Radiazione di Hawking analoga in...

Eleonora Rubinorelatore: Daniele Faccio

- relazione delle attività del primo anno -Università degli Studi dell’Insubria

Dottorato in Fisica XXV ciclo

Radiazione di Hawking analoga in laboratorio

PART I: • Hawking Radiation and Analogue Gravity models

• Ultrashort laser pulse filamentation

• Experiments: spontaneous and Bessel filament

PART II:

• A new mid-infrared laser source

PART III:

• Mode conversion (work in progress)

Overview

5 November 2010 Eleonora Rubino

Hawking radiation

Typical stellar mass black hole temperature:10 nK=> too low to be detected!

1974: S. Hawking predicted that the space-time curvature at the event horizon of a black hole is sufficient to exite photons out of the vacuum.

Hawking radiation glimpsed in artificial black hole© New Scientist, 28 September 2010


Essential ingredient is not the astrophysical BH, but rather the space-time curvature associated to the event horizon and a quantum field...

Event horizons and analogue gravity

“The circular jump is a white hole”Jannes et al., arXiv:1010.1701v1


“The same arguments that lead to black hole evaporation also predict a thermalspectrum of sound waves from a sonic horizon”

Unruh - 1981

physical systems analogue to black holes:

• Bose-Einstein condensates;

• Acoustic waves (phonons) in moving fluids;

• Moving refractive index perturbation (RIP) in dielectric media (Philbin et al., Science 2008: optical soliton in fiber).

faster water

slower water

Trapping RIP - phase horizon


Travelling RIP => intense ultrashort laser pulses in a nonlinear Kerr medium:

The moving δn creates a distortion of thespace-time metric seen by light rays.- PROBE: external seed, or quantum vacuum.

• photons decelerate and are arrested at

• blue shifted frequency

white hole

n(r, t) = n0 + n2I(r, t)

Prediction of the model


RIP steepness => blackbody temperature: T =�v2

2πc(1− vn/c)kB

dn

dx

c

n0 + δn< v <

c

n0

RIP velocity => spectral window:

Ultrashort laser pulse filamentation


Main features:

• long propagation range of tightly focused intensity peak:

• nearly single cycle shock front:

• possibility to control v:

> pulse splitting (spontaneous filament)> cone angle (Bessel filament)

-200 -100 0 100 2000

14

7

I (TW

/cm

)2

(fs)0.1 0.4

1.98

2.05

2.02

v (1

0 m

/s)8

x (cm)

(a) (b)TL

!"#!

!"$%

!"$&

'"())))))))))'"*))))))))))'"$))))))))'"# '"$#))))))))))))))'"##))))))))))))))'"+#!"$#+

!"$+

!"$+$

!"$+,

'"%))))))))))))))))'"&)))))))))))))!!"$$&

!"$#*

!"$#%

-

./0121-345)6 78

6/8 698 6:8

input 1055 nmspontanous filament

input 800 nmspontaneus filament

input 1055 nmBessel filament, 7° cone angle

medium: Fused silica

Experiments - setup


200 400 600 800 1000wavelength (nm)

p-e

coun

ts

0

300

600

spontaneous Raman

NBOHC !uorescence @ 650 nm

ODC !uorescence @ 470 nm

Kerr sample: 2 cm long fused silica (suprasil 311)

Hor. pol. input laser pulse, 1 ps 1055 nm Nd:glass.

Imaging of the filament at 90 degree:‣ imaging spectrometer + cooled CCD camera.

Suppression of spurious effect:

• FWM and SPM, or spectral broadening • Rayleigh scattering• Spontaneous Raman scattering • Fluorescences from glass defects

Experiments - spontaneous filament


!"#$#%&%'$(#)*'#+)$,

*-

*.-

*/- -0.

1*2334 2%4254

*-

*.6

*7-

-

-0.

1*2334 284294

:9;%&%)<$"*2)34*=6-*************>6-***************.6-*********66-

*-

*.-

*/-

*6********?06******=06-

-0.

1*2334 2@42'4

A*2334

1 ps, 50 microJ, 10 Hz, Nd:glass laser. Spontaneous filament in 2 cm long fused silica.

90° acquisitions, integrated over 3600 laser shots. 0.1 photons/pulse

c

n0 + δn< v <

c

n0

-200 -100 0 100 2000

14

7

I (TW

/cm

)2

(fs)0.1 0.4

1.98

2.05

2.02

v (1

0 m

/s)

8

x (cm)

(a) (b)TL

varying trailing pulse group velocity

Experiments - Bessel filament


n2 = 2.8± 0.5× 10−16 cm2/W

n2 = 3× 10−16 cm2/W

fit slope:

in fused silica:

Kerr effect:

Hawking radiation from ultrashort laser pulse filamentsF. Belgiorno, S.L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V.G. Sala, D. Faccio

Phys. Rev. Lett., in press.

vB =vGcos θ

θ = 7 deg

slightly superluminal RIP velocity:




PART II:


PART III:


Overview





PART II:

• A new mid-infrared laser source (LaserLab project - Vilnius University)

PART III:


Overview


MIR - justification


• ultrafast IR spectroscopy• biomedicine• laser-matter interaction• high harmonic generation - attosecond science• analogue Hawking radiation

✓ 2nd order nonlinear optics:• NOPAs in KTP, BIBO, PPSLT…

✓ 3rd order nonlinear optics:• gases: FWOPA in filamentation and guided-wave regime• solids: FWOPA in the visible and UV range…

MIR - four-wave optical parametric amplifier


(nm)0.4 0.6 0.8 1.0 1.2 1.4

2

4

6

8

Ext

.

(d

eg

)p

m

(b)

signal

near-IR idler

pump

diagnostics

30 fs, 4.8 J seed pulse (TOPAS white)

130 fs, 1.8 mJ

pump pulse

(Ti:Sapph.)

1 mm

fused silica

f

TF10, 60°

TF5, 60°

prisms pair

compressorAl(a)

pm 1 f2

fs

fp

@ Vilnius University, Laserlab project in collaboration with prof. A. Dubietis

Single-pass FWOPA in bulk fused silica:

➡ pump: 800 nm (1.8 mJ, 130 fs, Ti:sapph)

➡ seed: 550-650 nm (4.8 microJ, 30 fs, TOPAS white)

➡ IR idler: 1000-1500 nm

Diagnostics: - spectrum (fiber spectrometer QE65000 Ocean Optics);- spatial profile (InGaAs CMOS camera - Xenics, Xeva 202):- temporal profile (autocorrelator).

MIR - experimental results


500 550 600 650 700 750(nm)

(a)

0.6-0.6

-0.6

0.6

0

0

x (mm)

y (m

m)

(d)

0

0.5

1

40-40 0time delay (fs)

(c)

1.0 1.1 1.2 1.3 1.4 1.5 1.60

1

0.5

I (a.

u.)

(m)

(b)

0

1

0.5

I (a.

u.)

1

0.5

I (a.

u.)

visible seed pulse

infrared idler pulse

temporal and spatial profile after compressor stage

‣ 20 microJ, sub-30-fs across the whole range

‣ 17.6 fs FWHM at 1200 nm

‣ 1% pump-to-idler conversion efficiency

Generation of broadly tunable sub-30-fs infrared pulses by four-wave optical parametric amplificationE. Rubino, J. Darginavicius, D. Faccio, P. Di Trapani, A. Piskarskas and A. Dubietis

Opt. Lett., Submitted.




PART II:


PART III:


Overview


Mode conversion


input = 1 mode(seed)

ω+

ω−

ωin

output = 2 modes

• Co-moving Ref. Frame: 1 positive mode, 1 negative mode

• Lab Ref. Frame: 2 blue-shifted real modes!

The 2 mode-converted waves are generated at the phase horizon:

travellingRIP

δn

t-x diagram

ω� = 0→ → v = c/nv� = 0

Mode conversion - numerics


1D code: linear propagation of the field.

Intrinsic numerical dispersion (grid resolution):

labco-moving

P

N

N

P

c/vin

in

ph

ω� = 0

ω� − k� n− ω



P

Nin

v = 0.996c

τ = 5 cycles FWHM

λin = 4µm

δn = 2.39× 10−3



spectrum

in

field evolution

P

N

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