. C. Sit, D. J. Broer, and M. J. Brett, “Optical activity of Chiral Thin Film and Liquid Crystal Hybrids,” Liq. Cryst. 28, 1799–1803 (2001).
[Crossref]

Kowal, J.

N. O. Young and J. Kowal, “Optically active fluorite films,” Nature 183, 104–105 (1959).
[Crossref]

Lakhtakia, A.

A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculpted-thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33–46 (2001).
[Crossref]

A. Lakhtakia and W. S. Weiglhofer, “On light propagation in helicoidal bianisotropic mediums,” Proceedings of the Royal Society of London A 448, 419–437 (1995).
[Crossref]

Lu, T. M.

Y. P. Zhao, D. X. Ye, P. I. Wang, G. C. Wang, and T. M. Lu, “Fabrication of Si nanocolumns and Si square spirals of self-assembled monolayer colloid substrates,” Int. J. Nanosci. 1, 87–97 (2002).
[Crossref]

McCall, M. W.

A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculpted-thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33–46 (2001).
[Crossref]

Miguez, H.

S. R. Kennedy, M. J. Brett, H. Miguez, O. Toader, and S. John, “Optical properties of a three-dimensional silicon square spiral photonic crystal,” Photon. Nanostruct. 1, 37–42 (2003).
[Crossref]

Motohiro, T.

Noda, S.

A. Chutinan and S. Noda, “Spiral three-dimensional photonic-band-gap structure,” Phys. Rev. B 57, 2006–2008 (1998).
[Crossref]

Robbie, K.

G. Beydaghyan, K. Kaminska, T. Brown, and K. Robbie, “Enhaced birefringence in vacuum evaporated silicon thin films,” Appl. Opt. 43, 5343–5349 (2004).
[Crossref] [PubMed]

K. Kaminska, T. Brown, G. Beydaghyan, and K. Robbie, “Vacuum evaporated porous silicon photonic interference filters,” Appl. Opt. 42, 4212–4219 (2003).
[Crossref] [PubMed]

K. D. Harris, D. Vick, E. J. Gonzalez, T. Smy, K. Robbie, and M. J. Brett, “Porous thin films for thermal barrier coatings,” Surf. Coat. Technol. 138, 185–191 (2001).
[Crossref]

K. Robbie and M. J. Brett, “Sculptured thin films and glancing angle deposition: Growth mechanics and applications,” J. Vac. Sci. Technol. A 15, 1460–1465 (1997).
[Crossref]

K. Robbie and Ph.D. Thesis, University of Alberta, Edmonton, AB, (1998).

Robbie, K. J.

K. J. Robbie and M. J. Brett, “Method of depositing shadow sculpted thin films,” U S patent 5,866,204 (2 February 1999).

K. J. Robbie and M. J. Brett, “Glancing angle deposition of thin films,” U S patent 6,206,065 (27 March 2001).

K. J. Robbie and M. J. Brett, “Shadow sculpted thin films,” U S patent 6,248,422 (19 June 2001).

Sherwin, J. A.

A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculpted-thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33–46 (2001).
[Crossref]

Sit, J. C.

Smy, T.

K. D. Harris, D. Vick, E. J. Gonzalez, T. Smy, K. Robbie, and M. J. Brett, “Porous thin films for thermal barrier coatings,” Surf. Coat. Technol. 138, 185–191 (2001).
[Crossref]

R. N. Tait, T. Smy, and M. J. Brett, “Modelling and characterization of columnar growth in evaporated films,” Thin Solid Films 226, 196–201 (1993).
[Crossref]

R. N. Tait, T. Smy, and M. J. Brett, “Structural anisotropy in oblique-incidence thin metal-films,” J. Vac. Sci. Technol. A 10, 1518–1521 (1992).
[Crossref]

Steele, J. J.

J. J. Steele, K. D. Harris, and M. J. Brett, “Nanostructured oxide films for high-speed humidity sensors,” Mat. Res. Soc. Symp. Proc. 788, 473–478 (2004).

Taga, Y.

Tait, R. N.

R. N. Tait, T. Smy, and M. J. Brett, “Modelling and characterization of columnar growth in evaporated films,” Thin Solid Films 226, 196–201 (1993).
[Crossref]

R. N. Tait, T. Smy, and M. J. Brett, “Structural anisotropy in oblique-incidence thin metal-films,” J. Vac. Sci. Technol. A 10, 1518–1521 (1992).
[Crossref]

Takeuchi, E.

Q. H. Wu, L. De Silva, M. Arnold, I. J. Hodgkinson, and E. Takeuchi, “All-silicon polarizing filters for near-infrared wavelengths,” J. Appl. Phys. 95, 402–404 (2004).
[Crossref]

Thesis, Ph.D.

K. Robbie and Ph.D. Thesis, University of Alberta, Edmonton, AB, (1998).

Toader, O.

S. R. Kennedy, M. J. Brett, H. Miguez, O. Toader, and S. John, “Optical properties of a three-dimensional silicon square spiral photonic crystal,” Photon. Nanostruct. 1, 37–42 (2003).
[Crossref]

S. R. Kennedy, M. J. Brett, O. Toader, and S. John, “Fabrication of Tetragonal Square Spiral Photonic Crystals,” Nano Lett. 2, 59–62 (2002).
[Crossref]

van Popta, A. C.

Vick, D.

K. D. Harris, D. Vick, E. J. Gonzalez, T. Smy, K. Robbie, and M. J. Brett, “Porous thin films for thermal barrier coatings,” Surf. Coat. Technol. 138, 185–191 (2001).
[Crossref]

Wang, G. C.

Y. P. Zhao, D. X. Ye, P. I. Wang, G. C. Wang, and T. M. Lu, “Fabrication of Si nanocolumns and Si square spirals of self-assembled monolayer colloid substrates,” Int. J. Nanosci. 1, 87–97 (2002).
[Crossref]

Wang, P. I.

Y. P. Zhao, D. X. Ye, P. I. Wang, G. C. Wang, and T. M. Lu, “Fabrication of Si nanocolumns and Si square spirals of self-assembled monolayer colloid substrates,” Int. J. Nanosci. 1, 87–97 (2002).
[Crossref]

Weiglhofer, W. S.

A. Lakhtakia and W. S. Weiglhofer, “On light propagation in helicoidal bianisotropic mediums,” Proceedings of the Royal Society of London A 448, 419–437 (1995).
[Crossref]

Wu, Q.

Wu, Q. H.

Q. H. Wu, L. De Silva, M. Arnold, I. J. Hodgkinson, and E. Takeuchi, “All-silicon polarizing filters for near-infrared wavelengths,” J. Appl. Phys. 95, 402–404 (2004).
[Crossref]

A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculpted-thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33–46 (2001).
[Crossref]

Ye, D. X.

Y. P. Zhao, D. X. Ye, P. I. Wang, G. C. Wang, and T. M. Lu, “Fabrication of Si nanocolumns and Si square spirals of self-assembled monolayer colloid substrates,” Int. J. Nanosci. 1, 87–97 (2002).
[Crossref]

Young, N. O.

N. O. Young and J. Kowal, “Optically active fluorite films,” Nature 183, 104–105 (1959).
[Crossref]

Zhao, Y. P.

Y. P. Zhao, D. X. Ye, P. I. Wang, G. C. Wang, and T. M. Lu, “Fabrication of Si nanocolumns and Si square spirals of self-assembled monolayer colloid substrates,” Int. J. Nanosci. 1, 87–97 (2002).
[Crossref]

Adv. Mater. (1)

I. Hodgkinson and Q. Wu, “Inorganic chiral optical materials,” Adv. Mater. 13, 889–897 (2001).
[Crossref]

Appl. Opt. (6)

Appl. Phys. Lett. (1)

R. Azzam, “Chiral thin solid films: method of deposition and applications,” Appl. Phys. Lett. 61, 3118–3120 (1992).
[Crossref]

Int. J. Nanosci. (1)

Y. P. Zhao, D. X. Ye, P. I. Wang, G. C. Wang, and T. M. Lu, “Fabrication of Si nanocolumns and Si square spirals of self-assembled monolayer colloid substrates,” Int. J. Nanosci. 1, 87–97 (2002).
[Crossref]

J. Appl. Phys. (1)

Q. H. Wu, L. De Silva, M. Arnold, I. J. Hodgkinson, and E. Takeuchi, “All-silicon polarizing filters for near-infrared wavelengths,” J. Appl. Phys. 95, 402–404 (2004).
[Crossref]

J. Vac. Sci. Technol. A (2)

K. Robbie and M. J. Brett, “Sculptured thin films and glancing angle deposition: Growth mechanics and applications,” J. Vac. Sci. Technol. A 15, 1460–1465 (1997).
[Crossref]

R. N. Tait, T. Smy, and M. J. Brett, “Structural anisotropy in oblique-incidence thin metal-films,” J. Vac. Sci. Technol. A 10, 1518–1521 (1992).
[Crossref]

Liq. Cryst. (1)

S. R. Kennedy, J. C. Sit, D. J. Broer, and M. J. Brett, “Optical activity of Chiral Thin Film and Liquid Crystal Hybrids,” Liq. Cryst. 28, 1799–1803 (2001).
[Crossref]

Mat. Res. Soc. Symp. Proc. (1)

J. J. Steele, K. D. Harris, and M. J. Brett, “Nanostructured oxide films for high-speed humidity sensors,” Mat. Res. Soc. Symp. Proc. 788, 473–478 (2004).

Nano Lett. (1)

S. R. Kennedy, M. J. Brett, O. Toader, and S. John, “Fabrication of Tetragonal Square Spiral Photonic Crystals,” Nano Lett. 2, 59–62 (2002).
[Crossref]

Nature (1)

N. O. Young and J. Kowal, “Optically active fluorite films,” Nature 183, 104–105 (1959).
[Crossref]

Opt. Commun. (1)

A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculpted-thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33–46 (2001).
[Crossref]

Opt. Lett. (1)

Photon. Nanostruct. (1)

S. R. Kennedy, M. J. Brett, H. Miguez, O. Toader, and S. John, “Optical properties of a three-dimensional silicon square spiral photonic crystal,” Photon. Nanostruct. 1, 37–42 (2003).
[Crossref]

Phys. Rev. B (1)

A. Chutinan and S. Noda, “Spiral three-dimensional photonic-band-gap structure,” Phys. Rev. B 57, 2006–2008 (1998).
[Crossref]

Proceedings of the Royal Society of London A (1)

A. Lakhtakia and W. S. Weiglhofer, “On light propagation in helicoidal bianisotropic mediums,” Proceedings of the Royal Society of London A 448, 419–437 (1995).
[Crossref]

Surf. Coat. Technol. (1)

K. D. Harris, D. Vick, E. J. Gonzalez, T. Smy, K. Robbie, and M. J. Brett, “Porous thin films for thermal barrier coatings,” Surf. Coat. Technol. 138, 185–191 (2001).
[Crossref]

Thin Solid Films (1)

R. N. Tait, T. Smy, and M. J. Brett, “Modelling and characterization of columnar growth in evaporated films,” Thin Solid Films 226, 196–201 (1993).
[Crossref]

Other (6)

J. N. Broughton and M. J. Brett, “Electrochem. Solid-State Lett. 5, A279–A282 (2002).

K. Robbie and Ph.D. Thesis, University of Alberta, Edmonton, AB, (1998).

K. J. Robbie and M. J. Brett, “Method of depositing shadow sculpted thin films,” U S patent 5,866,204 (2 February 1999).

K. J. Robbie and M. J. Brett, “Shadow sculpted thin films,” U S patent 6,248,422 (19 June 2001).

K. J. Robbie and M. J. Brett, “Glancing angle deposition of thin films,” U S patent 6,206,065 (27 March 2001).

C. F. Borhen and D. R. Huffman, Absorption and scattering of light by small particles, (Wiley, New York, 1983), pp. 44–56.

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Figures (6)

Fig. 1.
Fig. 1. SEM images of helical obliquely deposited films deposited at (a) 30°, (b) 65°, (c) 80° and (d) 87° illustrate the wide range of attainable film porosities. Side views are shown in the left column, top-down views are shown in the right column.
Fig. 2.
Fig. 2. (a). Transmittance and (b) selective transmittance spectra of a helical film deposited at α = 65°.
Fig. 3.
Fig. 3. Peak selective transmittance wavelength vs. deposition angle α.
Fig. 4.
Fig. 4. Maximum selective specular transmittance of circularly polarized light in helical TiO2 thin films
Fig. 5.
Fig. 5. (a). Maximum selective diffuse transmittance of circularly polarized light in helical TiO2 thin films; (b) Maximum selective diffuse reflectance of circularly polarized light in helical TiO2 thin films.
Fig. 6.
Fig. 6. Maximum selective specular transmittance of circularly polarized light in helical TiO2 films (○ diffuse components included, ● diffuse components removed).

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

T ( LCP ) s T ( RCP ) s = 2 m 14 ( λ ) .
T ( LCP ) D T ( RCP ) D = T ( LCP ) T ( RCP ) [ T ( LCP ) S T ( RCP ) S ] .
ρ ρ o = 2 cos ( α ) 1 + cos ( α ) .

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