IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 72, NO. 1, JANUARY 2024 1045
Communica ion
Elec omagne ic Bandgap Based on a Compac Th ee-Hole Double-Laye
Pe iodic S uc u e
Luis Fe nando He an , Qiao Chen , F ancisco Mesa , and Osca Que edo-Te uel
Abs ac — We p opose and s udy a new ype o double-laye holey
s uc u e wi h a wide bandgap. The s uc u e can ha e glide symme y
in wo o hogonal di ec ions bu no 2-D glide symme y. We epo
esul s in e ms o dispe sion diag ams calcula ed wi h he eigensol e
o a comme cial sol e , as well as wi h a mul imode ans e ma ix
app oach ha pe mi s an accu a e calcula ion o he a enua ion cons an .
The esul s demons a e ha he bandgap o he p oposed s uc u e can
p o ide a wide ac ional bandwid h and a la ge a enua ion cons an
han hose o a 2-D glide-symme ic holey con igu a ion. The e o e, his
new ype o pe iodic s uc u e can be ad an ageous in p e en ing leakage
in gap wa eguide echnology o , in gene al, pa allel pla e con igu a ions
and il e s. The ope a ion o his new uni cell is expe imen ally
demons a ed wi h a double- lange con igu a ion be ween 40–60 GHz.
Index Te ms— Elec omagne ic bandgap (EBG), lange ansi ion, glide
symme y, holey pe iodic s uc u e, mul imodal analysis.
I. INTRODUCTION
Fully me allic wa eguides a e o en used in millime e -wa e appli-
ca ions due o hei low inse ion losses. When used o design de ices
ha in eg a e in o high- equency sys ems, wa eguides a e usually
spli in o wo pieces, so hei in e nal de ails can be ab ica ed
using he machining echnique. In p ac ice, his spli ing in oduces
a small ai gap be ween me al pieces due o manu ac u ing/assembly
impe ec ion and/o me al de o ma ion, which can cause signi ican
ene gy leakage a millime e -wa e equencies [1]. Leakage may also
occu in he in e connec ion be ween he wa eguides, whe e i is di -
icul o ensu e pe ec elec ical con ac [2]. Al hough con en ional
1-D pe iodic co uga ions/g oo es only p o ide a high supp ession
o leakage in he di ec ion o pe iodici y [3], he gap wa eguide
echnology [4],[5] based on bed-o -nails s uc u es can p ohibi wa e
p opaga ion in unwan ed di ec ions inside a pa allel-pla e wa eguide
(PPW). Howe e , he manu ac u ing p ocess o pe iodic pins can be
agile and cos ly when hei physical dimensions a e scaled down
o a magni ude o submillime e s in millime e -wa e equencies
Manusc ip ecei ed 16 July 2023; e ised 19 Oc obe 2023; accep ed
31 Oc obe 2023. Da e o publica ion 15 No embe 2023; da e o cu -
en e sion 9 Feb ua y 2024. This wo k was suppo ed in pa by
COST Ac ion SyMa unde G an CA18223 and in pa by COST
(Eu opean Coope a ion in Science and Technology). The wo k o Luis
Fe nando He an was suppo ed in pa by unde G an PID2020-114172RB-
C21/AEI/10.13039/501100011033 and in pa by he Gobie no del P incipado
de As u ias unde G an IDI/2021/000097. The wo k o F ancisco Mesa
was suppo ed by MCIN/AEI/10.13039/501100011033 unde G an PID2020-
116739GB-I00. (Co esponding au ho : Osca Que edo-Te uel.)
Luis Fe nando He an is wi h he Depa men o Elec ical Enginee ing,
Uni e si y o O iedo, 33003 O iedo, Spain (e-mail: [email p o ec ed]).
Qiao Chen and Osca Que edo-Te uel a e wi h he Di ision o Elec omag-
ne ic Enginee ing and Fusion Science, School o Elec ical Enginee ing and
Compu e Science, KTH Royal Ins i u e o Technology, SE 100 44 S ockholm,
Sweden (e-mail: [email p o ec ed]; [email p o ec ed]).
F ancisco Mesa is wi h he Depa men o Applied Physics 1, ETS
Ingenie ía In o má ica, Uni e sidad de Se illa, 41012 Se ille, Spain (e-mail:
[email p o ec ed]).
Colo e sions o one o mo e igu es in his communica ion a e a ailable
a h ps://doi.o g/10.1109/TAP.2023.3331502.
Digi al Objec Iden i ie 10.1109/TAP.2023.3331502
[6]. As an al e na i e, holey elec omagne ic bandgap (EBG) s uc-
u es ha e ecei ed inc easing in e es due o hei obus ness and
cos -e ec i eness [7]. I has ecen ly been demons a ed ha glide
symme y [8],[9] enables a numbe o ad an ages when applied
o pe iodic s uc u es, and in pa icula o holey EBG s uc u es
[10]. Two-dimensional glide-symme ic holey s uc u es we e i s
s udied in [11], e ealing ha glide symme y can be used o inc ease
he ope a ing bandwid h o a Lunebu g lens. Fu he mo e, glide
symme y has been shown o imp o e EBG bandwid h [12],[13] and
i s a enua ion [14], which a e bene icial p ope ies o gap wa eguide
echnology [15], il e s [16], leaky wa e an ennas [17],[18], and
educ ion o leakage in langes [19],[20].
The cha ac e is ics o pe iodic EBG s uc u es a e s udied p ima ily
by means o dispe sion analysis. The commonly used eigenmode
sol e (ES) o comme cial ull-wa e simula o s only compu es he
p opaga ion cons an s o pu ely p opaga i e modes, and hence only
p o ides he equency ange o he s opband. Howe e , knowledge
o he na u e o he s opband and i s a enua ion is c ucial o
ully cha ac e ize he beha io o he bandgap. This in o ma ion
can be ob ained om he comple e modal solu ions o e ed by
ad hoc analy ical/nume ical me hods such as he equi alen ci cui
app oach [21],[22] and he ans e se esonance me hod [23],[24]
widely used in single-sided me asu aces. When a pai o pe iodic
su aces possess glide symme y, highe o de in e ac ions be ween
hem canno always be easily modeled wi h an equi alen ci cui o
homogenized using he ans e se esonance me hod [25]. Al hough
a emp s o use he mode-ma ching echnique [26],[27] ha e been
epo ed o glide-symme ic co uga ions [26] and holey su aces
[27], his echnique is es ic ed o he analysis o some canonical
geome ies.
The mul imode ans e ma ix app oach [28],[29],[30],[31],[32],
[33] combines he abili y o ull-wa e simula o s [34],[35],[36] o
deal wi h complex geome y s uc u es [14],[37] and inhomogeneous
ma e ials [38],[39],[40] wi h he ad an age o ad hoc app oaches
o ob ain comple e modal solu ions (bo h phase and a enua ion
cons an s) and p o ide physical insigh [41].In[14], his app oach
p o ed o be capable o accu a ely cha ac e izing he glide-symme y
holey EBG s uc u e, including he ejec ion bandwid h, he le el
o a enua ion, he na u e o he mode (complex/e anescen /bound),
pa i y o he mode, and he di ec ional p ope y o he s opband.
In his wo k, we p opose and s udy he EBG p ope ies o a new
ype o glide-symme ic holey s uc u e ha has “b oken” glide sym-
me y in wo o hogonal di ec ions a he han 2-D glide symme y.
The ope a ion o his new uni cell is expe imen ally alida ed wi h
a double- lange expe imen al se -up.
II. DESCRIPTION OF THE PROPOSED PERIODIC UNIT CELL
The common opology o holey pe iodic me asu aces consis s o
wo me allic laye s sepa a ed by a na ow gap ha o ms a PPW.
In bo h op and bo om laye s, he e is a pe iodic dis ibu ion o holes,
and depending on i s speci ic pe iodic con igu a ion (o symme y),
© 2023 The Au ho s. This wo k is licensed unde a C ea i e Commons A ibu ion-NonComme cial-NoDe i a i es 4.0 License.
Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by-nc-nd/4.0/
1046 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 72, NO. 1, JANUARY 2024
Fig. 1. Holey uni cells. (a) Mi o . (b) One edge displaced mi o . (c) Glide
symme ic. (d) P oposed pe iodic uni cell. Top and bo om heigh s o he
holes (h) a e he same.
he s uc u e beha es di e en ly. The mos common con igu a ions
o a uni cell wi h holes in he uppe and lowe laye s a e: mi o ing,
mi o ing wi h a displacemen o one edge, and symme ic glide [12].
A schema ic o hese uni cells is illus a ed in Fig. 1(a)–(c). In all
cases, pis he pe iodici y o he uni cell, his he heigh o he
op and bo om holes, gis he ai gap be ween he bo om and op
laye s, and diis he diame e o he hole. Fo s uc u es wi h di e en
diame e s in he op and bo om holes, d1will e e o he bo om
holes and d2 o he op holes.
The no el uni cell p oposed in his wo k is illus a ed in Fig. 1(d).
This uni cell has one hole o diame e d1in he bo om me allic laye
and wo holes wi h diame e d2in he op me allic laye . The op-laye
holes a e shi ed in bo h plane di ec ions o hal he uni -cell pe iod
wi h espec o he mi o o he bo om hole. Unlike he o he uni
cells shown in Fig. 1, which ha e wo holes in o al, he p oposed
con igu a ion has h ee holes pe uni cell (p.u.c.). The diame e d2o
he holes in he uppe laye mus be selec ed so ha he adjacen holes
do no o e lap; ha is, i s maximum alue is gi en by d2,max =p/√2.
In he ollowing, uni cells will also be deno ed in e ms o he numbe
o holes p.u.c.; namely, he ones in Fig. 1(a)–(c) as “ wo-hole” uni
cells, while he p oposed no el uni cell will be deno ed as a “ h ee-
hole” uni cell.
III. PARAMETRIC STUDY
In his sec ion, we s udy he beha io o he p oposed h ee-hole
uni cell, Fig. 1(d), and compa e i wi h he o he h ee wo-hole uni
cells illus a ed in Fig. 1(a)–(c) h ough a de ailed pa ame ic s udy.
A. Cells Wi h he Same Pe iod
Fi s , we show he dispe sion diag ams o he ou holey s uc u es
in Fig. 2when he size o hei uni cells is he same. The emaining
pa ame e s o each uni cell a e op imized o ob ain he maximum
s opband. As p e iously epo ed in [10] and [15], a glide-symme ic
uni cell [Fig. 2(c)] exhibi s a wide s opband bandwid h han i s
co esponding nonglide e sions [Fig. 2(a) and (b)]. Howe e , he
p oposed h ee-hole uni cell has a much lowe equency bound
o he s opband wi h he same pe iodici y and simila bandwid h
[Fig. 2(d)]. We can obse e ha he beha io o he undamen al
mode o he mi o ed wo-hole uni cell and he one o he h ee-hole
uni cell a e quali a i ely simila , al hough he h ee-hole uni cell
limi s he p opaga ion in he 45◦di ec ion (M0) a a signi ican ly
lowe equency, hus educing he lowe equency bound o he
s opband and inc easing i s bandwid h. This is a ele an ea u e,
since i means ha his newly p oposed uni cell is mo e compac
han o he p e iously epo ed holey s uc u es.
An explana ion o he abo e ea u e could be expec ed o be ha
he p oposed h ee-hole uni cell has a highe illing ac o han i s
wo-hole coun e pa s. Howe e , a u he analysis o he s opband
beha io e eals ha he speci ic geome y o he h ee-hole uni
cell also has a signi ican impac . Fo example, Fig. 3compa es he
beha io o wo h ee-hole uni cells wi h he same illing ac o : he
Fig. 2. Dispe sion diag ams o he uni s cells in Fig. 1wi h he same
pe iodici y (p=3 mm). In all cases, h=2 mm and g=50 µm. (a) Mi o
(d=2.8 mm). (b) One edge displaced mi o (d1=2.6 mm, d2=1.6 mm).
(c) Glide symme ic (d=2.4 mm). (d) P oposed h ee-hole uni cell (d1=
2.6 mm, d2=1.6 mm).
Fig. 3. Dispe sion diag ams o wo h ee-hole uni cells. (a) P oposed
h ee-hole cell. (b) Th ee-hole uni cell wi h he op-laye holes shi ed by
p/2. In he inse o (b), he holes in he bo om laye a e colo ed blue, while
hose in he op laye a e colo ed ed.
one p oposed in Fig. 1(d) and a a ia ion o his cell wi h i s op laye
shi ed by an addi ional leng h o p/2. The compa ison o bo h plo s
in Fig. 3clea ly shows ha he alue o he illing ac o appea s
o be less ele an han he ela i e posi ion o he bo om and op
holes. I is somewha unexpec ed ha changing he ela i e posi ion o
he holes a ec s he s opband loca ion and bandwid h so d as ically.
I can be in e ed ha he beha io o he shi ed h ee-hole opology
in Fig. 3(b) is a so o hyb idiza ion be ween he wo-hole mi o
and glide wo-hole cases shown in Fig. 2(a) and (c), in he sense
ha he beha io o he i s mode in he M0 egion is simila o
he wo-hole mi o case in Fig. 2(a), while i s s opband is con ined
be ween he second and hi d o de o p opaga ion as in he wo-hole
glide case in Fig. 2(c).
A pa ame ic s udy has also e ealed ha among he pa ame e s
ha ha e mo e in luence on he bandwid h pe o mance o he
p oposed h ee-hole uni cell, bo h he op and bo om hole diame e s
ha e he g ea es impac on i . The e ec o he in luence o hese
wo pa ame e s is plo ed in Fig. 4, which shows he equencies
in he i s and second modes, and hus he absolu e bandwid h, o
di e en combina ions o d1and d2. This analysis was ca ied ou
using he same pe iod as in he p e ious igu es, p=3 mm. Bo h
diame e alues a e aken o hei p ac ical size limi s, he diame e
o he bo om hole is less han he pe iod o he uni cell, and he
diame e o he op hole is chosen o a oid o e lap [ hese limi s a e
(d1/p)lim =1 and (d2/p)lim =0.7]. An impo an obse a ion is
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 72, NO. 1, JANUARY 2024 1047
Fig. 4. Pa ame ic analysis o he p oposed h ee-hole cell o (a) equency
bounds o he i s and second modes and (b) ac ional bandwid hs. All da a
ha e been ob ained using a no malized heigh o h/p=0.66.
Fig. 5. Holey pe iodic me asu aces wi h he same lowe equency bound
o he s opband. (a) Mi o . (b) Mi o wi h one displaced edge. (c) Glide
symme ic. (d) P oposed pe iodic uni cell.
ha he s opband bandwid h inc eases as he diame e o he holes
g ows, sugges ing ha he la ge he a ea o he su ace occupied by
he holes, he wide he bandwid h ob ained. Howe e , his inc ease
shows a limi o an op imum combina ion o d1and d2. This ac
is be e obse ed in Fig. 4(b), whe e he ac ional bandwid h is
plo ed e sus he no malized hole diame e wi h espec o he uni -
cell pe iod. The op imal ac ional bandwid h is ob ained o d1/p=
0.86 and d2/p=0.54. I has been obse ed ha he a ia ion in hole
dep h does no ha e a signi ican in luence on ac ional bandwid h
o alues g ea e han h/p=0.5.
B. Cells Wi h Di e en Pe iods
Nex , we s udy he beha io o he s opband o all holey s uc u es
when hei uni -cell dimensions a e adjus ed o ha e he same
lowe equency bound so he ac ional bandwid h can be p ope ly
compa ed in all he s uc u es. The co esponding dispe sion diag ams
a e shown in Fig. 5, wi h he inse s ep esen ing each holey uni cell
wi h i s ac ual aspec a io o help compa e he sizes o he di e en
cells. All pa ame e s used o his compa ison ha e been selec ed o
ob ain he op imum s opband bandwid h [14]. These pa ame e s a e
shown in Table I.
The esul s o Fig. 5demons a e ha he h ee-hole uni cell
p oposed in his wo k exhibi s a wide ac ional s opband bandwid h
and a smalle pe iod size compa ed o he o he h ee wo-hole
s uc u es. Compa ed o he glide case, he h ee-hole uni cell has
TABLE I
HOLEY UNIT CELL PARAMETERS FOR FIG.5(DIMENSIONS IN mm)
Fig. 6. Bloch’s analysis o he p oposed uni cell [ ep oduced in (d)] wi h
dimensions in Table Iusing MMTMM o i s p opaga ion and a enua ion
cons an s along (a) 0X and (b) 0M, in compa ison wi h CST ES. (c) Roo
loci o he complex mode in (b) om 40.8 o 81 GHz. (d) Ske ch o he
p oposed h ee-hole uni cell.
36% less size and 20% mo e ac ional bandwid h. This esul shows
ha he p oposed h ee-hole uni cell has a e y high po en ial
o de ices whe e a high s opband is equi ed, wi h he addi ional
bene i o a educed size compa ed o o he wo-hole uni cells while
main aining i s obus ness and ease o manu ac u ing. Fu he mo e,
he educed size o he h ee-hole uni cell makes i s use con enien
a lowe equencies, whe e he la ge size o he o he wo-hole
uni cells could be imp ac ical. Howe e , i should be no ed ha size
educ ion can lead o a lowe a enua ion ac o p.u.c. (e−2αp). In ha
case, he minimum numbe o uni cells equi ed o achie e he a ge
a enua ion should be de e mined by in es iga ing he cha ac e is ics
o he s opband.
IV. BLOCH ANALYSIS USING MMTMM
In addi ion o he p e ious s udy, he mul imode ans e ma ix
me hod (MMTMM) [41] is applied in his sec ion o analyze an op i-
mal h ee-hole p.u.c. holey me asu ace (see dimensions in he i h
column o Table I). MMTMM allows us o ob ain no only he phase
cons an bu also he a enua ion cons an o any pe iodic s uc u e.
Al hough accu a e alues o he a enua ion cons an canno be easily
ob ained using comme cial elec omagne ic so wa e, MMTMM has
al eady demons a ed being a eliable ool o his ask [14],[41].
Fig. 6(a) shows bo h he phase shi and he no malized ( o he
wa enumbe o he ee space) a enua ion cons an along he edge
0X in he i s B illouin zone o he p oposed h ee-hole uni cell
wi h op imal dimensions using MMTMM. The igu e also included
he phase shi ob ained wi h he ES o he CST S udio Sui e
using pe iodic bounda ies in he p opaga ion di ec ions wi hin he
B illouin zones and PEC bounda ies on he es . Bo h esul s a e
1048 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 72, NO. 1, JANUARY 2024
Fig. 7. F equency beha io o he a enua ion o a ious no malized alues
o d2 o he h ee-hole uni cell wi h dimensions gi en in Table I. (a) Fi s
B illouin edge 0X. (b) Thi d B illouin edge M0.
pe ec ly co ela ed, showing bo h he alidi y o he MMTMM and
he pe o mance o he p oposed cell. The esul s also demons a e
he high le el o a enua ion/ ejec ion p o ided by he h ee-hole
s uc u e in he o bidden band, simila o he glide-symme ic holey
EBG epo ed in [14]. As demons a ed in Fig. 6(b), when applying
he MMTMM o he hi d edge 0M o he B illouin zone, a good
ag eemen in he phase cons an wi h he CST-ES esul s is ound
again excep o he appea ance o a complex mode in he o bidden
band. This mode canno be de ec ed wi h he CST-ES because i only
compu es p opaga i e modes. A de ailed discussion on he beha io
o his kind o complex modes can be ound in [14]. Simila o
he complex mode in [14], he complex mode in Fig. 6(b) spli s
a abou 77 GHz in o wo eal p opaga i e o wa d and backwa d
modes. The lowe b anch o he a enua ion cons an co esponds
o he e anescen modes in he s opband, while he uppe b anch
co esponds o he complex mode. To ob ain a be e pic u e o he
beha io o he complex mode, i s oo loci a e p esen ed in Fig. 6(c)
om i s onse equency a 40.8 GHz un il 81 GHz. I can be clea ly
obse ed ha he complex mode spli s a 77.4 GHz in o wo eal
p opaga i e o wa d and backwa d modes.
The e ec o a ying he op no malized diame e , d2(keeping
d1 ixed), on he a enua ion cons an is shown in Fig. 7. The alue
d1/pis aken as he op imal one ha p oduces he highes limi o he
s opband, as can be seen in Fig. 4(b). Fig. 7(a) shows ha he e ec
o no malized d2on he i s B illouin edge is no e y signi ican ,
excep o i s minimum alue. The maximum le el o a enua ion
is ob ained a he op imal no malized alue o d2/p=0.54, which
is he same alue ha achie es he maximum ac ional s opband
bandwid h. The in luence o d2/pis mo e signi ican a he hi d
B illouin edge, as obse ed in Fig. 7(a). In his egion, i can be seen
ha he change om he minimum no malized alue o i s maximum
signi ican ly a ec s he a enua ion ac o . Again, he op imal alue
o d2/p o a enua ion ma ches he op imal alue o he s opband.
The esul s shown in Fig. 7(b) show ha mos o he in luence on
he p opaga ion cha ac e is ics comes om he hi d B illouin edge
(kx=ky). This means ha p opaga ion in he 0M di ec ion is he
main esponsible o he good pe o mance o he p oposed uni cell
in e ms o s opband.
V. EXPERIMENTAL RESULTS
In o de o expe imen ally alida e he p e ious analysis, wo pai s
o WR-19 wa eguide space s we e manu ac u ed and measu ed in
a back- o-back con igu a ion. All space s a e compa ible wi h he
UG-383/U lange, wi h a 2.5 mm leng h. One o he pai s is a egula
space wi h no holes on i , as shown in Fig. 8(a), while he o he
uses he h ee-hole double-laye pe iodic s uc u e p oposed in his
wo k, as shown in Fig. 8(b). The dimensions o he holes a e gi en
in Table Ico esponding o he dispe sion diag am in Fig. 5(d). The
measu emen se up can be seen in Fig. 8(c), showing he back- o-back
Fig. 8. Manu ac u ed WR-19 wa eguide space s. (a) No holey egula
space . (b) Th ee-hole double-laye space . (c) Space s measu emen se up
in back- o-back con igu a ion.
Fig. 9. Measu emen s o he ansmission coe icien . (a) Compa ison o
he esponse wi h and wi hou holey s uc u e o ai gaps o 0 and 100 µm.
(b) Response o he holey s uc u e o di e en alues o he ai gap.
case. To measu e di e en ai gaps, a sepa a o is added be ween bo h
space s o achie e he desi ed ai gap.
Two di e en measu emen s ha e been pe o med o bo h pai s:
one wi h ze o ai gap be ween bo h space s and he o he wi h
an ai gap o 100 µm. The ansmission coe icien s (S21) a e
illus a ed in Fig. 9. Bo h s uc u es pe o m as expec ed when no
gap exis s be ween each space ; ha is, minimal losses a e ob ained.
Howe e , when he e is a 100 µm ai gap, he s anda d s uc u e
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 72, NO. 1, JANUARY 2024 1049
exhibi s conside able losses, wi h a dip appea ing a ound 47.5 GHz.
In con as , he holey s uc u e has small losses wi h no peaks in
he ope a ing band, 40–60 GHz. Fig. 9(b) shows a compa ison o
ansmission losses o he holey s uc u e wi h a ying ai gaps. I is
e iden ha he smalle he ai gap, he lowe he losses, al hough
hey emain almos insigni ican in compa ison o he nonholey
case. No e ha , in all cases, he measu ed e lec ion coe icien s
a e below −20 dB. The e o e, he losses in he nonholey s uc u e
can only be explained by he leakage due o he ai gap in he
in e ace be ween bo h space s. In conclusion, he h ee-hole s uc u e
d as ically educes leakage due o he space . These expe imen al
esul s clea ly demons a e he po en ial o he p oposed h ee-hole
s uc u e. This con igu a ion is a compac and e sa ile candida e o
di e en p ac ical scena ios whe e leakage mus be a oided.
VI. CONCLUSION
In his communica ion, a no el holey EBG is p esen ed, which
is based on a h ee-hole opology wi h di e en alues o he
op and bo om diame e s. The pe o mance o his uni cell has
been compa ed wi h o he simila holey EBGs, such as mi o , one-
edge displaced mi o , and glide-symme ic opologies. In pa icula ,
we ha e s udied he s opband beha io , main aining he uni cell
pe iod equal in all s uc u es and wi h he same lowe equency
bound o he s opband. The esul s show ha he p oposed uni
cell exhibi s a educ ion in size and an inc ease in he ac ional
bandwid h wi h espec o he glide-symme ic s uc u e. These esul s
sugges ha he p oposed uni cell could ha e po en ial uses in
p ac ical applica ions wi h limi ed space. Wi h a pa ame ic analysis,
he op imum pa ame e s o his uni cell ha e been ound o achie e
he maximum ac ional bandwid h o he s opband. A MMTMM
analysis was pe o med o de e mine he a enua ion o he p oposed
uni cell, which shows a desi ed high le el o a enua ion in he s op-
band, simila o o he glide-symme ic s uc u es p e iously s udied.
To illus a e he po en ial o he p oposed EBG s uc u e in a p ac ical
scena io, i has been used o educe leakage a he in e ace be ween
wo space s. Ou expe imen al esul s show a d as ic imp o emen
wi h espec o i s nonholey coun e pa .
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