Metamaterial Slow-wave Structures

for High-Power Microwave Devices

Kubilay Sertel

John. L Volakis

Students: Nil Apaydin, Panos Douris & Md. Zuboraj

Group velocity:

Wave Slow-down Using Anisotropic Materials

… …

Unit cell

H0

r r2 r1

F A2 A1

Periodic Magnetic Photonic Crystal

A1,2:Anisotropic dielectrics F: Biased ferrimagnetic layers

Slow-group velocity mode @ SIP

Corresponding K-ω diagrams

Isotropic Dielectric Medium

r

B

B:Isotropic dielectric

Periodic Isotropic Medium

1r

B1

B1,2:Isotropic dielectrics

2r

B2

… …

k

w

0g

v k

c

1p

v k

c

SIP due to anisotropy

k

w

Wave slow-

down(vg=0)

Field enhancement

2nd order relation (w’=0)

3rd order (w’=0, w”=0) k

w

RBE

2nd order relation (w’=0)

Phase velocity:

2.4 2.5 2.6 2.7 2.8 2.9 0

20

40

60

80

100

Frequency (GHz)

gro

up

de

lay (

ns)

SIP

Band edge

forward backward

Experimental Validation of Wave Slow-Down

In Volumetric Form In Printed Form

Band edge

SIPMPCs Free

Space

@ SIP: 7.2ns 0.18ns

Finite 9-unit-cell Printed MPC

Finite 8-unit-cell Printed MPC

4.40.440.1

3.960.440.1

4.4

0.44

MPC

@SIP: 96.1ns

Free

Space

0.33ns

3.96

0.44

Measured Group Delay (ns)

Finite 15-unit-cell Volumetric MPC

Wave velocity reduction by a factor of 286

Novel Slow-wave Structures and Antenna Designs

Utilizing Slow Group Velocity Modes

~Uniform Aperture

Illumination

High Directivity

|E|

dB

Ө (in degrees)

200 /L

140

450

15dB

)R/V 10log( Normalized INOC 82

Miniaturized Antennas w/ Optimal Gain BW

Gain Enhanced Dipole Antenna Embedded in MPC

Coupled

UncoupledUncoupled

L1C1

0

L2C2

0

L3 LM

L3 LM

C3

0

C3

0

CMLM

(V1

I1)

(V2

I2)

(V3

I3)

(V4

I4)

Inductive

coupling

Capacitive

coupling

Coupled

UncoupledUncoupled

Coupled

UncoupledUncoupled

L1C1

0

L2C2

0

L3 LM

L3 LM

C3

0

C3

0

CMLM

(V1

I1)

(V2

I2)

(V3

I3)

(V4

I4)

Inductive

coupling

Capacitive

coupling

MPC Antenna Element Broadside 6.2 dB Gain at 2.35GHz

1.05”

1.03”

Broadside 6.5 dB Gain at 2.22GHz

Mode Profile at 2.22 GHz

DBE Antenna Element

Printed Coupled Lines Emulating Slow Modes

Gain Enhancement via Leaky-

waves

5

Remarkably Large Bandwidth for Thin Conformal Arrays

71.75mm

(0.06λ-1.4 λ)

εr = 4

23.25mm

(0.02λ-0.45λ)

Bowtie Array with FSS in substrate

23.25mm

(0.02λ-0.45λ)

Infinite Unit Cell

270-5850 MHz (22:1)

•22:1 BW

•Low profile

•Efficiciency. ≥ 69%

•Excellent polarization

purity (AR ≥ 43 dB)

Interweaved Spiral Array (ISPA) w/

FSS in Substrate

Infinite Unit Cell

FSS in substrate:

Rs = 25Ω/□ 23.25mm

(0.014λ-0.5λ)

71. 5mm

(0.04λ-1.5 λ)

175-6350 MHz (36:1)

FSS in substrate:

Rs = 25Ω/□

•36:1 BW

•Low profile

•Efficiency ≥ 63%

•Circular polarization

εr = 4

6

Integrated UWB Balun and

Demonstrated Meta-structured Array Benefits

6

New thin Metastructured Array is

• Thinner

• Much greater bandwidth

• Has integrated balun and feed

(several balun/feed options)

• Lightweight 600-4500MHz

• Military datalinks:

• Link-16, DWTS, DDL, TTNT, TACAN, etc.

• Almost all commercial telecom waveforms

• Wideband SAR, TWRI

Measured Metastructured Aperture

•Much thinner integrated printed balun (trivial cost);

as thin as /15 at 600MHz, lowest operational

frequency.

• Measured array was 8x8 and had 7.3:1

VSWR<2 bandwidth with no FSS in substrate.

• Aperture: 9.4”x9.4” (89in2)

• Scanning verified to 60o with no sidelobes or

surface waves

• Beam steering over entire band (digital or optimal

beam formers required).

Nonreciprocal Leaky Wave Antenna

Using Coupled Microstrip Lines

-p -0.5p 0 0.5p p 3.5

3.6

3.7

3.8

3.9

4

4.1

Normalized wavenumber K( kd )

Fre

qu

en

cy(G

Hz)

H i =1450Oe

Guided Wave

Region

Guided Wave

Region

Leaky Wave

Region

H i =1600Oe

-k o d k

o d

+1

- d

-1

+ d

Ferrite substrate: εr=14,

4πMs=1000 G,

δH=10Oe, tan δε=0.0002

θ=sin-1(β-1/k0)

z

y

kz

β-1

k0

θ

1 2 N

…

h Hi

x

Permanent magnet

e-jβ-1y Hi

e-αy

ZL ZL

Nonreciprocal Leaky-wave Antenna

w 3 s 2

s 1

w 2

w 1

l 1 l 2 1

Hi

l

d

x

y coupled

uncoupled z x

l1=110, l2=120, w1=60,

w2=20, w3=30, s1=105,

s2=10,h=100, d=440(mils)

• leaky/fast wave: |β-1/k0|<1 radiates

Beam-steering capability

without frequency

modulation

due to tunable dispersion

properties with bias field

strength, Hi

• guided/slow wave: |β+1/k0|>1 does not radiate

Unit-cell Dispersion Diagram

Nonreciprocal Transmitting and Receiving Properties

Traditional Slow-wave Structure

for Travelling Wave Tubes

z

y

x

εr

εr dielectric liner

dielectric liner

Cerenkov Maser: Dielectric Lined Cylindrical Waveguide

Bunched

electron

beam, νe-

B0,

(static magnetic field)

e- e- e- e-

e- e- e- e-

electron gun collector

Slow-wave Structure

RF signal, νp

1)Microwave signal vp ≈electron velocity ve-

Cherenkov Radiation Condition

0 0.2p

0.4p

0.6p

0.8p

p

1.2p

1.4p

1.6p

0

10

20

30

40

50

Normalized wavenumber K=kd

fre

qu

en

cy(G

Hz)

Wide BW (constant vp)

p

eq

c

0eeV / m

-

*e and m are electron charge and mass. V0 =voltage applied to electron gun.

Corresponding K-ω diagram

2)Strong longitudinal E-field at waveguide center

(TMz modes) for mode coupling

Issues to be Addressed

in Designing High-Power Microwave Devices

Shortcomings:

•Limited wave slow-down

(depends on the filling ratio (a/b)

and r)

•Dielectric charging

•Surface breakdown

•Bulky design

z

y

x

Cerenkov Maser Advantages:

•Simple geometry

•Wider bandwidth

•Tunable operation

•Several MWs of output

microwave power

•Validated performance

Solution

•Purely metallic slow-wave metamaterial structures

Dielectric filling ratio=a/b

Additional wave slow-down (L) Metallic construction

Goal:

•Larger amplification (G0) •Wide bandwidth •Smallest configuration (L)

•Avoid

charging

Gai

n

Frequency

G0 G0/2 G0/2

Bandwidth

Gai

n

Device Length

G0

L

Possible Slow-wave Structures

for Travelling Wave Tubes Travelling Wave Tube with Periodic Slow-wave Liner

Dielectric/Ferrite

Corrugations

Concentric Metallic Rings Metal Corrugations Coupled Transmission Lines

on Dielectric

Limited wave slow-down

good for relativistic e-beams, ve-c

Cherenkov Radiation in Periodic Media

21

Electron

particle

ve-

vp=c/n

n=effective

refractive

index of the medium

Helix Double Helix Ring-Bar Structure Coupled Cavities OR

Enormous wave slow-down

(good for slower e-beams, 0.1c<ve-<0.3c)

Metallic Slow Wave Structures

Based on Helical Waveguide

Advantages of Helix WG

•Considerable wave slow

down.

•Purely metallic

construction.

•Wide BW operation.

Travelling Wave Tube

Electron-beam bunching Field Amplification

Operation Principle

ve- =(eV0/m)1/2

e and m are electron charge and mass.

V0 =voltage applied to electron gun.

Electron gun

V0

Gain-9.54+47.3CN (dB) (* J. R. Pierce, Travelling Wave Tubes, NY: D.Van Nostrand

Co, 1950)

2

03

2

02 4

axialE I

CP V

N=number of wavelengths

Needs to be as

large as possible to

obtain high gain.

Key Performance Parameters

for Helical Waveguides

5 10 150.1

0.2

0.3

0.4

0.5

Frequency(GHz)

p/c

helix

Normalized Phase velocity

Double-helix

Ez: Longitudinal field

strength along z axis

β:phase constant within

WG

P:net power flow along

helix

2)Interaction Impedance: K0=Ez2/(2β2P)

(*J. R. Pierce, Travelling Wave Tubes, NY: D.Van Nostrand Co, 1950)

2 4 6 8 10 12 140

50

100

Frequency(GHz)

K0(

)

Interaction Impedance K0

double helix

helix

Need Larger K0 for

stronger interaction

with the e-beam

•Double-helix allows for more energy transfer from the e-beam to the RF signal.

1)Phase velocity of EM wave=electron velocity vp= csinψ = ve- =(eV0/m)1/2* Ψ=cot-1(2πa/p)

*e and m are electron charge and mass,

V0 is the voltage applied to electron gun.

Double- Helix

a p

a=2.375mm

p=3.52mm

p

a

Helix

Strong transverse electric field!

Need

constant vp

for wider BW

3 4 5 6 7 8 9 10 11 12 13 0.1

0.2

0.3

0.4

0.5

Frequency(GHz)

p /c

3 4 5 6 7 8 9 10 11 12 13 0.1

0.2

0.3

0.4

0.5

Frequency(GHz)

g /c

Double-Helix

a

p

a=2.375mm

p=3.52mm

δ=0.15mm

Simpler

Ring-bar Structure

•Easier to fabricate

•Extra wave slow-down

•Higher K0(Ω)larger gain

Simplified Double-Helix : Ring-bar Structure

a

p

Normalized Phase &Group Velocity

Double Helix

Ring-bar WG

Double Helix

Ring-bar WG

slower

2 4 6 8 10 12 14 0

20

40

60

80

100

Frequency(GHz) K

0 (

)

Double Helix

Interaction Impedance K0(Ω)

Ring-bar WG

larger

Similar dispersion

δ

a1=2.375mm

a2=1.9mm

p=3.52mm

δ=0.15mm

a1

p

a2

Ring-bar

Inner Ring

(Inductive coupling)

δ

Design 1:

Double Ring-bar Structure for Miniaturization

E-field profile

Strong longitudinal field stronger coupling

between the RF signal and e-beam

Purely metallic construction

Connected inner and outer

rings (no charging or arcs)

Inductive&capacitive coupling

extra wave slow-down&miniaturization

Current Distribution

Coupled

UncoupledUncoupled

L1C1

0

L2C2

0

L3 LM

L3 LM

C3

0

C3

0

CMLM

(V1

I1)

(V2

I2)

(V3

I3)

(V4

I4)

Inductive

coupling

Capacitive

coupling

Coupled

UncoupledUncoupled

Coupled

UncoupledUncoupled

L1C1

0

L2C2

0

L3 LM

L3 LM

C3

0

C3

0

CMLM

(V1

I1)

(V2

I2)

(V3

I3)

(V4

I4)

Inductive

coupling

Capacitive

coupling

coupled

uncoupled

Performance of Double Ring-bar Structure

3 4 5 6 7 8 9 0

0.2

0.4

Frequency(GHz)

p

/c

3 4 5 6 7 8 9 0

0.2

0.4

Frequency(GHz)

g

/c

Phase & Group Velocities

More dispersive

(not desired)

slower

Ring-bar

Double ring-bar

3 4 5 6 7 8 9 0

50

100

150

200

Frequency(GHz)

K 0

(

)

Interaction Impedance

Larger K0

Ring-bar Double ring-bar

Ring-bar

Double ring-bar Extra wave slow-down

(0.18c<vp<0.32c)

Larger K0 over the bandwidth

(90Ω<K0<150 Ω)

More dispersive (not desired)

Operates between 3-7GHz

(vp=0.25c±0.07c)

a1=2.375mm

a2=1.9mm

p=3.52mm

δ=0.15mm

a1

p a2

δ

Design 2:

Modified Ring-bar Structure

for Additional Miniaturization

Jsurface Distribution (A/m)

Longer current path miniaturization

E-field Distribution (V/m)

Strong axial E-field strong radiation

Modified Ring-bar Structure

Concentric ring-

bars increase

the current path

and leads to

miniaturization.

Performance Using Modified Ring-bar Structure

2 4 6 8 10 12 140

0.2

0.4

Frequency(GHz)

p/c

3 4 5 6 7 8 90

0.2

0.4

Frequency(GHz)

g/c

Phase & Group Velocities

1.5 times slower

Similar dispersion

2 4 6 8 100

50

100

150

Frequency(GHz)

K0(

)

Regular ring-bar

Modified ring-bar

Interaction Impedance

Larger K0 at low

frequencies

1.5 times more wave slow-down (0.18c<vp<0.25c) Larger K0 up to 5.8GHz(75Ω<K0<150 Ω)

Similar dispersion

Operates between 3-7GHz(vp=0.215c±0.035c)

Further Miniaturization

Using CRLH Concept

4-port circuit model

Port 1

Port 3

Port 2

Port 4C

L

L

C

CC

Microstrip TRLs

Series Chip Capacitors Parallel Chip Inductors

Interdigital Capacitors

Shunt Inductors

Interdigital

Capacitors Shunt Inductors

-p 0 p

Normalized Wavenumber (K=kd)

wRBE

w02

w01

wSIP

Frequency band gap

Fre

qu

ency

K-w Diagram

SIP

Light line

low frequency

resonance

Coupled Transmission Lines

Port 1

Port 3

Port 2

Port 4

Microstrip TRLs

Coupled Transmission Lines w/

Lumped Elements

0 + d

- 1 + d

+1 - d

0 - d

- 2 p - p 0 p 2 p F

requency w

n= - 1 n=0 n=0 n=+1

Normalized Wavenumber (K=kd)

Strong Spectral

Asymmetry

but

high frequency

resonance

K-w Diagram

•Artificial anisotropy

•Nonreciprocal behavior

•Leaky-wave radiation from n=±1 harmonics

•Leaky-wave radiation from n=0 mode 18

β+1=β0-+2π/d

Leads to

miniaturization

by a factor of 3!

Ohio State’s Research

• Design slow wave structures using a variety of metamaterial liners

Purely metallic is our first focus

Material loading to be considered as well and examine their potential

Coupling, Power & Group Velocity consideration

• Demonstration and applications

-------------------Immediate Steps--------------------------------------

• Calculate interaction of SWS with e-beams using PIC code simulations.

– E-beam bunching

– Cherenkov radiation

– Field amplification

• Final prototype and performance evaluation for high power microwave source.

– Output power

– Power efficiency

– Bandwidth of operation