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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 13 — Jun. 21, 2010
  • pp: 14056–14062
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High transmission and low color cross-talk plasmonic color filters using triangular-lattice hole arrays in aluminum films

Qin Chen and David R. S. Cumming  »View Author Affiliations


Optics Express, Vol. 18, Issue 13, pp. 14056-14062 (2010)
http://dx.doi.org/10.1364/OE.18.014056


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Abstract

Three primary color (red, green and blue) filters consisting of subwavelength triangular-lattice hole arrays in an aluminum film on glass were simulated and fabricated. A silicon dioxide cap layer, deposited on the patterned aluminum film, was found to almost double the transmission efficiency for all the filters. The measured peak transmittance for each color filter was above 30%, exhibiting a wavelength spectrum with a full-width at half-maximum of approximately 100 nm. Simulation results of various structures with different cap layers revealed the enhanced coupling between surface plasmon resonances at both sides of the metal film in a symmetrical configuration. It was found that gratings with as few as three periods were sufficient to demonstrate filtering. The effect of metal thickness and hole size was investigated in detail.

© 2010 OSA

1. Introduction

A color filter that selectively transmits or reflects input light is an important element in complementary metal-oxide-semiconductor (CMOS) image sensors [1

1. P. Catrysse, B. Wandell, and A. E. Gamal, “An integrated color pixel in 0.18 μm CMOS technology,” in 2001 International Electron Devices Meeting-Technical Digest (IEEE, 2001), pp. 559–562.

], liquid crystal display devices [2

2. G. D. Sharp, K. M. Johnson, and D. Doroski, “Continuously tunable smectic A(*) liquid-crystal color filter,” Opt. Lett. 15(10), 523–525 (1990). [CrossRef] [PubMed]

] and light emitting diodes [3

3. Y. Cho, Y. K. Choi, and S. H. Sohn, “Optical properties of neodymium-containing polymethylmethacrylate films for the organic light emitting diode color filter,” Appl. Phys. Lett. 89(5), 051102 (2006). [CrossRef]

]. Filtering is at present most commonly realized by dye films but these filters yield inadequate color cross-talk properties as pixel sizes are reduced. Other color filtering techniques for imaging arrays have been investigated. One-dimensional (1D) gratings in silicon were shown to work as a bandpass color filter [4

4. Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Photon. Technol. Lett. 18(20), 2126–2128 (2006). [CrossRef]

]. Recently freestanding 1D gold coated gratings on a membrane were found to offer excellent optical transmission (87%) property in the midinfrared range [5

5. S. Collin, G. Vincent, R. Haïdar, N. Bardou, S. Rommeluère, and J. L. Pelouard, “Nearly perfect Fano transmission resonances through nanoslits drilled in a metallic membrane,” Phys. Rev. Lett. 104(2), 027401 (2010). [CrossRef] [PubMed]

]. However, devices based on a 1D structure have an intrinsic polarization dependency. A bull’s eye structure consisting of concentric grooves with a central hole was proposed as another candidate for color filters [6

6. E. Laux, C. Genet, T. Skauli, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2(3), 161–164 (2008). [CrossRef]

]. This method gave very good narrow band wavelength filtering, but the low fill ratio resulted in poor transmission efficiency. Ebbeson et al. investigated the subwavelength holes in metal films and observed unexpected optical properties such as enhanced transmission of light through the holes and wavelength filtering due to the excitation of surface plasmon resonance (SPR) [7

7. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]

]. Following this discovery, researchers started to use two-dimensional (2D) hole arrays in metal films as color filters. A square-lattice hole array in a freestanding silver film was reported to demonstrate color filtering function [8

8. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

]. Although the bandwidth of the transmission peak itself was small, multiple transmission peaks gave rise to cross talk. Furthermore, a freestanding structure limits practical application. Red and green color filters consisting of a square array of circular holes were designed and fabricated in a thin aluminum film [9

9. H.-S. Lee, Y.-T. Yoon, S.-S. Lee, S.-H. Kim, and K.-D. Lee, “Color filter based on a subwavelength patterned metal grating,” Opt. Express 15(23), 15457–15463 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-23-15457. [CrossRef] [PubMed]

]. Unfortunately the green filter devices exhibited a yellow color due to the high color cross-talk. A reflective light modulator has also been demonstrated in a square-lattice hole array in a metal film supported by a microelectromechanical systems [10

10. J. L. Skinner, A. A. Talin, and D. A. Horsley, “A MEMS light modulator based on diffractive nanohole gratings,” Opt. Express 16(6), 3701–3711 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-6-3701. [CrossRef] [PubMed]

]. The peak in the reflected light spectrum shifted when a voltage was applied to adjust the distance between the pixel array and the top glass plate of the devices.

For imaging applications, it is necessary to achieve low color cross-talk filtering and reasonably high transmission efficiency for three primary colors. It has been suggested that a triangular-lattice hole array will have a larger wavelength interval between the first two SPR peaks compared to a square-lattice hole array of a same period [7

7. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]

,11

11. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

]. So far very little experimental work on color filters, based on triangular-lattice hole arrays, has been reported. In addition, most research to date has used noble metals such as silver and gold. Gold, in particular, is incompatible with silicon microelectronics. In this Paper, we focus on transmitted color filters consisting of triangular-lattice hole arrays in aluminum films that are compatible with standard CMOS technology. Compared to silver and gold, aluminum is cheap and easy to fabricate although it has a slightly higher absorption loss. Aluminum also has good adhesion to many substrates making fabrication easier. Electron beam lithography and dry etch were used to fabricate subwavelength triangular-lattice hole arrays in aluminum films in this work. The measured transmission spectral responses agreed well with the simulation results using the finite-difference time-domain (FDTD) method. Good separation between the three primary colors with more than 30% transmission was demonstrated. Our results therefore show great potential for applications in CMOS image sensors.

2. Fabrication of red, green and blue filters

A uniform metal film of sufficient thickness will block all the incident light. However, periodic subwavelength structures in a metal film can help to excite SPR and selectively transmit light according to wavelength. The peak position, λmax, of the transmission spectrum at normal incidence can be approximated by
For a square arrayλmax=ai2+j2εmεdεm+εd,
(1)
For a triangular arrayλmax=a43(i2+ij+j2)εmεdεm+εd,
(2)
where a is the period of the array, εm and εd are the dielectric constants of the metal and the dielectric material in contact with the metal respectively, and i and j are the scattering orders of the array [7

7. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]

,11

11. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

]. As shown in Eq. (1) and (2), the period determines the transmission peak positions of SPRs for a given material configuration. Furthermore, the wavelength interval between the first two SPR peaks in a triangular array is larger than that for a square array of a same period.

The procedure for device fabrication is as follows. A 150 nm aluminum film was evaporated on to a clean microscope glass slide. ZEP520A electron beam resist was spin-coated on to the sample and exposed using a Vistec VB6 UHR EWF electron beam lithography tool. After development in o-xylene, the sample was etched using SiCl4 in a Plasmalab System 100. Figure 1(a)
Fig. 1 A SEM image of etched holes in a triangular array with a = 430 nm in an Al film on glass. The inset is a SEM image for a sample tilted at 30°.
shows a scanning electron microscope (SEM) image of patterned aluminum film on a glass substrate after removing the residual resist. Vertical and smooth sidewalls can be seen from the inset SEM image for which the sample was tilted at 30°. After dry etch and removal of the resist, a SiO2 layer, of varying thickness, was deposited on top of the patterned aluminum film by plasma enhanced chemical vapor deposition.

Spectral measurement was carried out on a microspectrometer TFProbe MSP300 that can sample the signal from a minimum area of 10 μm × 10 μm. Three primary color filters were written on to the same sample to ensured consistent measurement of the different structures. Due to the symmetrical properties of the hole array and the holes, the transmittance should not show any difference for illumination at different polarization angles. An unpolarized light beam from a halogen lamp was launched normally on to the back-side of the sample.

Figure 2
Fig. 2 (a)-(c) Measured transmission spectra of three primary color filters. (a) a red filter hole array with a = 430 nm, hole diameter d = 230 nm (b) a green filter hole array with a = 330 nm, d = 180 nm, (c) a blue filter hole array with a = 250 nm, d = 140 nm. Devices were measured with no SiO2 cap layer, with a 100 nm SiO2 cap layer and with a 200 nm SiO2 cap layer. The transmitted light image for a square patch consisting of each hole array with a 200 nm SiO2 cap layer is shown in the inset of each graph. (d) A SEM image of holes composing the letter ‘G’ with a = 330 nm. The transmitted light image of the structure with a 200 nm SiO2 cap layer is shown in the inset.
shows three graphs, one for each of the hole array designs. Each hole array has a pass-band in the red (Fig. 2 (a)), green (Fig. 2(b)) or blue (Fig. 2(c)) part of the visible spectrum. In each graph, three sets of data are shown for different coating layers on the aluminum hole arrays. These are for devices with: no coating; a 100 nm layer of SiO2; and a 200 nm layer of SiO2. As can be clearly seen from the data in Fig. 2, the addition of increasing amount of SiO2 has a progressive effect o each of the three filters. In all cases the peak wavelength grows slightly longer as SiO2 is added, and the peak transmission coefficient increases. In Fig. 2(a), the spectrum of the red filter without a SiO2 cap layer shows two peaks of almost equal magnitude. With the addition of the 200 nm SiO2 layer, the transmittance of the long wavelength peak, λL, significantly increased but that of the short wavelength peak, λS, decreased. The effect of this improvement was clearly visible to the naked eye. The transmitted light through the blue and green color filters also had an obvious enhancement of the brightness after deposition of 200 nm of SiO2. All the filters that had a 200 nm SiO2 cap layer demonstrated a peak transmission above 30%. The full-width at half-maximum (FWHM) of each filter is approximately 100 nm, therefore ensuring low color cross-talk. The transmitted light images for the three primary color filters with a 200 nm SiO2 cap layer are shown in the insets of Fig. 2(a)-(c). These images were captured by a CCD array integrated on the microspectrometer. Each color image consists of hole arrays that was 50 μm × 50 μm. A letter ‘G’ consisting of holes with a = 330 nm was fabricated as shown in Fig. 2(d), where the period number of hole array is as small as three. The clear green letter ‘G’ appeared under the white light illumination as shown in the inset. Unlike the structures in earlier work, there is no dimple around the etched holes in our structure [11

11. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

]. This means that the pixel size could be as small as 1 μm on a high resolution image sensor.

3. Device simulation

Commercial software, Lumerical FDTD Solutions [12

12. Lumerical FDTD Solution, http://www.lumerical.com/

], was used to numerically investigate the color filters and identify the transmission peaks in the measured spectra. A 3D model including a semi-infinite glass substrate and a semi-infinite air superstrate in the z-direction was used, with a triangular-lattice hole array formed in the xy plane as shown in Fig. 3
Fig. 3 Schematic of the simulation model. No SiO2 cap layer is shown.
. The repeating pattern defined by rectangle ABCD is the simulation window on the xy plane, where points A and C are at the center of two holes, and B and D are in the middle of the space between two neighboring holes. A uniform cell with space step Δx = Δy = Δz = 2 nm was used in the range −0.05 μm < z < 0.2 μm (including the metal slab). A nonuniform cell was used outside this range. Perfectly matched layers were used at the top and bottom boundaries

Symmetrical boundary conditions were used along the AB and AD edges. A broad-band plane wave source was launched normally to the metal film from the glass side. Transmitted light was recorded at a plane 0.8 μm above the top surface of the aluminum slab. The transmission was calculated by normalizing the transmitted light to the incident light.

A systematic simulation was done for hole arrays with a = 430 nm. Four structures were simulated as shown in Fig. 4
Fig. 4 Simulation results of four types of patterned aluminum hole arrays: (a) without a SiO2 cap layer, (b) with a 100 nm SiO2 cap layer, (c) with a 200 nm SiO2 cap layer, (d) a free-standing configuration with the Al film in air. The first column is the simulated transmission spectrum, where the two main transmission peaks are marked as λS and λL. The second column is the corresponding structure schematic in the xz plane, where the red region is SiO2, the blue region is Al and the green region is air. The third and fourth columns are the electric field intensity distributions in the xz plane at λS and λL, respectively. In the intensity images, the intensity increases from the blue region to the red region.
. In each case, the near-field data shown are for selected resonances of the devices at λS and λL. From the schematic of each structure, we can see that the near-field material index at the aluminum surface around the hole is not the same for the structures shown in Fgi. 4(a)-(b). The corresponding electric field intensity distributions of λS and λL are therefore different. The resonance at λS yields a strong field distribution around the top of the opening of the hole but the resonance at λL has a stronger field distribution around the bottom of the opening. We call the former ‘air mode’ and the latter ‘oxide mode’, which corresponding to the solutions at εd = εair and εd = εdioxide (εair and εdioxide are the dielectric constants of air and silicon dioxide respectively) in Eq. (2). In both case, i = 1 and j = 0, i.e. they are (1,0) resonance. Although the top surface of the aluminum film was not fully covered by air in Fig. 4(b), the resonance at λS was still dominated by the air mode because the electric field was concentrated around the metal corners that were exposed to air. The field intensity distributions for the air mode inside the hole in Fig. 4(a)-(b) gradually increase from the bottom to the top of the opening for the air mode. The opposite effect is seen for the oxide mode.

Simulated transmission spectra for three primary color filters in Fig. 2 are shown in Fig. 5
Fig. 5 (a)-(c) Simulated spectra of the structures in Fig. 2. (a) red filter, a = 430 nm, hole diameter d = 230 nm, (b) green filter, a = 330 nm, d = 180 nm, and (c) blue filter, a = 250 nm, d = 140 nm. (d) comparison of experimental and simulated transmission peak positions.
. The fill ratios (the ratio of the hole area to the unit cell area) of the holes are 26%, 27% and 28% for the red, green and blue filters, respectively. The simulated spectra of the green and red filters show a double peak characteristic of almost equal magnitude in the main transmission peak. However, the modes at λS were not as obvious in the measured spectra, as shown in Fig. 2, where small “shoulders” at wavelengths shorter than those of the main transmission peaks appeared for both green and red filters. This effect is possibly caused by the smoothed step profile from fabrication. The positions of λS and λL for both the experimental and simulated data for the devices with a 200 nm SiO2 cap layer are in approximately the same spectral positions as shown in Fig. 5(d). The small difference is probably caused by the approximation of the material parameters used for simulation and errors in the estimation of the structure dimensions. A slightly larger difference between simulation and experiment was abserved for the blue filter due to the larger fabrication error for the smaller structure. For all three filters, the experimental transmission peaks have a relatively large red shift compared to the simulation data. This was probably caused by the residual resist left on the samples after dry etch and uncompleted resist removal.

The transmission efficiency was also strongly affected by the size of the circular hole. Triangular arrays with a = 330 nm, but different hole sizes were fabricated. Spectra for devices with hole diameter d = 155 nm to 195 nm are shown in Fig. 6(a)
Fig. 6 (a) Measured transmission spectra for hole arrays with a = 330 nm with different hole diameters d (from 155 nm to 195 nm). (b) Simulated transmission spectra of hole arrays with a = 330 nm and d = 180 nm with different metal thicknesses.
. As the hole size increases, the magnitude of the main transmission peak increases from 20% to 46%. There is also a red shift and an increase in the FWHM from 60 nm to 150 nm. The transmission peak at the short wavelength side rose quickly with the increasing hole size. A simulation of a same hole array at a = 330 nm and d = 180 nm was done for different aluminum thickness. As shown in Fig. 6(b), the structure made with a thinner aluminum film has higher transmission but also a much larger bandwidth. The enhanced coupling of SPR when using thinner metal films increases the splitting of the two transmission peaks. In addition, the transmittance of the long wavelength side peak increased but that of the short wavelength side decreased to a very low level at a thickness of 50 nm. In summary, a hole array with larger hole size in a thinner metal film always offers a higher transmission, but with a larger bandwidth.

4. Conclusion

In conclusion, we have fabricated subwavelength holes in an aluminum film on glass using electron beam lithography and dry etch. The holes were patterned into a triangular array. The resonant modes of the filters were investigated in detail giving consideration to the hole size, grating period, and the mode characteristics of the top and bottom sides of the metal film where it was in contact with air or SiO2. The device parameters, including metal film thickness and the thickness of the over-coating of SiO2 were explored in order to optimize the spectral characteristics thus maximizing transmission and reducing color cross-talk. Triangular-lattice hole arrays with a fill ratio of approximately 27% in an 150 nm thick aluminum film, covered with a 200 nm SiO2 layer, gave a transmittance of more than 30% and a FWHM of approximately 100 nm for all three primary color filters. A hole array with a period number as small as three was found to work well as a filter. The materials and dimensions we have studied are consistent with present CMOS process technology. Using this method, color-selective filters for red, green and blue may be made in a single process step and demonstrate low color cross-talk.

Acknowledgement

This work was supported by a UK EPSRC research grant.

References and links

1.

P. Catrysse, B. Wandell, and A. E. Gamal, “An integrated color pixel in 0.18 μm CMOS technology,” in 2001 International Electron Devices Meeting-Technical Digest (IEEE, 2001), pp. 559–562.

2.

G. D. Sharp, K. M. Johnson, and D. Doroski, “Continuously tunable smectic A(*) liquid-crystal color filter,” Opt. Lett. 15(10), 523–525 (1990). [CrossRef] [PubMed]

3.

Y. Cho, Y. K. Choi, and S. H. Sohn, “Optical properties of neodymium-containing polymethylmethacrylate films for the organic light emitting diode color filter,” Appl. Phys. Lett. 89(5), 051102 (2006). [CrossRef]

4.

Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Photon. Technol. Lett. 18(20), 2126–2128 (2006). [CrossRef]

5.

S. Collin, G. Vincent, R. Haïdar, N. Bardou, S. Rommeluère, and J. L. Pelouard, “Nearly perfect Fano transmission resonances through nanoslits drilled in a metallic membrane,” Phys. Rev. Lett. 104(2), 027401 (2010). [CrossRef] [PubMed]

6.

E. Laux, C. Genet, T. Skauli, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2(3), 161–164 (2008). [CrossRef]

7.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]

8.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

9.

H.-S. Lee, Y.-T. Yoon, S.-S. Lee, S.-H. Kim, and K.-D. Lee, “Color filter based on a subwavelength patterned metal grating,” Opt. Express 15(23), 15457–15463 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-23-15457. [CrossRef] [PubMed]

10.

J. L. Skinner, A. A. Talin, and D. A. Horsley, “A MEMS light modulator based on diffractive nanohole gratings,” Opt. Express 16(6), 3701–3711 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-6-3701. [CrossRef] [PubMed]

11.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

12.

Lumerical FDTD Solution, http://www.lumerical.com/

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(050.6624) Diffraction and gratings : Subwavelength structures
(130.7408) Integrated optics : Wavelength filtering devices

ToC Category:
Diffraction and Gratings

History
Original Manuscript: April 12, 2010
Revised Manuscript: May 20, 2010
Manuscript Accepted: May 21, 2010
Published: June 15, 2010

Citation
Qin Chen and David R. S. Cumming, "High transmission and low color cross-talk plasmonic color filters using triangular-lattice hole arrays in aluminum films," Opt. Express 18, 14056-14062 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-13-14056


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References

  1. P. Catrysse, B. Wandell, and A. E. Gamal, “An integrated color pixel in 0.18 μm CMOS technology,” in 2001 International Electron Devices Meeting-Technical Digest (IEEE, 2001), pp. 559–562.
  2. G. D. Sharp, K. M. Johnson, and D. Doroski, “Continuously tunable smectic A(*) liquid-crystal color filter,” Opt. Lett. 15(10), 523–525 (1990). [CrossRef] [PubMed]
  3. Y. Cho, Y. K. Choi, and S. H. Sohn, “Optical properties of neodymium-containing polymethylmethacrylate films for the organic light emitting diode color filter,” Appl. Phys. Lett. 89(5), 051102 (2006). [CrossRef]
  4. Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Photon. Technol. Lett. 18(20), 2126–2128 (2006). [CrossRef]
  5. S. Collin, G. Vincent, R. Haïdar, N. Bardou, S. Rommeluère, and J. L. Pelouard, “Nearly perfect Fano transmission resonances through nanoslits drilled in a metallic membrane,” Phys. Rev. Lett. 104(2), 027401 (2010). [CrossRef] [PubMed]
  6. E. Laux, C. Genet, T. Skauli, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2(3), 161–164 (2008). [CrossRef]
  7. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]
  8. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
  9. H.-S. Lee, Y.-T. Yoon, S.-S. Lee, S.-H. Kim, and K.-D. Lee, “Color filter based on a subwavelength patterned metal grating,” Opt. Express 15(23), 15457–15463 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-23-15457 . [CrossRef] [PubMed]
  10. J. L. Skinner, A. A. Talin, and D. A. Horsley, “A MEMS light modulator based on diffractive nanohole gratings,” Opt. Express 16(6), 3701–3711 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-6-3701 . [CrossRef] [PubMed]
  11. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]
  12. Lumerical FDTD Solution, http://www.lumerical.com/

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