3-D photonic bandgap structures in the microwave regime by fused deposition of multimaterials

3-D photonic bandgapstructures in themicrowave regime byfused deposition ofmultimaterials

Mauricio E Pilleux

Mehdi AllahverdiYouren Chen

Yicheng Lu Mohsen A Jafari and

Ahmad Safari

The authors

Author information may be found at the end of the article

Keywords

Design Layered manufacturing Alumina Ceramics

Abstract

Three-dimensional photonic bandgap (PBG) structuresusing alumina (Al2O3) as the high permittivity materialwere modeled and then the structures were fabricated byFused Deposition of Multi-materials (FDMM) technologyA nite element method and a real-time electromagneticwave propagation software were used to simulate anddesign the layered PBG structures for applications in themicrowave frequency range The modeling predicted a 3-Dphotonic bandgap in the 165ndash235 GHz range FDMMprovides a computer-controlled process to generate 3-Dstructures allowing high fabrication exibility andefciency Electromagnetic measurements displayed thepresence of a bandgap between 171ndash233 GHz showinga good agreement with the predicted values These PBGstructures are potential candidates for applications inadvanced communication systems

Electronic access

The research register for this journal is available at

httpwwwemeraldinsightcomresearch_registers

The current issue and full text archive of this journal is

available at

httpwwwemeraldinsightcom1355-2546htm

1 Introduction

Photonic bandgap (PBG) crystals are periodic

dielectric structures that alternate high and

low permittivity materials in order to obtain

an electromagnetic stop-band in a desired

direction depending upon the periodicity of

the structure PBG crystals were proposed in

the late 1980rsquos and since then there have been

extensive theoretical and experimental works

devoted to this new reg eld in order to

understand and exploit the properties of these

structures (Berger 1999 Dowling et al

2000) The dielectric or metallic periodic

structure gives rise to a forbidden band of

frequencies or photonic bandgap which

essentially changes the electromagnetic wave

propagation properties through the structure

These structures have received increasing

interest in recent years because of their

capability to conreg ne electromagnetic (EM)

waves in all three spatial dimensions

(Yablobovitch 1993 1997) A variety of

potential applications such as thresholdless

lasers high quality-single mode LEDs

microwave antennas light diodes an all kinds

of optical circuits have been suggested and

some have already been demonstrated

(Joannopoulos et al 1995)

For the microwavemillimeter wave region

in which our interest is focused applications

involve control of signal propagation quiet

oscillators frequency selective surfaces

narrow band reg lters and antenna substrates

For the latter case if a conventional substrate

is used then a large portion of the antenna

radiation is emitted into the substrate (since it

has a higher dielectric constant than air) and a

great part of this radiation is trapped inside

the substrate because of total internal

remacr ections In consequence not only more

than 50 percent of the radiated energy is lost

but also heat dissipation and temperature

effects arise in the substrate Instead if an

appropriate PBG substrate is selected then

the energy can be directed towards the

radiating direction (total remacr ection by the

PBG structure) thus improving the antenna

directivity and eliminating the substrate heat

Rapid Prototyping JournalVolume 8 middot Number 1 middot 2002 middot pp 46ndash52q MCB UP Limited middot ISSN 1355-2546DOI 10110813552540210413301

This project was supported by the New Jersey

Commission on Science and Technology under the

Research Excellence Program We wish to

acknowledge the helpful assistance provided by

Mr Ferdus Safari and by Mr Kian Seyed We also

appreciate the assistance of Dr Edip Niver with the

microwave characterization

46

dissipation There have been many reports for

the application of PBG structures as antenna

substrates such as (Brown and McMahon

1996 Sievenpiper et al 1999) Our research

will focus on the design and fabrication of 3-D

PBG structures with applications in the

millimeter-wave band Such structures are

made by a rapid prototyping technique

discussed below

Many groups have performed research in

photonic structures using alumina as the high

permittivity dielectric material (Masuda et al

1999 Jessensky et al 1998 Shingubara et al

1997 Feiertag et al 1997) The use of anodic

porous alumina formed by the anodization of

aluminum in an appropriate acid solution

has attracted attention as a starting material

for 2-D PBG structures with typical

dimensions in the nano- or micrometers since

this process is a typical example of a naturally

occurring ordered structure (Masuda et al


1997) Also Feiertag et al developed a

microfabrication technique for building 3-D

PBG structures using x-ray lithography with

bandgaps in the infrared region (Feiertag et al

1997) These structures have a lattice

constant of 85 mm and are made with 22 mm

diameter rods

Jin et al made microwave measurements on

a 2-D octagonal quasiperiodic photonic

crystal composed of an array of 23 pound 23 rows of

alumina cylinders (Jin et al 1999) The

diameter of the alumina cylinders was

612 mm so the reg lling fraction was 49

percent The authors found a bandgap

between 89 and 105 GHz that the position

and width of the bandgap did not depend on

the incidence direction and that it can appear

even if the arrayrsquos dimensions are lowered to

11 rows of cylinders Because of these

characteristics this photonic quasicrystal

seems to be more suitable for waveguide

applications than as a periodic photonic

crystal For this purpose waveguides were

fabricated by removing 3 rows of cylinders

leaving a 157-mm wide empty path from one

side of the array to the opposite one which

was approximately half of a wavelength at the

gap center The results show a high efreg ciency

of straight and bending guides

For the fabrication of PBG structures in the

mm-range there are few rapid prototyping

processes available Fused Deposition of

Ceramics (FDC) or its modireg ed version for

multimaterials presents several advantages

for the fabrication of the PBG periodic

structures for use in the microwave region

since the minimum part shapes are in the

order 05 mm (Danforth et al 1998 Safari

et al 1998a Safari et al 1998b Jafari et al

2000) The main advantage of this technique

is the rapid prototyping of the complex design

which means that the geometry and the

dimensions of a sample can be easily modireg ed

by the use of a CAD software FDMM makes

it possible to build PBG structures up to

frequencies close to 100 GHz

In this paper we present the application of

a novel fabrication technique fused

deposition of multimaterials (FDMM) to the

manufacturing of PBG structures in order

demonstrate the feasibility of the technique

for this purpose The advantage of FDMM is

the rapid fabrication of complex designs using

a computer-controlled system with no need

for mold or any hard tooling Conventional

fabrication processes require initial making of

bulk pieces of dielectric materials followed by

machining andor etching to form the desired

structures with alternating high and low

dielectric constant materials On the other

hand FDMM deposits the desired materials

only where required by the design and

therefore is capable of making complex PBG

structures

2 Experimental procedure

The modeling was based on a reg nite element

shareware Fortran program written by the

Photonics Research Team of Imperial College

(London UK) and was adapted to this

research in order to incorporate the specireg c

structures that were modeled (Pendry et al

1992 Pendry 1996) Frequency-domain

modeling was also performed using the High

Frequency Structure Simulator (HFSS)

commercial software from Ansoft

Corporation (Pittsburgh PA) This is a

powerful program that can perform real-time

simulation of the wave propagation though

2-D or 3-D dielectric or metallic periodic

structures of any complex geometry The

electromagnetic measurements were carried

out in a Network Analyzer (Hewlett Packard

model HP8510C) with open-ended

waveguides

The geometry of the structure that was

built by FDMM in this work is shown in

Figure 1 The size of the unit cell and in

consequence the spacing between bars and

3-D photonic bandgap structures in the microwave regime

Mauricio E Pilleux et al

Rapid Prototyping Journal

Volume 8 middot Number 1 middot 2002 middot 46ndash52

47

the geometry of the cross-section of each bar

of the structure was chosen so that the

bandgap would lie in the 15 plusmn 95 GHz

frequency range Alumina was used as the

high permittivity dielectric material (relative

permittivity 1r = 96) and air as the low

permittivity one

The fabrication of the PBG structures was

performed using the multimaterial deposition

equipment designed and fabricated at Rutgers

University and is described elsewhere (Jafari

et al 2000) The feedstock materials for the

FDMM process were reg laments of alumina

and ICW-06 wax (Stratasys Inc Eden

Prairie MN) The alumina reg lament was

fabricated using A152-SG alumina powder

(Alcoa New Milford CT) which was coated

with a surfactant by mixing 150 g of alumina

in a 30 gL solution of stearic acid in toluene

and then mixing the slurry for 4 h The

mixture was then reg ltered and then air dried in

order to remove the solvent The loss on

ignition test at 550 8 C for 1 h indicated that the

stearic acid adsorption was 19 wt percent

Once the coated alumina powder was dried it

was mixed with ECG-9 thermoplastic binder

(developed at Rutgers University) (McNulty

et al 1998a b) in a Haake System 9000 high-

shear mixer (Haake-Fisons Paramus NJ)

with a twin-roller blade mixing bowl operating

at 100 rpm The alumina powder volume

fractions successfully used were 60 and 62 vol

percent solids loading The compounded

alumina-binder system was then extruded at

90 8 C into continuous reg laments several meters

long through a 178-mm diameter nozzle

using the same system but with a single screw

extruding attachment

Using the input from the PBG modeling a

CAD reg le was made in order to fabricate the

structure using the FDMM equipment The

geometry of the PBG structure required the

use of a supporting material below the

alumina rods during fused deposition and

ICW-06 wax was utilized for this purpose

The part was fabricated by the successive

deposition of the wax and the alumina-loaded

reg lament in a layer-by-layer manner The

alumina reg lament was loaded into a liquereg er

heated to 130 8 C having a 500 mm diameter

nozzle The wax reg lament was deposited using

a similar liquereg er and nozzle at a working

temperature of 72 8 C The CADCAM system

gave instructions to the FDMM equipment so

that the liquereg er would move and deposit

material in a predereg ned tool pathTo avoid bending of the alumina bars while

performing the binder burnout (BBO)

process it was necessary to initially remove

the wax from the fabricated structure so that it

could be replaced by a temperature resistant

support material during the BBO process

The wax removal was carried out in an oven

by placing the as-fabricated part for 10 min at

a temperature of 110 8 C This time-

temperature combination allowed the removal

of the wax without deforming the alumina-

polymer structure The dewaxed structure

was subsequently reg lled with zirconia powder

in order provide a refractory mechanical

support to avoid bending of the alumina bars

when subjected to the BBO cycle The BBO

was carried out by heating the structure to

550 8 C for 1 h immediately followed by a

partial sintering at 1050 8 C for 1 h The

heating from 100 to 350 8 C was carried out at

10 8 Ch in order to avoid any excessive

degassing of the sample from the calcination

of the organic components that might deform

the structure Finally sintering was carried

out at 1600 8 C for 1 h in a different furnace

3 Results and discussion

31 Design and simulation

The objective of the theoretical simulation of

the PBG structures was to solve Maxwellrsquos

equations inside the desired PBG geometry

As previously indicated our simulation used

two different computational methods to

investigate the PBG structure The reg rst one

the Fortran-code software was used to

reformulate Maxwellrsquos equations on a lattice

by dividing the space into a set of small cells

with a coupling between neighboring ones

(OEgrave zbay et al 1994) Then it calculated the

Figure 1 CAD drawing of the unit cell of the PBG structurefabricated by FDMM Each bar is 28 mm long with a2 pound 2 mm2 square cross-section and a pitch separation of8 mm The lling ratio of the structure is 38 percent





48

propagation of the EM reg elds through a

periodic dielectric structure in layer-by-layer

manner by means of a transfer matrix (Pendry

et al 1992) The transfer matrix can then be

used to evaluate the bulk dispersion and

transmission through a reg nite thickness slab of

the material since its eigenvectors are the

solutions for the electric and magnetic reg eld at

each point for a given frequency v Then the

band structure k = k(v) can be calculated

from these eigenvalues Since the transfer

matrix dereg nes how the waves cross a slab of

the material the transmission coefreg cients can

also be calculated The input to the program is

the geometry of the periodic structure as well

as the frequency v (or energy) of interest

The Transfer Matrix method was applied

to calculate the energy bandgap of the

alumina structure with rectangular rods as

shown in Table I and Figure 2 We

demonstrated that the reg lling ratio (ie the

ratio between the volume of material in the

unit cell and the total volume of the unit cell)

and the dielectric constant ratios are the major

factors that affect the bandgap existence and

the width of the bandgap frequency The

lattice constants of the structure determine

the starting frequency and the width of the

bandgap The shape of the dielectric rod is not

important since the results with square and

cylindrical rods were similar and the rods can

be either of a high permittivity material

surrounded by air or they can be made of air

embedded in a dielectric material The

frequency of the bandgap scales linearly with

the unit cell length which is dereg ned by thesize and the space between the rods This is

due to the linearity of Maxwellrsquos equations

Our second approach was to solveMaxwellrsquos equations in the frequency-domain

and for this purpose the High Frequency

Structure Simulator (HFSS) software wasused The wave-guide simulator method was

used to calculate the EM wave distribution in

the propagation direction (z-direction) The

inputs for the program were the geometry of

the structure which is dereg ned in terms of its

unit cell the monochromatic source and the

boundary conditions at the surface edges The

structure used was made of rectangular

alumina rods of 2 pound 2 mm2 cross section with

a pitch separation of 8 mm between rods The

structure exhibits a bandgap starting around

147 GHz with a bandgap width of 8 GHz

The modeling indicated that the structure

behaved like a Bragg remacr ector ie all the

incident energy was remacr ected The

transmission coefreg cient calculated by the

HFSS program has the same bandgap range

as that shown in Figure 2 using the T-matrix

approach

4 FDMM fabrication

The FDMM process was used to fabricate the

PBG structure shown in Figure 1 ie each

2 pound 2 mm2 square cross-section alumina bar

was 28 mm long with a pitch separation of

8 mm The bars were deposited parallel to

each other in each layer and perpendicular to

the direction of the immediate upper and

lower neighboring layers For every second

layer there was a shift in the position of the

rods by a half lattice constant (every reg fth layer

is identical so that a unit cell was constituted

of 4 rows of bars)

The FDMM fabrication of the PBG

structures was made with the multimaterial

deposition equipment using alumina-loaded

and wax reg laments as feedstock materials The

fabrication was made by the successive

deposition of the reg laments in a layer-by-layer

manner reg nishing each layer before

proceeding to the next one The main

problem encountered was the lack of adhesion

of the alumina layers to the underlying wax

layer The deposition parameters (deposition

speeds and mass macr ow rate) were adjusted to

overcome this problem thus improving the

adhesion of the two materials so that the

Table I Comparison between the results of the simulationand the electromagnetic measurements of the PBGstructure with square alumina rods The cross section ofthe rods is 2 mm and the pitch is 8 mm

Bandgap (GHz) Dvgapvmidgap

165plusmn235 35171plusmn233 31

Figure 2 Transmission loss of the alumina structure with square cross-sectionrods (2 pound 2 mm2)





49

successive layers could be deposited

appropriately Figure 3shows an as-fabricated

PBG structure with the support wax

surrounding itThe BBO cycle procedure used was the

same one as for the fabrication of other

electroceramic materials made with this

method (McNulty et al 1998a b) The wax

removal was optimized so that the alumina

rods would not bend due to their own weight

while the wax was macr owing around it for

removal The optimum temperature for the

wax removal was 110 8 C and at this

temperature it only required 10 min for the

wax to macr ow away from alumina bars In the

BBOpresintering cycle the parts were

embedded in zirconia powder in order to

provide support for the overhanging alumina

bars This procedure proved effective for

supporting the bars while not reacting with

the structure The removal of the zirconia was

simple and done using a macr ow of pressurized

air Following this the sintering cycle

densireg ed the structure leaving the typical

reg nished structure shown in Figure 4

Electromagnetic measurements were

carried out on a stack of 4 ordf unit cellsordm of the

sintered PBG structures Each unit cell

consisted of 4 stacks of bars so the

measurement involved 16 layers of bars with

the incident radiation perpendicular to the

ordf topordm side of the unit cell shown in Figure 4 A

stop band was detected between 171 and

233 GHz These results are in good

agreement with the simulation results for this

structure shown in Table I The

rearrangement of the stacks of ordf unit cellsordm

among each other gave identical results

In summary the feasibility of FDMM as a

manufacturing tool to fabricate complex 3-D

PBG structures that can be applied in the

microwave frequency region has been

demonstrated It appears that the complex

ceramic structure fabricated in this research

cannot be made by traditional molding

methods (Knitter et al 2001) A practical

fabrication procedure for example would

involve the fabrication of individual bars and

stacking them using templates In contrast

rapid prototyping seems to be a unique way to

make such complex structures To our

knowledge another rapid prototyping

technique called Robocasting was used to

fabricate similar PBG structures (Cesarano

et al 2001)

5 Conclusions

A photonic bandgap (PBG) structure was

designed and modeled so that it would have

a bandgap in the microwave frequency

Figure 3 The photograph shows the deposition of alumina(bright) and ICW-06 wax (dark) The wax had to beremoved before BBO and sintering of the part





50

region Computer simulation was performed

using T-Matrix and frequency-domain

approaches The results with both methods

showed a bandgap in the required frequency

region Further electromagnetic

measurements conreg rmed the existence of the

bandgap in the predicted region The

modeling demonstrated that the photonic

bandgap can be predicted in a structure of a

given geometry and material thus allowing

the engineering of PBG structures for specireg c

applications The experimental values

recorded for the bandgap are in good

agreement with those predicted by the

models indicating the effectiveness of the

simulation in predicting the real behavior of

the structure

FDMM has demonstrated its feasibility as a



microwave frequency region PBG structures

were prototyped using alumina and wax the

latter was used as a supporting material

during deposition of alumina rods The

successful removal of the wax and the use of a

structural supporting agent during the BBO-

presintering cycle allowed successful

sintering of the structure In short FDMM is

found to be a promising tool for the

fabrication of PBG crystals in the microwave

frequency range

(Mauricio E Pilleux Mehdi Allahverdi and

Ahmad Safari are at the Ceramic amp Materials

Engineering Department Rutgers The State

University of New Jersey Piscataway New

Jersey 08854 USA Youren Chen and

Yicheng Lu are at the Electrical amp Computer



Jersey 08854 USA Mohsen A Jafari is at the

Industrial Engineering Department Rutgers

The State University of New Jersey

Piscataway New Jersey 08854 USA)

References

Berger B (1999) ldquoPhotonic crystals and photonicstructuresrdquo Current Opinion in Solid State andMaterials Science 4 pp 209-16

Brown ER and McMahon OB (1996) ldquoHigh zenithaldirectivity from a dipole antenna on a photoniccrystalrdquo Applied Physics Letters 68 No 9pp 1300-2

Cesarano J Smay JE Lin SY Stuecker JN and LewisJA (2001) ldquoSolid freeform fabrication of photonicband gap structures in the 100 GHz regimerdquo 103rdAnnual Meeting of the American Ceramic SocietyA3B-12-2001-P p 40

Contopanagos H Zhang L and Alexopoulos N (1998)ldquoThin frequency-selective lattices integrated in novelcompact MIC MMIC and PCA architecturesrdquo IEEETransactions on Microwave Theory and Techniques46 pp 1936-48

Danforth SC Agarwala M Bandyopadhyay ALangrana N Jamalabad VR Safari A and vanWeeren R (1998) ldquoSolid freeform fabricationmethodsrdquo United States Patent No 5738817

Dowling JP Everitt H and Yablonovitch E (2000)ldquoPhotonic amp Sonic Band-Gap Bibliographyrdquohttphomeearthlinknet jpdowlingpbgbibhtmlThis site is continuously updated and has acomprehensive list of bibliographic references on thesubject

Feiertag G Ehrfeld W Freimuth H Kolle H Lehr HSchmidt M Sigalas MM Soukoulis CMKiriakidis G Pedersen T Kuhl J and Koenig W(1997) ldquoFabrication of photonic crystals by deepx-ray lithographyrdquo Applied Physics Letters 71No 11 pp 1441-3

Jafari MA Han W Mohammadi F Safari A DanforthSC and Langrana N (2000) ldquoA novel system forfused deposition of advanced multiple ceramicsrdquoRapid Prototyping Journal 6 No 3 pp 161-74

Jessensky O Muller F and Gosele U (1998) ldquoSelf-organized formation of hexagonal pore arrays inanodic aluminardquo Applied Physics Letters 72 No 10pp 1173-5

Jin C Cheng B Man B Li Z Zhang D Ban S andSun B (1999) ldquoBand gap and wave guiding effectin a quasiperiodic photonic crystalrdquo Applied PhysicsLetters 75 No 13 pp 1848-50

Joannopoulos J Meade RD and Winn JN (1995)Photonic Crystals Princeton University PressPrinceton NJ

Knitter R Bauer W Gohring D and Hauszligelt J (2001)ldquoManufacturing of ceramic microcomponents by arapid prototyping process chainrdquo AdvancedEngineering Materials 3 No 1ndash2 pp 49-54

Masuda H Ohya M Asoh H Nakao M Nohtomi Mand Tamamura T (1999) ldquoPhotonic crystal usinganodic porous aluminardquo Japanese Journal ofApplied Physics Part 2 38 No 12A pp L1403-5

McNulty TF Mohammadi F Bandyopadhyay AShaneeld DJ Danforth SC and Safari A

Figure 4 PBG ldquounit cellrdquo structure fabricated by FDMMafter sintering at 1600 8 C for 1 h





51

(1998a) ldquoDevelopment of a binder formulation forfused deposition of ceramicsrdquo Rapid PrototypingJournal 4 No 4 pp 144-50

McNulty TF Shaneeld DJ Danforth SC and Safari A(1998b) ldquoDispersion of lead zirconate titanate forfused deposition of ceramicsrdquo Journal of theAmerican Ceramic Society 82 No 7 pp 1757-60

Ozbay E Michel E Tuttle G Biswas R Sigalas M andHo K-M (1994) ldquoMicromachined millimeter-wavephotonic band-gap crystalsrdquo Applied PhysicsLetters 64 No 16 pp 2059-61

Pendry JB (1996) ldquoCalculating photonic bandgapstructuresrdquo Journal of Physics Condensed Matter 8pp 1085-108

Pendry JB and MacKinnon A (1992) ldquoCalculation ofphoton dispersion relationsrdquo Physical ReviewLetters 69 No 19 pp 2772-5

Safari A Danforth SC Bandyopadhyay A Janas VFand Panda RK (1998a) ldquoOriented piezo electricceramics and ceramicpolymer compositesrdquo UnitedStates Patent No 5796207

Safari A Janas VF Bandyopadhyay A Panda RKAgarwala M and Danforth SC (1998b) ldquoCeramicComposites and methods for producing samerdquoUnited States Patent No 5818149

Shingubara S Okino O Sayama Y Sakaue H andTakahagi T (1997) ldquoOrdered two-dimensionalnanowire array formation using self-organizednanoholes of anodically oxidized aluminumrdquoJapanese Journal of Applied Physics Part 1 36No 12B pp 7791-5

Sievenpiper D Zhang L Broas RFJ Alexopolous NGand Yablonovitch E (1999) ldquoHigh-ImpedanceElectromagnetic Surface with a Forbidden BandrdquoIEEE Transactions on Microwave Theory andTechniques 47 No 11 pp 2059-74

Yablonovitch E (1993) ldquoPhotonic band-gap structuresrdquoJournal of the Optical Society of America 10 No 2pp 283-95

Yablobovitch E (1997) ldquoInhibited spontaneous emissionin solid state physics and electronicsrdquo PhysicalReview Letters 58 No 20 pp 2059-62





52

dissipation There have been many reports for

the application of PBG structures as antenna

substrates such as (Brown and McMahon

1996 Sievenpiper et al 1999) Our research

will focus on the design and fabrication of 3-D

PBG structures with applications in the

millimeter-wave band Such structures are

made by a rapid prototyping technique

discussed below

Many groups have performed research in

photonic structures using alumina as the high

permittivity dielectric material (Masuda et al


1997 Feiertag et al 1997) The use of anodic

porous alumina formed by the anodization of

aluminum in an appropriate acid solution

has attracted attention as a starting material

for 2-D PBG structures with typical

dimensions in the nano- or micrometers since

this process is a typical example of a naturally

occurring ordered structure (Masuda et al


1997) Also Feiertag et al developed a

microfabrication technique for building 3-D

PBG structures using x-ray lithography with

bandgaps in the infrared region (Feiertag et al

1997) These structures have a lattice

constant of 85 mm and are made with 22 mm

diameter rods

Jin et al made microwave measurements on

a 2-D octagonal quasiperiodic photonic

crystal composed of an array of 23 pound 23 rows of

alumina cylinders (Jin et al 1999) The

diameter of the alumina cylinders was

612 mm so the reg lling fraction was 49

percent The authors found a bandgap

between 89 and 105 GHz that the position

and width of the bandgap did not depend on

the incidence direction and that it can appear

even if the arrayrsquos dimensions are lowered to

11 rows of cylinders Because of these

characteristics this photonic quasicrystal

seems to be more suitable for waveguide

applications than as a periodic photonic

crystal For this purpose waveguides were

fabricated by removing 3 rows of cylinders

leaving a 157-mm wide empty path from one

side of the array to the opposite one which

was approximately half of a wavelength at the

gap center The results show a high efreg ciency

of straight and bending guides

For the fabrication of PBG structures in the

mm-range there are few rapid prototyping

processes available Fused Deposition of

Ceramics (FDC) or its modireg ed version for

multimaterials presents several advantages

for the fabrication of the PBG periodic

structures for use in the microwave region

since the minimum part shapes are in the

order 05 mm (Danforth et al 1998 Safari

et al 1998a Safari et al 1998b Jafari et al

2000) The main advantage of this technique

is the rapid prototyping of the complex design

which means that the geometry and the

dimensions of a sample can be easily modireg ed

by the use of a CAD software FDMM makes

it possible to build PBG structures up to

frequencies close to 100 GHz

In this paper we present the application of

a novel fabrication technique fused

deposition of multimaterials (FDMM) to the

manufacturing of PBG structures in order

demonstrate the feasibility of the technique

for this purpose The advantage of FDMM is

the rapid fabrication of complex designs using

a computer-controlled system with no need

for mold or any hard tooling Conventional

fabrication processes require initial making of

bulk pieces of dielectric materials followed by

machining andor etching to form the desired

structures with alternating high and low

dielectric constant materials On the other

hand FDMM deposits the desired materials

only where required by the design and

therefore is capable of making complex PBG

structures

2 Experimental procedure

The modeling was based on a reg nite element

shareware Fortran program written by the

Photonics Research Team of Imperial College

(London UK) and was adapted to this

research in order to incorporate the specireg c

structures that were modeled (Pendry et al

1992 Pendry 1996) Frequency-domain

modeling was also performed using the High

Frequency Structure Simulator (HFSS)

commercial software from Ansoft

Corporation (Pittsburgh PA) This is a

powerful program that can perform real-time

simulation of the wave propagation though

2-D or 3-D dielectric or metallic periodic

structures of any complex geometry The

electromagnetic measurements were carried

out in a Network Analyzer (Hewlett Packard

model HP8510C) with open-ended

waveguides

The geometry of the structure that was

built by FDMM in this work is shown in

Figure 1 The size of the unit cell and in

consequence the spacing between bars and





47







permittivity one




























































































48


























































approach

4 FDMM fabrication












of 4 rows of bars)























49






















































et al 2001)

5 Conclusions









50

















the structure














frequency range













References




















51
















52







permittivity one




























































































48


























































approach

4 FDMM fabrication












of 4 rows of bars)























49






















































et al 2001)

5 Conclusions









50

















the structure














frequency range













References




















51
















52


























































approach

4 FDMM fabrication












of 4 rows of bars)























49






















































et al 2001)

5 Conclusions









50

















the structure














frequency range













References




















51
















52






















































et al 2001)

5 Conclusions









50

















the structure














frequency range













References




















51
















52

















the structure














frequency range













References




















51
















52
















52

3-D photonic bandgap structures in the microwave regime by fused deposition of multimaterials

Documents

Transcript of 3-D photonic bandgap structures in the microwave regime by fused deposition of multimaterials