ER(nr)

non-resonant reflection

(resonant) atomic response

window

dilute vapour

IR = |ER(nr) + Eat|²

(non-resonnant) reflection

at the interface

Eat

atomic respons

e

"ordinary" selective reflection

imaginary part of Eat ... is not detected!!

real part: interferes with non-res. reflected amplitude → detected signal

Observable = reflected intensity: IR = |ER(nr) + Eat|² |ER(nr)|² . {1+ 2Re(Eat/ ER(nr))}

How to detect the imaginary part?? Some proposals have been made:

► Brewster incidence (ER(nr)=0) ? (Akul'shin et al, Soviet J. Q. E. 19(1989), 416)

the sub-doppler feature of SR spectroscopy is lost;

► multidielectric coating? (theor. work by Vartanyan and Trager, Opt Commun 110(1994), 315)

the coating may be damaged by the atomic vapour

► metallic coating? (Chevrollier et al, Phys Rev E63(046610), 2001)

  considerable attenuation of the atomic signal, due to the required metal thickness

amplitude-and-phase diagram

depending on the relative phase between the two NR reflected beams, two opposite regimes are expected

- close to a reflection maximum:

No qualitative change:

SR signal still displays real part of the atomic response

- close to a reflection minimum:

then:

- Re(Eat) does not interfere with Erefl1 + Erefl2 → not detected

- Im(Eat) interferes with Erefl1 + Erefl2 → DETECTED!

- the Im(Eat) x (Erefl1+Erefl2) signal changes sign around refl. minimum

selective reflection with a parallel window(qualitative approach)

Irefl = |ER(nr)1 + ER(nr)2 + Eat|²

windowdilute vapour

1

2

12

1

2

1

2

2

1

Eat

amplitude-and-phase diagram

How to change the interference condition in the window?

very easily, by changing the window temperature

For 0.5 mm sapphire window and 852nm:

T 30°C 2 change of the interference

(see Jahier et al, Appl Phys B71 (2000), 561 for the use of the

"temperature tuning" of the windows for reflection-loss free vapour cells)

The experiment

Twindow 190-230°C

Tside-arm=160°C

Cs vapour,

3x1014/cm3

sapphire window

diaphragm (rejects fluorescence)

signal = Irefl , vs Twindow & laser

852nm laser diode

F'= 4

F'= 3

F'= 2

-The interference pattern is obvious

- The atomic signal is small... (dilute vapour)

off-resonance background subtraction

- the atomic signal is more evident

- (still a "wavy" offset pattern: the subtracted, off-resonance background has a non negligible dependance on the laser frequency)

The raw signal on

the Cs D1 line

(6S 6P3/2,, F'=2,3,4)

The raw and derivative

signals

raw derivative

(model)

Re(Eat): dispersive

"ordinary" selective reflection

mixed

mixed

Im(Eat): absorptive

(model)

zoom at... The minimum reflection regime

the hidden side of the

selective reflection signal

The model

window

dilute vapour

ER(at)

E0

ER(nr)

n2

n1=1

n3 = n1

window

Continuity equations at the two boundaries between the three media:

- air, n1=1

- (sapphire) window, n2=1.76

- vapour, n3=1

Maxwell equations for the propagation of the backward atomic field in the vapour (without using the slowly varying envelope approximation)field envelope atomic polarisation

)()/²()(2²

)(²0 zPk

zzEik

zzE

assuming cell length >> absorption length (no backward beam coming from z=)

then0)(//

)2exp(1)2exp(

2123

23211212 E

irrirttrE vapourwindowR

atEirr

itt)2exp(1

)exp(2123

3212

=ER(nr) (ordinary reflection from a parallel window ,

with = n2k x thickness)

= ER(at) (the atomic contribution)

(where the tij's and rij's are the amplitude transmission and reflection

coefficients) and the backward atomic field is generated by the vapour atomic polarisation:

L

at dzikzzPikE0

)2exp()(2

Defining the atomic response by and assuming the

absence of saturation and non-linearity, we get (,D: homogeneous and Doppler widths):

b2123

02312

)2exp(1)exp( irr

iEttEat

HFS

F DFF

Csb

ixdxxdN

0

²)exp(²

b

ConclusionThe model and experiment agree very well (no fitted parameter!) on

the size and the temperature dependance of the spectra.

By using a "temperature tunable" window, one can detect at will

- the real (dispersive) part

- or the imaginary (absorptive) part of the atomic response.

S/N is better near the reflection minimum.

Changing from one regime to the other is obtained very easily,

just by changing the window temperature by a few degree C.

Possible application: temperature-tunable locking of a laser frequency

on the zero of the derivative signal

SELECTIVE REFLECTION SPECTROSCOPY

WITH A HIGHLY PARALLEL WINDOW:

PHASE TUNABLE HOMODYNE DETECTION

OF THE RADIATED ATOMIC FIELD

A. V. Papoyan, G. G. Grigoryan, S. V. Shmavonyan, D. Sarkisyan,

 Institute for Physical research, NAS of Armenia, Ashtarak-2, 378410, ARMENIA

J. Guéna, M. Lintz , M.-A. Bouchiat,

LKB, Département de Physique de l'ENS 24 rue Lhomond, 75 231 Paris cedex 05, FRANCE

(to be published in Eur. Phys. J. D)