Atomic optical filters are widely utilized in free-space optical communication, laser frequency stabilization, and other fields due to their narrow bandwidth, high transmission, and excellent noise suppression capabilities. Several methods are commonly employed to achieve these filters. The Faraday anomalous dispersion optical filter (FADOF) and Voigt anomalous dispersion optical filter (VADOF) use magnetic fields to induce birefringence in atomic vapor, resulting in the rotation of the polarization plane of the signal light. These methods have been extensively researched. While magneto-optical rotation filters have narrow bandwidths, they are typically on the order of GHz. Another type, the induced-dichroism atomic optical filter (IDAOF), utilizes circularly polarized laser light to polarize the atomic medium and induce polarization plane rotation without needing a magnetic field, achieving narrower bandwidths on the order of MHz. Thus, developing ultra-narrow bandwidth and high transmission atomic optical filters at various wavelengths and with different atoms is a significant research focus.

We realize an ultra-narrow bandwidth nonlinear optical filter at an operating wavelength of 852 nm based on the ¹³³Cs atom 6S_1/2→6P_3/2 hyperfine transitions. The filter is achieved by leveraging circular dichroism, the saturated absorption effect, and the Faraday effect. The experimental setup (Fig. 2) divides the 852 nm laser provided by the extended cavity diode laser into two parts: one beam serves as high-power pump light and is circularly polarized by adjusting the optical axis direction of a λ/4 wave plate, while the other beam, with lower power, acts as the signal light and passes through a ¹³³Cs atomic vapor cell (5 cm length, no buffer gas). A pair of Glan-Taylor prisms with an extinction ratio up to 10⁵∶1 and perpendicular polarization directions is placed on both sides of the ¹³³Cs vapor cell. The temperature of the ¹³³Cs vapor cell can be adjusted from room temperature to 150 ℃ with an accuracy of less than 1 ℃. The temperature-controlled ¹³³Cs vapor cell is placed in a custom-made axial magnetic field generating device, where the magnitude of the axial magnetic field, parallel to the light propagation direction, is conveniently controlled by adjusting the number of magnetic columns within the range of 0-0.1 T. The linearly polarized signal light and circularly polarized pump light are overlapped in the ¹³³Cs vapor cell, with the beam diameter of the pump laser being larger than that of the signal light for better spatial overlap. The transmitted signal light after the filter enters the photodetector and is recorded by the digital storage oscilloscope.

In the experiment, we measure in detail the dependencies of the nonlinear optical filter on various experimental parameters, including the power of the 852 nm circularly polarized pump laser and linearly polarized signal light, the temperature of the ¹³³Cs vapor cell, and the magnitude of the axial magnetic field. The typical results are shown in Fig. 3: under the weak axial magnetic field of 5.5×10^-4 T, the transmission of the nonlinear optical filter is significantly improved compared to the IDAOF alone, when the frequency of the 852 nm laser is scanned over the 6S_1/2(F=4)→6P_3/2 and 6S_1/2(F=3)→6P_3/2 transitions, respectively. With the increasing power of the circularly polarized pump laser, the transmission of the nonlinear optical filter also increases and then tends to saturate, as shown in Fig. 4. On the one hand, the intensive pump laser enhances the circular dichroism effect, causing the polarization plane of the linearly polarized signal light to rotate by a larger angle, thus improving the transmission of the optical filter. On the other hand, the strong pump laser excites more atoms from the ground state 6S_1/2 to the excited state 6P_3/2, resulting in weaker absorption of the signal light by the atomic medium, known as the saturation effect, further improving the transmission of the optical filter. When the temperature of the ¹³³Cs vapor cell varies between 30 ℃ and 55 ℃, the transmission of the filter first increases and then decreases. As the temperature rises, the number of atoms interacting with the light fields increases, thus improving the transmission of the optical filter. However, too high a temperature leads to increased absorption of the signal light, and the transmission of the optical filter decreases accordingly, as shown in Fig. 5, with the optimized temperature being 40 ℃. To achieve an ultra-narrow bandwidth nonlinear filter, we use a weak axial magnetic field, which improves the transmission of the optical filter while ensuring a narrow bandwidth. Under most experimental conditions, the bandwidth of the filter is less than 60 MHz, as shown in Fig. 4-6. Finally, we explore the influence of signal light power on the performance of the optical filter. When the power changes from 50 µW to 400 µW, the peak transmission and bandwidth of the nonlinear filter show a slow increasing trend (Fig. 7).

We comprehensively utilize circular dichroism, the saturation effect, and the Faraday effect to realize a resonant ultra-narrow-bandwidth nonlinear optical filter at 852 nm based on the ¹³³Cs 6S_1/2→6P_3/2 transitions. Compared with the previous FADOF of the ¹³³Cs atom at 852 nm with a bandwidth ~GHz, the bandwidth of this nonlinear optical filter is reduced by two orders of magnitude. With the optimized experimental parameters, we find that the peak transmission of the filter can reach 30% and the bandwidth is less than 60 MHz when the temperature of the ¹³³Cs vapor cell is 40 ℃ near room temperature and the weak axial magnetic field intensity is 5.5×10^-4 T. This resonant ultra-narrow bandwidth optical filter may be suitable for optical systems such as frequency-stabilized lasers and atomic clocks.