Experimental demonstration of reflection minimization at two-dimensional photoniccrystal interfaces via antireflection structuresTeun-Teun Kim, Sun-Goo Lee, Myeong-Woo Kim, Hae Yong Park, and Jae-Eun Kim Citation: Applied Physics Letters 95, 011119 (2009); doi: 10.1063/1.3176949 View online: http://dx.doi.org/10.1063/1.3176949 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/95/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Two dimensional metallic photonic crystals for light trapping and anti-reflective coatings in thermophotovoltaicapplications Appl. Phys. Lett. 104, 021115 (2014); 10.1063/1.4862180 A flexible Bloch mode method for computing complex band structures and impedances of two-dimensionalphotonic crystals J. Appl. Phys. 111, 013105 (2012); 10.1063/1.3674281 Experimental studies of the internal Goos–Hänchen shift for self-collimated beams in two-dimensionalmicrowave photonic crystals Appl. Phys. Lett. 93, 131901 (2008); 10.1063/1.2980033 Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition Appl. Phys. Lett. 93, 121114 (2008); 10.1063/1.2992066 Enhanced light extraction efficiency from organic light emitting diodes by insertion of a two-dimensionalphotonic crystal structure J. Appl. Phys. 96, 7629 (2004); 10.1063/1.1815049

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Experimental demonstration of reflection minimization at two-dimensionalphotonic crystal interfaces via antireflection structures

Teun-Teun Kim,1 Sun-Goo Lee,2 Myeong-Woo Kim,1 Hae Yong Park,1 and Jae-Eun Kim1,a�

1Department of Physics, KAIST, Daejon 305-701, Republic of Korea2Photonics Research Laboratory, Division of Intelligent System Research, Korea Institute of Scienceand Technology (KIST), Seoul 130-791, Republic of Korea

�Received 20 May 2009; accepted 22 June 2009; published online 10 July 2009�

We experimentally confirm that the antireflection structures effectively minimize unnecessaryreflections of self-collimated microwave beams at the interfaces of a two-dimensional photoniccrystal, which is composed of cylindrical alumina rods. Optimized design parameters for theantireflection structures are obtained from the one-dimensional antireflection coating theory and thefinite-difference time-domain simulations. Measured transmittance through the photonic crystalsamples with and without the antireflection structures agree well with the simulation results. Themeasured results show that the photonic crystal with an antireflection structure yields about 90%transmission of incident power on the average in the frequency range of 12.0 to 13.0 GHz. © 2009American Institute of Physics. �DOI: 10.1063/1.3176949�

Photonic crystal �PC� structure, which consists of a pe-riodic array of dielectric material in space has been the sub-ject of intensive research in recent years. Since a PC struc-ture has forbidden propagation frequency ranges which arecalled photonic band gaps �PBGs�, there have been a numberof attempts to control the flow of light using the effect ofPBGs.1,2 In particular, it is well known that self-collimatedbeams of light can propagate with almost no diffraction in aPC.3,4 The group velocity of light given by vg=�k��k� de-termines the propagation direction of light in a PC which isalways normal to the equifrequency contours �EFCs�. Thus,self-collimation effect occurs in a PC whose band structurehas EFCs with flat sections. There are many attempts to ap-ply this phenomenon to optical integrated circuits, such aswaveguides, mirrors, beam splitters, super lenses, demulti-plexers, and so on.5–8

In general, the reflection at the ends of PC structuresmay seriously affect the performance of devices because thePCs are truncated and of finite sizes. Thus, the reduction ofunwanted reflection at the interfaces between a two-dimensional PC and uniform dielectrics is considered to bean important subject and still remains as a crucial problem. Anumber of solutions were proposed by using multilayeredgratings, adiabatic transitions, or antireflection layers.9–11

However, the proposed methods are complex and difficult tomanufacture for practical applications to the dispersion basedPC devices. Very recently, it was theoretically suggested thatthe reflection minimization at the PC interfaces can be opti-mized using the conventional antireflection coating �ARC�theory.12

In this letter, we experimentally demonstrate the reduc-tion in reflection at the ends of a square PC composed ofalumina rods in microwave range. The unwanted reflection atthe PC interfaces can be reduced by adding ARC structureswhich are optimized by changing the radii and positions ofrods. The measured transmissions are compared with the nu-merical results obtained by the finite-difference time-domain�FDTD� simulations.13

When the light beam meets interfaces at the normal in-cidence �see Fig. 1�a��, the reflection coefficient is given by

r =r12 + r23 exp�2i��

1 + r12r23 exp�2i��, �1�

where � is the phase change occurred during the time thelight goes across the region 2 and rij is the reflection coeffi-cient of the light propagating from the region i to j.14 Thedestructive interference between the two reflected beams oc-curs when the following two conditions are satisfied simul-taneously:

�r12� = �r23� , �2�

a�Electronic mail: jekim@kaist.ac.kr.

Region 1

(n1)

Region 2

(n2)

Region 3

(n3)

h

r12

r23

Antireflection Layer

(a)

(b)

Antireflection Structure

a

2Rdarc

Air Air

2Rarc

FIG. 1. �Color online� �a� In the conventional 1D case, the refractive indexn2 and the thickness h of an antireflection layer are the antireflection param-eters. �b� In the 2D PC case, the radius of rods RARC and the distance dARC

between the ARC structure and the crystal truncation are the design param-eters of the ARC structure.

APPLIED PHYSICS LETTERS 95, 011119 �2009�

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ei�2�+�23−�12� = − 1, �3�

where �rij� and �ij are the amplitude and the phase factor ofthe reflection coefficient rij, respectively. As a simple ex-ample, when the refractive index n2=�n1n3 and the opticalthickness h=� /4, we can easily see that no reflection occursfrom Eqs. �2� and �3�. If the region 3 is replaced by a one-dimensional �1D� PC, the zero reflection can also be ob-tained by using the r12 given by the Fresnel equations and r23given by the FDTD numerical calculations. To apply this 1Dcase to two-dimensional �2D� PCs, the radius RARC of the rodand the distance dARC between the ARC and the 2D PC arechosen as the design parameters of the ARC structure asdepicted in Fig. 1�b�. The value of RARC satisfying the con-dition given by Eq. �2� is to be found and then the value ofdARC to satisfy Eq. �3� at the optimized value of RARC.

Our 2D PC sample which has a band gap ranging from14.39 to 19.92 GHz is composed of 17�2a�28�2a squarearray of cylindrical alumina rods in air. The radius of rod is2 mm, the length 100 mm, and the lattice constant a 5 mm.The dielectric constant of the rods is approximately 9.7 in themicrowave region. The 2D PC sample with the ARC struc-ture shown in Fig. 2 is placed between two antennas, whichact as a source and a receiver, respectively. The source andreceiver horn antennas are set to pass the TM �the electricfield parallel to the axis of alumina rods� polarized micro-waves. Two acrylic plates with periodically drilled holes areplaced at the top and bottom of the structure to hold thealumina rods vertically. Also an aluminum foil is attached oneach of the acrylic plates to ensure the microwaves to be theplane waves between these two conducting sheets. The ex-perimental characterization was performed with a setupwhich consists of a network analyzer �Agilent 8722ES� andtwo microwave horn antennas �ETS Lindgren 3160–08�. Toremove any loss or other problems caused by cables or con-necting parts of the setup, the resulting frequency-dependentdata were normalized with the transmittance without the PCsample.

The EFCs are calculated using the plane wave expansionmethod15 to find the frequency range and the propagationdirection of the self-collimated light beam. It is well knownthat in an inhomogeneous medium the light propagates self-collimatedly in the same direction as the direction normal tothe flat EFCs. As can be seen in Fig. 3�a�, we find the lightsof microwave frequencies in the vicinity of 12.5 GHz canpropagate self-collimatedly along the �M direction in our2D square lattice PC. The self-collimation phenomena in ourPC can be verified by observing the beam profile as a func-

tion of position. Figure 3�b� shows the experimentally mea-sured transmission powers without any ARC structure and�c� with the ARC structure applied for the lights of frequen-cies from 12.1 to 12.9 GHz propagating along the �M direc-tion as a function of position. The black line with rectangularpoints indicates the transmittance measured without the PCat 12.5 GHz as the reference. The position-dependent trans-mitted power profiles which decrease as the receiver antennamoves away from the center of the sample show that theself-collimation phenomenon exists for the lights of frequen-cies around 12.5 GHz in our PC sample. In particular, Fig.3�c� shows that the broad band of self-collimated frequenciesis obtainable adding the ARC structure.

To find the optimal values of RARC and dARC for the lightof 12.5 GHz by using the FDTD simulations, we first calcu-lated �r23�, the reflection coefficient of the PC when the lightis incident on it from air, and then �r12�, the reflection coef-ficient of the ARC structure when the light propagates fromair to it, as shown in Fig. 1�b�. It is found that �r12�= �r23�=0.459 at RARC=1.15 mm�=0.23 a�. The total reflectance isobtained by using the FDTD simulations as a function ofdARC when RARC=1.15 mm and found that the reflectancebecomes zero when dARC=3.60 mm�=0.72 a�. Next, theFDTD simulations are performed for the PC sample of17�2a in the �M direction. We apply the Bloch periodicboundary condition in the x direction and the perfectlymatched layer �PML� absorbing boundary condition is usedin the y direction. The ARC structures of the same param-eters are introduced to both the input and output PC inter-faces.

Acrylic plateAluminum

foil

Alumina rods

x

yz

FIG. 2. �Color online� Schematic diagram of the PC with the ARC structure.Two acrylic plates, each with an aluminum sheet attached hold the samplevertically.

(b)

Normalizedtransmission(dB)

Ref.

12.1 GHz

12.3 GHz

12.5 GHz

12.7 GHz

12.9 GHz

-6 -4 -2 0 2 4 6

-40

-30

-20

-10

0

Position ( 2a)

(a)

kx(2π/a)

0 0.2 0.4-0.2-0.4

-0.4

-0.2

0

ky(2π/a)

0.2

0.4

12.3 GHz

12.7 GHz

12.5 GHz

Γ Χ

Μ

Ref.

12.1 GHz

12.3 GHz

12.5 GHz

12.7 GHz

12.9 GHz

-6 -4 -2 0 2 4 6

Position ( 2a)

-40

-30

-20

-10

0

(c)

FIG. 3. �Color online� �a� Equifrequency surfaces of the 2D PC which areobtained by the plane-wave expansion method. The inset represents thecross-sectional view of the 2D square lattice PC composed of alumina rods��=9.7� in air. �b� Transmittance of microwaves without any ARC structureand �c� with the ARC structure applied for the frequency range of 12.1 to12.9 GHz propagating along the �M direction as a function of position. Theblack line with rectangular points indicates the reference transmission whichis measured without the PC at 12.5 GHz.

011119-2 Kim et al. Appl. Phys. Lett. 95, 011119 �2009�

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Figure 4�a� displays the transmission spectra of the PCobtained with the FDTD calculations with �red line� andwithout �black line� the ARC structure in the spectral rangebetween 11.5 and 14.0 GHz. Shown in Fig. 4�b� are theexperimentally measured transmission spectra of the PCsample with and without the ARC structure applied in thesame frequency range. One can see that a good agreementexists between the FDTD simulations and our experimentallyobtained results. When the ARC structure is not introduced,the transmitted light power through the PC exhibits oscilla-tory behavior in both the simulated and measured spectra.This phenomenon is caused by the constructive and destruc-tive interferences of multiply reflected and transmitted lightbeams at the PC interfaces. But with the ARC structure em-ployed �the red curves in Figs. 4�a� and 4�b��, the oscillationsin the transmission spectra disappear exhibiting nearly flattransmission spectra in the frequency range of 12.0 to about13.0 GHz. Almost 100% transmission through the PC is ex-pected from the FDTD simulations in the frequency range of12.0 to 13.0 GHz, but measured spectra with small fluctua-tions yield about 90% transmission of incident power on theaverage. This difference between the simulation and experi-mental results may be due to the limitation of 2D calcula-tions in which the vertically leaky modes are not consideredand/or other experimental losses such as the loss tangent forthe alumina at microwave frequencies.16 Thus, it is demon-strated that the application of optimal ARC structure caneffectively suppress the unwanted reflection at the 2D PCinterfaces.

In conclusion, we have experimentally demonstrated asimple and effective method to eliminate unwanted reflection

at the interfaces between a 2D PC composed of a squarearray of alumina rods and a homogeneous background mate-rial. Transmission of light beams can be improved by opti-mizing the parameters of the ARC structure such as RARC

and dARC. This result opens promising perspectives towardimproved performance of PC devices for practical applica-tions.

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Frequency (GHz)Frequency (GHz)

Normalizedtransmission(dB)

Normalizedtransmission(dB)

11.5 12.0 12.5 13.0 13.5 14.0 11.5 12.0 12.5 13.0 13.5 14.0

0

-10

-20

-30

-40

0

-10

-20

-30

-40

W/O ARC

ARCWith

W/O ARC

ARCWith

FIG. 4. �Color online� �a� Transmission spectra ob-tained with the 2D FDTD calculations for the PCsample with �red line� and without the ARC �black line�structure. �b� Experimentally measured transmissionspectra of the PC sample which are composed of alu-mina rods with �red line� and without the ARC �blackline� structure.

011119-3 Kim et al. Appl. Phys. Lett. 95, 011119 �2009�

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