e r(nr) non-resonant reflection
DESCRIPTION
The minimum reflection regime. "ordinary" selective reflection. Conclusion. (model). zoom at. The raw and derivative signals. How to change the interference condition in the window? very easily, by changing the window temperature For 0.5 mm sapphire window and l= 852nm : - PowerPoint PPT PresentationTRANSCRIPT
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)