PHOTONIC CRYSTALS
ENHANCED TRANSMISSION and BEAMING via PHOTONIC CRYSTAL SURFACE MODES
A interesting property of metal surfaces is the surface plasmons due to the negative permittivity of the metals at some frequency range. Recently, surface plasmons attracted great interest in the scientific community due to the possibiliy of enhanced transmission through a sub-wavelength hole on a metallic surface. Ebessen et. al demonstrated the enhanced transmission of electromagnetic wave through a sub-wavelength hole surrounded by concentric grooves. Moreover, several researchers have demonstrated the beaming effect due to surface plasmons. The possibility of enhanced transmission through a sub-wavelength is of great scientific and thechnological importance. Many novel applications may be realized, such as sub- _wavelenth imaging, large capacity dense optical storage media, sub-wavelength waveguides.
An intrinsic property of metals greatly limits the performance of surface plasmon based applications. Namely, the ohmic losses is an important issue for metals. This brings the following question in mind: is it possible to obtain optical modes that share similar properties to surface plasmons by using dielectric structures? The anology with semiconductor crystals suggest that photonic crystals may support such modes. Photonic crystals support surface propagating electromagnetic waves provided that the surface of the photonic crystal is appropriately terminated. The corrugation may be achieved by reducing the rod radius at the surface of the photonic crystal or by using rods of different shape. The photonic crystal that we used in our study is a 2 dimensional square array of circular alumina rods. The radius of the rods is 1.55 mm. The dielectric constant of alumina is 9.61 and the lattice constant is 11 mm. For this study we changed the radius of the rods at the surface of the photonic crystal from 1.55 mm to 0.76 mm. The plane-wave expansion method can be used to calculate the modes of a fnite size photonic crystal such as the one used in our work by employing a large enough supercell. The supercell has rectangular geometry and it consists of 40 layers long along y axis and 1 unit cell along x axis. 15 unit cells along y axis contains alumina rods and the rest is free space. The modes of our finite size photonic crystal (infinitely periodic along one of the axis and finite in the other axis) can be classified into 4 parts: 1) modes extending both in air and photonic crystal , 2) modes extending in air but decaying in photonic crystal , 3) modes decaying in air but extending in photonic crystal , 4) modes bound to the surface of the photonic crystal (Figure 1).
Figure 1: Modes of the finite size photonic crystal a) electric field profile of mode extending both in air and photonic crystal b) electric field profile of mode extending in air but decaying in photonic crystal c) electric field profile of mode decaying in air but extending in photonic crystal d) electric field profile of surface mode.
Figure 2 shows that when the corrugation is added a band below the light line appears in the band structure (This band is shown with blue solid curve ).This band is inside the photonic band gap and extends from 11.9 GHz to 12.8 GHz. The electric field corresponding to these modes is bound to the surface i. e., the electric field for these modes is evanescent both in air and inside photonic crystal. However, these modes have real wave vectors parallel to the PC surface. As a result, these modes are surface propagating waves.
Figure 2: TM band structure of the finite size photonic crystal when the radius of the rods at the surface of the photonic crystal is reduced to 0.76 mm.
Since the surface propagating modes lie below the light line they can not be excited by incident plane waves. A conversion mechanism is required. The conversion may be achieved either by transforming the incident plane wave to an evanescnet wave or by a translation of the wavevector. Wave vector translation can be achieved by adding a grating-like structure to the surface of the corrugated photonic crystal, i.e., by adding an extra layer with a suitable lattice constant. We added an extra layer in front _of the corrugated photonic crystal surface. The added layer is composed of alumina rods with a radius of 1.55mm and a lattice constant of 22 mm. The _coupling to the surface modes of the photonic crystal can then be observed by measuring the reflection spectrum. We measured the reflection spectrum _by using HP-8510C vector network analyzer and transmitting-receiving horn antennas. When the grating-like layer is added to the surface of the _corrugated photonic crystal, the resulting structure exhibits a dip in the reflection spectrum around 12.4 GHz. The magnitude of the reflection coefficient _is -32 dB at 12.4 GHz. The dip in the reflection spectrum clearly shows that due to the grating-like structure the incident EM waves effectively couples _to the surface modes of the corrugated photonic crystal around 12.4 GHz.
_Figure 3: Measured reflection spectrum from (A) bare photonic crystal surface (B) from _the corrugated layer added photonic crystal surface (C) from the corrugated photonic _crystal surface when the grating-like structure is added.
Waveguide structures are important components for photonic devices. Several waveguide structures based on photonic crystals have been proposed and demonstrated. One major problem with the photonic crystal based waveguides is the low transmission efficiency. The low transmission efficiency is usually attributed to the poor coupling between the incident wave and the waveguide modes of the photonic crystal waveguide. The coupling efficiency may be improved by means of a matching. This matching may be obtained by utilizing the surface modes.
Our photonic crystal waveguide was obtained by removing one row of rods from a 21x15 square array of circular alumina rods. The crystal is 15 layers long along the propagation direction. The photonic crystal waveguide structure has waveguiding band between 9.7 GHz and 13.1 GHz. The overall transmission efficiency through out the waveguiding band is around %10 when compared to free space transmission. At 12.45 GHz the transmission efficiency is %11. These results show that the transmission efficiency of our photonic crystal waveguide is low. We added an extra layer of rods with a radius of 0.76 mm and a grating-like layer to the input surface of the photonic crystal. This arrangement creates surface modes and enables efficient coupling of incident waves to the surface modes. Addition of these extra layers resulted in enhanced transmission through the photonic crystal waveguide. The transmission was increased to %53 for the photonic crystal waveguide with the surface modulation. These results indicate that efficient coupling to the photonic crystal waveguide modes can be achieved via surface propagating waves (Figure 4).
Figure 4: A) The measured, B) the calculated transmission spectrum through the photonic crystal waveguide, C) the measured, D) the calculated transmission spectrum through the photonic crystal waveguide when the surface corrugation and the grating-like structure is added in front of the input surface of the photonic crystal waveguide.
The EM waves emitted through a sub-wavelength aperture quickly diffract in all directions. The photonic crystal waveguide that we used in this study has a width smaller than the operation wavelength. The operation wavelength is around 2.5 cm, whereas the waveguide width is 1.9 cm. Hence,the EM waves emitted through the photonic crystal waveguide would difract in all directions from the photonic crystal waveguide aperture. Our experiments confirm this expectation (Figure 5).
Figure 5: A) The measured intesity distribution at the exit side of the photonic crystal waveguide. Y-axes is parallel to the photonic crystal surface.
On the other hand, when an extra layer of rods with a radius of 0.76 mm and a grating-like layer was added to the output surface of the photonic crystal the EM waves leaving the aperture of the PC waveguide was confined to a narrow spatial region (Figure 6).
_Figure 6: A)The measured intesity distribution at the exit side of the photonic crystal waveguide when the corrugation and grating-like layer are added _to the exit surface of the photonic crystal waveguide. Y-axes is parallel to the photonic crystal surface.
Negative refraction and subwavelength focusing using photonic
crystals
Metallodielectric photonic crystals with negative refraction and
focusing
Highly directional radiation using sources embedded in photonic
crystals
Coupling and phase analysis of cavity structures in photonic
structures
Enhanced transmission and beaming via photonic crystal surface
modes
Plasmonic Structures
With Highly Directional Beaming Properties
| About NANOTAM | Facilities | People | Research |Publication | Seminars |
| Home | News | Bilkent University | Contact |
© Copyright - com.web.tr. This page is best viewed with IE v.5.0 or higher, at minimum 1024x768 resolution.