> Ibjbj"]^NNNN---Z\\\\\\$7+V-)---NN-NNZ-Z:$,ZN!P
Dispersion plots for photonic crystals from infinitely long perfectly conducting spirals
C. R. Simovski1
1 Department of Physics, St. Petersburg State Institute of Fine Mechanics and Optics
Sablinskaya Street 14, 197101 St. Petersburg, Russia
email: simovsky@phd.ifmo.ru
Abstract
An analytical model of dispersion is presented for 2D lattice of inclusions. These inclusions are infinitely long perfectly conducting helices at microwaves. It is shown that such structure possess high opportunities for the dispersion properties control and can be used as the excellent polarization filters. We studied photonic crystal from the grid of array of spirals. This grid consists of two orthogonal sets of parallel spirals. In our model we ignore the interaction between mutually orthogonal spirals. So, the plane-wave reflection from such a grid is considered as two additive reflections from both parallel sets of spirals. For the purpose of computer calculations, we use a model of a spiral excitation as that of a line of magnetic current and a line of electric current flowing along the axis of the spiral. We suggest that this substitution changes not too much. The model of such a spiral has been already developed by V.V. Yatsenko [1]. This theory allows to get values of reflection coefficients from the dense (period is smaller than the wavelength) arrays of infinitely long spirals from perfectly conducting wires. Another restriction is that the spiral step is much smaller than the wavelength. After evaluating the reflection (R) and transmission (T) coefficients of a single grid we apply the method of S.L. Prosvirnin [2]. It allows us to get the dispersion equation for the periodical layered structure of arbitrary parallel layers, knowing only the R and T. There are two conditions under which this theory works. First, the distance between layers must be lager than the maximal internal period of a layer ( distance between spirals and the step). Second, the reflection tensor must be of the following structure (in the dyadic form): INCORPORER Equation.3 , where INCORPORER Equation.3 and INCORPORER Equation.3 are two orthogonal orts. This condition is implied in our problem formulation.
Main results obtained for realistic parameters of conducting spirals at microwaves are as following:
the group velocity can be negative at the frequencies lower the edge of the first band gap, so we can have for such crystals an effect of backward waves at low frequencies. Here we can consider the lattice as a continuous medium. It shows in this case the properties similar to those of a meta-material ( INCORPORER Equation.3 and INCORPORER Equation.3 are both negative).
with another set of parameters we obtain that the eigenwave polarization is perfectly circular. E.g. the left-handed polarization is prohibited (first band gap) and the right-handed is allowed ( for it the frequency belongs to the second pass-band).
So, we expect that such structures can possess very interesting properties.
References
[1] V.V. Yatsenko, Int. J. of Appl. Electromagn. Mechanics. 9, 191 (1998).
[2] S.L. Prosvirnin, Proc. 8-th Int. Conf. on Electromagn. Complex Media, Lisbon, Portugal, 27-29 Sept. 2000, 241.
YZijlnTU]^:
!"#+,DEFGLMefghwx
OPhijkpq㓊jB*EHUjԊ?
UVmHmH
jEHUj^?
UVmH
jEHUjL?
UV jUjB*EHUj?
UVmHjB*UB*NHB*NHCJPJPJCJmHCJH*>*CJCJ3YZjkl
B
$7Wdhd
&Fd
d
d
d
7$dddxYZjkl
Bt
\
1234BW6CJ
6B*CJB*CJCJ5CJmH B*NHB*jB*UjlB*EHUjԊ?
UVmHB
$7Wd. A!"#$%DdhB
SA?2.Nå/(7
zE
D`!Nå/(7
zE@&|xڝ?K@]cV TE:8!`-AH['_@pAGQPA\\A0$'{{/G (>fz%ĕmKՅFg($cLGlt(S&y6=®|u#W6VyMUKfE7ka[оVKI(bd =h{|ԍ\I l?Dہ)'6N2x<~xVV+m10V&wyR;{|[NqlR5K]
xU|\"iDd<
CA2m hXI`!A hX ȽHxcdd`` @c112BYL%bpu;1 ϟ
h7T
obIFHeA*L
N`A $37X/\!(?717k30I] h8W!H @c112BYL%bpuw
"t
FMicrosoft Equation 3.0DS EquationEquation.39q%{
2gEquation Native
-_1065950046 Fn!n!Ole
CompObjfObjInfoEquation Native -_1066063028Fn!n!Ole
FMicrosoft Equation 3.0DS EquationEquation.39q
FMicrosoft Equation 3.0DS EquationEquation.39qCompObjfObjInfoEquation Native )_1066063054F`&x!`!Ole
CompObjfObjInfoEquation Native )
Oh+'0
4@L
Xdlt|%ssAntnio L. TopantntNormal.dotTbisbisd2sbMicrosoft Word 8.0@@6eb@1Table*SummaryInformation(DocumentSummaryInformation8!CompObj)jC~!@C~!z
՜.+,D՜.+,Hhp
Instituto de Telecomunicaes-1%Titre 6>
_PID_GUIDAN{2470C181-A796-11D5-BFBB-0000B436C415}
FDocument Microsoft Word
MSWordDocWord.Document.89q
[0@0Normal_HmH sH tH 4@4Titre 1$$@&a$5\22Titre 2$@&
5CJ\88Titre 3$$@&a$
5CJ\88Titre 4$
7@@@&CJ2A@2Police par dfaut6B6Corps de texte$a$6>@6Titre$a$5CJ OJQJ\FP@FCorps de texte 2$
a$CJNQ"NCorps de texte 3
7BCJmHsH4Z24
Texte brutOJQJmH "B
"+DFLegO
h
j
p
:::::8@0(
B
S ?aiSWXb@
D
&FJKUW[gkp{XZil
ABAntnio L. TopaZD:\Conferncias\Bianisotropics\Bianisotropics 2000\Organizing Committe\Web Page\sample.docAntnio L. Topa[D:\Conferncias\Bianisotropics\Bianisotropics 2000\Organizing Committe\Web Page\sample2.docAntnio L. Topa[D:\Conferncias\Bianisotropics\Bianisotropics 2000\Organizing Committe\Web Page\sample2.docAntnio L. Topa[D:\Conferncias\Bianisotropics\Bianisotropics 2000\Organizing Committe\Web Page\sample2.docbisbis$C:\WINDOWS\Bureau\Nouveau\sample.docConstantin R. SimovskiC:\TEMP\sample.docConstantin R. Simovski$C:\WINDOWS\TEMP\2B>:>?8O sample.asdConstantin R. Simovski$C:\WINDOWS\TEMP\2B>:>?8O sample.asdConstantin R. SimovskiC:\TEMP\simov.docbisbisCC:\WINDOWS\Bureau\biaj\abstracts\Nouveau dossier\21-12\simovski.docTc0b(wh^`.h^`.hpLp^p`L.h@@^@`.h^`.hL^`L.h^`.h^`.hPLP^P`L.hho(.b(wT@77X277p@GTimes New Roman5Symbol3&Arial]
MS MinchoArial Unicode MSMCentury Schoolbook?5 Courier New"qe\\ΚAfz
"r0d%Antnio L. Topabisbis