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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 14 — Jul. 5, 2010
  • pp: 14547–14552
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Investigation of polarized light emitting diodes with integrated wire grid polarizer

Örs Sepsi, István Szanda, and Pál Koppa  »View Author Affiliations


Optics Express, Vol. 18, Issue 14, pp. 14547-14552 (2010)
http://dx.doi.org/10.1364/OE.18.014547


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Abstract

The polarization properties of light emitting diodes with integrated wire grid polarizers are investigated. Rigorous coupled wave analysis and Monte-Carlo ray tracing are used for modeling the gratings and the entire LED structure respectively. We show that it is more advantageous to place the polarizer onto the LED encapsulation rather than onto the die. With the proposed arrangement the average extinction ratio is 2.37 in the uncollimated case and 76.86 in the collimated case, while the light extraction efficiency is significantly higher than that of the LED + external polarizer combination. The achieved results compare favorably to other polarized LED solutions proposed in the literature.

© 2010 OSA

1. Introduction

Light emitting diodes (LED) attract more and more attention and are in the focus of interest of both industrial and fundamental research. They provide high energy efficiency, long lifetime, portability and flexibility [1

1. E. F. Schubert, Light Emitting Diodes (Cambridge University Press, 2006).

,2

2. G. B. Stringfellow, and M. G. Craford, “High Brightness Light Emitting Diodes,” in Semiconductors and Semimetals, R. K. Wiliardson and E. R. Weber eds. (Academic Press, 1997), Vol. 48.

]. Native LED radiation is unpolarized, but polarized LED would be very useful in several applications like high-contrast imaging [3

3. J. C. Ramella-Roman, K. Lee, S. A. Prahl, and S. L. Jacques, “Polarized Light Imaging with a Handheld Camera,” Proc. SPIE 5068, 284–293 (2003). [CrossRef]

,4

4. J. S. Baba, S. S. Gleason, J. S. Goddard, and J. M. Paulus, “Application of Polarization for Optical Motion-Registered SPECT Functional Imaging of Tumors in Mice,” Proc. SPIE 5702, 97–103 (2005). [CrossRef]

], optical communications [5

5. R. Otte, L. P. de Joung, and A. H. M. van Roermund, Low-Power Wireless Infrared Communications (Kluwer Academic Publishers, 1999).

] and LCD backlighting [6

6. P. Yeh, and C. Gu, Optics of Liquid Crystal Displays (John Wiley, Canada, 1999).

].

Several papers deal with LEDs having polarized light output. Schubert et al. demonstrated two possible solutions for this problem: a polarization selective encapsulation based on Brewster's effect for unpolarized white light source [7

7. M. F. Schubert, A. Noemaun, S. Chhajed, J. K. Kim, E. F. Schubert, and Ch. Sone, “Encapsulation shape with non-rotational symmetry designed for extraction of polarized light from unpolarized sources,” Opt. Express 15(16), 10452–10457 (2007). [CrossRef] [PubMed]

] and a polarization-enhancing reflector for a partially polarized GaInN LED dies [8

8. M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Linearly polarized emission from GaInN lightemitting diodes with polarization-enhancing reflector,” Opt. Express 15(18), 11213–11218 (2007). [CrossRef] [PubMed]

].

Wheatley et al. patented a solution [9

9. J. A. Wheatley, C. A. Leatherdale, and A. J. Ouderkirk, “Polarized LED,” International Patent, WO 2006/052328 A1 (2006).

], in which the emitting surface of the LED die is coated with a wire grid polarizer (WGP), and on the opposite surface a polarization recycler takes place. The WGP transmits one component of the wave, with polarization perpendicular to the grating lines, and reflects the component of parallel polarization. The light reflected by the WGP has another chance to get out of the LED if its polarization changes inside. This concept is useful practically if the total polarized output of the LED is significantly higher than the output of a standard LED combined with a standard polarizer.

In this study the concept of polarized LED with wire grid polarizer is investigated and the idea mentioned above is reviewed and modified in order to achieve better performance. In the first step, the performance of the WGP is examined for the purpose of polarized LED applications. The well-established rigorous coupled wave analysis (RCWA) is used to compute transmittance, absorption and extinction ratio of WGPs with different grating parameters. In the second step, a complete high power AlGaInP LED model is built up, using a commercial ray tracing software combined with a custom RCWA module.

2. Investigation of the wire grid polarizer

2.1 Modeling the wire grid polarizer

The optical properties of the WGP are investigated using the RCWA method [14

14. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995). [CrossRef]

,15

15. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13(9), 1870–1876 (1996). [CrossRef]

]. This method has been proven to be efficient in the simulation of periodic gratings of a wide range of materials and geometries.

In this section two different constructions are investigated. The first sample is Grating-on-die (GD), which matches the structure as described in [9

9. J. A. Wheatley, C. A. Leatherdale, and A. J. Ouderkirk, “Polarized LED,” International Patent, WO 2006/052328 A1 (2006).

], i.e. the WGP is placed between the semiconductor and the encapsulation. The second sample is Grating-on-encapsulation (GE), a new construction in which the grating is placed between the interface of the encapsulation and air. The simulations are performed for both cases for plane interface, thus the curved surface of the encapsulation is not taken into account. This assumption can be confirmed with the fact, that the radius of curvature is always much larger than the dimensions of the grating.

The samples consist of a superstrate, a single layer uniperiodic binary metallic grating and a substrate. The cross section of both configurations is the same, simple rectangular profile on flat surface [15

15. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13(9), 1870–1876 (1996). [CrossRef]

]. The refractive index of the die is approximated with ndie = 3.3 (according to AlGaInP LED chip). The encapsulation refractive index is approximated with nenc = 1.5. The grating consists of aluminum grids (refractive index: nAL = 1.32 + 7.52 i) of a grating period of 150 nm, a grating height of 150 nm and a linewidth of 60 nm. The calculations are performed at a single wavelength of 620 nm taken from a typical AlGaInP red LED specification, but the same calculations can be implemented for any other wavelengths and the finite spectral width of the LED can also be taken into account.

2.2 Comparison of Grating-on-die (GD) and Grating-on-encapsulation (GE)

The performance of the polarizers are investigated at general angle of incidence. Figure 1(a)
Fig. 1 (a) Extinction ratio and (b) average absorption for unpolarized incident wave. The WGP is placed onto the encapsulation (Grating on encapsulation: line + symbol) or onto the LED die (Grating on die: solid line).
shows the extinction ratio of the gratings defined by the ratio of the power that can be observed by an external analyzer aligned in the x-direction and the power with the external analyzer aligned in the y-direction. Figure 1(b) displays the absorption of an unpolarized incident wave by the gratings. In spherical coordinates, the curves depend on the polar angle and are drawn at a few azimuth angles.

It can be seen from the figures, that GE achieves better performances than GD both in extinction ratio and in extraction efficiency. On the one hand, the extinction ratio of GE is an order of magnitude higher than that of GD for each azimuth angle [Fig. 3(a)
Fig. 3 (a) Schematics of the combination of the geometrical optical model with the diffraction optical model. (b) Schematic drawing of the simulation setup. D1 and D2 denotes the detectors, which detects the uncollimated and collimated waves respectively. L denotes a theoretical “perfect” collimating lens, and (P) denotes an optional polarizer for the LED + external polarizer configuration.
]. On the other hand, the average absorption of GE – when an unpolarized wave hits the surface – is much lower than that of GD for each azimuth angle.

Besides that, there is another aspect in which GE is superior. From the geometry of the LED source it is clear, that the wave coming from the chip and hitting the encapsulation surface falls nearly at normal incidence onto the surface. On the contrary inside the chip, the waves fall on the interface of the chip and the encapsulation in polar angles uniformly distributed. Consequently a large amount of light is trapped inside the LED die by total internal reflection. Thus one can conclude, that if these conditions hold, it is reasonable to put the WGP onto the encapsulation rather than onto the chip surface. In this case the large absorption arising from the larger polar angle region in GD can be avoided and the high extinction ratio of GE at near normal incidence is insured.

3. Investigation of the polarized LED source

3.1 Modeling the polarized LED structure

The LED source is modeled using a conventional ray tracing software. With this method arbitrary LED configurations can be designed with appropriate geometry and parameter set. In our research a high efficiency, transparent substrate AlGaInP LED [16

16. F. A. Kish, F. M. Steranka, D. C. DeFevere, D. A. Vanderwater, K. G. Park, C. P. Kuo, T. D. Osentowski, M. J. Peanasky, J. G. Yu, R. M. Fletcher, D. A. Steigerwald, M. G. Craford, and V. M. Robbins, “Very high-efficiency semiconductor wafer-bonded transparent-substrate (AlxGa1-x)0.5In0.5P/GaP light-emitting diodes,” Appl. Phys. Lett. 64(21), 2839–2841 (1994). [CrossRef]

,17

17. N. F. Gardner, H. C. Chui, E. I. Chen, M. R. Krames, J.-W. Huang, F. A. Kish, S. A. Stockman, C. P. Kocot, T. S. Tan, and N. Moll, “1.4x efficiency improvement in transparent-substrate (AlxGa1-x)0.5In0.5P light-emitting diodes with thin (≤2000 Å) active regions,” Appl. Phys. Lett. 74(15), 2230–2232 (1999). [CrossRef]

] is investigated. The model consists of an LED chip (assumed to be non-absorbing), an encapsulation (spherical, with n = 1.5 refractive index) and a mirror [Fig. 2(a)
Fig. 2 (a) Schematic diagram of the LED model with WGP placed onto all sides of the chip. (b) Schematic design of the WGP on the encapsulation LED model. The density of the lines doesn't correspond to the grating period, the lines mark only the direction of the grating lines.
]. The chip area is 500 × 500 μm2, the chip height is 250 μm. The refractive index of the chip is assumed to be 3.3, and absorption is neglected for this wavelength. Spherical encapsulation is assumed with diameter of 5 mm.

We investigate three different theoretical LED configurations. The first one is an unpolarized LED + external polarizer combination. The external polarizer is also designed as a WGP for better comparison. The second one is a standard LED with a WGP placed onto all sides of the LED chip [Fig. 2(a)]. The third one is also a standard LED with a WGP placed onto the curved encapsulation surface. In this last case the polarizing WGP is designed similarly to the circles of latitude on the globe. Figure 2(b) shows the schematic diagram of such an encapsulation. For both configurations the grating period as well as the grating height are 150 nm and the line/period ratio is 0.4.

In the case of the spherical surface the WGP is approximated with wire grids on a locally plane surface. The grating has a constant period and an appropriate direction. The distortion of the parallel lines due to the spherical surface as well as the variation of the line spacing are not included in our model. We use the locally flat surface approximation, because the radius of curvature of the sphere is much larger than the size (period, height) of the grating. Practically the grating can be imagined on the whole curved surface as consisting of multiple segments, where the size of one segment is much smaller than the area of the sphere, but much larger than the grating period. Similar modeling method is used by Kim et al. [18

18. D. Kim and E. Sim, “Segmented coupled-wave analysis of a curved wire-grid polarizer,” J. Opt. Soc. Am. A 25(3), 558–565 (2008). [CrossRef]

].

The direction of the grating lines on the curved surface can also be optimized, to reach higher extinction ratio as well as higher efficiency. In the optimized setup the direction of the lines is adjusted so that the polarization of the outcoupled wave lies in the globally defined xz-plane. In this case higher extinction ratio is expected.

Throughout this research uncollimated as well as collimated LED sources are tested. In the uncollimated case a virtual polarization sensitive detector is placed at 10 cm far from the source. In the collimated case the LED source is placed into the focal point of a “perfect” collimating lens with focal length of 10 cm. Behind the collimating lens there is another virtual detector. The simulation setup can be seen on Fig. 3(b).

3.2 Comparison of the modeled LED sources

For a detailed examination of the polarized LED using WGPs, various structures are modeled and compared. Table 1

Table 1. Optical output of the examined LED models.

table-icon
View This Table
. shows the results of the three previously defined configurations: a LED + external polarizer configuration, a setup with a WGP placed onto all sides of the chip and a configuration, where the WGP is placed onto the spherical encapsulation. For comparison of the total extraction efficiency the equivalent unpolarized LED is also simulated. In addition, an improved WGP on the encapsulation setup – where the direction of the grating lines are optimized – is also listed in the table.

In the LED + external polarizer case, with the applied external wire grid polarizer the extinction ratio of the collimated case is very high, about 2000. However, the drawback of this setup can be also right seen. The total extraction efficiency is highly reduced compared to the unpolarized LED source, i.e. more than the half of the extracted light is lost (58.3%).

Two configurations of the WGP on the encapsulation setup are also investigated. The grating lines of the first one are similar to Fig. 2(b). The direction of the grating lines of the second one are optimized in order to reach higher extinction ratio in the collimated case. The extraction efficiency in both cases is about 13% (43.9% and 45.2% explicit loss), definitely higher as the extraction efficiency of the LED + external polarizer combination. This fact shows that these configurations have a polarization recycling property, i.e. a part of the light reflected by the WGP undergoes reflection and polarization change and thus can escape again with proper polarization state. Note that although explicit polarization recycler grating is not included in our model, the polarization recycling property is present because the inner structure of the LED indicates phase change of the reflected light.

The presented WGP on the encapsulation setups show also strong polarized properties in the collimated case. Moreover the extinction ratio of the optimized case is over 70. This seems much lower than the extinction ratio of the LED + external polarizer configuration, however this value is also well suited to most practical applications. On the other hand, the significantly higher extraction efficiency of this setup is a remarkable advantage in contrast to the LED + external polarizer configuration.

In addition, the optimized WGP on the encapsulation setup is investigated with the use of a pyramidal light extracting structure placed onto the chip surface. This technique is widely used to enhance the light extraction efficiency of high power LED sources [19

19. T.-X. Lee, K.-F. Gao, W.-T. Chien, and C.-C. Sun, “Light extraction analysis of GaN-based light-emitting diodes with surface texture and/or patterned substrate,” Opt. Express 15(11), 6670–6676 (2007). [CrossRef] [PubMed]

]. Our simulations show that the total extraction efficiency is over 30% and the (collimated) extinction ratio of this setup is about 100. This result shows that the proposed setup is compatible to high extraction efficiency power LEDs at slightly improved extinction ratio.

Although the feasibility of the presented polarized LED remains a challenge because of the non-planar WGP, recent studies show that fabrication of gratings with similar parameters on curved surface can be possible for example with nanoimprint lithography techniques [20

20. Y.-P. Chen, Y.-P. Lee, J.-H. Chang, and L. A. Wang, “Fabrication of concave gratings by curved surface UV-nanoimprint lithography,” J. Vac. Sci. Technol. B 26(5), 1690–1695 (2008). [CrossRef]

,21

21. Z. Li, Y. Gu, L. Wang, H. Ge, W. Wu, Q. Xia, Ch. Yuan, Y. Chen, B. Cui, and R. S. Williams, “Hybrid nanoimprint-soft lithography with sub-15 nm resolution,” Nano Lett. 9(6), 2306–2310 (2009). [CrossRef] [PubMed]

].

4. Conclusion

We have investigated the combination of light emitting diodes and WGP structures in order to produce polarized light output. Both RCWA and Monte-Carlo analysis show that it is advantageous to place the WGP on the encapsulation surface rather than on the die. Putting the WGP onto the die, the internal absorption increases as well as the extinction ratio reduces.

A complete LED model was built up to determine the optical properties of this configuration. AlGaInP diode structure was modeled using Monte-Carlo ray tracing method. The model includes the main parts of a conventional LED structure as well as optional light extracting structure and the wire grid polarizer.

In conclusion the average extinction ratio was found to be 2.37 in the uncollimated case and 76.86 in the collimated case, while the light extraction was significantly higher than that of the LED + external polarizer combination. Moreover with additional light extracting structure on the chip surface, over 30% extraction efficiency and an extinction ratio of about 100 was estimated.

The presented results were not optimized for any special application, but the proposed model can be used for the design of polarized LED applications requiring high extinction ratio, power and specific angular distribution.

Acknowledgements

The authors would like to thank to Dr. Gábor Erdei for his helpful advices and discussions.

References and links

1.

E. F. Schubert, Light Emitting Diodes (Cambridge University Press, 2006).

2.

G. B. Stringfellow, and M. G. Craford, “High Brightness Light Emitting Diodes,” in Semiconductors and Semimetals, R. K. Wiliardson and E. R. Weber eds. (Academic Press, 1997), Vol. 48.

3.

J. C. Ramella-Roman, K. Lee, S. A. Prahl, and S. L. Jacques, “Polarized Light Imaging with a Handheld Camera,” Proc. SPIE 5068, 284–293 (2003). [CrossRef]

4.

J. S. Baba, S. S. Gleason, J. S. Goddard, and J. M. Paulus, “Application of Polarization for Optical Motion-Registered SPECT Functional Imaging of Tumors in Mice,” Proc. SPIE 5702, 97–103 (2005). [CrossRef]

5.

R. Otte, L. P. de Joung, and A. H. M. van Roermund, Low-Power Wireless Infrared Communications (Kluwer Academic Publishers, 1999).

6.

P. Yeh, and C. Gu, Optics of Liquid Crystal Displays (John Wiley, Canada, 1999).

7.

M. F. Schubert, A. Noemaun, S. Chhajed, J. K. Kim, E. F. Schubert, and Ch. Sone, “Encapsulation shape with non-rotational symmetry designed for extraction of polarized light from unpolarized sources,” Opt. Express 15(16), 10452–10457 (2007). [CrossRef] [PubMed]

8.

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Linearly polarized emission from GaInN lightemitting diodes with polarization-enhancing reflector,” Opt. Express 15(18), 11213–11218 (2007). [CrossRef] [PubMed]

9.

J. A. Wheatley, C. A. Leatherdale, and A. J. Ouderkirk, “Polarized LED,” International Patent, WO 2006/052328 A1 (2006).

10.

Y. Ekinci, H. H. Solak, C. David, and H. Sigg, “Bilayer Al wire-grids as broadband and high-performance polarizers,” Opt. Express 14(6), 2323–2334 (2006). [CrossRef] [PubMed]

11.

Z. Y. Yang and Y. F. Lu, “Broadband nanowire-grid polarizers in ultraviolet-visible-near-infrared regions,” Opt. Express 15(15), 9510–9519 (2007). [CrossRef] [PubMed]

12.

J. J. Wang, L. Chen, X. Liu, P. Sciortino, F. Liu, F. Walters, and X. Deng, “30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by UV-nanoimprint litography,” Appl. Phys. Lett. 89(14), 141105 (2006). [CrossRef]

13.

J. J. Wang, F. Walters, X. Liu, P. Sciortino, and X. Deng, “High-performance, large area, deep ultraviolet to infrared polarizers based on 40 nm line/78 nm space nanowire grids,” Appl. Phys. Lett. 90(6), 061104 (2007). [CrossRef]

14.

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995). [CrossRef]

15.

L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13(9), 1870–1876 (1996). [CrossRef]

16.

F. A. Kish, F. M. Steranka, D. C. DeFevere, D. A. Vanderwater, K. G. Park, C. P. Kuo, T. D. Osentowski, M. J. Peanasky, J. G. Yu, R. M. Fletcher, D. A. Steigerwald, M. G. Craford, and V. M. Robbins, “Very high-efficiency semiconductor wafer-bonded transparent-substrate (AlxGa1-x)0.5In0.5P/GaP light-emitting diodes,” Appl. Phys. Lett. 64(21), 2839–2841 (1994). [CrossRef]

17.

N. F. Gardner, H. C. Chui, E. I. Chen, M. R. Krames, J.-W. Huang, F. A. Kish, S. A. Stockman, C. P. Kocot, T. S. Tan, and N. Moll, “1.4x efficiency improvement in transparent-substrate (AlxGa1-x)0.5In0.5P light-emitting diodes with thin (≤2000 Å) active regions,” Appl. Phys. Lett. 74(15), 2230–2232 (1999). [CrossRef]

18.

D. Kim and E. Sim, “Segmented coupled-wave analysis of a curved wire-grid polarizer,” J. Opt. Soc. Am. A 25(3), 558–565 (2008). [CrossRef]

19.

T.-X. Lee, K.-F. Gao, W.-T. Chien, and C.-C. Sun, “Light extraction analysis of GaN-based light-emitting diodes with surface texture and/or patterned substrate,” Opt. Express 15(11), 6670–6676 (2007). [CrossRef] [PubMed]

20.

Y.-P. Chen, Y.-P. Lee, J.-H. Chang, and L. A. Wang, “Fabrication of concave gratings by curved surface UV-nanoimprint lithography,” J. Vac. Sci. Technol. B 26(5), 1690–1695 (2008). [CrossRef]

21.

Z. Li, Y. Gu, L. Wang, H. Ge, W. Wu, Q. Xia, Ch. Yuan, Y. Chen, B. Cui, and R. S. Williams, “Hybrid nanoimprint-soft lithography with sub-15 nm resolution,” Nano Lett. 9(6), 2306–2310 (2009). [CrossRef] [PubMed]

OCIS Codes
(080.2740) Geometric optics : Geometric optical design
(230.3670) Optical devices : Light-emitting diodes
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Optical Devices

History
Original Manuscript: April 2, 2010
Revised Manuscript: May 21, 2010
Manuscript Accepted: June 5, 2010
Published: June 23, 2010

Citation
Örs Sepsi, István Szanda, and Pál Koppa, "Investigation of polarized light emitting diodes with integrated wire grid polarizer," Opt. Express 18, 14547-14552 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-14-14547


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References

  1. E. F. Schubert, Light Emitting Diodes (Cambridge University Press, 2006).
  2. G. B. Stringfellow, and M. G. Craford, “High Brightness Light Emitting Diodes,” in Semiconductors and Semimetals, R. K. Wiliardson and E. R. Weber eds. (Academic Press, 1997), Vol. 48.
  3. J. C. Ramella-Roman, K. Lee, S. A. Prahl, and S. L. Jacques, “Polarized Light Imaging with a Handheld Camera,” Proc. SPIE 5068, 284–293 (2003). [CrossRef]
  4. J. S. Baba, S. S. Gleason, J. S. Goddard, and J. M. Paulus, “Application of Polarization for Optical Motion-Registered SPECT Functional Imaging of Tumors in Mice,” Proc. SPIE 5702, 97–103 (2005). [CrossRef]
  5. R. Otte, L. P. de Joung, and A. H. M. van Roermund, Low-Power Wireless Infrared Communications (Kluwer Academic Publishers, 1999).
  6. P. Yeh, and C. Gu, Optics of Liquid Crystal Displays (John Wiley, Canada, 1999).
  7. M. F. Schubert, A. Noemaun, S. Chhajed, J. K. Kim, E. F. Schubert, and Ch. Sone, “Encapsulation shape with non-rotational symmetry designed for extraction of polarized light from unpolarized sources,” Opt. Express 15(16), 10452–10457 (2007). [CrossRef] [PubMed]
  8. M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Linearly polarized emission from GaInN lightemitting diodes with polarization-enhancing reflector,” Opt. Express 15(18), 11213–11218 (2007). [CrossRef] [PubMed]
  9. J. A. Wheatley, C. A. Leatherdale, and A. J. Ouderkirk, “Polarized LED,” International Patent, WO 2006/052328 A1 (2006).
  10. Y. Ekinci, H. H. Solak, C. David, and H. Sigg, “Bilayer Al wire-grids as broadband and high-performance polarizers,” Opt. Express 14(6), 2323–2334 (2006). [CrossRef] [PubMed]
  11. Z. Y. Yang and Y. F. Lu, “Broadband nanowire-grid polarizers in ultraviolet-visible-near-infrared regions,” Opt. Express 15(15), 9510–9519 (2007). [CrossRef] [PubMed]
  12. J. J. Wang, L. Chen, X. Liu, P. Sciortino, F. Liu, F. Walters, and X. Deng, “30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by UV-nanoimprint litography,” Appl. Phys. Lett. 89(14), 141105 (2006). [CrossRef]
  13. J. J. Wang, F. Walters, X. Liu, P. Sciortino, and X. Deng, “High-performance, large area, deep ultraviolet to infrared polarizers based on 40 nm line/78 nm space nanowire grids,” Appl. Phys. Lett. 90(6), 061104 (2007). [CrossRef]
  14. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995). [CrossRef]
  15. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13(9), 1870–1876 (1996). [CrossRef]
  16. F. A. Kish, F. M. Steranka, D. C. DeFevere, D. A. Vanderwater, K. G. Park, C. P. Kuo, T. D. Osentowski, M. J. Peanasky, J. G. Yu, R. M. Fletcher, D. A. Steigerwald, M. G. Craford, and V. M. Robbins, “Very high-efficiency semiconductor wafer-bonded transparent-substrate (AlxGa1-x)0.5In0.5P/GaP light-emitting diodes,” Appl. Phys. Lett. 64(21), 2839–2841 (1994). [CrossRef]
  17. N. F. Gardner, H. C. Chui, E. I. Chen, M. R. Krames, J.-W. Huang, F. A. Kish, S. A. Stockman, C. P. Kocot, T. S. Tan, and N. Moll, “1.4x efficiency improvement in transparent-substrate (AlxGa1-x)0.5In0.5P light-emitting diodes with thin (≤2000 Å) active regions,” Appl. Phys. Lett. 74(15), 2230–2232 (1999). [CrossRef]
  18. D. Kim and E. Sim, “Segmented coupled-wave analysis of a curved wire-grid polarizer,” J. Opt. Soc. Am. A 25(3), 558–565 (2008). [CrossRef]
  19. T.-X. Lee, K.-F. Gao, W.-T. Chien, and C.-C. Sun, “Light extraction analysis of GaN-based light-emitting diodes with surface texture and/or patterned substrate,” Opt. Express 15(11), 6670–6676 (2007). [CrossRef] [PubMed]
  20. Y.-P. Chen, Y.-P. Lee, J.-H. Chang, and L. A. Wang, “Fabrication of concave gratings by curved surface UV-nanoimprint lithography,” J. Vac. Sci. Technol. B 26(5), 1690–1695 (2008). [CrossRef]
  21. Z. Li, Y. Gu, L. Wang, H. Ge, W. Wu, Q. Xia, Ch. Yuan, Y. Chen, B. Cui, and R. S. Williams, “Hybrid nanoimprint-soft lithography with sub-15 nm resolution,” Nano Lett. 9(6), 2306–2310 (2009). [CrossRef] [PubMed]

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