5
Discussion of the Experimental Results
The experimental setup, which was the focus of the previous chapter, allows accu-rate measurements of the ESFADOF transmission characteristics. The influence of several important control parameters on the ESFADOF transmission character-istics has been systematically investigated by employing the measurement prin-ciple of Sec. 4.4 together with the described extensive data post-processing. The results of this study will be the contents of Sec. 5.2. They have been obtained by employing vapor cell I and demonstrate Rubidium ESFADOF operation and its operational limits. Section 5.3 focuses on these limits. In addition, Sec. 5.4 examines the results obtained with vapor cell II, which allows the employment of higher magnetic fields. As proof of concept, these measurements demonstrate the general feasibility of the ESFADOF edge-filter as Brillouin-lidar detector system.
In order to facilitate the upcoming discussion of this chapter, it is useful to have a closer look on the general influence of the investigated control parameters.
Fig. 5.1: Schematic of the experimental implications towards an optimized transmission: The ESFADOF design as well as the experimental parameters have to be adapted in order to suit the Brillouin-lidar requirements. The specific realizations as well as the exact choice of all external parameters have to comply with severe restrictions due to the manufacturing process and the airborne compatibility.
The arrows indicate direct influence.
therefore intended to give an overall overview of the implications of the vapor cell temperature and the pump geometry on the ESFADOF device.
5.1.1 Vapor Cell Temperature
Generally speaking, ESFADOF spectra depend on several different terms which themselves are influenced by the temperature of the vapor (cf. also Secs. 3.5 and 3.6):
1. The Rb vapor density: The density of the Rb vapor increases exponentially with the temperature [78]. The corresponding dependency as well as a plot of the temperature dependent Rb density can be found in appendix A and Fig. A.1. Generally speaking, increasing the Rb vapor density mainly in-creases the opacity of the vapor.
Due to the fact, that the accessible vapor volume is limited by the measure-ment geometry (cf. Fig. 4.1), increasing the vapor density results in more atoms, which interact with the high magnetic fields close to the permanent ring magnets at the cell entrance. This increases the dispersion and leads to significantly higher transmissions of the ESFADOF spectra.
Moreover, radiation trapping processes profit from high vapor densities as well (cf. Sec. 3.6.3). Increasing the opacity of the vapor simultaneously increases the amount of trapped radiation [138, 139]. Generally speaking, increasing the vapor density increases the trapping volume around the pump laser beam, up to a certain threshold density. When increasing the vapor density further the contrary effect appears and the trapping volume shrinks. In order to shed light on this effect, Scholz et al. performed measurements concerning the influence of the vapor density on the spatial extent of the trapping region [171]. They investigated the radial extent of the trapping volume in optically pumped and pressure broadenend Sodium vapor. Their experiments prove that beyond a certain density threshold the trapped radiation remains confined to a smaller volume compared to lower vapor densities. They quote temperature thresh-olds of 220◦C and 240◦C for their experimental conditions, which comprise also additional Argon partial pressures of 20 hPa and 200 hPa respectively. In addition, Scholz et al. solved the radiation trapping problem numerically and reproduced the measurements with good agreement. The authors showed that the confinement of the radiation increases also with increased Argon partial pressure, i.e. with an increased spectral overlap of the pump laser with the atomic transition. However, their results can not be transformed to Rb vapor quantitatively, as they investigated pressure broadened Sodium vapor. More evidence on that topic delivers the radial profile of the pumped region. A rea-sonable indicator for the diameter of the trapping region is the energy pooling fluorescence. In particular, the 6P3/2 →5S1/2 and 6P1/2 →5S1/2 transition fluorescence (420 nm and 421 nm respectively) allow an excellent spectral discrimination from the pump laser. By imaging this fluorescence on a screen, it is possible to gain a rough estimation of the trapping diameter. Figure 5.2 shows the corresponding measurements for different cell temperatures. The
150 200 250 300 TCell / °C
20 30 40 50 60
σ / Pixel -100 0 100
Position / Pixel 0.0
0.5 1.0
Normalized intensity
2σ
200°C Gaussian fit
Fig. 5.2: Temperature dependence of the trapping volume: The confine-ment of the trapped radiation upon the increase of the number density is clearly visible for temperatures>160◦C. The inset shows a cross section through one corresponding radial profile and a Gaussian fit to the data. The dashed line is a cubic spline fit and underlines the confinement. Please note that the pre-sented measurement estimates the radial profile by imaging the energy-pooling fluorescence of the vapor cell. The surround-ing oven did not allow a perpendicular access, so that the fitted profile widthsσcan only be compared relative to each other.
circles mark the measured full width half maximum of an arbitrary cross sec-tion through the imaged fluorescence and the dashed line a cubic spline fit through these points. The shrinking of the trapping volume, when increasing the cell temperatures beyond 160◦C, is clearly apparent. The employed tech-nique gives only a rough estimate of the absolute diameter, however the values can be compared relatively, which proves that the confinement of the trapped radiation has to be taken into account for temperatures beyond 160◦C.
For the sake of completeness, it has to be mentioned that for pump intensities, which exceed the saturation intensity of the vapor by orders of magnitude, nonlinear radiation trapping effects appear. Stacewicz et al. and Scholz et al. performed extensive measurements on this topic [172–174]. By exciting sodium vapor with laser pulses of several kW/cm2in intensity, they have been able to demonstrate the saturation of the vapor far beyond the pumped volume.
The fact that subnatural decays, i.e. decays faster than the natural lifetime of the excited atoms, result from the nonlinearity of these high pumped vapors, is striking. However, the available intensities of the employed cw pump laser do not reach values to observe this effect.
2. The energy pooling quenching rate: The energy pooling quenching rate de-pends on the mean velocity of the Rb atoms, vRMS =q
3kBT
mRb , which itself has a square root dependency on the local vapor temperature. However, the small cross section of this process,σEP5P3/2↔5D=3×10-14cm2[140], will only extract a minor amount of Rb atoms from the 5P3/2 state (cf. Sec. 3.6.2).
3. The Doppler width: The Doppler width,νD=2νq2 ln 2 kmc2BT, is also propor-tional to the square root of the local vapor temperature and affects the width of the ESFADOF spectra directly. However, the exponential increase of the Rb vapor density covers this effect as long as the vapor remains saturated.
5.1.2 Pump Geometry
Besides the vapor cell temperature, the choice of the implemented pump geometry has the strongest effect on the ESFADOF transmission spectrum and offers some distinct control parameters, such as the pump laser intensity, its detuning from the D2 line center, its spectral width and its polarization. These parameters allow to tailor the ESFADOF spectra within certain limits as they directly influence the population of the lower ESFADOF state:
1. The pump intensity: The amount of excited state atoms is directly influenced by the pump intensity. Saturating the vapor is advantageous in order to ob-tain the maximum ESFADOF transmission. In addition, as the energy-pooling quenching rate is proportional to the square of the excited state population (cf.
Sec. 3.6.2), increasing the 5P3/2population also increases the losses. However, this loss channel saturates also with the saturation of the vapor.
A quite more advantageous effect when increasing the pump intensity emerges from the imprisonment of the pump radiation within the vapor cell (cf.
Sec. 3.6.3). Trapped photons can undergo a high number of absorption and reemission cycles within the highly opaque vapor before they eventually reach the initially pumped region again or escape from the vapor cell [139].
Meanwhile they experience a significant change in frequency and polariza-tion [138, 139, 175]. These photons can be absorbed again by atoms within the initially pumped region and hence populate excited states, whose spectral overlap with the initial pump laser almost vanishes. This effect is of particular importance, as the confinement of the trapped radiation reinjects a significant amount of the trapped radiation back into the interaction volume. Hence, this effect can be regarded as an advantage and Sec. 5.2.2 further elaborates on this discussion.
2. The detuning of the pump laser: The spectral overlap between the pump laser and the 5S1/2→5P3/2 pump transition influences the amount of absorbed radiation. Due to the spectrally narrow laser source, this additional degree of freedom potentially offers the possibility to tailor the ESFADOF spectral char-acteristics to some extent. However, it can not be uncoupled from radiation trapping effects and the inhomogeneous magnetic fields. Its influence will be examined in Sec. 5.2.3.
3. The polarization of the pump laser: For the Brillouin-lidar detector, sym-metric ESFADOF transmission spectra are advantageous. Hence, an extensive polarization of the Rb vapor has to be avoided, as it suppresses complemen-tary transitions. In view of the high inhomogeneity of the employed magnetic fields a linear polarization perpendicular to the quantization axis appears to be advantageous, as it potentially suppliesσ+andσ- transitions. In addition, the optical pumping process benefits from the frequency and polarization redis-tribution of the trapped radiation within the saturated vapor. In fact, the best results have been obtained by injecting a linear polarized pump beam into the ESFADOF vapor cell, which is why the following discussion will be restricted to a linear polarization of the pump beam.
4. The spectral width of the pump laser: At this point, the spectral width of the pump laser needs some distinct consideration. For the sake of completeness, it has been included as an accessible parameter, though it is not exploited in the present experimental setup. The spectral width of the pump laser is imposed by the ECDL master oscillator, which seeds the tapered amplifier. Typical values of the spectral width are of the order of a few MHz, which means that the pump laser reaches only distinct velocity groups within the Zeeman- and Doppler-broadened absorption profile. This is of particular importance, as the large hyperfine-structure of the Rb 5S1/2→5P3/2 transition in combina-tion with the high magnetic fields lead to a considerable spreading of the Rb 5S1/2→5P3/2 absorption spectrum. Increasing the spectral width of the pump laser to the extent that it almost perfectly matches the spectral absorption pro-file of the Zeeman and Doppler broadened Rb vapor, would certainly improve the energy deposition into the vapor. In addition, the frequency redistribution due to the radiation trapping process would become less important and, as an appreciated side effect, it would become easier to simultaneously pump σ+ andσ− transitions when applying strong magnetic fields. Hence symmetric ESFADOF transmission spectra can be expected, when mapping the spectral width of the pump laser with the spectral width of the involved pump transi-tions. A significant increase in absolute transmission can also be expected.
Recently, Gourevitch et al. published the development of a high power vol-ume Bragg laser diode (VOBLA), which operates around 780 nm and offers a spectral width of 7 GHz and up to 2 W of laser power [176]. In view of the above discussion, this development is a very promising tool, as it would allow an optimized spectral overlap between the pump laser and the Doppler-and Zeeman- broadened absorbtion profile. The Brillouin-lidar requirement of approx. 500 mT result in a spectral width of the Rb 5S1/2→5P3/2 transition, which easily exceeds 7 GHz.