THz generation and transport

Sara CasalbuoniDESY Hamburg

S. Casalbuoni, DESY

Overview

• Motivation • Design goals • Simulation tools - POP ZEMAX

- Mathematica code (B. Schmidt, DESY)

• THz beam extraction• Optical design• Simulation of the THz radiation transfer line• Summary and outlook

S. Casalbuoni, DESY

Motivation

CDR/CTR

140 m, = 1000, Eel = 500 MeV

Bunch length measurements with interferometer

S. Casalbuoni, DESY

Design goals

• Flat frequency response

• Low frequency response limit as low as possible BUT– Finite dimensions of transfer line tube and mirrors (ɸ ≈ 200mm)– Long transfer line ~20m

• High frequency structures expected from μbunching up to 30THz(10μm)

S. Casalbuoni, DESY

30THz

Diamond window

S. Casalbuoni, DESY

Vacuum needed

0 200 400 600 800 10000.0

0.2

0.4

0.6

0.8

1.0

Transmission through 20m of Humid Air (50% RH)

Tra

smis

sio

n

(m)

vacuum pressure(mbar) 1000 100 10 1 0.1 0.01

from B. Schmidt

S. Casalbuoni, DESY

LL

yx

L

yxLd

Lyx

L

y

L

xLdyxLd

dddi

eELyxE

ikd

Surf

22

|||,|

1;)()(

),0,,(~

),,,(~

2222

222222

),(

Simulation ToolsZEMAXCommercially availablePOP (Physical Optic Propagation)

B. Schmidt (DESY)Mathematica

2 CODES

Huygens-Fresnel principle:Every point of a wave front may be considered as a centre of a secondary disturbance which gives rise to spherical wavelets, and the wave-front at any later instant may be regarded as the envelope of these wavelets. The secondary wavelets mutually interfere.

ƞ

ξy

x

L

d

first order second orderFraunhofer near field, Fresnel

≃Lfinite size screen

Kirchhoff integral

S. Casalbuoni, DESY

Input for CTR

rII

rII

ck

;)(kb/I

)(kb/K )/(k)(kr/)(kr/K )/(kIr)(k,E

~

;)(kb/I

)(kb/K )/(k)(kr/)/(kK )(kr/Ir r)(k,E

~

//2radius pipebradius beamcoordinate radialr

0

01111r

0

01111r

Fourier Transform with respect to the longitudinal coordinate ζ=z-vt of the radial electric field Er of a uniform bunch charge distribution of radius ρ moving with velocity v in straight line uniform motion (M. Geitz, PhD Thesis).

sinE~ E

~cosE

~ E

~atan(y/x)

ryrx

S. Casalbuoni, DESY

Ginzburg-Frank

L

x

Lx

LxLxI

))/(sin1(

)/(sin)/(

22

22

Valid: - if CTR screen radius ≳ effective CTR radius a ≳ λ -if L ≫ λ 2 ⇒ far field (Castellano & Verzilov, Phy.Rev.ST-Accel. Beams ,1998)

⇒ frequency independent

-8 -6 -4 -2 0 2 4 6 80.0

0.2

0.4

0.6

0.8

1.0

Inte

nsi

ty

(a.u

.)

S. Casalbuoni, DESY

from P. Schmüser

Both conditions satisfied

=300μmL=10m

a=30mm

S. Casalbuoni, DESY

from P. Schmüser

Finite size CTR screen

=1.5mmL=20m

a=30mm

S. Casalbuoni, DESY

from P. Schmüser

Near field

=300μm

L=0.5m

a=30mm

S. Casalbuoni, DESY

L=0.5m a=30mm

from P. Schmüser

Both conditions violated

=1.5mm

and exact SQRT

S. Casalbuoni, DESY

ZEMAXCommercially availablePOP (Physical Optic

Propagation)

B. Schmidt (DESY)Mathematica

Both make use of scalar Fresnel diffraction theory

2 CODES

Valid if objects and apertures >> λ|x-ξ|,|y-η|<<L

ξ

ƞ

x

y

L

Fourier transform of

ck

ddeeEeLi

LyxE LyxikLik

Surf

Lyxik

2;

2

2/)(2/)(

),(

2/)( 2222

),0,,(~1

),,,(~

ddeEdi

LyxE ikd

Surf

),(

),0,,(~1

),,,(~

Simulation Tools

S. Casalbuoni, DESY

Free propagation

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0 (mm) f(THz) 1 0.3 0.1 3 0.01 30 0.001 300

Inte

nsity

(a.

u.)

X (mm)

if a ≲ λ and/or L ≲ λ 2 ⇒ I (x, L,ω) frequency dependent

L=1 m; a=10 mm; =1000

S. Casalbuoni, DESY

Dimensions of the CTR screen

-10 -5 0 5 100

1

2

3

ZEMAX Mathematica

screen intensity @window/@screen (mm)

10 0.74 20 0.84 25 0.83 30 0.79 40 0.70

Inte

nsity

(a.

u.)

X (mm)

window =20mm

L=40mm; =1000λ=1.5mm ⇒ f=200GHz

S. Casalbuoni, DESY

CDR screen

intensity @window/@screen 0.75 0.55 0.78

20 mm

ɸ=20 mm, slit=1mm

ʘ ʘʘ

window =20mmL=40mm; =1000λ=1.5mm ⇒ f=200GHz

ɸ=20 mm

S. Casalbuoni, DESY

Optical design: technical drawing

from O. Peters

S. Casalbuoni, DESY

Optical design

CTR screen ɸ=25mm

diamond window ɸ=20mm

M1 f=630mm ɸ=188mm

M2 f=4500mm ɸ=188mm

M3 f=3500mm ɸ=188mm

M4 f=3000mm ɸ=188mm M5 f=100mm

ɸ=100mmfinal screen

40mm 560mm 3410mm 8990mm 3100mm 2400mm 100mm

M1600mm

M2 M3

M4M5

8990mm

2400mm100mm

3100mm

3410mm

S. Casalbuoni, DESY

Simulation of the THz radiation transfer line with ideal thin lenses

λ=1.5mm ⇒ f=200GHz; =1000

Intensity @final screen/@window=0.49

CTR screen ɸ=25mm Diamond window ɸ=20mm M1 M2

M3 M4 M5 final screen ɸ=8mm

S. Casalbuoni, DESY

-10 0 100.000

0.001

0.002

0.003

-60 0 600.00000

0.00002

-100 -50 0 50 1000.00000

0.00001

0.00002

-100 -50 0 50 1000.000000

0.000005

0.000010

-100 -50 0 50 1000.00000

0.00002

0.00004

0.00006

-50 0 500.00000

0.00005

-10 -5 0 5 100.000

0.005

0.010

M5M4M3

M2

Inte

nsity

(a.

u.)

Mathematica ZEMAX

M1

final screen

Inte

nsity

(a.

u.)

X (mm)

X (mm)

Inte

nsity

(a.

u.)

X (mm)

diamond window

Simulation of the THz radiation transfer line with ideal thin lenses

λ=1.5mm ⇒ f=200GHz =1000CTRscreenɸ=25mmDiamond windowɸ=20mm

Intensity @final screen/@window=0.49

S. Casalbuoni, DESY

-10 0 100.000

0.001

0.002

0.003

-60 0 600.00000

0.00002

-100 -50 0 50 1000.00000

0.00001

0.00002

-100 -50 0 50 1000.000000

0.000005

0.000010

-100 -50 0 50 1000.00000

0.00002

0.00004

0.00006

-50 0 500.00000

0.00005

-10 -5 0 5 100.000

0.005

0.010

M5M4M3

M2

Inte

nsity

(a.

u.)

intensity @final screen/@CTR screen

CTR 0.49 Gauss beam 0.85

w0=9mm

M1

final screen

Inte

nsity

(a.

u.)

X (mm)

X (mm)

Inte

nsity

(a.

u.)

X (mm)

diamond window

Good also for a Gaussian beam

λ=1.5mm ⇒ f=200GHz =1000CTRscreenɸ=25mmDiamond windowɸ=20mm

S. Casalbuoni, DESY

Simulation of the THz radiation transfer line at different frequencies

-4 -2 0 2 40.000

0.005

0.010

(mm) f(THz) 1.5 0.2 0.3 1 0.01 30

= 1000 CTR screen = 25mmdiamond window = 20mm

final screen =8mm

Inte

nsity

(a.

u.)

X (mm)

Intensity @final screen/@window

0.490.900.99

S. Casalbuoni, DESY

Transfer function

0.1 1 10

1E-5

1E-4

1E-3

0.01

0.1

1

Inte

nsi

ty @

fina

l scr

ee

n/@

win

do

w

f(THz)

λ(mm) 3 0.3 0.03

S. Casalbuoni, DESY

Half screen and horizontal polarization: frequency response

-4 -2 0 2 40.00

0.01

0.02

(mm) f(THz) 1.5 0.2 0.3 1 0.01 30

= 1000 CTR screen = 25mmdiamond window = 20mm

final screen =6mm

Inte

nsity

(a.u

.)

X (mm)

Intensity @final screen/@window

0.520.91 0.99

ʘ

S. Casalbuoni, DESY

Gaussian beam λ=500nm

M3 M4 M5 final screen

w0=1mm Diamond window ɸ=20mm M1 M2

S. Casalbuoni, DESY

Summary and outlook

• 2 simulation tools: very good agreement

• Optical design for the THz beam line transfer @140m in TTF2: tested for CTR, CDR and Gaussian beam

• Outlook

-”ideal” mirror surface

-tests for stability against beam displacement and mirrors misalignment

-effect of tilting CTR screen

S. Casalbuoni, DESY

Electric field of a charge in the laboratory system

krK

kqrkE

derkErkE

ctzvtz

rvtz

rqEE

r

rqrE

r

ikrr

rz

10

2/32220

32/322

2

0

4),(

~

),(),(~

)(4;0

sin1

)1(

4)(

q

)(rE

observation point

r

vθ

S. Casalbuoni, DESY

L ≫ λ 2 far field⇒

22

22222

1)(

)(12

)(

LL

L

k

characteristic size of theCTR screen

S. Casalbuoni, DESY

Paraboloid mirrorsCTR screen ɸ=25mm Diamond window ɸ=20mm M1 M2

M3 M4 M5 final screen

S. Casalbuoni, DESY

Paraboloid mirrors

-10 0 100.000

0.001

0.002

0.003

-60 0 600.00000

0.00002

-100 -50 0 50 1000.00000

0.00001

0.00002

-100 -50 0 50 1000.000000

0.000005

0.000010

-100 -50 0 50 1000.00000

0.00002

0.00004

0.00006

-50 0 500.00000

0.00005

-10 -5 0 5 100.000

0.005

0.010

m4m3

m2

Inte

nsity

(a.

u.)

m1

m5

final screen

paraxial lenses paraboloids

Inte

nsity

(a.

u.)

X (mm)

X (mm)

Inte

nsity

(a.

u.)

X (mm)

window

S. Casalbuoni, DESY

Transfer function

0.1 1 10

1E-5

1E-4

1E-3

0.01

0.1

1

lenses paraboloids

Inte

nsi

ty @

fina

l scr

ee

n/@

win

do

w

f(THz)

S. Casalbuoni, DESY

Paraboloid mirrors: half screen and horizontal polarization

Half CTR screen ɸ=25mm Diamond window ɸ=20mm M1 M2

M3 M4 M5 final screen

Intensity @final screen/@window 0.64