TeraHertz Kerr effect in GaP crystal

   

J. Degert, M. Geye, E. Abraham, E. Freysz

Laboratoire Ondes et Matière d’Aquitaine

University of Bordeaux

France

Dept. Physics, Bangalore, October 24 2011

Outline

1. Introduction:

2. THz spectroscopy application to the GaP crystal

3. THz- Kerr effect in GaP

4. Conclusions and prospects

Conventional Kerr effect experiment

Set-up

To lock-in amplifier

• The pump induces a nonlinear third-order polarization in an isotropic medium • The medium becomes birefringent

• The birefringence induced in medium placed in between two crossed polarisers is sensed by a probe-beam whose polarization is at 45° with respect to the pump beam .

• Pump and probe pulses can be delayed to perform time-resolved experiment

Photodiode

probe pulse

Pump pulse

Liquid or Crystal

/2l

Polariser/4l

Crossed Polariser

Dt

Conventional Kerr effect experiment

• This technique is usually applied in the optical spectral range, in degenerate wavelength configuration, in transparent and isotropic medium

• Liquids• Glasses

• The dispersion and absorption of the medium is usually negligible• No dispersion and absorption of the pump or probe pulses mismatch• No group velocity mismatch• Automatic phase matching

• Only one nonlinear third order coefficient as to be known: all the other are related !

• We will see the situation is quite different, if you perform a THz Kerr effect experiment in a cubic crystal (GaP) using a visible pulse as a probe

The first THz Kerr effect experiment

Kerr effect: Change of refraction induced by an electric field

Hence a initially isotropic liquid may become anisotropic when properly excited by the electric field of a THz pulse

),,';'(2

3 )()( )3(

,,,0

22 xxxxnnwithtIntn

• M.C. Offmann et al., Appl. Phys. Letters 95, 231105 2009

THz Kerr effect in liquid

' )'(

exp)'()()(0

2

0

022

2 dtt

tEn

Ennt

Thze

• M.C. Offmann et al., Appl. Phys. Letters 95, 231105 2009

THz spectroscopy of GaP

THz-TDS of our GaP CrystalTHz-TDS of our GaP Crystal

The set-up

THz-TDS of our GaP CrystalTHz-TDS of our GaP Crystal

0 1 2 3 4 5 6 7

3.3

3.4

3.5

3.6

Ref

ract

ive

ind

ex

Frequency (THz)

0 1 2 3 4 5 6 70

10

20

30

40

Ab

sorp

tio

n c

oef

fici

ent

(cm

-1)

Frequency (THz)

0 1 2 3 4 5 6 7 8 9 10

1E-11

1E-10

1E-9

EO

sig

nal

(A

)

Frequency (THz)

ref GaP

0 5 10 15

-10

0

10

20

30

EO

sig

nal

(n

A)

time (ps)

ref GaP

FT

Absorption band @ 4.5, 5.5 and ~6.5 THzPhonon @ 11 THz

THz-TDS of our GaP CrystalTHz-TDS of our GaP Crystal

First conclusions:• We have a dispersion of the index of refraction and a small

absorption in the THz range

• We are using a 43m cubic crystal: according to Kleinmann’s relation two nonlinear coefficients have to be considered

• We have a large index mismatch in THz and near I.R. spectral range:

n(THz) ~ 3.4n(l~800nm) ~ 3.66

THz Kerr effect in GaP

03 pr32i ij j

j

P t t E te

dc In the reference frame of the crystal (OXYZ), the THz induced third order polarization is:

3 pu pu*ij ijkl k l

kl

t d R t E Edc t t t t

with

Response function

Eprobe

ETHz

X

45°

x

yˆ ˆX z

Z

Y

q

Geometry of the experiment

c-axis 001Z

THz pulse

Oxyz = reference frame of the laboratory

optical axis 100ˆz X

Theoretical background IThird order non linear polarization

Theoretical background IThird order non linear polarization

03 pr3

2 2, ,i iiP t t E t i x y

edc

22 pu

22 pu

3 31 2 4

2 43 3

2 42 4

sin sin

sin sin

xx

yy

u ut b E t

u ut b u E t

dc q q

dc q q

with

Rough approximation: R(t) is purely electronic !!! 3ijkl ijklR t ts d

+ Crystal symmetry: 43m0

0

iiii

iijj ijji ijij

a

b

s

s s s

+ An other approximation: THz and optical pulse are phase matched in GaP

In the frame of the laboratory (Oxyz)

u = a/b

Theoretical background Third order non linear polarization

Theoretical background Third order non linear polarization

Detection set-upGaP

<100>L=1 mm

λ/4

Wollaston

tSs

Sp

PD1

PD2

I SKerr(t)=Ss–Sp

2

prKerrS dt E t tt t fD

phase retardation of the probe pulse accumulated in GaPtfD

pr pr pr

2 32y x yy xxn n L L

np p

dc dcl l

22 pu

pr pr

31 3 2

2sin

Lb u u E t

np

ql

2 22 pu prKerr 1 3 2sinS b u u dt E t E tq t

Theoretical background Kerr effect signal

Theoretical background Kerr effect signal

C. P. A.

λ0 = 795 nm

τp = 35 fs

1 kHzBeamsplitter

(R=90%)

THz120 kV/cm

GaP <100>1 mm

Pellicle

Si-filter λ/4

Wollaston

BalancedDetector

Lock-inAmplifier

Computer

Delay

Probepulse

700 µJ

Type I BBO 100 µm

f = 25 cm

Eprobe

ETHz

X

45°

x

yz

Kerr effect in a GaP crystal: Experimental set-up

Kerr effect in a GaP crystal: Experimental set-up

EMax (THz)= 120 kV.cm-1

-40 -20 0 20 40 60 80 100 120 140

Inte

gra

ted

Ker

r S

ign

al (

a.u

.)

2Kerr 1 3 2sinS d K u ut t q

Eprobe

ETHz

X

45°

x

yˆ ˆX z

Z

Y

q

OXYZ = crystal frameOxyz = lab frame

Fit u = siiii/siijj 8

Angular dependenceAngular dependenceWe checked the THz Kerr effect was linear with respect to

the THz pump intensity

0 1 2 3 4 5

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

SK

err (n

A)

delay (ps)

= 0°

0 1 2 3 4 5

-0.1

0.0

0.1

0.2

0.3

0.4

SK

err (

nA

)

delay (ps)

= 40°

0 1 2 3 4 5-0.2

0.0

0.2

0.4

0.6

0.8

1.0

SK

err (

nA

)

delay (ps)

= 90°

Temporal dependenceTemporal dependence

If the vf (THz) =vg (800 nm) then S(t)~I THz (t)

Not our case

Conclusions and prospects

Conclusions:1. We have investigate the THz Kerr effect in a <100> GaP crystal2. The angular dependence results from the symmetry of the crystal 3. The temporal dependence of the Kerr signal is mainly affected by the velocity

mismatch and the dispersion of the THz pulse during its propagation within the crystal. The latter is related to c(1) (THz)

4. In near future we would like to investigate the dispersion of c(3) (THz,THz,visible)

Our prospects in Nonlinear THz optics:Resonnant• Self induced transparency• THz photon echosNon-resonnant• Self focusing, self phase modulation, THz solitons….

Our laser research in fiber laser

• Average power 20 W at 74 MHz• Pulse duration tunable from 20 ps down to 120 fs• Wavelength tunable from 1010 nm to 1080 nm

-40 -20 0 20 400.0

0.5

1.0

-6 -3 0 3 60.0

0.5

1.0

-4 -2 0 2 40.0

0.5

1.0

0.07 nm filter

Inte

nsi

ty (

a.u

.)

Delay (ps)

(a)

-1.0 -0.5 0.0 0.5 1.00.0

0.5

1.0(d) 0.07 nm filter

In

ten

sity

(a.

u.)

(nm)

(b) 0.9 nm filter

Inte

nsi

ty (

a.u

.)Delay (ps)

(c) 4 nm filter

Inte

nsi

ty (

a.u

.)

Delay (ps)

-2 -1 0 1 20.0

0.5

1.0(e) 0.9 nm filter

(nm)

In

ten

sity

(a.

u.)

-10 0 100.0

0.5

1.0 (f) 4 nm filter

(nm)

In

ten

sity

(a.

u.)

• Demonstration of ignition of combustion chambers

• Patent on laser ignition of aeronautic engines.• Four-wave mixing in birefringent LMA fibers

Prospectives:• Fondamental research: nanosecondes fiber laser tunable in the visible spectral range• Applied reseach: Application to laser ignition to actual aeronautic engines

• Développement of fiber lasers for ignition of aeronautic engines in partner-ship with a french compagnie (Turbomeca)

Our laser research in fiber laser