Photonics Research

The spatio-temporal structured light in four-dimensional field refers to the light that has been precisely engineered with specific patterns in both spatial and temporal domains. The manipulation of spatio-temporal structured light holds the potential to drive significant advancements in optical microscopy and imaging, optical trapping, as well as medical and biological applications. Conventional methods for manipulating spatio-temporal structured light primarily rely on the linear optical elements. However, the high manufacturing complexity, special material requirements, low damage thresholds, and high costs of these optical elements present significant challenges to efficiently manipulating structured light fields in the short-wavelength range.

 

The nonlinear effect, utilizing nonlinear media, provides a versatile toolkit for the construction, manipulation, and detection of structured light across different wavelengths. Among the numerous existing nonlinear media, alkali atoms stand out due to their novel characteristics, including flexible tunability, easily saturable characteristics, purity without impurities, and high-power handling capability. Therefore, the nonlinear wave mixing process in atomic vapor provides a powerful mechanism for manipulating spatio-temporal structured light across a range from visible to shorter wavelengths.

 

To this end, Professor Jinpeng Yuan and Professor Lirong Wang of Institute of Laser Spectroscopy of Shanxi University proposed the high-performance transfer of spatio-temporal optical Ferris wheel (OFW) beam based on nonlinear frequency conversion. The spatial and temporal characteristics of spatio-temporal OFW beam are efficiently imprinted from near-infrared to blue-violet wavelength in a diamond-type energy level system of 85Rb atoms. The perfectly coincident multi-petal intensity profiles of input and output spatio-temporal OFW beams confirm the flawless transfer of spatial characteristic. The isochronous rotation velocities and directions of the beams verify the precise transfer of temporal characteristic. The relevant research results were recently published in Photonics Research, Volume 12, Issue 11, 2024. [Sandan Wang, Jinpeng Yuan, Lirong Wang, Liantuan Xiao, Suotang Jia, "Trans-spectral transfer of spatio-temporal optical Ferris wheel with nonlinear wave mixing," Photonics Res. 12, 2559 (2024)]

 

In the experiment, optical vortices with left and right circular polarization are superimposed onto the optical frequency comb to generate the optical vortex comb beam. Then, the spatio-temporal OFW beam with periodic rotating point-symmetry multi-petaled bright spot is generated through the interference between two vortex comb beams with opposite topological charges (l₁ = |l₂|) and offset frequency difference (Δf). Furthermore, the generated probe spatio-temporal OFW beam with 776 nm and the other 780 nm Gaussian pump beam interact with 85Rb atoms in a co-propagating configuration. Finally, the 420 nm signal blue-violet OFW beam with spatio-temporal characteristic is effectively reproduction with the four-wave mixing (FWM) process.

 

Fig. 1 Experimental intensity profiles of the vortex comb beams with different topological charges (a) l1 = 1, 2, 3, 5, 7, and 9 and (b) l2 = -1, -2, -3, -5, -7, and -9, respectively. Spatial distribution of (c) input 776 nm probe spatio-temporal OFW beams and (d) output 420 nm signal beams with topological charge difference Δl = 2, 4, 6, 10, 14, and 18, respectively.

 

The intensity profiles of left circularly polarized vortex comb (LVC) beams with l1 = 1, 2, 3, 5, 7, and 9 are shown in Fig. 1(a). The right circularly polarized vortex comb (RVC) beams with l2 = -1, -2, -3, -5, -7, and -9 are described in Fig. 1(b). There are the same profiles of vortex comb beams when l1 = |l2|. Figure 1(c) are experimentally obtained 776 nm spatio-temporal OFW beams by the interference of above two vortex comb beams with the same laser intensity and opposite topological charge l1 = |l2|. The intensity profiles of the generated 776 nm spatio-temporal OFW beams show plentiful spatial distribution with point-symmetry multi-petaled bright spot. The bright spot numbers m = 2, 4, 6, 10, 14, and 18 are determined by m = Δl = |l1 - l2|. The generated 420 nm signal beams in FWM process are shown in Fig. 1(d), which exhibit the same point-symmetry multi-petaled bright spot with 776 nm probe beams at the same Δl. This result indicates that the spatial characteristic of spatio-temporal OFW beam is effectively transferred from input probe to output signal beams.

 

Fig. 2 Temporal characteristic transfer of spatio-temporal OFW beam with Δl = 6 when Δf = 2 Hz and Δf = -2 Hz, respectively. (a) and (c) show the rotating patterns of 776 nm probe and 420 nm signal beams. (b) and (d) show the maximum beam intensity azimuthal angle ϕmax as a function of the rotation time.

 

The temporal characteristic transfer of spatio-temporal OFW beam in FWM process is displayed by the periodic rotation of probe and signal beams at different Δl and Δf. Figure 2(a) depicts the temporal rotation evolutions of 776 nm probe beam and 420 nm signal beam with rotation period of 3 s when the Δl = 6 and Δf = 2 Hz. It can be found that the probe and signal beams all preserve its six-petaled spatial pattern with clockwise rotation synchronously. In addition, the maximum beam intensity azimuthal angle ϕmax is measured to extract the rotation velocity with the time evolution, as shown in Fig. 2(b). The ϕmax of probe and signal beams increases linearly with the increasing t, corresponding to the vp = 2.09 rad/s of the probe beam and vs = 2.07 rad/s of the signal beam, respectively.

 

Furthermore, the temporal characteristic transfer of spatio-temporal OFW beam is described by the rotation direction of probe and signal beams. When the Δf is positive, the probe and signal beams are rotated synchronously in the clockwise direction, which is shown in Fig. 2(a). On the contrary, the rotating direction of the two beams is counterclockwise with the negative value of Δf [Fig. 2(c)]. Meanwhile, the rotation velocity of input probe and output signal beams is vp = -2.08 rad/s and vs = -2.11 rad/s with Δl = 6 and Δf = -2 Hz, respectively, as shown in Fig. 2(d). These results indicate that the temporal characteristic of the spatio-temporal OFW beam is effectively transferred from the input probe to the output signal beams.