Nonlinear optical processes can be greatly enhanced for quasi-resonant atomic and molecular systems, allowing phenomena like efficient frequency up-conversion, four-wave mixing, slow light or image storage to be studied at low light intensities. On resonance, absorption hinders the build-up of strong coherences; this can be counteracted by excitation via two-photon resonances and in particular by using electromagnetically induced transparency (EIT). Here we report the generation of 1.1mW of 420nm blue light by enhanced frequency up-conversion in a hot rubidium vapor. This is made possible by long lived two-photon coherences at frequencies that allow propagation under phase-matching conditions. Depending on the polarization of the pump lasers, up-conversion can be enhanced or almost completely suppressed.

Alkali metal vapors are versatile tools for spectroscopy and nonlinear optics in atomic physics and have long been used for studies of 2-photon spectroscopy [1, 2, 3], dispersion [4] and EIT [4, 5]. In both isotopes of rubidium, the 5S_1/2–5P_3/2 (780nm) and 5P_3/2–5D_5/2 (776nm) transitions (Fig. 1a) are easily accessible with simple diode laser systems [6]. The extremely strong dipole moment of the infrared 6P_3/2–5D_5/2 transition (Fig. 1b) means that two-photon pumping with 776 and 780nm light facilitates three-photon coherence between ground state and the 6P_3/2 level. Excitation and decay via other levels (5P_1/2, 6P_1/2, 5D_3/2) is excluded by large detuning and selection rules. Similar alkali metal transitions have proven ideal for studies of amplified spontaneous emission versus four-wave mixing [7, 8], superfluorescence [11], multi-photon ionization processes [8], and sensitive atomic imaging [9, 10].

Recent papers [12, 13, 14] have reported the generation of tens of µWatts of coherent 420nm blue light by pumping the Rb 5S–5P–5D transition. In our experiment we obtained up to 1.1mW of coherent blue light for similar input pump powers. We have studied and optimized blue light generation for a variety of experimental parameters, namely input beam polarization and frequency, and Rb vapor pressure. In our system we have measured a maximum of 1.1mW of coherent blue light close to two-photon resonance of the input lasers at Δ₇₈₀ = −Δ₇₇₆≅1.6GHz. Optimal conditions include a Rb vapor pressure of 10⁻³ mbar and cocircularly polarized input beams at maximum available powers of 17mW at 776nm and 25mW at 780nm. This corresponds to a conversion efficiency of η = P ₄₂₀/(P ₇₇₆ P ₇₈₀) ~ 260%/W.

 

Fig. 1. a) The Rb energy level scheme. b) Relevant Rb transition parameters [15]. c) Experimental image showing how co-propagating focussed 780 and 776nm laser beams create a coherent 420nm (and invisible 5.2µm) beam.

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Fig. 2. a) Experimental schematic, abbreviations used are: PD (photodiode), VC (vapor cell) N/PBS (non/polarizing beamsplitter) and ECDL (external cavity diode laser). b) Power in the coherent 420nm beam as a function of 780nm (red) and 776nm (black) input power. For each trace the power of the other input beam was maximal and detunings and polarization were optimized, see text.

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The essence of the experimental setup is shown in Fig. 1c), with a more detailed view in Fig. 2a). Laser beams from Faraday-isolated 776nm and 780nm extended-cavity diode lasers are overlapped on a non-polarizing beamsplitter and focussed into a 75mm long Rb vapor cell. The pump beams have maximum powers of 17mW and 25mW respectively which for elliptical beams with waists of 0.6mm × 1.1mm yield an estimated focal intensity of ≈ 2×10⁶W/m² each. Note that the 780nm beam area after the cell varies with frequency, differing by more than an order of magnitude due to Kerr lensing.

We have measured the conversion efficiency as a function of the 776 and 780nm input power (Fig. 2b), with all other parameters fixed at their optimum values stated above. We note that conversion efficiency depends on the Rabi frequencies and detunings of the pump beams, so that for low pump powers the chosen detunings are not ideal. The pump power was varied by rotating half wave plates in the individual input beams, and monitored via the polarizing beamsplitter (PBS) shown in the dashed region of Fig. 2a). Although the blue light begins to saturate with 780nm input power, it is linear in 776nm input power in the regions accessible by our diode lasers, promising a further increase in blue light power for stronger 776nm pumping.

The atomic density and associated vapor temperature were measured to high resolution via absorption spectroscopy of a low power (5µW) 780nm probe beam [16]. This avoided any inaccuracy due to the inhomogeneity of the external cell temperature. For our setup optimal blue light generation occurs at a temperature of 120±1°C, corresponding to a Rb vapor pressure of 9×10⁻⁴ mbar, nearly 4 orders of magnitude higher than at room temperature. While higher temperatures, and therefore atomic densities, facilitate the nonlinear up-conversion process, they also increase absorption of the pump and output beams. Overall, the system is fairly robust: more than half of the maximum blue beam efficiency could be achieved over a temperature range of 104–131°C corresponding to a factor of 5 in Rb pressure, and focussing the nearinfrared light from 0.4 to 4 times the optimal free-space focal intensity yielded similar (> 75% of optimal) conversion efficiency.

In order to investigate the up-conversion process we have measured fluorescent and coherent blue light generation over a wide range of input beam frequencies, see Fig. 3c)–f). Data was taken for low and high Rb temperatures of 90°C and 120°C respectively, corresponding to vapor pressures of 1×10⁻⁴ mbar and 9×10⁻⁴ mbar. The frequency of the 780nm beam was measured via saturated absorption spectroscopy in a room temperature Rb cell, and that of the 776nm beam by monitoring the two-photon absorption of a weak 776nm probe beam counterpropagating through the hot cell (Fig. 2a).

We have modeled fluorescence and coherent light generation (Fig. 3a) and b) from optical Bloch equations for the 5 atomic levels, using a similar model to Ref. [13], evaluated with Doppler broadening (FWHM~580MHz for the 776 and 780nm light at ~100°C) and for Rabi frequencies (Ω₇₈₀ = 1.4GHz, Ω₇₇₆ = 0.4GHz, Ω_IR = 30MHz, Ω₄₂₀ = 20MHz) similar to the estimated experimental focal values in the low pressure cell. The model does not explicitly include propagation, and neglects the hyperfine structure of the upper states. Nevertheless, numerical solutions for the steady state of the optical Bloch equations allowed us to interpret many of the observed features. Fluorescence (top row of Fig. 3) arises from a transfer of population to the 5D level and subsequent fast decay to the 6P level. Our model shows that this happens mainly when the system is pumped at two-photon resonance between the Stark-shifted atomic levels, and to a lesser extent, for resonant driving of the 776nm transition. The model (Fig. 3a) describes the observed fluorescence well (Figs. 3c and e), even though it does not account for propagation effects or 780nm pump Kerr lensing which increase at higher temperature.

The generation of coherent blue light requires coherences between the ground state 5S hyperfine levels and the 6P level. While the detuning of the blue (and IR) light is experimentally unknown, our simulations suggest that coherent blue light conversion occurs at three-photon resonance. For the (relatively) small blue light and IR intensities in the experiment the 6P level is unshifted, so three-photon resonance coincides with two-photon resonance. Phase-matching is a prerequisite of efficient coherent light generation. Our model shows that phase-matching Δk = n ₇₈₀ k ₇₈₀+n ₇₇₆ k ₇₇₆−n_IRk_IR−n ₄₂₀ k ₄₂₀≈0 is satisfied along most of the three-photon resonances. We model blue light generation (Fig. 3b) as Doppler-broadened coherences adjusted to account for Kerr lensing and absorption of the 780nm pump beam. This is an approximation to a full analysis which would require the study of field and density matrix propagation for non-collinear beams. At lower vapor pressure, we observe coherent blue light over a range of detunings near two-photon resonance (Fig. 3d), reminiscent of observations in Ref. [13, 14]. Strikingly, when the Rb pressure in the cell is high, the experiment shows an increase of blue beam generation by 1.5 orders of magnitude, however only over a restricted range of input detunings (Fig. 3f), with highest conversion efficiency for two-photon (and three-photon) resonance at Δ₇₈₀ = −Δ₇₇₆ = 1.6GHz. We attribute the suppression of blue light generation outside this region to Kerr-lensing of the 780nm input beam. Furthermore, absorption of 780nm light contributes to the absence of light generation from the ⁸⁷Rb isotope.

 

Fig. 3. Relative blue fluorescence (top row) and blue beam (bottom row) power as a function of 780 and 776nm light detuning. Theoretical simulations of the 5-level Bloch equations are shown in a) and b). Graph a) shows the Doppler-broadened population in the 6P level corresponding to blue fluorescence. Fig. b) shows the Doppler-broadened coherences between ground and the 6P level, corresponding to coherent blue light generation. The blue coherences are adjusted to account for Kerr lensing and absorption of the 780nm pump beam. Graphs c) and d) show measurements at a cell temperature of 90°C, and e) and f) at 120°C. At low pressure, coherent light is generated over a range of detunings at twophoton resonance. At high pressure Kerr-lensing of the pump beams and phase-matching become more pronounced, restricting blue light generation to a narrow frequency window. The backdrops show 780nm saturated absorption in a cold cell.

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A scan (Fig. 4) of the 780nm input frequency, keeping the 776nm detuning constant at the optimized value of Δ₇₇₆ = −1.6GHz, shows clearly the strong frequency dependence of fluorescence and blue light generation. The theoretical model (Fig. 4a) of blue fluorescence accompanied by 776nm absorption agrees well with the experiment (Fig. 4c). Coherences on the 420nm transition between the 5S level and 6P level are present at two-photon resonance for the two hyperfine ground levels of ⁸⁵Rb and ⁸⁷Rb, and mark out four frequency regions of potential blue light generation, Fig. 4b). Kerr-lensing depletes and deflects the 780nm pump laser at three of these resonances, so that only the coherence at Δ₇₈₀ = 1.6GHz survives. The same detuning also exhibits a local minimum of absorption of the 780nm input laser. We note that Kerr lensing will change beam direction and hence also modify the phase-matching condition. Increasing the atomic density and hence the optical path length, makes propagation effects and phase-matching more critical and adds further complexity as more 5µm and 420nm fields are generated. Experimentally, the strongest blue light generation was observed near a minimum of lensing for the 780nm beam, Fig. 4d).

 

Fig. 4. Coherent and fluorescent blue light as a function of Δ₇₈₀ for Δ₇₇₆ = −1.6GHz. Graph a) shows theoretical blue fluorescence (420_F, blue) as well as transmission of the 776nm (776_T, black) pump beam, including Doppler-broadening. Graph b) shows the blue beam coherences (420_B, blue), as well as the Doppler-broadened theoretical transmission (780_T, red) and Kerr-lensing ( ${780}_{n_2}\propto \frac{\Delta n_{780}}{\Delta I_{780}}$ intensity-dependent refraction, black) of the 780nm beam, which favors the coherence at 1.6GHz. Measurements of blue fluorescence accompanied by 776nm absorption c), and blue beam generation d) are shown for different input polarizations: counter-circular (red), crossed-linear (green), co-linear (blue) and co-circular (purple). Vertical lines indicate ⁸⁵Rb and ⁸⁷Rb 780nm resonances.

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We finally report the crucial effect of input polarization on blue light generation, shown in Fig. 4c) and d). For these experiments the PBS in the dashed region of Fig. 2a) had to be removed. We simultaneously monitored the blue beam power (PD_B), the blue fluorescence in the cell (PD_F), absorption of the 776nm beam (PD₇₇₆), and the detuning of the 780nm laser (PD_SAS). Measurements were taken for four different relative input polarizations of the 776nm and 780nm input beams: co-linear, crossed-linear, co-circular and counter-circular. Care was taken to compensate for grating polarization-dependence in the 776nm pump beam measured at PD₇₇₆. By analyzing the 776nm laser absorption (Fig. 4c), we can estimate that it is possible to create a coherent 420nm photon for every six 776nm photons absorbed. Note that the blue beam generation is suppressed by a factor of 500 when counter-circular polarization is used, although there is still a similar amount of blue fluorescence and 776nm beam absorption, indicating that the transfer of population to levels 5D_5/2 and 6P_3/2 is not forbidden by two- and three-photon absorption selection rules. This implies that the excitation of three-photon coherences between the 5S_1/2 ground state and the 6P_3/2 state depend crucially on polarization. Optical pumping favors blue light generation for the case of co-circularly polarized pump beams, however, the inhibition of blue light generation for counter-circular polarization suggests an interference effect. This may be attributed to a cancelation of the coherences due to the phase of the atomic dipoles. One can envisage that this property will be useful for applications in optical switching, where flipping 780nm (or 776nm)pump polarization would switch the blue beam power.

As our system is not saturating with pump power, increasing the pump power or using a build-up cavity could generate tens of mW of blue light. By accessing higher lying D _5/2 levels one should be able to generate similar powers at UV wavelengths by transitions via the corresponding P _3/2 levels. It is interesting to consider the application of such light sources for laser cooling where the narrower linewidth on these blue/UV transitions will lead to much lower Doppler temperatures [17]. In initial experiments we have observed 420nm linewidths of less than 8MHz, at the resolution limit of our etalon. The scheme should generalize to all alkali metals, and has recently been realized in cesium [20].

In conclusion, we have observed a polarization-dependent factor of 26 increase in blue light conversion efficiency under comparable conditions to previous experiments. Our observations of the frequency-dependent characteristics of the 776nm beam absorption, blue fluorescence and blue beam power show good agreement with our theoretical framework, particularly for low experimental temperatures, indicating the importance of three-photon resonance coinciding with vanishing susceptibility on the 780nm transition. In the low Rb pressure regime with the weaker blue beam afforded by crossed-linear polarizations we observe similar experimental behavior (frequency dependence and conversion efficiency) as observed in Refs. [12, 13] and we attribute our increased efficiency to polarization enhancement as well as a higher apparent Rb vapor pressure. It is clear that propagation must be included for proper modeling of the system at high temperatures due to the strong absorption/refraction processes at work in the cell. There are still many open questions in this surprisingly rich atomic vapor system. We envisage future experiments in isotopically enhanced vapor cells (to simplify the system’s absorptionemission characteristics) and sapphire vapor cells which will allow us access to the ‘missing link’ of the closed loop structure [18, 19], the 5.2µm light.