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Abstract
We report high-efficiency optical amplification with near-extreme-limit gain from a diode-pumped Cs vapor cell. We used wavelength-division multiplexing to couple 852 nm pump and 895 nm seed lasers to achieve nearly overlapping spatial modes in the Cs vapor cell. We investigated the amplification factor as a function of the focal length of the lens focusing on the combined pump and seed signals and determined the optimal focal length under our experimental conditions. The small-signal amplification factor from the Cs vapor cell reached >30 dB at 240 mW pump power, and the optimal optical amplification factor per pump power was 4171/W.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Alkali atom vapors have attracted significant research attention as gain media for optical amplification since Schawlow and Townes first proposed an optical maser based on potassium vapor [1]. Subsequently, coherent light amplification in optically pumped Cs vapor was measured at an infrared wavelength of 3.2 µm by selective optical pumping [2]. A considerably efficient diode-pumped alkali-vapor laser (DPAL) based on Cs vapor was also subsequently demonstrated [3–16]. The main advantage of the DPAL is its high quantum efficiency of 95.3% for Cs atomic vapor due to the difference in wavelength between the pump laser and the amplified beam being smaller than that of a solid-state or fiber laser [4–6].
In this context, high-efficiency diode-pumped alkali amplifiers (DPAAs) are promising candidates for high-power DPAL implementations because they simplify the use of multiple pump sources and adequately address the problem of excessive heat dissipation into the gain medium [17]. The implementation of high-efficiency DPAA is closely related to a better understanding of the gain properties of alkaline vapor media. Previous studies on DPAA have investigated the high gain coefficient of an alkali-vapor medium as a function of the vapor-cell temperature, which is related to the density of the alkali atoms [17–24]. However, it has been reported that the measured Cs gain coefficients are less than half the calculated values [18]. Recently, the experimental Cs gain coefficient reportedly reached ∼75% of the theoretical value owing to the improvement of the spatial-mode matching of the pump and seed beams and the consideration of the hyperfine structure of Cs atoms [23].
In this work, our primary goal was to experimentally realize the highest possible DPAA efficiency for Cs vapor. We used a narrowband pump laser, implemented spatial-mode matching of the pump and seed beams, and carefully selected certain hyperfine states of the Cs atom [23]. Furthermore, to operate a highly efficient DPAA under optimal conditions, we determined the optimal focal length of the “combining” lens used in the setup for realizing the maximum output power of amplification under our experimental conditions. We investigated the gain coefficient as a function of the vapor-cell temperature and compared it with the numerically calculated result under the conditions for effective optical pumping and amplification.
2. Experimental setup
Figure 1(a) shows the experimental scheme for achieving highly efficient DPAA from Cs vapor mixed with ethane buffer gas. The setup uses a wavelength-division multiplexing (WDM) device to couple 852 nm pump and 895 nm seed lasers. In our experiment, we used two distributed Bragg reflector (DBR) lasers as the pump and seed lasers, with linewidths of ∼2 MHz and beam diameters of 1.0 mm. The gain-medium Cs vapor cell for DPAA comprised a 20 mm-long vapor cell containing 133Cs and 500 Torr ethane (C2H6) buffer gas, with the cell temperature varied from room temperature to ∼100.5 °C.
Fig. 1. (a) Experimental setup for highly efficient diode-pumped alkali amplification (DPAA) from a Cs vapor gain cell using a wavelength division multiplexing (WDM) device (MOPA, master oscillator power amplifier for pump laser; OI, optical isolator; FC, fiber collimator; BF, bandpass filter). (b) Energy-level diagram of the fine structure of the D1 and D2 transitions of 133Cs atoms and collisional mixing process (CMP) with ethane (C2H6) buffer gas for population inversion and gain in the Cs vapor; three-level atomic model ($|1 \rangle$, $|2 \rangle$, and $|3 \rangle$) for highly efficient DPAA of Cs vapor.
To obtain the maximum optical gain, as shown in the energy-level diagram in Fig. 1(b), the optical frequencies of the pump and seed lasers were set near the 6S1/2(F = 4) − 6P3/2(F′ = 5) transition of the D2 line and the 6S1/2(F = 4) − 6P1/2(F′ = 4) transition of the D1 line, respectively, considering the hyperfine-state dependence of the DPAA gain [23]. We finely adjusted the optical frequencies of the pump and seed lasers via saturated absorption spectroscopy (SAS) measurements of the D1 and D2 lines from two independent pure Cs vapor cells for the seed and pump lasers. Furthermore, for highly efficient DPAA operation, the pump and seed lasers were coupled into two input ports of the WDM and combined at the output port of a single-mode optical fiber for spatial-mode overlapping in the Cs vapor gain cell. Finally, we determined the optimal focal length of the lens used in the setup (L1) for achieving the maximum output power of the amplifier under our experimental conditions. The distance (d) between the L1 lens and the center of the Cs vapor cell is corresponding to the focal length of the L1 lens. The pump and seed beams were simultaneously focused into the vapor cell using lens L1 with a 75 mm focal length.
3. Experimental results and discussion
3.1 Highly efficient small-signal DPAA
To achieve the maximum possible efficiency of DPAA of Cs vapor under the specified spectral and spatial optimal conditions, we plotted the optical amplification as a function of the pumping power (Fig. 2) under the following experimental conditions: a small seed power of 0.1 mW, pumping power of 200 mW, and Cs vapor cell temperature of 100.5 °C, corresponding to a Cs vapor density of ∼1 × 1013 cm−3. As seen in Fig. 2, the amplification factor is 770 at a pumping power of 200 mW, reaching ∼30 dB at a pumping power of 240 mW. Although our experimental condition corresponded to small-signal amplification, we achieved the highest amplification factor of 1168 (>30 dB) at a pumping power of 280 mW. In the pump-power regime from 100 mW to 200 mW, we estimated the single-pass optical gain slope per pump power to be 5450/W, as indicated by the blue dashed line in Fig. 2. Generally, the amplified spontaneous emission (ASE) efficiency increases as the pump power increases [17]. However, under our experimental conditions with weak continuous wave (CW) pumping of <200 mW, we assumed that the ASE effect was extremely weak [16].
Fig. 2. Optical amplification in Cs vapor cell as a function of the pumping power under the condition of the 6S1/2(F = 4) − 6P3/2 pump transition and the 6S1/2(F = 4) − 6P1/2 amplification transition; amplification factor as a function of the pumping power considering the fraction factor (η = 0.7), with the plot showing both experimental (blue circles) and calculation results for a three-level atomic system (red curve).
To clarify the highly efficient small-signal DPAA demonstrated in our work, we compared the amplification factor per pump power reported by other studies [19–24], as listed in Table 1. Although the seed and pump powers listed in Table 1 are all different, our small-signal amplification factor per pump power is comparable with those of the previous related works. In this work, considering the pump power, the amplification efficiency is higher than that obtained in the study by Cai et al. [24]. As mentioned above, the causes underlying this high amplification are the selective pump transition, complete spatial-mode overlapping, and optimal lens focal length selection for achieving the maximum output power of the amplifier.
Table 1. Comparison of amplification factors per pump power pertaining to DPAA with longitudinal pumping.
3.2 DPAA calculation in three-level atomic model
In our experiment, because the collisional broadening of 10 GHz owing to the 500-Torr ethane buffer gas is larger than the hyperfine splitting of the 6P1/2 and 6P3/2 states, we didn’t consider the branching ratios of the pumping and lasing to different hyperfine levels. We considered the pressure broadening and the intrinsic cross-sections of the D1 and D2 lines. Considering the three-level atomic system ($|1 \rangle$, $|2 \rangle$, and $|3 \rangle$ levels) corresponding to the 6S1/2, 6P1/2, and 6P3/2 states, respectively, in Fig. 1(b), the population (n1, n2, n3) of each level is selected longitudinally through the gain volume along the propagation axis of the pump laser with its Gaussian beam [4]. The rate equation governing the population distribution is as follows [17,22,25,26]:
In the calculation of the amplification factor, we assumed a Gaussian beam propagation in an end-pumped gain cell containing Cs vapor. In our experiment, the pump and seed beams propagated from an output port (a single-mode optical fiber) of the WDM. Although the numerical aperture of the single-mode fiber and the beam waist diameter have slight difference of <5% due to the wavelength difference between the pump and seed lasers, we assumed the same spatial profile of the pump and laser beams. Figure 2 compares the calculated amplification factor (red solid line) with the experimental results (blue circles). The calculation parameters were: Cs cell length of 20 mm, cell temperature (red circles) of 100.5 °C, and ethane buffer gas at a pressure of 500 Torr, corresponding to the experimental conditions [28]. The beam waist of the pump laser was measured to be ∼ 60 µm when using a lens with a 75 mm focal length, and the $\eta$ value was set to 0.7. Although the simple atomic model used for DPAA analysis differs from an actual atomic system with hyperfine structures and Zeeman sublevels, we note that the experimental results are in close agreement with the calculated ones.
3.3 DPAA as a function of the cell temperature
Next, we examined the signal amplification characteristics according to the cell temperature. The vapor-cell temperature, which is related to the atomic density and collision ratio of Cs atoms with the buffer gas, significantly affects the feature of small-signal amplification. Figure 3(a) shows the amplification factor as a function of the cell temperature under a pump power of 200 mW and a seed power of 0.1 mW when using a lens with a 75 mm focal length. The blue circles in Fig. 3(a) indicate the experimental results. The red curve shows the calculated result under the same calculation parameters as those considered in Fig. 2 in the temperature range from 75 °C to 110 °C. The vapor number density was estimated from the vapor pressure of the Cs atoms according to the cell temperature [27]. Under our experimental conditions, amplification saturation occurred at ∼103 °C because of the reabsorption of the seed beam and reduction in the pump power at the end of the dense Cs atomic medium.
Fig. 3. (a) Amplification factor and (b) gain coefficient as functions of the cell temperature. The blue circles indicate the experimental results and the red curve the theoretical results in a three-level atomic system, obtained by considering a Gaussian beam with an end-pumped free-propagation gain cell.
Furthermore, we calculated the gain value from the experimental results shown in Fig. 3(a) using Eq. (5); The blue circles in Fig. 3(b) show the estimated gain coefficient, where the maximum value of 3.34(2) cm−1 was obtained at a cell temperature of 105 °C. The red curve in Fig. 3(b) indicates the theoretical results corresponding to Eq. (5). The overall trend of gain coefficient obtained from the experiment as a function of cell temperature agrees well with those by theoretical calculation.
3.4 Optimal focal length for highly efficient DPAA
For highly efficient amplifier operation, we consider an optimal focal length of the lens for achieving the maximum output power under our experimental conditions. The pump and seed beams were simultaneously focused and propagated to the far end of the high-density Cs vapor cell to achieve maximal efficiency. Subsequently, we investigated the dependence of optical amplification on the lens focal length. For an end-pumped free-propagation gain medium, the optimal focal length of the lens for highly efficient amplifier operation is dependent on the pump power, cell temperature, and cell length.
Figure 4 shows the optical amplification as a function of the focal length of the lens for the pump and seed beams in the focal length range of 40–500 mm under the following experimental conditions: pump power of 200 mW and gain length of 20 mm in the two cases of cell temperatures of (a) 96 °C (red squares) and (b) 105 °C (blue circles). The maximum amplification factor is obtained at a focal length of ∼75 mm. Upon comparing the cases of the two different cell temperatures, the optimal focal length at the higher temperature is slightly smaller than at 96 °C because of the different atomic number densities. The high atomic density of Cs atomic vapor requires a high-intensity pump beam for effective DPAA, corresponding to a higher maximum optical amplification, accompanied by a sharp decrease in the amplification factor as a function of the focal length of the lens.
Fig. 4. Optical amplification as a function of the focal length of the lens used in the setup for focusing the combined pump and seed beams in the focal length range of 40–500 mm. Two cases of cell temperature are considered: 96 °C (red squares and red solid-line indicate experimental and calculated values, respectively) and 105 °C (blue circles and blue solid line indicate experimental and calculated values, respectively).
When the focal length of the lens is >300 mm, the amplification factor is minimal because the pump beam is completely absorbed before it reaches the end of the dense Cs atomic medium; subsequently, the amplified seed beam is reabsorbed and emitted as fluorescence. The intensity and beam diameter of the pump and seed beams, as functions of the position in the gain medium, vary because the beam waist, Rayleigh range, and divergence angle are determined by the focal length of the lens. When the focal length increases, the volume of the amplification mode also increases. For focal lengths >300 mm, the pump power is depleted before it is delivered from the pump excitation source to the end of the gain medium. However, when the focal length of the L1 lens is <50 mm, the amplification factor decreases rapidly. In this case, the Rayleigh range is <6 mm, shorter than the 20 mm-long gain medium. The diverging pump beam in the dense Cs atomic medium is exhausted before it propagates from the pump excitation source to the end of the gain medium.
Furthermore, we calculated the amplification factor as a function of the focal length of the lens; the results are indicated by the red and blue solid line in Fig. 4. In the calculation, the intensity variation of the pump and seed beams along the cell length was obtained from the Gaussian beam propagation in the presence of the focused lens. Although the simple atomic model used for the calculation of the performance of the DPAA in Cs vapor cells differs from a real atomic system with hyperfine structures, the calculated amplification factor curves are in good agreement with the experimental results.
4. Conclusion
We experimentally and numerically demonstrated high-efficiency small-signal DPAA using a WDM device coupling pump and seed lasers for the first time. We also determined the optimal focal length of the lens used to focus the seed and pump lasers for achieving the maximum amplified output power under our experimental conditions: a 20 mm-long DPAA gain medium, seed power of 0.1 mW, and pump power of 200 mW. At the optimal lens focal length of ∼75 mm, we obtained a highly efficient amplification factor of ∼30 dB at a pumping power of 240 mW under optimal spectral and spatial conditions; furthermore, we experimentally observed the highest optical amplification slope of the small-signal per pump power (=5450/W). We confirmed that our DPAA setup is highly efficient in comparison with other previous approaches. In particular, considering the three-level atomic system via the gain volume along the propagation axis of the pump laser with a Gaussian beam, we numerically calculated the amplification factor as a function of the pump power, Cs vapor-cell temperature, and focal length of the combining lens. Our experimental DPAA results are consistent with the calculated results and with the calculated gain near the extreme DPAA limits when using a Cs vapor cell with 500 Torr C2H6 buffer gas. Although our setup was operated under small-signal, sub-watt-level pump laser conditions, we believe that our high-efficiency DPAA based on the Cs vapor cell can provide insights into understanding and designing highly efficient alkali laser MOPA systems.
Funding
MSIT of Korea under the ITRC support program (IITP-2022-2020-0-01606); National Research Foundation of Korea (NRF-2020M3E4A1080030, NRF-2021R1A2B5B03002377).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper may be available from the corresponding author upon reasonable request.
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