We describe the direct measurement of actual transmittance of sodium samples with thickness of a 2 mm and 3 mm in a spectral range >115 nm, resulting in >50% transmittance of 3 mm thick solid and liquid sodium samples including transmission of a pair of the windows at the wavelength of 120 nm, giving an extinction coefficient of ~10−6 to ~10−7 which represents the sodium with a few cm thickness to be partially transparent for this wavelength. To confirm the measurement, we perform simple imaging experiments by the ultra-violet light passing through a 8 mm-thick sodium sample to illuminate a mesh as an object, resulting in obtaining a clear image.
© 2013 Optical Society of America
Optical property of alkali metals including sodium was intensively investigated in the 20th century [1, 2]. In 1930s, Wood proposed sodium as transparent material in the vacuum ultra-violet (VUV) spectral range since he had observed anomalous optical constant of a thin layer of sodium in a bulb . In 1960s, Sutherland et al. proposed optical transparency based on the measured dielectric optical constants of the real and the imaginary parts represented as ε1, ε2, respectively in the solid state based on their original experimental results and the summary of the previous works . They measured the refractive index relevant to ε1 with the interference and critical angle methods for reflected light resulting in obtaining plasma wavelength of 218 nm (the plasma energy of 5.69 eV) . Although the absorption processes such as the ionization and the plasmon excitation [5, 6] in the wavelength range of <218 nm may prevent clear transparency, the sodium can be partially transparent down to the threshold of the electron excitation wavelength of 40.5 nm (the energy of 30.6 eV) . The most important constants for the transparency are the extinction coefficient relevant to ε2. Sutherland et al measured them with a sample having a sub-μm thick solid sodium layer coated on a Quartz and lithium-fluoride (LiF) substrates . On the basis of the pioneering works, we should extend the characterization into much thicker sodium region to clarify the value of the extinction coefficient.
Recently, Fukuda et al. proposed a visualization technique for observing sophisticated hydrodynamic behavior in liquid sodium as a sample of conductive fluid . In this case, we need the accurate optical constants especially for the ε2. We also need the constants in the liquid state where the enhanced electron-ion collisions are expected to enhance the transmittance . On the other hand, the plasmon excitation is proposed theoretically to make enhanced absorption . The experimental data of transmittance in liquid state is really desirable.
Here we present successful characterization of a spectral transmission of several mm thick sodium samples with temperature dependency from the solid state to the liquid state. Based on the measured transmittance, we try to obtain an image of a test piece illuminated by VUV light passing through a sodium sample with thickness of up to 8 mm, resulting in obtaining successfully the image of 100 μm diameter bars. The present experimental results confirm the partially transparent property of a bulk sodium sample in the VUV region.
2. Experimental setup
Experimental setup is represented schematically in Fig. 1. We use a deuterium lamp having a magnesium fluoride (MgF2) window as a continuous VUV source whose wavelength is longer than 115 nm. The VUV light enters into the MgF2 window followed by a solid sodium sample and another MgF2 window where the thickness of each window is 1mm as shown in Fig. 2. The samples are assembled in a glove box. In it, whole the equipments for making the samples are heated and dried for a few days to reduce the water contamination significantly before the actual use. We assemble a sample on the heater at the temperature of 120 degrees centigrade which is slightly higher than the melting point of 97 degrees centigrade where the surface tension of the molten sodium for the operation is suitable. Whole surface of a sodium sample is covered with MgF2 windows shielded with a copper o-ring in one side and a cylindrical support structure made of stainless steel to protect the undesired chemical reactions. Note that a sample holder has an enough empty room for sodium escaping from a main part of the holder without causing additional pressure to MgF2 windows. During transmission experiments, the flatness of the MgF2 window is monitored with a He-Ne laser beam reflected at the surface of the window with an accuracy of 0.1 mrad, resulting in no detectable deviation from the flat surface during the experiments. After the preparation of the samples, we take them out from the glove box to vacuum container. We try to minimize the exposure time of the samples in the air for less than a minute although the samples are protected against the air. Empirically the samples keep their transmittance for 2~3 months in the experiments.
The thickness of the sodium layer is 2 mm and 3 mm to obtain thickness dependent spectral transmittance to determine the extinction coefficient. The notation M1 and M2 represent mirrors having a 100% reflectivity. Transmitted light is spectrally resolved by the Seya-Namioka type grating spectrometer. An entrance slit (S1) and an exit slit (S2), each of which has a 100 μm slit width, are placed at the proper position according to the grating curvature as shown in Fig. 1, where the light source image is transferred to the slits. A photomultiplier coupled with the slit (S2) detects a monochromatic spectral component. The total spectral resolution is <1 nm at the wavelength of 150 nm mainly owing to the aperture width of the two slits. We have tested to take each datum as follows. We perform successively 3, 5, 10 and 20 times data acquisition at specific wavelength to be averaged over the acquisition time. We find that 3 and 5 times acquisition gives us the fluctuation ratio of between 10−2 and 10−3, where the fluctuation ratio is defined as an amplitude of fluctuation divided by a signal level. On the other hand, 10 and 20 times acquisition gives us the ratio of 10−4. Rather large fluctuation just after changing the wavelength may be caused by the mechanical stability of the optical system. Anyway, we have decided to choose the 10 times data acquisition at each step throughout the experiment.
3. Experimental results and discussions
Figure 3 represents the spectral intensity profiles of the deuterium lamp itself and transmitted light through the 2 mm and 3 mm-thick sodium samples. We concentrate on the data analyses in the spectral range of <180 nm because the intensity of the lamp outside this range is low. Figure 4 shows the spectral transmittance of the MgF2 windows with thickness of 1mm for each and that of the sodium samples combined with the windows having thicknesses of 2 mm and 3 mm. For obtaining net sodium transmission caused by absorption, firstly we measure the transmittance of a single window as shown in Fig. 4. Next, we measure the transmittance of a pair of windows without a sodium sample as shown also in Fig. 4. The transmittance of the pair of windows should be squared by that of the single window. In this respect, rather good coincidence is visible. Then we subtract the reflection loss of each layer to layer boundary taking into account the refractive indexes of MgF2 [12, 13] and sodium [14, 4] as shown in Fig. 5. For example, we watch the data around the wavelength of 130 nm in Fig. 4, the reflection loss is dominant. The extinction coefficient of MgF2 is calculated to be ~10−6 to ~10−7 around the wavelength of 120 nm. The coefficient depends upon the reflection loss calculated using the refractive index of MgF2 which include 10% error bars [12, 13]. Note that below 120 nm, the transmittance decreases rapidly due to increasing the extinction coefficient of MgF2. We also subtract the reflection losses including sodium layer and we finally obtain the net transmittance due to absorption for the 2 mm- and 3 mm-thick sodium samples. Note that error bars on the measured transmittance of two sodium samples arise from the accuracy of the spectral intensities. The difference between the two extinction coefficients obtained independently with use of 2 mm and 3 mm sodium samples is <20% in the entire spectral range. In Fig. 4, the error bars of the extinction coefficient are estimated to be larger when the coefficient becomes smaller where the absorption loss of the sodium samples is an order of a few % which is the limit of the dynamic range of the measurement. We also note that the accuracy of the extinction coefficient of sodium depends upon the accuracy of the refractive indexes especially in the high transmission region such as the wavelength of ~120 nm, because the reflection losses of sodium-MgF2 interface dominate compared with the absorption loss. Estimated error bars indicated on this curve is also shown in Fig. 4. Note that the error bar at the wavelength <118 nm is significantly larger than that at the rest of the spectral range. Anyway, the wavelength range between 200 nm and 100 nm, the extinction coefficient of sodium which has not been listed in the handbook  is measured in the present experiment.
When we raise the temperature of the windows measured by a thermo-couple very slowly, for example it takes an hour from 23 to 152 degrees centigrade, the transmittance of the MgF2 windows does not change within a measurement accuracy of <10−3. We also measure the spectral transmittances of the sodium sample with thickness of 3 mm as a function of the temperature, resulting in very small difference such as <0.03 over the entire spectral range compared with the one shown in Fig. 4. The result encourages us to make a visualization technique in and through the liquid sodium medium although we need further characterization of temperature dependency in the liquid state.
In order to confirm the partial transmittance of sodium, we perform an imaging experiment as shown schematically in Fig. 6. Figure 7 represents a clear tungsten mesh image in the VUV region where the diameter of the bars is 100 μm. A VUV light at the lamp is transferred by the MgF2 lens having a focusing length of 100 mm to illuminate the mesh passing through a 8 mm-thick sodium sample. The mesh image is transferred by the other MgF2 lens to the phosphor plate, at which the VUV light is converted into visible light and the signal is transferred via a set of fibers to two-dimensional Charge Coupled Device (CCD) detector. The photo is represented under the optimized sensitivity. In the photo, the blackened region and the slightly dark region correspond to the areas covered with a 1 mm-thick glass plate having a shortest transmission wavelength of ~270 nm and that covered with a 1 mm-thick fused silica plate  having the wavelength of ~160 nm as indicated in the photo. The image caused by these optical elements confirms that a clear image in this configuration is owing to the VUV light. If we watch the wavelength range close to 120 nm in Fig. 4, the absorption coefficient of <0.2-0.5/cm derived from the extinction coefficient of ~2-5 x 10−7 indicates that the useful thickness of sodium for visualization is at least a few cm if we use an intense 120 nm light source coupled with an efficient optical system.
Another interesting point of the present work includes physical interpretation of such high transmittance. According to the conventional theory, the absorption due to the interband transition is ineffective, rather than that due to the Drude model  in this spectral range. If we assume the electron-electron relaxation time of 0.1ps , expected transmittance is ~10−3 for a 1mm-thick sodium sample which is far lower than the present experimental result. In the classical Drude theory, transmittance of substances strongly depends upon the electron-electron relaxation time or effective electron mass. If we assume that the electron mass is that in the vacuum, the present results requires the relaxation time of an order of 10 ps which is at least slower by 2 orders of magnitude than that expected in the previous theoretical and experimental works in 1960s [6,8]. It is interesting to note that recently, extremely slow relaxation time has been found in heavy-fermion metal , It also suggests that the present result may show us unresolved interesting role of quantum mechanical processes of a metallic sodium.
We believe that the present results show a clear demonstration of the partially transparent thick metallic sodium in the VUV spectral range proposed firstly by Wood . The measured extremely small extinction coefficient provides us a good theoretical problem in the field of optical property of alkali metals. From the practical point of view, we can set up a continuous real time transmission imaging experiment for a few cm thick sodium sample if we use proper optical setup including an intense VUV source. Such an experiment opens up a way to design and construction of a visualization device for transmitted images through or inside a solid or liquid sodium medium.
We are deeply indebted to the members of International Nuclear Information & Training Center and Applied Laser Technology Institute at Tsuruga Head Office, Japan Atomic Energy Agency.
References and links
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