Hollow cathode lamps (HCLs) with alkaline-earth metal are attracting growing attention nowadays as sources of intense atomic spectral lines in various physical devices applied in atomic absorption and emission spectroscopy^[1–3]. Furthermore, the atom unit most frequently employed in a traditional Faraday anomalous dispersion optical filter (FADOF)^[4] is a vapor cell with atomic density determined by thermal equilibrium^[5–8]. Hence, the samples of atomic filters have to be heated to high temperatures to get an atomic density high enough to guarantee the transmittance^[9,10]. To overcome this limitation, an innovative method of utilizing an HCL to realize a Sr element FADOF was proposed, as the HCLs can provide the high atomic density at room temperature^[11]. Moreover, since the state-of-the-art HCLs cover about 70 kinds of high melting point metal elements, we believe that, due to its rich spectral lines, without heating, scalability, low fabrication cost, and potential applications in various atomic spectra^[12–16] they can be used in submarine communication systems as well as excited-state FADOFs without the use of a pump laser^[5,6].

Basic knowledge about HCLs is meaningful for the exploration of further applications^[17,18]. The HCLs have rich atomic spectral lines; nevertheless, the spectral measurements are often contaminated by buffer gas-line interference^[14–23]. A new method of measurement, as shown in Fig. 1, element-balance-detection technology, is introduced by us, which can remove the effect of the buffer gas-line via the subtraction relation between two spectral signals of Ca HCL and Sr HCL, as shown in Figs. 2 and 3. This method is simply described as follows: two spectral signals of Ca HCL and Sr HCL both include the buffer gas-line; in order to distinguish the atom lines between the spectral signals, we conduct a subtraction operation of two signals to make the buffer gas-lines offset each other. Although the components of the buffer gas may be different, the results imply that the subtraction procedure is coping better with this problem. Hence, the element-balance-detection technology is applicable for similar situations in atomic spectroscopy measurement, which exists in the interference of impurity lines.

In this Letter, we measured the intensities of fluorescence spectral lines of Ca and Sr atoms in two different HCLs, respectively. In the wavelength range of 350–750 nm in the visible spectral region, using the individual strongest line (Ca 422.67 nm, Sr 460.73 nm) as the bench mark, we calculated the population ratios between the excited states by rate equations and spontaneous transition probabilities. The measured results showed that the intensities of the spectral lines of Ca and Sr atoms are significantly different.

The measurement setup is schematically shown in Fig. 1. Figure 2 shows the energy diagrams of the transitions related to the Ca and Sr atoms’ spectral signal. The Sr HCL and Ca HCL are powered by Power1 and Power2 (generating a current range of 0 to 20 mA), respectively, which are placed across the cathode and anode terminals. The intensities of the fluorescence spectral lines of Ca and Sr atoms were strikingly different along with the current increase. The USB2000+ spectrometer in connection with a personal computer (PC) produced by Ocean Optics Company in USA with a resolution of 1.5 nm is used to measure the fluorescence spectra. One path is Ca HCL spectral signal 1, and the other path is Sr HCL spectral signal 2. Since the spectrometer has only one channel, signals 1 and 2 were not measured simultaneously. The measured signals can be adjusted by a suitable attenuator (coefficient), which is an appropriate constant coefficient, to adjust the amplitude when processing the data. The measured spectral signals are shown in Fig. 3.

When the distance of the spectrometer from the HCLs is set appropriately, the current of Power1 and Power2 is set to be 17 and 20 mA, respectively. The relative intensities of the spectral lines of Ca atoms and Sr atoms can be detected, as shown in Fig. 3. In order to display the signal clearly, it is divided into four pictures according to the wavelength ranges, as shown in Fig. 4. The wavelength ranges of Figs. 4(a), 4(b), 4(c), and 4(d) are 340–440, 440–540, 540–640, and 640–740 nm, respectively.

By reference to the NIST atomic spectra database^[24], the spontaneous transition probabilities Aμη and the wavelengths involved in the calculation are listed in Table 1 (Ca) and Table 2 (Sr). Data in columns 1–4 are wavelengths, spectral signal intensities, spontaneous transition probabilities, and transition level, respectively.

The intensities of the atomic lines depend on the number of sputtered metal atoms, which depends on the kinetic energy of the buffer gas ions, which, in turn, is dictated by the lamp current.

The intensity (P) of the transition signal between two energy levels can be expressed as Pλ=nμAμηhυλ, where λ is the transition wavelength, nμ is the atomic density in the level numbered μ (μ=a,b,c,…), Aμη is the spontaneous transition probability between the μ and η energy levels, υ is the transition frequency, and h is the Planck constant^[22,25,26]. The Ca atoms’ transition signal intensity studied can be clearly expressed with Eqs. (1)–(13). The Sr atoms’ transition signal intensity studied can be clearly expressed with Eqs. (14)–(36): P397=niAijhυ397,(1)P423=nbAbahυ423,(2)P430=nkAkjhυ430,1+nnAnmhυ430,2,(3)P443=nrArmhυ443,1+nuAumhυ443,2,(4)P445=npApjhυ445,1+nrArjhυ445,2+nuAujhυ445,3,(5)P519=ncAcbhυ519,(6)P527=nlAlohυ527,(7)P560=nsAsohυ560,1+nvAvqhυ560,2,(8)P612=nhAhmhυ612,(9)P643=nwAwohυ643,(10)P645=nfAfqhυ645,1+nfAfthυ645,2,(11)P646=nxAxqhυ646,(12)P649=nyAythυ649,1+nyAyqhυ649,2,(13)P358=nfAfjhυ358,(14)P363=nb′aAb′ahυ363,(15)P409=nxAxnhυ409,1+nyAynhυ409,2,(16)P461=nbAbahυ461,(17)P474=nkAkmhυ474,(18)P478=nkAkjhυ478,(19)P481=nhAhghυ481,(20)P483=nuAumhυ483,(21)P487=nrArjhυ487,1+nuAujhυ487,2,(22)P489=nzAznhυ489,1+nyAynhυ489,2,(23)P496=noAoghυ496,(24)P523=nlAlqhυ523,1+niAiqhυ523,2,(25)P545=npApqhυ545,(26)P548=npApnhυ548,(27)P550=nsAsqhυ550,(28)P554=nvAvqhυ554,(29)P581=niAichυ582,(30)P662=na′Aa′thυ662,(31)P679=neAemhυ679,(32)P688=neAejhυ688,(33)P689=njAjahυ689,(34)P707=neAeghυ707,(35)P731=ndAdchυ731.(36)

From Eqs. (1)–(13), the 423 nm transition of Ca atoms has only one spectral line corresponding to the transition, 4s4pP11→4s2S10. Given that the population at the |b> energy level is the maximum, the value of nb is used as the bench mark to calculate the results of nμ/nb. The calculated results of nμ/nb of Ca atoms are shown in Table 3. Because the number of unknowns is larger than the number of equations, we finally get several sets of algebraic results; those are the results obtained in the bottom lines in Table 3.

From Eqs. (14)–(36), the 461 nm transition of Sr atoms also has only one spectral line corresponding to the transition, 5s5p P11→5s2S10. Given that the population at the |b> energy level is the maximum, the value of nb is used as the bench mark to calculate the results of nμ/nb. The calculated results of nμ/nb of Sr atoms are shown in Table 3. By reference to the NIST atomic spectra database^[24], because of the absence of the spontaneous transition probability between the corresponding energy levels Afj, Ab′t, Axn, and Ayn, we can only use the symbols to calculate the equations and display the results.

As shown in Table 3, the populations at the other energy levels are also very large. However, due to the wavelength spacing of 1 nm between 643, 645, and 646 nm, the overlap of signals and the relative lower resolution of 1.5 nm of the spectrometer may bring measurement errors. But, this problem can be solved by using a high-resolution spectrometer. In addition, because the measurable range of the spectrometer, 400–1000 nm, did not cover all the lines of Ca and Sr atoms, some higher excited states may not be considered. Hence, the calculated population ratios have the errors ±0.25. Since the state-of-the-art commercial HCLs cover about 70 kinds of high melting point metal elements and can excite large amounts of levels of neutral atoms, they thus provide abundant transitions for frequency standard fields, etc.^[27–31]

In conclusion, population ratios between the excited states according to the spontaneous transition probabilities with rate equations and the measured intensities of fluorescence spectral lines of Ca atoms and Sr atoms in HCL within the visible spectral region from 350 to 750 nm are calculated; the population density of the energy level is also obtained. Sufficient populations at the excited states are found when the HCLs are lit. The HCLs with populations at excited states can be used to realize the frequency stabilization reference of the laser frequency standard^{[12,23,32–40]}.