Ma que
´se al. Reply: The Commen [1] by Kond a ’e
and Smi no (KS) p o ides an al e na i e explana ion o
he esul s in Re . [2]. I is no unusual o explain a
physical phenomenon om a ious pe spec i es.
Howe e , KS i mly s a e ha he heo y in Re . [2] is
w ong. In ou opinion, KS s a om a se ious misin e -
p e a ion. Al hough i is ob ious ha a wa eguide illed
wi h an iso opic ‘‘medium ha ing "1and 
e <0’’ does no ansmi elec omagne ic wa es,
such a model is no conside ed anywhe e in Re . [2]. In
ou wo k, he wa eguide loaded wi h a single ow o spli
ing esona o s (SRRs) is jus conside ed as he uni cell
o a quasicon inuous (a a la ge scale) e ec i e medium
(see Fig. 6 in [2] o Fig. 3 in [3]). The hollow wa eguide
beha es as a 1D plasma wi h e ec i e pe mi i i y e 
01!2
c=!2. Fo he dominan mode, he a e age
ields ac oss he wa eguide sec ion a e ans e se, and
he pola iza ion o he uni cell a ising om he walls
cu en , Pp=a3, is ela ed o he a e age elec ic ield
by P0!c=!2hEi. The uni cell magne iza ion is
p opo ional o he a e age magne ic ield h ough a
( esonan ) scala e ec i e magne ic suscep ibili y, e .
This ollows om he symme y o he s uc u e (see
Fig. 2 in [2]): he a e age magne ic ield is no mal o
he SRR axis, he unique possible di ec ion o magne i-
za ion. As a i s app oxima ion, e was chosen o be
he e ec i e magne ic suscep ibili y (along he xaxis) o
he in ini e 3D SRR medium. Since he a e age ields a e
ans e se, hey o m a TEM plane wa e whose dispe -
sion ela ion is k!
e e
p[e 01e ].
Thus, i is he whole sys em consis ing o he wa eguide
plus he SRRs ha beha es as he uni cell o a 1D le -
handed medium in ou pic u e. No e ha he SRR-loaded
wa eguide is ea ed as a disc e e sys em a he scale o
he uni cell dimensions (xyza), bu as a
homogeneous medium a he la ge scale o a ia ion o
he a e age elec omagne ic ield (2=k). Al hough
KS’s in e p e a ion leads o exac ly he same quan i a i e
esul o he dispe sion ela ion [see Eq. (5) o KS [1] and
Eqs. (1) and (2) o [2]], he applica ion o his analysis o
he single ow o ings in Re . [2] does no seem o be
plausible. Ul ima ely, wha KS assume is ha he elec o-
magne ic wa es p opaga ing along he loaded wa eguide
a e he supe posi ion o wo plane wa es wi h wa e
ec o s kx=a ; kz, p opaga ing along an in ini e
homogeneous aniso opic medium wi h xx 0.How-
e e , a he scale o he a ia ions o such hypo he ical
plane wa es, 2= 
k2
xk2
z
q<2a, he SRR sys em
should be iewed as a disc e e pe iodic s uc u e a he
han as a con inuous medium. In con as , a he la ge
scale sugges ed in Re . [2], Fig. 6, and in Re . [3], Fig. 3,
he con inuous-medium pe spec i e is ully jus i ied, p o-
ided a.
In o de o illus a e he abo e poin , we ha e ca ied
ou an expe imen simila o ha epo ed in Fig. 5(a) o
Re . [2] including wo addi ional SRRs loca ed be ween
he h ee SRRs conside ed in Re . [2] bu ha ing hei
axes pa allel o he wa eguide axis. Following he a ion-
ale implici in KS’s Commen [1], he esul ing s uc u e
would be, oughly speaking, equi alen o a wa eguide
illed wi h a homogeneous medium ha ing zz xx 
e ope a ing a cu o . Howe e , he expe imen al e-
sul s in Fig. 1 show ha he addi ional SRRs do no a ec
he quali a i e beha io o he de ice. This esul is in
ag eemen wi h ou poin o iew, which conside s he
whole sys em as he uni cell o a 1D le -handed medium
(wi h he e ec i e pe meabili y o he SRR subsys em
along he xaxis, e , and he e ec i e pe mi i i y o he
wa eguide, e ). We belie e ha his expe imen conclu-
si ely suppo s ou in e p e a ion.
This esea ch was suppo ed by Spanish MCyT and
EU-FEDER unds unde P ojec No. TIC2001-3163.
R. Ma que
´s, J. Ma el, F. Mesa, and F. Medina
Uni e si y o Se illa,
41012-Se illa, Spain
Recei ed 21 May 2003; published 8 Decembe 2003
DOI: 10.1103/PhysRe Le .91.249402
PACS numbe s: 42.70.Qs, 41.20.Jb, 42.25.Bs, 73.20.M
[1] I. G. Kond a ’e and A. I. Smi no , p eceding Commen ,
Phys. Re . Le . 91, 249401 (2003).
[2] R. Ma que
´se al., Phys. Re . Le . 89, 183901 (2002).
[3] R. Ma que
´se al., Mic owa e Op . Technol. Le . 35,405
(2002).
FIG. 1. Rough 1D le -handed medium simula ion wi h addi-
ional SRRs.
PHYSICAL REVIEW LETTERS week ending
12 DECEMBER 2003
VOLUME 91, NUMBER 24
249402-1 0031-9007=03=91(24)=249402(1)$20.00 2003 The Ame ican Physical Socie y 249402-1