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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 16 — Aug. 12, 2013
  • pp: 18733–18741
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Fabrication of metal-oxide nano-hairs for effective index optical elements

Indumathi Raghu Srimathi, Aaron J. Pung, Yuan Li, Raymond C. Rumpf, and Eric G. Johnson  »View Author Affiliations


Optics Express, Vol. 21, Issue 16, pp. 18733-18741 (2013)
http://dx.doi.org/10.1364/OE.21.018733


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Abstract

We present a method for fabricating high aspect ratio metal-oxide, sub-wavelength grating structures. These “nano-hair” structures are composed of alumina cylindrical pillars, partially embedded in a supporting fused silica substrate. The fabricated nano-hair structures demonstrate phase control of the transmitted beam while maintaining a peak transmitted power greater than 93% around a central wavelength of λo = 1.55 µm. Based on this principle, discrete and continuous phase functions can be encoded by controlling the lithographic process.

© 2013 OSA

1. Introduction

Diffraction gratings play an important role in modern technology with applications in spectrometry, polarizers, beam splitters, laser cavities, interferometry, and laser pulse compression [1

1. T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73(5), 894–937 (1985). [CrossRef]

]. In particular, subwavelength gratings with lateral periods smaller than the wavelength of incident light allow only the 0th diffractive order to propagate through the grating; all the other higher orders are evanescent in the perturbation region and substrate. The effective refractive index is dictated by the fill fraction of the subwavelength grating [2

2. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

]. Early demonstrations of subwavelength gratings to form artificial dielectric optical components included binary blazed grating profiles [3

3. W. Stork, N. Streibl, H. Haidner, and P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16(24), 1921–1923 (1991). [CrossRef] [PubMed]

, 4

4. H. Haidner, J. T. Sheridan, and N. Streibl, “Dielectric binary blazed gratings,” Appl. Opt. 32(22), 4276–4278 (1993). [CrossRef] [PubMed]

]. Since a closed form approximation does not exist for the effective index of 2D subwavelength gratings, numerical techniques are often used to estimate effective indices. Usually a fitting-based approximation is applied to existing numerical methods and the effective indices are deduced [5

5. F. T. Chen and H. G. Craighead, “Diffractive phase elements based on two-dimensional artificial dielectrics,” Opt. Lett. 20(2), 121–123 (1995). [CrossRef] [PubMed]

, 6

6. C. Zhang, S. Liu, T. Shi, and Z. Tang, “Fitting-determined formulation of effective medium approximation for 3D trench structures in model-based infrared reflectrometry,” J. Opt. Soc. Am. A 28(2), 263–271 (2011). [CrossRef] [PubMed]

]. The design and fabrication of arbitrary grating geometries has been made possible due to the progress in the field of lithography, enabling numerous optical functions to be realized in modern optics.

Dispersion characteristics of many artificial dielectric structures have been tailored to demonstrate increasing optical functionality. Subwavelength structures have played an important role in realizing achromatic blazed gratings that can operate over a broad spectral range [7

7. C. Sauvan, P. Lalanne, and M. S. Lee, “Broadband blazing with artificial dielectrics,” Opt. Lett. 29(14), 1593–1595 (2004). [CrossRef] [PubMed]

]. Polarization independent response was obtained by using holes and pillar geometries [8

8. H. J. Hyvärinen, P. Karvinen, and J. Turunen, “Polarization insensitive resonance-domain blazed binary gratings,” Opt. Express 18(13), 13444–13450 (2010). [CrossRef] [PubMed]

, 9

9. B. Wang, X. P. Zhang, W. J. Song, P. Cui, Y. Zhang, and G. T. Fei, “Fabrication of transmission phase gratings on porous anodic alumina,” Opt. Lett. 35(5), 727–729 (2010). [CrossRef] [PubMed]

]. The non-deterministic phase response of a computer generated hologram was also approximated with effective medium theory using non-repeated subwavelength square pillar structures [10

10. W. Freese, T. Kämpfe, E. B. Kley, and A. Tünnermann, “Design of binary subwavelength multiphase level computer generated holograms,” Opt. Lett. 35(5), 676–678 (2010). [CrossRef] [PubMed]

]. Other diffractive optical elements designed and fabricated using subwavelength structures include diffractive lenses [11

11. F. T. Chen and H. G. Craighead, “Diffractive lens fabricated with mostly zeroth-order gratings,” Opt. Lett. 21(3), 177–179 (1996). [CrossRef] [PubMed]

, 12

12. J. N. Mait, A. Scherer, O. Dial, D. W. Prather, and X. Gao, “Diffractive lens fabricated with binary features less than 60 nm,” Opt. Lett. 25(6), 381–383 (2000). [CrossRef] [PubMed]

], array generators [13

13. G. Bloom, C. Larat, E. Lallier, M. S. Lee-Bouhours, B. Loiseaux, and J. P. Huignard, “Design and optimization of a high-efficiency array generator in the mid-IR with binary subwavelength grooves,” Appl. Opt. 50(5), 701–709 (2011). [CrossRef] [PubMed]

], and antireflective structures [14

14. E. B. Grann, M. G. Varga, and D. A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. A 12(2), 333–339 (1995). [CrossRef]

, 15

15. C. H. Chang, J. A. Dominguez-Caballero, H. J. Choi, and G. Barbastathis, “Nanostructured gradient-index antireflection diffractive optics,” Opt. Lett. 36(12), 2354–2356 (2011). [CrossRef] [PubMed]

]. Furthermore, subwavelength structures have been used to modify both the spectral and spatial properties of the reflected beam that utilizes a space varying structure for a Guided Mode Resonance filter for beam shaping [16

16. P. Srinivasan, M. K. Poutous, Z. A. Roth, Y. O. Yilmaz, R. C. Rumpf, and E. G. Johnson, “Spatial and spectral beam shaping with space-variant guided mode resonance filters,” Opt. Express 17(22), 20365–20375 (2009). [CrossRef] [PubMed]

].

However, the majority of these diffractive phase elements are based on a homogeneous material system including silicon [4

4. H. Haidner, J. T. Sheridan, and N. Streibl, “Dielectric binary blazed gratings,” Appl. Opt. 32(22), 4276–4278 (1993). [CrossRef] [PubMed]

], fused quartz [5

5. F. T. Chen and H. G. Craighead, “Diffractive phase elements based on two-dimensional artificial dielectrics,” Opt. Lett. 20(2), 121–123 (1995). [CrossRef] [PubMed]

, 11

11. F. T. Chen and H. G. Craighead, “Diffractive lens fabricated with mostly zeroth-order gratings,” Opt. Lett. 21(3), 177–179 (1996). [CrossRef] [PubMed]

], silicon nitride [7

7. C. Sauvan, P. Lalanne, and M. S. Lee, “Broadband blazing with artificial dielectrics,” Opt. Lett. 29(14), 1593–1595 (2004). [CrossRef] [PubMed]

], and gallium arsenide [13

13. G. Bloom, C. Larat, E. Lallier, M. S. Lee-Bouhours, B. Loiseaux, and J. P. Huignard, “Design and optimization of a high-efficiency array generator in the mid-IR with binary subwavelength grooves,” Appl. Opt. 50(5), 701–709 (2011). [CrossRef] [PubMed]

]. Since the effective index of the grating is a function of its refractive indices and grating geometry, use of different materials can be compensated by altering the fabrication parameters to obtain the desired phase response. However, the Fresnel losses associated with a high-index material must be overcome, often requiring an antireflection coating to optimize the zero order diffraction efficiency. Some of these issues can be mitigated with a low index material such as fused silica, but other challenges are encountered with the fabrication of a high aspect ratio structure [17

17. A. G. Lopez and H. G. Craighead, “Subwavelength surface-relief gratings fabricated by microcontact printing of self-assembled monolayers,” Appl. Opt. 40(13), 2068–2075 (2001). [CrossRef] [PubMed]

]. In high power laser applications, the laser damage threshold and dn/dT parameters of a material system are crucial to the overall success of the device. The role of thermo-optic coefficients in optical materials has been extensively studied [18

18. G. Ghosh, Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic Press, 1998).

]. Numerically, the thermo-optic coefficient of fused silica and alumina (Al2O3) are an order of magnitude lower than that of silicon, silicon nitride and gallium arsenide. Considering their relatively low index contrast, these material systems are attractive candidates in high power laser systems. While other material systems may exist that have similar properties, practical application is restricted by limitations in the fabrication process as thermal stresses are induced during deposition of thick coatings. It is for this reason that the fused silica / alumina material system was chosen for these devices.

While high aspect ratio devices offer the ability to fully control the phase response, current designs require thick metal-oxide film depositions. However, mechanical stresses arising from lattice mismatch during deposition can cause the coatings to crack and delaminate from the substrate. Furthermore, lithographic patterning and reactive ion beam etching processes can introduce etch loading and sidewall distortions leading to under-cutting or T-topping of the devices. To circumvent these issues, an etch and conformal deposition is utilized. In this approach, lithography and etching are performed on a fused silica substrate, which is then coated using a conformal deposition process to back fill the etched holes. The density and fill fraction of these holes can then be used to encode the desired phase based on the effective index.

The phase, φ, encoded on a wave-front transmitting through the nano-hair structure at normal incidence has a composite phase that is a sum of the contribution due to the embedded portion and the air surrounded portion of the nano-hairs. This can be expressed as
ϕ=n¯kod=n¯1k0ha+n¯2k0hb.
(1)
where ko = 2π/λo. These effective indices for the two cascaded regions can be exploited for a number of dispersive properties based on their geometries and surrounding media. Moreover, by changing the duty cycle, or period, the phase can be modulated as a function of position across the surface.

2. Device design and analysis

For a grating to be subwavelength at a specific wavelength λo, the lateral period Λ of the grating has to obey the following condition at normal incidence:
Λ<λomax(nc,ns).
(2)
where nc and ns are the refractive indices of the cover and substrate materials respectively. The period of the grating has to lie in the subwavelength regime for 3 different regions for the optical nano-hair structures: (a) pillars above the substrate consisting of air/alumina, (b) pillars embedded in the substrate where the material system is alumina/fused silica, and (c) substrate region made up of fused silica. The refractive indices of alumina and fused silica are 1.62 and 1.44 respectively at λo = 1.55 µm. Based on the numerical values computed for the three regions from Eq. (2), the period of the grating was chosen to be 1.00 µm.

Rigorous coupled-wave analysis (RCWA) [20

20. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71(7), 811–818 (1981). [CrossRef]

] was utilized to simulate the spectral and phase response of the device at λo = 1.55 µm as a function of fill fraction. The simulated hexagonal grating geometry has a lateral period of Λ = 1.00 µm, and pillar heights below (hb) and above (ha) the substrate of 1.60 µm and 1.90 µm, respectively. Furthermore, the response of the device is polarization insensitive due to the symmetry of the hexagonal gating lattice. As shown in Fig. 2
Fig. 2 RCWA simulations at λo = 1.55 µm of (left) peak transmittance, and (right) phase variation with fill fraction at normal incidence.
, the amplitude of the transmitted beam is > 97% for the simulated 30% - 80% variation in fill fraction. The phase variation plotted as a function of the duty cycle is the overall phase φ experienced by the nano-hair structures.

One of the concerns with sub-wavelength structures is the scattering introduced throughout the structure. In order to understand this, field computations were performed in the incident, pillar region (air and embedded regions), and the substrate. The Ex, Ey, and Ez field components in these regions are plotted in Fig. 3
Fig. 3 Field profile in the optical nano-hair structure for the 0.58 duty cycle case showing confinement of the fields in the pillars. Illumination is at normal incidence.
for an intermediate duty cycle value of 0.58 illuminated at normal incidence. From the field profiles, it is evident that scattering at the intended wavelength (λo = 1.55 µm) is not an issue, and that the field remains planar in each nano-hair. However, a slight difference in the field profile can be seen between the ha and hb regions of the nano-hair. This difference is a result of the two regions have slightly different effective indices.

In order to demonstrate the nano-hairs for optical phase encoding, a binary phase plate with azimuthally alternating phase sections was chosen. This design has alternating regions of nano-hairs with open areas as illustrated in Fig. 4
Fig. 4 (a) A step phase plate with azimuthally alternating N phase sections, and (b) Proposed nano-hair geometry to mimic the phase function of the optical element in (a).
.

In the example under consideration, the phase plate consisted of N = 16 sections (m = 0,…, (N-1)). The phase variation in each section m can be expressed as a mathematical function of the form:

Φ(m)=(1)m;2πNθ2πN(m+1),;m=0,...,(N1).
(3)

By combining the phase plate geometry along with the optical nano-hair structure (Fig. 4(b)), alternate 0 and π phase can be introduced between the different sections.

3. Device fabrication

Fabrication of the nano-hair structures starts with the lithography and patterning of a fused silica substrate. This is then followed with an etch process to create the deep holes that are then filled using a conformal deposition process. Once the holes are filled, the top surface is etched away to reveal the top of the posts. This template is then subjected to an etch process to expose the desired amount of the posts as highlighted in Fig. 5
Fig. 5 Illustration of the fabrication sequence. (a) Chrome coated fused silica substrate, (b) Patterned photoresist on the substrate, (c) Photoresist pattern transferred to the chrome layer, (d) Grating patterns transferred to the substrate using an oxide etcher, (e) Alumina deposited on the patterned substrate using an ALD, (f) Planar alumina on top of the structure etched using a III-V etcher, and (g) Fused silica etched around the filled alumina holes finally forming the optical nano-hair structures.
.

The nano-hair fabrication starts with a 100 mm diameter UV grade fused silica substrate topped with 200 nm of chrome. The wafers were cleaned and coated with a 1 µm thick layer of AZ MiR 701 photoresist. Following a post applied bake, a GCA i-line 5X-reduction stepper tool was used to print the necessary exposures using a two-step exposure process. The first exposure is with the base hexagonal grating lattice of period 1.00 µm with a hole diameter of 0.78 µm over a 10 by 10 mm die size. The second exposure biases the existing grating with a binary, large-feature azimuthally varying binary pattern. In the doubly-exposed areas, overexposure washes out the grating design, ultimately removing it from the substrate. This leaves behind alternating regions of patterned and non-patterned surface in the form of pie wedges to produce a phase offset.

The developed pattern was then transferred into the chrome layer using a wet chromium etch 1020AC solution. The preserved surface topology of the chrome and photoresist layers allows both materials to act as etch masks in the etch process. A Unaxis Versaline Inductively Coupled Plasma (ICP) oxide etcher transferred the pattern into the substrate to a depth of 3.50 µm using CHF3 and O2 gas chemistry. The flow rates of CHF3 and O2 were 70 sccm and 2 sccm respectively, where sccm is stands for standard cubic centimeters per minute. The ICP power was 800 W and the RF power 40 W. The etch rate of fused silica obtained was 240 nm/min. The photoresist to fused silica etch selectivity was 1.8: 1 and that of chrome to fused silica was 10: 1. Any residual organic matter on the surface of the wafer was removed using an oxygen plasma following the transfer etch. Unused chrome was cleared from the substrate via wet chrome etchant.

The etched and cleaned holes in fused silica were conformally coated with alumina by atomic layer deposition (ALD) using an Oxford OpAL tool with a Trimethyl Aluminum (TMA) precursor. TMA has high vapor pressure and is directly drawn into the chamber without any bubbling during the ALD cycle. The precursor attaches itself to the surface of the wafer by chemisorption and this is followed by an Ar gas purge. At this stage, oxygen plasma is used to form an atomic layer of alumina. A short post plasma purge completes one ALD cycle which takes ~5 s to complete and the deposition rate of alumina formed this way was found to be 0.122 nm/cycle. The conformal nature of the deposition is crucial because it allows for precise coating over structures of any aspect ratio. Since the largest hole radius obtained from the fabrication was 0.39 µm, a thickness of 0.50 µm for the Al2O3 was deposited on the wafer. This completely filled the cylindrical holes, submerging the grating beneath a planarized Al2O3 layer on top of the structure. This step is key, since any other deposition would require 3.50 µm of alumina and would likely create air voids in the desired structures. The ALD has an inherent advantage in the conformal aspect as compared to other methods.

Following the alumina deposition, a STS III-V ICP Compound Semiconductor etch system with a BCl3-based etch chemistry was used to selectively remove 0.50 µm of the planarized alumina coating from the top of the device. The flow rate of BCl3 used in the etch process was 50 sccm. The etcher uses a planar type inductively coupled radio frequency (13.56 MHz) plasma coil arrangement. The coil and platen powers used in the process were 800 W and 250 W respectively. The etch rate of alumina was 40 nm/min. This fabrication sequence of filling up etched grooves/holes using an ALD deposition and removing the planarized layer from top by etching the metal-oxide to encapsulate a grating has been discussed in [21

21. A. J. Pung, S. R. Carl, I. R. Srimathi, and E. G. Johnson, “Method of fabrication for encapsulated polarizing resonant gratings,” IEEE Photon. Technol. Lett. 25(15), 1432–1434 (2013). [CrossRef]

]. Once the top surface of the Al2O3 is removed, the nano-hair structures are created by etching away the fused silica surrounding the alumina filled cylindrical holes using the ICP oxide etcher. The gas chemistry in the oxide etcher does not react with alumina and thus forms a natural etch stop. The fused silica was etched to a depth of 1.90 µm; however, taller pillar structures may be made if the initial transfer etch is deeper, since the conformal deposition is not as sensitive to the hole depth. The final result is an array of 1.90 µm tall alumina pillars surrounded by air and buried in the fused silica substrate, providing mechanical support to the standing pillars. Top-down scanning electron microscope (SEM) images of the fabricated devices are shown in Fig. 6
Fig. 6 Top-down scanning electron micrograph of the proposed optical nano-hair structure at (a) 2000X, and (b) 6000X magnification.
. The fill fraction of the exposed region was measured to be 0.78.

4. Device testing

Based on the RCWA simulations, the phase modulation calculated for the fabricated structures was found to be 0.90π. Based on the numerical values, the far field diffraction pattern of the structure was simulated based on the binary phase pattern in Eq. (3). The simulated intensity pattern is shown in Fig. 7(a)
Fig. 7 (a) Simulated far field diffraction pattern for the optical necklace beam at λo = 1.55 µm, and (b) Experimentally measured far field diffraction pattern at λo = 1.55 µm of optical nano-hair structures using an IR camera on structures corresponding to a phase shift of 0.90π.
.

The far field patterns of the fabricated structure was measured experimentally at λo = 1.55 µm using an Agilent tunable laser source with output power of 100 µW. The output of the laser was coupled with a fiber collimator that has a 1/e2 value of 1.364 mm, and directed to be normally incident on the device. A CCD near-IR camera was used to collect the image of the transmitted diffraction pattern. Normalized to the incident illumination, 93.5% transmitted power was measured through the device plane. This value is consistent with the numerical simulations that predicted a drop in transmission of 2% on one interface with the nano-hair structures and 4% on the other interface without the structures. This measurement confirms that all the incident power is transmitted through the device in the zero diffraction order and there is no power coupled into the higher orders. The experimental measurement of the far field diffraction pattern through the fabricated device is shown in Fig. 7(b), showing good agreement with the simulated far field diffraction profile.

5. Extension of the device concept

The same fabrication steps outlined in Section 3 were followed with a few variations. The exposure dose, while fabricating the base hexagonal grating lattice, was adjusted so that a fill fraction of 0.58 was obtained. The second exposure was performed using the binary mask as before. In this case, the exposure dose was adjusted to obtain a duty cycle variation in the areas that were doubly exposed. The top down SEM image of the devices with duty cycle variations is shown in Fig. 8. The duty cycle variation between the single and double exposure areas can be clearly seen from the images. Variations in fill fraction range from 0.58 to 0.78. This approach can further be applied to create much more complex duty cycle variations based on additive lithography steps of binary and analog intensity masks in lithographic patterning, for space variant guided mode resonant devices based on duty cycle variations as presented in [16

16. P. Srinivasan, M. K. Poutous, Z. A. Roth, Y. O. Yilmaz, R. C. Rumpf, and E. G. Johnson, “Spatial and spectral beam shaping with space-variant guided mode resonance filters,” Opt. Express 17(22), 20365–20375 (2009). [CrossRef] [PubMed]

, 22

22. P. Srinivasan, Z. A. Roth, M. K. Poutous, and E. G. Johnson, “Novel method for the fabrication of spatially variant structures,” J. Micro/Nanolith. MEMS-MOEMS 8, 013010–013018 (2009).

].

The morphology of the fabricated nano-hair structure with the fill fraction variation is shown in Fig. 9
Fig. 9 SEM micrograph of the fabricated alumina optical nano-hair structures on a fused silica substrate. The dielectric pillars are clearly visible and the height was measured to be 1.90 µm. The fill fraction variation is also distinctly seen.
. The SEM micrograph was obtained by tilting the substrate, allowing the heights of the pillars to be measured at 1.90 µm. In comparison with the RCWA simulations of Fig. 2, the phase in transmission was evaluated to be 0.45π.

6. Conclusion

In conclusion, we introduced a novel method for the fabrication of metal-oxide nano-hairs for applications with the effective index in optical elements. These structures are based on partially embedded metal-oxide rods in a low index optical substrate for subwavelength gratings with high index of refraction for modulation of the local effective index. Successful design, simulation, fabrication, and testing of these devices have been shown. The functionality of the device is based on approximating a heterogeneous grating layer as a homogeneous effective index medium in two independent regions – cylinders buried in the substrate with a portion remaining as pillars surrounded in air. The fabrication sequence utilizes conventional photolithographic techniques to pattern and etch the devices. Moreover, the exploitation of ALD with the patterning and etching of fused silica provide a well-controlled process that can easily be scaled to high volume and higher aspect-ratio structures. By modifying the local fill fraction, stepped and/or continuous phase functions can be realized. This can be used as a powerful alternative to fabricating 3D profiles using simple fabrication steps and the experimental data presented validates this statement. The proposed technique can provide better impedance matching at the interfaces by reducing the refractive index discontinuity, especially for a high contrast structure. Although fused silica and Al2O3 nano-hairs were exploited in this example, ongoing work with hafnium oxide (HfO2) is currently under investigation.

Acknowledgments

This work was supported by HEL-JTO/AFOSR MRI – “3D Meta-Optics for High Energy Lasers” FA9550-10-1-0543.

References and links

1.

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73(5), 894–937 (1985). [CrossRef]

2.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

3.

W. Stork, N. Streibl, H. Haidner, and P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16(24), 1921–1923 (1991). [CrossRef] [PubMed]

4.

H. Haidner, J. T. Sheridan, and N. Streibl, “Dielectric binary blazed gratings,” Appl. Opt. 32(22), 4276–4278 (1993). [CrossRef] [PubMed]

5.

F. T. Chen and H. G. Craighead, “Diffractive phase elements based on two-dimensional artificial dielectrics,” Opt. Lett. 20(2), 121–123 (1995). [CrossRef] [PubMed]

6.

C. Zhang, S. Liu, T. Shi, and Z. Tang, “Fitting-determined formulation of effective medium approximation for 3D trench structures in model-based infrared reflectrometry,” J. Opt. Soc. Am. A 28(2), 263–271 (2011). [CrossRef] [PubMed]

7.

C. Sauvan, P. Lalanne, and M. S. Lee, “Broadband blazing with artificial dielectrics,” Opt. Lett. 29(14), 1593–1595 (2004). [CrossRef] [PubMed]

8.

H. J. Hyvärinen, P. Karvinen, and J. Turunen, “Polarization insensitive resonance-domain blazed binary gratings,” Opt. Express 18(13), 13444–13450 (2010). [CrossRef] [PubMed]

9.

B. Wang, X. P. Zhang, W. J. Song, P. Cui, Y. Zhang, and G. T. Fei, “Fabrication of transmission phase gratings on porous anodic alumina,” Opt. Lett. 35(5), 727–729 (2010). [CrossRef] [PubMed]

10.

W. Freese, T. Kämpfe, E. B. Kley, and A. Tünnermann, “Design of binary subwavelength multiphase level computer generated holograms,” Opt. Lett. 35(5), 676–678 (2010). [CrossRef] [PubMed]

11.

F. T. Chen and H. G. Craighead, “Diffractive lens fabricated with mostly zeroth-order gratings,” Opt. Lett. 21(3), 177–179 (1996). [CrossRef] [PubMed]

12.

J. N. Mait, A. Scherer, O. Dial, D. W. Prather, and X. Gao, “Diffractive lens fabricated with binary features less than 60 nm,” Opt. Lett. 25(6), 381–383 (2000). [CrossRef] [PubMed]

13.

G. Bloom, C. Larat, E. Lallier, M. S. Lee-Bouhours, B. Loiseaux, and J. P. Huignard, “Design and optimization of a high-efficiency array generator in the mid-IR with binary subwavelength grooves,” Appl. Opt. 50(5), 701–709 (2011). [CrossRef] [PubMed]

14.

E. B. Grann, M. G. Varga, and D. A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. A 12(2), 333–339 (1995). [CrossRef]

15.

C. H. Chang, J. A. Dominguez-Caballero, H. J. Choi, and G. Barbastathis, “Nanostructured gradient-index antireflection diffractive optics,” Opt. Lett. 36(12), 2354–2356 (2011). [CrossRef] [PubMed]

16.

P. Srinivasan, M. K. Poutous, Z. A. Roth, Y. O. Yilmaz, R. C. Rumpf, and E. G. Johnson, “Spatial and spectral beam shaping with space-variant guided mode resonance filters,” Opt. Express 17(22), 20365–20375 (2009). [CrossRef] [PubMed]

17.

A. G. Lopez and H. G. Craighead, “Subwavelength surface-relief gratings fabricated by microcontact printing of self-assembled monolayers,” Appl. Opt. 40(13), 2068–2075 (2001). [CrossRef] [PubMed]

18.

G. Ghosh, Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic Press, 1998).

19.

B. H. Kleemann, M. Seesselberg, and J. Ruoff, “Design concepts for broadband high-efficiency DOEs,” J. Eur. Opt. Soc. Rapid Publ. 3, 08015 (2008). [CrossRef]

20.

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71(7), 811–818 (1981). [CrossRef]

21.

A. J. Pung, S. R. Carl, I. R. Srimathi, and E. G. Johnson, “Method of fabrication for encapsulated polarizing resonant gratings,” IEEE Photon. Technol. Lett. 25(15), 1432–1434 (2013). [CrossRef]

22.

P. Srinivasan, Z. A. Roth, M. K. Poutous, and E. G. Johnson, “Novel method for the fabrication of spatially variant structures,” J. Micro/Nanolith. MEMS-MOEMS 8, 013010–013018 (2009).

OCIS Codes
(220.3740) Optical design and fabrication : Lithography
(220.4000) Optical design and fabrication : Microstructure fabrication
(050.2065) Diffraction and gratings : Effective medium theory
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: June 19, 2013
Revised Manuscript: July 19, 2013
Manuscript Accepted: July 21, 2013
Published: July 30, 2013

Citation
Indumathi Raghu Srimathi, Aaron J. Pung, Yuan Li, Raymond C. Rumpf, and Eric G. Johnson, "Fabrication of metal-oxide nano-hairs for effective index optical elements," Opt. Express 21, 18733-18741 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-16-18733


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References

  1. T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE73(5), 894–937 (1985). [CrossRef]
  2. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP2, 466–475 (1956).
  3. W. Stork, N. Streibl, H. Haidner, and P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett.16(24), 1921–1923 (1991). [CrossRef] [PubMed]
  4. H. Haidner, J. T. Sheridan, and N. Streibl, “Dielectric binary blazed gratings,” Appl. Opt.32(22), 4276–4278 (1993). [CrossRef] [PubMed]
  5. F. T. Chen and H. G. Craighead, “Diffractive phase elements based on two-dimensional artificial dielectrics,” Opt. Lett.20(2), 121–123 (1995). [CrossRef] [PubMed]
  6. C. Zhang, S. Liu, T. Shi, and Z. Tang, “Fitting-determined formulation of effective medium approximation for 3D trench structures in model-based infrared reflectrometry,” J. Opt. Soc. Am. A28(2), 263–271 (2011). [CrossRef] [PubMed]
  7. C. Sauvan, P. Lalanne, and M. S. Lee, “Broadband blazing with artificial dielectrics,” Opt. Lett.29(14), 1593–1595 (2004). [CrossRef] [PubMed]
  8. H. J. Hyvärinen, P. Karvinen, and J. Turunen, “Polarization insensitive resonance-domain blazed binary gratings,” Opt. Express18(13), 13444–13450 (2010). [CrossRef] [PubMed]
  9. B. Wang, X. P. Zhang, W. J. Song, P. Cui, Y. Zhang, and G. T. Fei, “Fabrication of transmission phase gratings on porous anodic alumina,” Opt. Lett.35(5), 727–729 (2010). [CrossRef] [PubMed]
  10. W. Freese, T. Kämpfe, E. B. Kley, and A. Tünnermann, “Design of binary subwavelength multiphase level computer generated holograms,” Opt. Lett.35(5), 676–678 (2010). [CrossRef] [PubMed]
  11. F. T. Chen and H. G. Craighead, “Diffractive lens fabricated with mostly zeroth-order gratings,” Opt. Lett.21(3), 177–179 (1996). [CrossRef] [PubMed]
  12. J. N. Mait, A. Scherer, O. Dial, D. W. Prather, and X. Gao, “Diffractive lens fabricated with binary features less than 60 nm,” Opt. Lett.25(6), 381–383 (2000). [CrossRef] [PubMed]
  13. G. Bloom, C. Larat, E. Lallier, M. S. Lee-Bouhours, B. Loiseaux, and J. P. Huignard, “Design and optimization of a high-efficiency array generator in the mid-IR with binary subwavelength grooves,” Appl. Opt.50(5), 701–709 (2011). [CrossRef] [PubMed]
  14. E. B. Grann, M. G. Varga, and D. A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. A12(2), 333–339 (1995). [CrossRef]
  15. C. H. Chang, J. A. Dominguez-Caballero, H. J. Choi, and G. Barbastathis, “Nanostructured gradient-index antireflection diffractive optics,” Opt. Lett.36(12), 2354–2356 (2011). [CrossRef] [PubMed]
  16. P. Srinivasan, M. K. Poutous, Z. A. Roth, Y. O. Yilmaz, R. C. Rumpf, and E. G. Johnson, “Spatial and spectral beam shaping with space-variant guided mode resonance filters,” Opt. Express17(22), 20365–20375 (2009). [CrossRef] [PubMed]
  17. A. G. Lopez and H. G. Craighead, “Subwavelength surface-relief gratings fabricated by microcontact printing of self-assembled monolayers,” Appl. Opt.40(13), 2068–2075 (2001). [CrossRef] [PubMed]
  18. G. Ghosh, Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic Press, 1998).
  19. B. H. Kleemann, M. Seesselberg, and J. Ruoff, “Design concepts for broadband high-efficiency DOEs,” J. Eur. Opt. Soc. Rapid Publ.3, 08015 (2008). [CrossRef]
  20. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am.71(7), 811–818 (1981). [CrossRef]
  21. A. J. Pung, S. R. Carl, I. R. Srimathi, and E. G. Johnson, “Method of fabrication for encapsulated polarizing resonant gratings,” IEEE Photon. Technol. Lett.25(15), 1432–1434 (2013). [CrossRef]
  22. P. Srinivasan, Z. A. Roth, M. K. Poutous, and E. G. Johnson, “Novel method for the fabrication of spatially variant structures,” J. Micro/Nanolith. MEMS-MOEMS8, 013010–013018 (2009).

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