12 Nonreciprocal Circuit

8/6/2019 12 Nonreciprocal Circuit

1/14

14. Nonreciprocal circuits

14.1 Loss-less characteristics of circuits

isolators

circulators

14.2 Microwave response of magnetic material

14.3 Isolator

14.4 Edge-guided mode

14.5 Circulator14.6 Application of circulators

Bi-directional transmission

Applicable to a phase modulatorAdd Drop Multiplexer


2/14

Isolator is never a loss-less device.

Loss-less or lossy ?

Check whether S-matrix can be unitary or not.(1) Isolator

Sa

2

1

2

1

01

00

a

a

b

b

ISS

10

00

(2) Circulator

3

2

1

3

2

1

001

100

010

a

a

a

b

b

b

ISS

Circulator can be a loss-less device.


3/14

Microwave response of magnetic material

Apply a magnetic field along the z-direction, then

operating frequency

22

0

s

-

-

1 rz

220

s0

-1

r

(Ms: saturation magnetization) ss M00 )/8.2( OeMHzH

Poldars tensor 0

00

0

0

rz

r

r

j

j


4/14

h

b

)(

0

)(

0

)(

)(

0000

0

rx

x

rxr

xr

x

x

rz

r

r

jh

h

hj

h

jh

h

j

j

h

b

)(0)(

0)(

)(

000

0

0

rx

x

rxr

xr

x

x

rz

r

r

jh

h

hj

h

jh

h

j

j

Electromagnetic field in magnetic material

H and B of RF field :

tj

e

h

tj

e

b

right-handed circularly polarized wave:

)2

cos(]Re[

cos]Re[

tjeh

tehjhh

hh

tj

y

tj

x

xy

yx jih

left-handed circularly polarized wave:

)

2

cos(]Re[

cos]Re[

tjeh

teh

jhh

hh

tj

y

tj

x

xy

yx jih


5/14

Faraday rotatoion

linearly polarized wave: 0,cos0 zyx eetEe

)}2

cos(cos{2

)}2

cos(cos{2

cos

00

0

ttE

ttE

tEex

jiji

ii

r-circular polarized l-circular polarized)(0 r )(0 r

)}sin()cos({2

)}2

cos()cos({2

0

0

ztztE

ztztE

ji

ji )}sin()cos({

2

0 ztztE

ji

ztzEztztE

ex2

cos2

cos)}cos(){cos(2

00

ztzEztztE

ey2

cos2

sin)}sin(){sin(2

00

)(22

zFPolarization plane rotates by an angle

in the reverse direction: 00 HH

ss MM )(0 r)(0 r

F


6/14

Isolator

polarizer + Faraday rotator + polarizer

edge guided mode

Polarizer

Polarizer

Polarizer

Polarizer

45degFaraday rotator

45degFaraday rotator

H

H


7/14

Edge-guided mode

x

y

d

H0

z

plateferritein0x

EH

HE

j

j

jj

r

r

0

0

001

0

)()(

)()(

)()(

220

22

0

00

y

E

jz

E

H

y

E

z

EjH

Ej

z

H

y

H

HHjjy

EHjHj

z

E

xx

rr

r

z

x

r

x

r

ry

x

yz

zryx

zyrx

002

2

2

2

2

xeffxx E

z

E

y

E eff

r

r

)( 22

)()( 022

2

2

jz

Ey

Exeff

x


8/14

Edge-guided mode

eff022 zjyy

x eBeAeE )(

)()(0

22

2

2

jz

Ey

E

xeff

x

zjy

reff

z

zjy

reff

x

reff

y

zjy

x

eAejH

eAeEH

eAeE

0

00

11

yEx at0

0on0 yHz

r

r

r

0

0

r

eff022

zjy

r

y eAeH

0

Ex, Hy

y


9/14

zjy

r

y eAeH

0

Edge-guided mode

r

Ex,Hy

y

Reversing the propagation direction (-->-)

forward

r

back

)(


10/14

Junction type circulator

eigen excitation of 3 port rotationally symmetric circuit

1

1

1

3

10u

3/2

3/2

1

3

1

j

j

e

eu

3/2

3/2

1

3

1

j

j

e

eu

)(3

1

)(3

1

)(3

1

3

2

3

2

031

3

2

3

2

021

011

SeSeSS

SeSeSS

SSSS

jj

jj

iii S

SSS

SSSSSS

UU

112131

311121

213111


11/14

Junction type circulator -- design

basic configuration: 84.12

rzrR

0U excitation: e

excitation:U

excitation:U

Disk center is replaced with open circuit.

f0 : disk center - port electrical length

CL //0

CL //0

0

0

jeS

j

c

c

c

c

e

CL

LjZ

CL

L

jZ

Z

Lj

Cj

Z

LjCjS

0

2

0

0

2

0

0

0

1

1

1

1

1

1

j

c

c

e

CL

LjZ

CL

LjZ

S

0

2

0

0

2

0

1

1


12/14


Ms, H0 -->

-

-/3

/3

0

0

+

-

,,e

CL ,0disk and line structure -->

3

3

0


13/14


330 ,,

jjj eSeSeS

001

100

010

)(3

1

0)(3

1

0)(3

1

3

2

3

2

031

3

2

3

2

021

011

S

eSeSeSS

SeSeSS

SSSS

jjj

jj

Circulator !


14/14

Application of circulator

(1) Bi-directional transmission(2) Isolator is constructed in combination with an anti-reflection terminator.

(3) Applicable to a phase modulator

(4) Add Drop Multiplexer (ADM)

fiber Bragg grating1,2,3... 1,2,3...

2

2

Add

Drop

Circulator

Circulator

Documents

12 Nonreciprocal Circuit