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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 6 — Mar. 17, 2008
  • pp: 4270–4277
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Reflection minimization at two-dimensional photonic crystal interfaces

Sun-Goo Lee, Jin-sun Choi, Jae-Eun Kim, Hae Yong Park, and Chul-Sik Kee  »View Author Affiliations


Optics Express, Vol. 16, Issue 6, pp. 4270-4277 (2008)
http://dx.doi.org/10.1364/OE.16.004270


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Abstract

We propose a method to design antireflection structures to minimize the reflection of light beams at the interfaces between a two-dimensional photonic crystal and a homogeneous dielectric. The design parameters of the optimal structure to give zero reflection can be obtained from the one-dimensional antireflection coating theory and the finite-difference time-domain simulations. We examine the performance of a Mach-Zehnder interferometer utilizing the self-collimated beams in two-dimensional photonic crystals with and without the optimal antireflection structure introduced. It is shown that the optimal antireflection structure significantly improves the performance of the device.

© 2008 Optical Society of America

1. Introduction

Recently, unique dispersion properties of photonic crystals (PCs) which give rise to the interesting light propagation phenomena such as self-collimated beam propagation [1

1. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999). [CrossRef]

, 2

2. J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 8, 1246–1257 (2002). [CrossRef]

], negative refraction [3

3. S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, “Refraction in media with a negative refractive index,” Phys. Rev. Lett. 90, 107402 (2003). [CrossRef] [PubMed]

, 4

4. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001). [CrossRef] [PubMed]

], and superprism effects [5

5. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998). [CrossRef]

] have attracted much attention because they could provide new mechanisms to control the light propagation in PCs. The propagation direction of light in a PC is determined by the direction of the group velocity of light in the PC, v g=∇k ω(k). Thus, the equifrequency contours (EFCs), the cross sections of the dispersion surfaces of the Bloch modes in momentum space, are essential to investigate the propagation properties of lights in PCs and to design the dispersion based PC optical devices such as non-channel waveguides [6

6. D. Chigrin, S. Enoch, C. Sotomayor Torres, and G. Tayeb, “Self-guiding in two-dimensional photonic crystals,” Opt. Express 11, 1203–1211 (2003). [CrossRef] [PubMed]

, 7

7. D.W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29, 50–52 (2004). [CrossRef] [PubMed]

, 8

8. P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačiv́, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and Erich P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5, 93–96 (2006). [CrossRef] [PubMed]

], beam splitters [9

9. X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251–3253 (2003). [CrossRef]

, 10

10. S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005). [CrossRef]

, 11

11. M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 90, 113121 (2007). [CrossRef]

, 12

12. S. Shi, A. Sharkawy, C. Chen, D. Pustai, and D. Prather, “Dispersion-based beam splitter in photonic crystals,” Opt. Lett. 29, 617–619 (2004). [CrossRef] [PubMed]

, 13

13. V. Zabelin, L. A. Dunbar, N. Le Thomas, R. Houdré, M. V. Kotlyar, L. O’Faolain, and T. F. Krauss, “Self-collimating photonic crystal polarization beam splitter,” Opt. Lett. 32, 530–532 (2007). [CrossRef] [PubMed]

], super lenses [14

14. Z. Y. Li and L. L. Lin, “Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,” Phys. Rev. B 68, 245110 (2003). [CrossRef]

, 15

15. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopou, and C. M. Soukoulis, “Subwavelength resolution in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. Lett. 91, 207401 (2003). [CrossRef] [PubMed]

, 16

16. V. P. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Photonic crystals - imaging by flat lens using negative refraction,” Nature 426, 404 (2003). [CrossRef] [PubMed]

], demultiplexers [17

17. T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of Photonic crystal superprism and superlens,” Opt. Express 13, 10768–10776 (2005). [CrossRef] [PubMed]

, 18

18. K. B. Chung and S. W. Hong, “Wavelength demultiplexers based on the superprism phenomena in photonic crystals,” Appl. Phys. Lett. 81, 1549–1551 (2002). [CrossRef]

] and so on.

In general, the unwanted reflection at the interfaces between a two-dimensional (2D) PC and an outside uniform dielectric has been a crucial problem in realizing PC devices. Several approaches have been proposed to reduce the reflection at the 2D PC interfaces. Baba et al. elongated holes in the first layer [19

19. T. Baba and D. Ohsaki, “Interfaces of photonic crystals for high efficiency light transmission,” Jpn. J. Appl. Phys. 40, 5920–5924 (2001). [CrossRef]

] and Witzens et al. added multilayered diffraction grating at the end of a PC [20

20. J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004). [CrossRef]

]. Momeni and Adibi gradually varied hole sizes at the interfaces so that the group velocity and the field profile varied slowly [21

21. B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal,” Appl. Phys. Lett. 87, 171104 (2005). [CrossRef]

]. Here, we present a different compact and systematic method which is suitable for practical applications to the dispersion based PC devices.

Fig. 1. Structural parameters for ARC. (a) In the 1D case, the ARC parameters are the refractive index n 2 and the thickness h of an antireflection layer. (b) In the 2D PC case, the ARC parameters are the radius of rods Rarc and the distance darc between the ARC structure and the crystal truncation. The antireflection structure becomes a part of the host PC when Rarc=R and darc=a/√2.

In this paper, we describe a method to minimize the reflection at the interfaces between a 2D PC and a background dielectric material by using the concept of ARC. We show that the ARC structures composed of rods or holes can be optimized for minimum reflection at the interfaces by using the finite-difference time-domain (FDTD) simulations [24

24. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Boston, 1995).

]. To stress the effectiveness of the proposed method, we simulate the performance of a Mach-Zehnder interferometer (MZI) for self-collimated beams in 2D PCs with and without the optimized ARC structure introduced. The simulated results show that the performance of the MZI can be significantly improved by the introduction of the ARC structure into the PC.

2. Model and Method

When a light beam is normally incident from region 1 onto region 2 which is placed between two semi-infinite homogenous media (region 1 and 3) as shown in Fig. 1(a), the reflection coefficient is given by

r=r12+r23e2iβ1+r12r23e2iβ,
(1)

where β is the phase change occurred during the time the light goes across region 2 and rij is the reflection coefficient of light propagating from region i to j [25

25. M. Born and E. Wolf, Principles of Optics, (Cambridge University Press, Cambridge, 2002).

]. The reflectance of the incident light, the square of the amplitude of the reflection coefficient r given by Eq. (1), becomes zero when the following two conditions are satisfied simultaneously:

r12=r23,
(2)

and

ei(2β+δ23δ12)=1,
(3)
Fig. 2. (a) |r 12|, the amplitude of the reflection coefficient of the ARC structure, as a function of Rarc. |r 23| represents the amplitude of the reflection coefficient of the semi-infinite square lattice PC consisting of dielectric rods in air. (b) Total reflectance of the PC with the ARC structure is calculated as a function of darc when Rarc=0.2064 a (red solid) and Rarc=0.4347 a (black dotted). The reflectance oscillates with a period of about a half wavelength of the incident beam. Simulations are performed for the light of frequency f=0.194 c/a (wavelength λ=5.1546 a).

where |rij| and δij correspond to the amplitude and the phase factor of the reflection coefficient rij, respectively. In the simple case shown in Fig. 1(a), the optimal ARC parameters, the refractive index n2=n1n3 and the optical thickness h=λ/4, are easily obtained from Eqs. (2) and (3) by using the reflection coefficients given by the Fresnel equations. When region 3 is replaced by a 1D PC, the ARC parameters can also be optimized by using the r 12 given by the Fresnel equations and r 23 given by the numerical calculations as described in Ref. [23

23. J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, “Systematic design of antireflection coating for semi-infinite one-dimensional photonic crystals using Bloch wave expansion,” Appl. Phys. Lett. 82, 7–9 (2003). [CrossRef]

].

We introduce ARC structures to minimize the reflection at the ends of 2D PCs. In a practical point of view, it is reasonable to apply ARC structures composed of rods or holes at the interfaces between a 2D PC and a homogeneous background medium to reduce the reflection. Thus, the radius Rarc of the rod (hole) and the distance darc between the ARC and the PC truncation are chosen as the design parameters of the ARC structure as depicted in Fig. 1(b) that shows the case for a 2D square lattice PC composed of dielectric rods in air. The ARC structure becomes a part of the host PC when Rarc=R and darc=a/√2. The ARC parameters for this configuration can also be optimized from Eqs. (2) and (3), provided that rij are properly modified. Note that, in this analysis, r 12 is the reflection coefficient of the ARC structure embedded in air and r 23 is that of the semi-infinite PC when the light is incident upon it from the air. In the conventional ARC approach the perfect transmission of incident light is resulted from the resonance in the region 2 of Fig. 1(a), whereas in the 2D PC case this is taking place in the air region located between the end of PC and the ARC structure (see Fig. 1(b)). Therefore, the reflection coefficient r 23 in the classical ARC is replaced by the reflection coefficient of the PC starting from the air. We can optimize the parameters for the specific light frequency of interest by using the FDTD simulations. First, the value of Rarc is found to satisfy the condition given by Eq. (2) and then the value of darc to satisfy Eq. (3) at the optimized value of Rarc.

To see the effects of the ARC structures on the reflection of light beam, both the 2D rod-type and hole-type PCs will be considered. In recent years, the self-collimated light propagation in 2D PCs have inspired great interests due to its potential applications in implementing on-chip photonic integrated circuits [26

26. D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90, 231114 (2007). [CrossRef]

, 27

27. Y. Zhang, Y. Zhang, and B. Li, “Optical switches and logic gates based on self-collimated beams in two-dimensional photonic crystals,” Opt. Express 15, 9287–9292 (2007). [CrossRef] [PubMed]

]. However, there has been no study on the reflection minimization of self-collimated beams at the 2D PC interfaces. Hence, we will mainly focus our attention on the reflection minimization of self-collimated beams at the 2D PC interfaces.

Fig. 3. (a) Configuration of the simulations. Periodic boundary condition is used in the x-direction and PMLs are placed at the ends of computational domain in the y-direction. Transmission spectra of two different sized PC samples of 2D square array of dielectric rods in air for the cases (b) without the ARC and (c) with the ARC structure. The red solid and black dotted lines represent the transmission through the PC samples of sizes 12√2 a and 16√2 a, respectively.

3. Results and Discussion

The transmission spectra of the PC are obtained with and without the ARC structure when darc=0.74 a and Rarc=0.2064 a. The minimum value of darc is chosen here to minimize the spreading of light beam which may occur during the propagation through the air layer between the ARC structure and the PC and thereby to improve the coupling efficiency. The FDTD simulations are performed for two different PC samples of sizes 12√2 a and 16√2 a in the ΓM-direction. The ARC structures of the same parameters are introduced at both the input and output PC interfaces. The computational geometry is shown in Fig. 3(a). In the x-direction the Bloch periodic boundary condition is applied and the perfectly matched layer (PML) absorbing boundary condition [28

28. J. -P. Berenger, “A perfectly matched layer for the absorption of electomagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]

] is used in the y-direction. Fig. 3(b) shows the calculated transmission spectra of the PC without the ARC structure and one can compare them with those shown in Fig. 3(c) which are obtained with the ARC structure applied. The transmission of light beam through the PC without the ARC structure not only strongly oscillates but also depends on the size of the PC; the period of oscillation becomes shortened as the size of PC increases because the optical path of light is increased. The variations in the transmitted power of light result from the constructive or destructive interferences of multiple beams which are reflected and transmitted at the PC interfaces. Hence, it is reasonably expected that the oscillations in the transmission spectra will disappear if the reflection totally vanishes. One can clearly see that the light beams of frequencies around f=0.194 c/a show almost perfect transmission, irrespective of the PC size. More than 99% of the incident power is transmitted through the PC samples for the the lights in the frequency range from 0.188 to 0.202 c/a.

Fig. 4. Transmission spectra of a 2D square lattice PC of air holes for the cases of (a) without the ARC and (b) with the ARC structure.

The ARC structure is also introduced into a 2D square lattice PC which consists of air holes with the hole radius r=0.35 a in a high index material of ε=12.0. According to Ref. [9

9. X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251–3253 (2003). [CrossRef]

], the H-polarized lights, which have the magnetic field parallel to the hole axis, of frequencies around f=0.190 c/a propagate with almost no beam spreading along the ΓM-direction in the PC of the same structure. The optimal values of the ARC parameters are found to be Rarc=0.2565 a and darc=0.58 a for the light of frequency f=0.190 c/a. The transmission spectra are calculated for the cases with and without the optimal ARC structure when the sample size is 16√2 a. Figure 4(b) demonstrates that the reflection at the 2D PC interfaces can be efficiently eliminated by the application of the optimal ARC structure. Comparing Fig. 4(b) with Fig. 3(c), one can notice that the frequency range from 0.170 to 0.205 c/a which exhibit over 99% transmission in the hole-type PC is much wider than that of the rod-type PC. Because the reflection of light beam at the hole-type PC interface is smaller than that at the rod-type PC interface, the frequency range in which the incident light exhibits high transmission gets wider.

The reflection at the ends of PC structures may crucially affect the performance of devices because the PCs are truncated and of finite sizes. Thus, the reflection minimization at a crystal truncation is one of the important issues to implement practical PC devices. To compare the performance of a PC device with and without a ARC structure, we choose a PC MZI based on the self-collimated beams as depicted in Fig. 5(a). Recently, Zhao et al. theoretically demonstrated that the phase difference of the two split self-collimated beams at the line-defect beam splitter is π/2 in the PC with the same structural parameters considered in this study [26

26. D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90, 231114 (2007). [CrossRef]

]. Hence, the normalized output intensity I 1/I 0 measured at the port 1 is ideally unity and I 2/I 0 at the port 2 is zero due to the constructive and destructive interferences, respectively. We calculate the transmission spectra at the ports 1 and 2 around the frequency f=0.194 c/a when the ARC structure is (Fig. 5(b)) and is not (Fig. 5(c)) introduced. In the simulations, a Gaussian pulse with a waist of w=3 a is launched into the input interface of the MZI. Figure 5(b) shows that the transmission of light at the port 1 exceeds 92% with almost no fluctuation for the lights in the frequency range between 0.190 and 0.198 c/a. On the other hand, Fig. 5(c) shows that the transmitted power at the port 1 strongly fluctuates from 23% to 94% due to the reflection at the input and output interfaces of the device. These results reveal that the performance of the PC MZI is significantly improved by the introduction of the ARC structure into the PC.

Fig. 5. (a) Schematic diagram of a PC Mach-Zehnder interferometer composed of two 50:50 beam splitters and two perfect mirrors. The radius of rods in the line-defect is 0.275 a. Transmission spectra at the two output ports when (b) the ARC structure is and (c) is not introduced.

Finally, we applied the ARC method to the propagation of light beam of frequency f=0.160 c/a at which the light does not exhibit self-collimated propagation in the larger size rod-type PC structure employed in this study. The obtained results showed more than 99% transmission for the lights in the frequency range from 0.153 to 0.170 c/a with the optimal ARC structure applied.

In this study, the loss of light due to the out-of-plane scattering, which could diminish the coupling efficiency, is not considered as all the FDTD simulations have been performed for 2D geometry. For practical applications, therefore, a detailed three-dimensional study is required and that may be the issue of future work.

4. Conclusion

In conclusion, we propose an effective method to minimize the reflection at the interfaces between a 2D PC and a homogeneous background material. It is shown that the reflection at the 2D PC interfaces can be efficiently eliminated by optimizing the parameters of the ARC structure such as Rarc and darc. We also show that the performance of a PC MZI based on the self-collimated beams can be significantly improved by the introduction of the optimal ARC structure. The proposed method can be important for implementing other PC devices.

Acknowledgments

This work was partially supported by Ministry of Science and Technology through QSRC, Photonics 2020, and APRI-Research Program of GIST.

References and links

1.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999). [CrossRef]

2.

J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 8, 1246–1257 (2002). [CrossRef]

3.

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, “Refraction in media with a negative refractive index,” Phys. Rev. Lett. 90, 107402 (2003). [CrossRef] [PubMed]

4.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001). [CrossRef] [PubMed]

5.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998). [CrossRef]

6.

D. Chigrin, S. Enoch, C. Sotomayor Torres, and G. Tayeb, “Self-guiding in two-dimensional photonic crystals,” Opt. Express 11, 1203–1211 (2003). [CrossRef] [PubMed]

7.

D.W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29, 50–52 (2004). [CrossRef] [PubMed]

8.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačiv́, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and Erich P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5, 93–96 (2006). [CrossRef] [PubMed]

9.

X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251–3253 (2003). [CrossRef]

10.

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005). [CrossRef]

11.

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 90, 113121 (2007). [CrossRef]

12.

S. Shi, A. Sharkawy, C. Chen, D. Pustai, and D. Prather, “Dispersion-based beam splitter in photonic crystals,” Opt. Lett. 29, 617–619 (2004). [CrossRef] [PubMed]

13.

V. Zabelin, L. A. Dunbar, N. Le Thomas, R. Houdré, M. V. Kotlyar, L. O’Faolain, and T. F. Krauss, “Self-collimating photonic crystal polarization beam splitter,” Opt. Lett. 32, 530–532 (2007). [CrossRef] [PubMed]

14.

Z. Y. Li and L. L. Lin, “Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,” Phys. Rev. B 68, 245110 (2003). [CrossRef]

15.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopou, and C. M. Soukoulis, “Subwavelength resolution in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. Lett. 91, 207401 (2003). [CrossRef] [PubMed]

16.

V. P. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Photonic crystals - imaging by flat lens using negative refraction,” Nature 426, 404 (2003). [CrossRef] [PubMed]

17.

T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of Photonic crystal superprism and superlens,” Opt. Express 13, 10768–10776 (2005). [CrossRef] [PubMed]

18.

K. B. Chung and S. W. Hong, “Wavelength demultiplexers based on the superprism phenomena in photonic crystals,” Appl. Phys. Lett. 81, 1549–1551 (2002). [CrossRef]

19.

T. Baba and D. Ohsaki, “Interfaces of photonic crystals for high efficiency light transmission,” Jpn. J. Appl. Phys. 40, 5920–5924 (2001). [CrossRef]

20.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004). [CrossRef]

21.

B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal,” Appl. Phys. Lett. 87, 171104 (2005). [CrossRef]

22.

H. A. Macleod, Thin-film optical filters, (Adam Hilger Ltd, Bristol, 1986). [CrossRef]

23.

J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, “Systematic design of antireflection coating for semi-infinite one-dimensional photonic crystals using Bloch wave expansion,” Appl. Phys. Lett. 82, 7–9 (2003). [CrossRef]

24.

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Boston, 1995).

25.

M. Born and E. Wolf, Principles of Optics, (Cambridge University Press, Cambridge, 2002).

26.

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90, 231114 (2007). [CrossRef]

27.

Y. Zhang, Y. Zhang, and B. Li, “Optical switches and logic gates based on self-collimated beams in two-dimensional photonic crystals,” Opt. Express 15, 9287–9292 (2007). [CrossRef] [PubMed]

28.

J. -P. Berenger, “A perfectly matched layer for the absorption of electomagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]

OCIS Codes
(260.2030) Physical optics : Dispersion
(310.1210) Thin films : Antireflection coatings
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: January 28, 2008
Revised Manuscript: February 29, 2008
Manuscript Accepted: March 2, 2008
Published: March 13, 2008

Citation
Sun-Goo Lee, Jin-sun Choi, Jae-Eun Kim, Hae-Yong Park, and Chul-Sik Kee, "Reflection minimization at two-dimensional photonic crystal interfaces," Opt. Express 16, 4270-4277 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-6-4270


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References

  1. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999). [CrossRef]
  2. J. Witzens, M. Loncar, and A. Scherer, "Self-collimation in planar photonic crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002). [CrossRef]
  3. S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a negative refractive index," Phys. Rev. Lett. 90, 107402 (2003). [CrossRef] [PubMed]
  4. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001). [CrossRef] [PubMed]
  5. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, 10096-10099 (1998). [CrossRef]
  6. D. Chigrin, S. Enoch, C. Sotomayor Torres, and G. Tayeb, "Self-guiding in two-dimensional photonic crystals," Opt. Express 11, 1203-1211 (2003). [CrossRef] [PubMed]
  7. D.W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, "Dispersion-based optical routing in photonic crystals," Opt. Lett. 29, 50-52 (2004). [CrossRef] [PubMed]
  8. P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljaciv, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and Erich P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nat. Mater. 5, 93-96 (2006). [CrossRef] [PubMed]
  9. X. Yu and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003). [CrossRef]
  10. S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of selfcollimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 181106 (2005). [CrossRef]
  11. M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 113121 (2007). [CrossRef]
  12. S. Shi, A. Sharkawy, C. Chen, D. Pustai, and D. Prather, "Dispersion-based beam splitter in photonic crystals," Opt. Lett. 29, 617-619 (2004). [CrossRef] [PubMed]
  13. V. Zabelin, L. A. Dunbar, N. Le Thomas, R. Houdr’e, M. V. Kotlyar, L. O’Faolain, and T. F. Krauss, "Selfcollimating photonic crystal polarization beam splitter," Opt. Lett. 32, 530-532 (2007). [CrossRef] [PubMed]
  14. Z. Y. Li and L. L. Lin, "Evaluation of lensing in photonic crystal slabs exhibiting negative refraction," Phys. Rev. B 68, 245110 (2003). [CrossRef]
  15. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopou, C. M. Soukoulis, "Subwavelength resolution in a twodimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003). [CrossRef] [PubMed]
  16. V. P. Parimi,W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals - imaging by flat lens using negative refraction," Nature 426, 404 (2003). [CrossRef] [PubMed]
  17. T. Matsumoto, S. Fujita, and T. Baba, "Wavelength demultiplexer consisting of Photonic crystal superprism and superlens," Opt. Express 13, 10768-10776 (2005). [CrossRef] [PubMed]
  18. K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002). [CrossRef]
  19. T. Baba and D. Ohsaki, "Interfaces of photonic crystals for high efficiency light transmission," Jpn. J. Appl. Phys. 40, 5920-5924 (2001). [CrossRef]
  20. J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, "Mode matching interface for efficient coupling of light into planar photonic crystals," Phys. Rev. E 69, 046609 (2004). [CrossRef]
  21. B. Momeni and A. Adibi, "Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal," Appl. Phys. Lett. 87, 171104 (2005). [CrossRef]
  22. H. A. Macleod, Thin-film Optical Filters, (Adam Hilger Ltd, Bristol, 1986). [CrossRef]
  23. J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, "Systematic design of antireflection coating for semiinfinite one-dimensional photonic crystals using Bloch wave expansion," Appl. Phys. Lett. 82, 7-9 (2003). [CrossRef]
  24. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Boston, 1995).
  25. M. Born and E. Wolf, Principles of Optics, (Cambridge University Press, Cambridge, 2002).
  26. D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, "Photonic crystal Mach-Zehnder interferometer based on self-collimation," Appl. Phys. Lett. 90, 231114 (2007). [CrossRef]
  27. Y. Zhang, Y. Zhang, and B. Li, "Optical switches and logic gates based on self-collimated beams in twodimensional photonic crystals," Opt. Express 15, 9287-9292 (2007). [CrossRef] [PubMed]
  28. J. -P. Berenger, "A perfectly matched layer for the absorption of electomagnetic waves," J. Comput. Phys. 114, 185-200 (1994). [CrossRef]

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