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olarization response of two-dimensional metallichotonic crystals studied by terahertzime-domain spectroscopy

umiaki Miyamaru and Masanori Hangyo

The polarization characteristics of a terahertz �THz� wave transmitted through two-dimensional �2-D�metallic photonic crystals �MPCs� are investigated. The 2-D MPCs studied in this paper are metal slabsperforated periodically with circular holes. We measured the polarization characteristics of the THzwave using a THz time-domain spectroscopic system with wire grid polarizers in the time and frequencydomains. The linearly polarized incident THz wave changes its polarization direction and becomeselliptic after it transmits through the sample. This phenomenon is highly sensitive to the incident angle.It is shown that the frequency range at which the polarization rotation occurs is related to the latticeconstant of a photonic crystal, indicating the importance of photonic band modes of the 2-D MPC in themechanism of the phenomenon. © 2004 Optical Society of America

OCIS codes: 230.5440, 240.6680, 260.3910.

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hotonic crystals with structures of the order of anptical wavelength have been the focus of attention inecent years because of their potential use in opticalpplications. These materials have photonicandgaps at wavelengths comparable with the latticeonstant of a periodic structure if the structure isppropriately designed. By use of photonic crystals,any attractive optical devices can be manufactured,

uch as waveguides,1–3 and filters.4As materials for photonic crystals, metals have be-

ome important in recent years. Since metals inter-ct strongly with light, fascinating optical devices cane constructed.5–9 Two-dimensional �2-D� metallichotonic crystals �MPCs�, which are metal plates per-orated periodically with circular holes, have beennown as high transmittance bandpass filters in theillimeter and terahertz �THz� wave regions.10,11

ecently, anomalous transmission properties causedy surface-plasmon polaritons have been reported bybbesen et al.12,13 for this type of 2-D MPCs with holeiameters smaller than the incident wavelength in

F. Miyamaru �miyamaru@rcsuper.osaka-u.ac.jp� and M. Hangyore with the Research Center for Superconductor Photonics, Osakaniversity, Yamadaoka 2-1, Suita, Okaka. 565-0871, Japan.Received 1 July 2003; revised manuscript received 14 October

003; accepted 11 November 2003.0003-6935�04�061412-04$15.00�0© 2004 Optical Society of America

412 APPLIED OPTICS � Vol. 43, No. 6 � 20 February 2004

he visible region. Interesting characteristics of a-D MPC are expected not only in the transmissionroperties but also in the polarization properties, be-ause metals bend the electric field of the incidentlectromagnetic wave strongly. However, little in-estigation of the polarization characteristics for the-D MPC has been reported so far.In a previous paper, an interesting feature of the

-D MPC was reported, that is, the polarization ro-ation caused by slight tilting of the incident angle.14

or the 2-D MPC, the photonic band modes consist ofurface-plasmon polariton modes localized at theetal surface. Such photonic band modes play im-

ortant roles in the high transmittance bandpassharacteristics of the 2-D MPC in the THz wave re-ion as well as in the visible region. The photonicand modes of the 2-D MPC can also be important forhe phenomenon of polarization rotation of the THzave transmitted through the 2-D MPC. Here we

nvestigate the incident angle dependence of the phe-omenon of the polarization rotation and the relationetween this phenomenon and the photonic bandodes of the 2-D MPC.The 2-D MPCs have a triangular lattice structureith circular holes. Figure 1 is a photograph of a-D MPC. The transmission characteristics of the-D MPC are determined by three parameters, i.e.,iameter of circular holes d, lattice constant s, andhickness of metal plate t. The principal axes of tri-ngular lattices a and b are also shown in Fig. 1.

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We measured the transmission characteristics ofhe 2-D MPC in the THz wave region by using theHz time-domain spectroscopic system. With thisystem we measured the temporal waveform of theHz wave transmitted through the 2-D MPC. Toeasure the polarization characteristics of the 2-DPC in the time domain, we inserted three wire grid

olarizers into a conventional THz time-domain spec-roscopic setup. The incident THz beam diameteras limited by the 10-mm-diameter aperture located

n front of the sample. The sample size was largerhan the aperture size, and the finite size effect15 ofhe transmission characteristics could be negligible.etails about the experimental setup are described inprevious paper.14

Figure 2�a� shows the measured waveform of thencident THz wave. The incident THz wave is al-

ost a one-cycle pulse and is linearly polarized.igure 2�b� shows the measured waveform of the THzave transmitted through a 2-D MPC at � � 3° and� 45°, where � is the incident angle and � is the

zimuth angle. The azimuth angle is the angle be-ween the polarization of the THz wave and the prin-ipal axis a of the 2-D MPC. The dashed and solidurves indicate the waveforms of Ex and Ey, which arehe parallel and perpendicular components of theHz wave transmitted through the 2-D MPC withespect to the incident THz wave polarization, respec-ively. More than a twenty-cycle oscillation is ob-erved in Ex of the THz wave whereas the incidentHz wave is almost a one-cycle pulse. Such oscilla-

ion is due to the bandpass characteristics of the 2-DPC.16 The electric field amplitude of Ey has a fi-

ite amplitude although the electric field of the inci-ent THz wave is linearly polarized along the xirection. The phase of Ey is slightly shifted withespect to that of Ex. For clarity, the enlarged figures shown in the inset. These results indicate thathe polarization of the THz wave rotates and that itecomes elliptical after transmitting through a 2-DPC.14

To investigate this phenomenon in detail, we mea-ured the incident angle dependence of Ex and Eyransmitted through the 2-D MPC. Figures 3�a�–�e� show the temporal variation of the electric fieldmplitude of Ex and Ey for incident angles of 3°, 6°, 9°,2°, and 15°, respectively. Azimuth angle � is fixed

t 45°. The electric field amplitudes of Ex and Eytrongly depend on the incident angle, indicating thatolarization of the THz wave can be changed by tilt-ng the incident angle slightly. Figures 3�f �–3�j�how the ellipticity spectra of the THz wave for theame incident angles of Figs. 3�a�–3�e�. Ellipticity �s obtained from the Fourier components Ex��� andy��� calculated from the time-domain waveformsx�t� and Ey�t� transmitted through the 2-D MPC,17

espectively, as

���� � tan�12

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��� �AEy

���

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here � is the frequency of the THz wave. AEx���

nd AEy��� are amplitudes of the Fourier components

f Ex��� and Ey���, and � is the phase delay betweenhem. In Fig. 3�f � there are two positive peaks andne negative peak at 0.28, 0.32, and 0.3 THz, respec-ively. The ellipticity in other spectral regions isearly zero. This means that the polarization rota-ion occurs only in the spectral region from 0.28 to.32 THz in Fig. 3�f �. The two positive peaks shift tohe lower and higher frequency sides when the inci-ent angle increases Figs. 3�g�–3�j��. The reason

ig. 2. Measured waveforms of the THz wave. �a� The incidentHz wave. �b� The THz wave transmitted through a 2-D MPC forx �dashed curve� and Ey �solid curve�, which are the parallel anderpendicular polarization components of the THz wave transmit-ed through the 2-D MPC with respect to the incident THz waveolarization, respectively. The inset shows the enlarged wave-orm in the time range from 40 to 80 ps.

ig. 1. Photograph of the 2-D MPC with hole diameters of d �.68 mm and spacing between holes of s � 1.1 mm. The samples made of an aluminum slab with thickness t � 0.5 mm.

20 February 2004 � Vol. 43, No. 6 � APPLIED OPTICS 1413

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he ellipticity peak shift is considered is as follows.orto et al.18 reported that the photonic band modesf a 2-D MPC are constructed from surface-plasmonolariton modes19 that are excited on the surface of a-D MPC by an incident THz wave. The resonantrequency at which the incident THz wave couples tohotonic band modes of the 2-D MPC changes whenhe incident angle is varied following the dispersionelation of the photonic band modes. In the case ofone-dimensional slit array of Porto et al., the lowest

wo resonant frequencies at k � 0 �k is the in-planeave vector� shift to lower and higher frequency sideshen the wave-vector component increases along the

urface. Although, in the case of 2-D MPC, the dis-ersion relation of the photonic band mode dependsn the direction of the wave vector �ex., –M or –Kirection�, the trend of the resonant frequency shift isonsidered to be similar to that of a one-dimensionallit array. The ellipticity peak shift observed inigs. 3�f �–3�j� agrees with the resonant frequencyhift of the photonic band modes qualitatively.rom this we conclude that the polarization rotationf the THz wave is closely related to the photonicand modes that are constructed from the surface-lasmon polaritons.To obtain the relation between the lattice constant

f the 2-D MPC and this phenomenon, we measuredhe ellipticity spectra of the THz wave for four sam-

ig. 3. �a�–�e� THz waveforms of Ex �dotted curve� and Ey �solidurve� components, �f �–�j� ellipticity spectra obtained from theaveforms of Ex and Ey components for various incident angles

rom 3° to 15°.

414 APPLIED OPTICS � Vol. 43, No. 6 � 20 February 2004

les with different lattice constants. Figures 4�a�–�d� show the ellipticity spectra of the THz wave forhe 2-D MPCs with lattice constants of 0.86, 1.00,.32, and 1.67 mm. The hole diameter is d � 0.74m and the thickness of the metal plate is t � 0.5 mm

or all the samples. Incident angle � and azimuthngle � are � � 3° and � � 45°, respectively. In Fig.�a� there are positive and negative peaks at 0.37 and.39 THz, respectively. The spectral region in whicholarization rotation occurs shifts to the lower-requency side where the lattice constant of the 2-D

PC increases. The resonant frequency �res at nor-al incidence �� � 0°� for a triangular lattice is ex-

ressed as

�res �2c

�3nsps, (3)

here nsp is the effective refractive index of theurface-plasmon polaritons and c is the speed of lightn vacuum. Since the dispersion relation betweenhe frequency and the wave number of the surface-lasmon polariton is almost the same as that of theight in vacuum,19 we can assume that nsp � 1 in Eq.3�. The resonant frequencies at normal incidenceor four samples are indicated by arrows in Fig. 4.trictly speaking, at � � 3°, the resonant frequencyplits into some frequencies and shifts with respect tohat at � � 0°. The resonant frequency at � � 3° is,owever, close to that at � � 0°. The spectral ranget which the polarization rotation occurs agrees wellith the resonant frequency for all the samples.ur experimental results provide the evidence that

he photonic band modes constructed from theurface-plasmon polariton modes play an important

ig. 4. Measured ellipticity spectra for the 2-D MPCs with latticeonstants of �a� 0.86, �b� 1.0, �c� 1.3, and �d� 1.7 mm. The arrowshow the resonant frequencies of the surface–plasmon polaritonodes at normal incidence.

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ole in the polarization rotation of a THz wave trans-itted through a 2-D MPC.In summary, we investigated the polarization char-

cteristics of a 2-D MPC using THz time-domainpectroscopy. The polarization rotation of the THzave transmitted through the 2-D MPC is observedy tilting the incident angle slightly. Such polariza-ion rotation phenomenon is highly sensitive to thencident angle. Since this phenomenon is observedround the resonant frequency at which the incidentHz wave couples with the photonic band modes, it isonsidered that the phenomenon of the polarizationotation of the THz wave transmitted through the-D MPC is related to the photonic band modes of the-D MPC.

We thank M. Tani and T. Nagashima for fruitfuliscussions. This research was partially supportedy a Grant-in-Aid for Scientific Research from theinistry of Education, Culture, Sports, Science, andechnology, Japan.

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