E R(nr) non-resonant reflection
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Transcript of E R(nr) non-resonant reflection
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)