22G17
Simultaneous formation of microwave plasma and negative refractive index
state with metamaterial effects
メタマテリアル効果によるマイクロ波プラズマと負屈折率状態の同時形成現象
Osamu Sakai and Satoshi Iio
酒井 道, 飯尾 聡
Department of Electronic Science and Engineering, Kyoto University
Kyoto-daigaku Katsura, Nishikyo-ku, Kyoto 615-8510, Japan
京都大学 工学研究科電子工学専攻 〒615-8510 京都市西京区京都大学桂Microwave plasmas with high electron density can be generated in a metamaterial structure with negative
permeability. In a conventional scheme in which the permeability is unintentionally positive, the cutoff
phenomenon against propagating microwaves restricts electron density which represents positivepermittivity in the discahrge space; when the electron density exceeds the cutoff density, the refractive
index becomes imaginary, and the waves cannot propagate furthermore. However, since the concept of“metamaterials” allows us to obtain a negative-permeability state, the refractive index becomes real andnegative when a plasma has high electron density, leading to negative permittivity, and with negativepermeabity. In this study, we predict bifuration of solutions in a nonlinear system where a high-densitymicrowave plasma is geenrated wimultaneously with negative refractive index, and demonstrated
experimentals results which cannot be comprehended using previous understandings.

1. Introduction
Plasma reactors in which plasmas are generated
by high-power microwaves are one of the mainprocessing tools in the industrial fabrication for
semiconductor devices. In a reactor without anexternal magnetic field, electron density islimited up to the so-called cutoff density sincerefractive index becomes imaginary in an
overdense plasma and microwaves for plasma
generation cannot propagate inside it. To
overcome this difficulty to obtain high-density
microwave plasmas, one solution is to excite
surface waves which can support plasma
generation with higher density than the cutoff
density, and surface wave reactors are suitable fora large-area plasma processing such as thin film
deposition and surface treatment of flat substrates[1]. In such plasma reactors, electron density
usually depends on the frequency of the excitedsurface wave, and is not a direct function of input
microwave power.
In our recent report, we proposed anotherscheme for high-density microwave plasmas inwhich the concept of metamaterials [2,3] areapplied [4]. In ordinary materials, permeability is
positive and unity except some materials such as
ferrites in microwave regions. However, using
metamaterials which contains much smaller
periodic length of microstructure than a given
electromagnetic wave, a volumetric metamaterial

becomes a negative-permeability (negative-  )space which includes free spaces with small
volume fraction of metallic components. In such aspace without a plasma, microwave cannot
propagate since permittivity  is positive andthe refractive index N is imaginary, according
to the relation:N   .

(1)

When there is an overdense plasma whose  isnegative, N becomes real and negative, andmicrowave can propagate to sustain a high-density
plasma. Interesting point is that electron density isunlimited, unlike the cases of the surface wave
excitation.
One missing point in the above argument isthat a state should pass through an imaginary- N
state when a microwave starts to propagate andignite plasma with fairly low density. In this report,we briefly overview a process underlying thisscheme using theoretical predictions. We also
demonstrate extraordinary phenomena observed inexperiments; transmitted microwave increased
when plasmas were generated, which cannot be
explained with our usual experimentalist’s
knowledge saying that microwaves should decrease
due to power absorption after plasma generation.

2. Theoretical Prediction
The detailed prediction based on numerical andanalytical approaches is found in our recent report[JAP2011], and here we describe the points
associated with experimental results.
We performed numerical calculation of
propagating microwaves at 2.45 GHz using afinite-difference time-domain (FDTD) method.
When we set negative  in a certain area, thewaves cannot propagate in cases of positive  ;electric fields inside the structure is extremely low.
On the other hand, they can propagate in cases ofnegative  with large electric field though thecalculated region, and their properties indicate
negative- N state such as reversed phase velocity
and negative refraction angle on the interface.
In contrast, when we see a formula of  in aplasma expressed in the Drude model, given as  1

pe 2
 2 (1  j m / )e 2 ne 1,
 0 me 2 (1  j m / )(2)

where is the wave frequency, the electron
plasma frequency, the electron elastic collision
frequency, ne is the electron density, theelementary charge, the vacuum permittivity, andthe electron mass. Because  does not include a
step-wise function of ne around zero, the electricfields inside the structure varies smoothly, unlike
the step-wise function. This discrepancy between
two facts yields bifurcations of solution of  .
3. Experimental Results
We installed a rectangle waveguide inside avacuum chamber, and double split ring resonators(DSRRs)[3] with a resonance frequency around2.45 GHz occupied the inside of the waveguide forabout 10 cm along the axis, which indicate that in the region of the DSRRs may become negative.
Before and after this region, we set directional
couplers to detect input and output microwave
power at 2.45 GHz. Ar gas at 0.5 kPa occupied theentire volume of the chamber.
DSRRs work as wave energy “condenser” due to
its resonant property as well as a component of anegative- material, leading to enhancement of
the electric field near the structure. Microwaves
with several tens of watts ignited plasmas aroundthe DSRRS, and the microwave
When plasmas were ignited around the DSRRs,
we observed increase of transmitted microwaves;this is an abnormal phenomenon for plasma
generation, since input energy is consumed in theplasma region. However, according to theprediction shown in Section 2, this increase is quitereasonable for possible generation of thenegative- N state with an overdense plasma.
Further experiments will verify detailed spaceparameters and their features in the region aroundthe DSRRs.
4. Conclusion
A negative-  state induces quite different
phenomena which have not been observed inconventional discharge spaces. The concept of thisnew scheme is based on the recent progress of
researches on metamaterials, and leads tohigh-density microwave plasma generation.
Experimental results were partly predicted bytheoretical approaches.
Acknowledgments
This work was partly supported by aGrant-in-Aid for Scientific Research from theJapanese Ministry of Education, Culture, Sports,
Science and Technology.
References[1] I. P. Ganachev and H. Sugai H: Surf. Coat. Technol.
200 (2005) 792.
[2] A. Sihvola, Advances in Electromagnetics ofComplex Media and Metamaterials (Kluwer,Dordrecht, 2002)[3] J. B. Pendry, A. J. Holden,D. J. Robbins and W. J.
Stewart: IEEE Trans. Microw. Theory Tech. 47(1999) 2075.
[4] O. Sakai: J. Appl. Phys. 109 (2011) 084914.