1. E R(nr) non- resonant reflection (resonant) atomic response windo w dilute vapou r I R = | E R(nr) + E at | ² (non-resonnant) reflection at the interface E at atomic respons e "ordinary" selective reflection imaginary part of E at... is not detected!! real part: interferes with non-res. reflected amplitude → detected signal Observable = reflected intensity: I R = | E R(nr) + E at | ²  | E R(nr) | ². {1+ 2Re(E at / E R(nr) )} How to detect the imaginary part?? Some proposals have been made: ► Brewster incidence (E R(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(E at ) does not interfere with E refl1 + E refl2 → not detected - Im(E at ) interferes with E refl1 + E refl2 → DETECTED ! - the Im(E at ) x (E refl1 +E refl2 ) signal changes sign around refl. minimum selective reflection with a parallel window (qualitative approach) I refl = | E R(nr)1 + E R(nr)2 + E at | ² windo w dilute vapou r 1 2 1 2 1 2 1 2 2 1 E at 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 T window 190-230°C T side- arm =160°C Cs vapour, 3x10 14 /cm 3 sapphire window diaphragm (rejects fluorescence) signal = I refl, vs T window & 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  6P 3/2,, F'=2,3,4) The raw and derivative signals rawderivative    (model) Re(E at ): dispersive "ordinary" selective reflection mixed Im(E at ): absorptive              (model) zoom at... The minimum reflection regime the hidden side of the selective reflection signal The model window dilute vapour E R(at) E0E0 E R(nr ) n2n2 n 1 =1 n 3 = n 1 windo w  Continuity equations at the two boundaries between the three media: - air, n 1 =1 - (sapphire) window, n 2 =1.76 - vapour, n 3 =1  Maxwell equations for the propagation of the backward atomic field in the vapour (without using the slowly varying envelope approximation) field envelopeatomic polarisation  assuming cell length >> absorption length (no backward beam coming from z=  ) then =E R(nr) (ordinary reflection from a parallel window, with  = n 2 k x thickness ) = E R(at) ( the atomic contribution) (where the t ij 's and r ij 's are the amplitude transmission and reflection coefficients) and the backward atomic field is generated by the vapour atomic polarisation: Defining the atomic response by and assuming the absence of saturation and non-linearity, we get ( ,  D : homogeneous and Doppler widths): Conclusion The 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)