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Abstract
Intense vector supercontinuum (SC) radiation with spatial polarization is obtained by using 800nm femtosecond vector laser beams in the air. The SC generated by azimuthally, radially, cylindrically polarized beams, and higher-order vector beams are investigated, respectively. The results show that the SC generated by vector beams is greatly enhanced compared to that by a Gaussian beam. The energy density of SC radiation reaches the order of 1µJ/nm in a bandwidth of 258 nm from 559 nm to 817 nm and 0.1 µJ/nm from 500 nm to 559 nm. Furthermore, by checking the polarization distribution of SC in different wavelengths from visible to near-infrared bands, we find that the SC maintains nearly the same polarization distribution as pump pulses. This work provides an effective and convenient way to generate powerful SC vector beams which may facilitate potential applications including optical communication, micro/nano-fabrication, and super-resolution microscopy.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As intense femtosecond laser pulses propagate in transparent media, the most spectacular and visually perceptible phenomenon is the white-light supercontinuum (SC) generation. The generation of the SC is due to a coupling action of several nonlinear effects including self-phase modulation, electron generation and self-steepening [1,2], and has been realized in various media [3–5]. The SC has many unique properties, such as ultra-broadband spectrum, high brightness, and high spatial and temporal coherence. Not only that, but the pulse width of the SC source can also maintain the same order of magnitude as the initial laser pulse [6,7]. Therefore, based on these benefits, the SC has been widely used in many fields of fluorescence microscopy [8], LIDAR [9], biomedical imaging [10], optical coherence tomography [11], cavity ring-down spectroscopy [12], attosecond pulses generation [13], and so on. However, to meet the requirements of different applications, the design of modulated SC sources is highly desired. Many experiments and simulations have been carried out to optimize the SC by using shaped pulse [14], manipulating pulse chirp [15,16], changing medium properties [17], modulating spatial phase of input beam [18], and so on. Besides the above-mentioned methods, polarization modulation is another efficient way to influence filamentation and SC. Elliptical, linear, and circular polarizations have been used to control the length, plasma density, clamped intensity of filamentation, and intensity and bandwidth of SC emission [19–26]. These studies demonstrated that laser polarization plays a vital role in filamentation and SC generation.with
The intense femtosecond vector SC is highly desired in many potential applications, such as nonlinear spectroscopy, femtosecond vector optical field, micro/nano-fabrication, and so on. However, it is difficult to generate broad vector polarized beam. It is nearly impossible to get vector SC by using nonlinear crystal due to the polarization-dependent phase matching condition [27,28]. Huang et al. have generated discrete multicolor annular ultrafast vector beams by using the technology of cascaded four-wave mixing [29]. S. Yisa et al. reported that the vector SC can be generated by an electrically tunable q-plate [30]. However, the wavelength tuning range has been limited to be a narrowband of ∼100nm due to effective range of wavelength selection for electric q-plate. Recently, T. Wakayama et al. introduced independently vector and vortex into the pre-generated SC to generate vector SC [31]. The Octave-wide SC with higher-order mode and orbital angular momentum can also be achieved from specially designed optical fiber [32,33]. However, the method strongly depends on the special optical elements, and in case of high-power SC with high conversion efficiency, these methods may face serious challenges. In our recent work, powerful and broadband SC vortices have been generated from femtosecond vortex beams by using multiple thin fused silica plates [34]. The generated vortex SC preserves the vortex phase profile of the initial beam, however, whether it carries linear polarization as same as the initial beam is unknown, although it is expected to carry. Up to now, it is still a challenge to generate vector SC with high power and high conversion efficiency. To our best knowledge, there is no study on producing the intense femtosecond vector SC.
In this work, the intense femtosecond vector SC radiation carrying space-variant polarization distribution is generated from the filamentation of femtosecond vector beams in air. The polarizations of SC beams are demonstrated to have the same polarizations of the initial beams.
2. Experiment setup
The sketch of the experimental setup is shown in Fig. 1. The laser source is an amplified Ti:Sapphire femtosecond laser system (Spectra-Physics, Solstice Ace) with a central wavelength of 800 nm, pulse duration of 50 fs, and the repetition rate of 1 kHz. Pulse energy of 4.1mJ is used for filamentation and SC radiation in our experiment. The Gaussian beam with horizontal polarization passes through a q-plate to generate different vector beams, including azimuthally, radially, cylindrical, 2- and 3-order vector polarized beams, respectively [27,35,36]. Then the air filamentation is induced by the vector beam with a lens with a focal length f =500mm. A CCD camera (Andor, ikon) is used to capture the far-field image of the SC beam and the side luminescence image of the filaments. The integrating time of CCD camera is set to 1ms. The mechanical shutter of CCD camera is pre-opened ∼35ms before the acquisition. To avoid CCD camera saturation, the output SC is reflected by a thin fused silica plate with a quite small angle (<10°). The SC polarization state is not influenced by the small reflection angle which is far smaller than the Brewster-angle. Several suitable bandpass filters are placed before CCD camera to record the intensity profile in the desired spectral regions, and a QB21 filter is used to filter out the influence of fundamental laser light. An additional ultra-broadband wire grid (WG) polarizer (Thorlabs, WP25L-UB) is used to exam the polarization state [37]. Besides, the SC is collected into an integrating sphere and recorded by a spectrometer (Ocean Optics Inc., USB-4000).
Fig. 1. Experimental setup (QP: q-plate, IL: imaging lens, FS: fused silica plate, IS: integrating sphere, Filters: QB21 and suitable bandpass filters, WG: wire grid polarizer).
3. Results and discussion
The side luminescence images of filaments of laser beams with different polarization distributions are taken by a CCD camera and shown in Figs. 2(a)–2(f). For comparison, the horizontal polarized Gaussian beam is also considered in our experiment. It can be seen that the intensity and the location are strongly influenced by the initial laser polarizations. The detailed evolution of the on-axis intensity of filamentation along the propagation distance is plotted in Fig. 2(g), where the black dotted curve represents that of Gaussian beam. First, we can see that compared to the Gaussian beam case, the onsets of filamentation of all vector beams are postponed, which is due to that the vector beam has a higher self-focusing critical power than the Gaussian beam [38]. The onset of filamentation is usually defined by a position where the signal starts to be obvious higher than the background. In this work, the onset of the filamentation is defined by a fixed fluorescence intensity of 1500 (CCD counts). Second, the Gaussian beam has the longest filamentation among these beams. However, the radially, azimuthally and cylindrically polarized beams (can be called the 1-order vector polarized beams [39]) have an obvious higher intensity than the Gaussian beam, while the 2- and 3-order beams have much lower intensity. But the reason is still unknown. Maybe it is similar with that of vortex beam observed by Vlasov et al. [40]. Third, although the peak fluorescence intensities of the 1-order beams are at almost the same level, the intensity profiles have some difference. We notice that in our experiment that the filamentation evolution is highly influenced by the position of the polarization singularity. If the polarization singularity deviates slightly from the beam center, the intensity of the filament will be different. Unfortunately, in practice the laser beam does not have an ideal Gaussian intensity distribution. Therefore, to generate each vector beam by rotating the q-plate, the position of the singularity is optimized by monitoring far-field beam pattern. We believe that this optimization will influence the filamentation evolution to some extent. Furthermore, it is still unknown yet how the polarization states of the three vector beams influence the filamentation processes, which deserves further studies.
Fig. 2. The side luminescence images of the filaments at different polarization states of (a) radially, (b) azimuthally, (c) cylindrically polarized beams, (d) Gaussian, (e) 2-order and (f) 3-order vector polarized beams in the air taken with a CCD camera with an exposure time of 1 ms. (g) The corresponding on-axis intensity of filament luminescence along with the propagation distance. The red arrow represents the laser propagation direction and the white dotted line represents the geometric focus of the lens.
The SC spectra generated by the vector beams are shown in Fig. 3(a). The pump laser spectrum is also plotted. It can be seen that the spectral broadening mainly occurs in the visible region. For the 1-order vector beams, the spectral broadenings are almost identical, and the cut-off wavelengths in the blue-side extension are 500 nm, much shorter than that of Gaussian beam. The shorter cut-off wavelength results from the contribution of the higher peak intensity [41], as shown in Fig. 2. Moreover, the SC energy density of the 1-oder vector beams is greatly enhanced, especially in the blue-side of the SC, compared to the Gaussian case. The energy density of SC reaches the order of 1µJ/nm in a bandwidth of 258nm from 559nm to 817 nm, and 0.1µJ/nm from 500nm to 835nm. For the 2- and 3-order vector beams, the bandwidths of the spectral region with energy density higher than 1µJ/nm decrease to 215nm and 173nm, respectively. It indicates that the spectral broadening becomes narrower with the vector order increasing, which is due to the weaker ionization as shown in Fig. 2. Furthermore, the conversion efficiency of SC, defined by the energy ratio of the continuum part (except pump spectral range from 750nm to 840nm) to the whole, is calculated and plotted in Fig. 3(b). The error of the conversion efficiency is also indicated by using the standard deviation of 6 measurements. The conversion efficiency is about 49.1% for the Gaussian beam, 46.6% for the 1-order vector beams, 29.1% for the 2-order vector beam, and 19.7% for the 3-order vector beam. The conversion efficiency for the case of Gaussian beam is slightly higher than that of 1-order vector beams, which is due to the contribution of the longer filamentation [41].
Fig. 3. (a) The output SC spectra generated from filamentation of azimuthally, radially, cylindrically, 2-order, 3-order vector polarized beams and Gaussian beam, respectively, and (b) corresponding SC conversion efficiency. The initial pump laser spectrum is also plotted for reference.
To verify whether SC carries the same polarization distribution as the pump pulse does, we use the WG polarizer to exam the polarization of SC beam in several selected spectral ranges. The spatial distributions of the spectral components generated from different vector beams are shown in Fig. 4. The different spectral ranges which are achieved by using different filters are shown in Fig. 4(g). For the cases of no WG polarizer, the intensity of different spectral ranges shows annular distribution (Figs. 4(a, c and e)). First, zero or low intensity at the center of the beam for new generated spectral components is preserved, as shown in Figs. 4(a, c and e), which indicates that the polarization singularity should also exist in different spectral ranges of the SC, i.e. the SC should be a vector SC. To verify it, a WG polarizer is put before the CCD camera. The rotation angle of the WG is set to 0° to only transmit horizontal-polarization component of light. The patterns of the SC beams with different orders in different wavelength ranges are shown in Figs. 4(b, d and f), where we can see clearly horizontally and vertically distributed lobes due to the filling by the WG polarizer. On the other hand, it can be seen from Fig. 4 that the spatial distributions of different spectral components have some differences. The shorter wavelength component is located on the ring with a larger radius. Such spatial distribution is called conical emission, a typical characteristic of SC, which is due to the spatiotemporal self-phase modulation by electron generation [42]. Many earlier works have demonstrated this phenomenon for Gaussian beam [42–44]. In recent years, this phenomenon from structured beams such as vortex beam or Airy pattern beam has also been observed in theory and experiment [40,45,46].
Fig. 4. Measured far-field SC beam distribution in the cross section (a, c and e) without or (b, d and f) with WG polarizer for (a and b) azimuthally polarized beam, (c and d) 2-order and (e and f) 3-order vector polarized beam after passing different filters of BP: bandpass; SP: short pass; and (g) corresponding SC spectra after different filters.
Besides, the radius also increases as the order of beam vector increases because they have a relationship of $r \propto \sqrt l $ (where r is the radius of vector beam and l is the order) [47]. As shown in Fig. 4(b), we observe two vertical distributed lobes whose orientation is consistent with the polarization direction of the WG polarizer. With the increase of the vector beam orders (see in Figs. 4(d) and 4(f)), the vector beams change into 2l lobes. It indicates that polarization distributions of SC radiation from the radially, 2-order and 3-order vector laser pulses are maintained as same as that of incident pules.
Furthermore, we rotate the WG polarizer to analyze the spatial polarization distribution of the SC beams. The SC patterns of azimuthally and 2-order vector polarized beams are shown in Fig. 5. For reference, the initial distributions of the pump laser beams are also provided in Figs. 5(a) and 5(d). The transmission direction angle of the WG polarizer is adjusted from 0° to 180° step by step. The black arrows at the top of Fig. 5 represent the polarization direction of the WG polarizer. The results show that for the azimuthally polarized beam, there are two lobes and their orientation is vertical to the transmission direction of the WG polarizer for both of short pass 700 nm and without filter cases (Figs. 5(b) and 5(c)). Four lobes are observed for the case of the 2-order vector beam. The variation with the rotation of WG polarizer is almost the same as the pump pulse.
Fig. 5. The intensity profiles of the (a-c) azimuthally and (d-f) 2-order vector polarized beams when there is (b and e) no filter or (c and f) SP700 nm filters, for several typical rotation angles of the WG. (a and d) The intensity distribution of pump laser is also shown.
Furthermore, the SC polarization with different spectral components is quantified by the degree of polarization (DOP), which can be defined by P = (Imax-Imin)/(Imax+Imin), whose value is equal to 0 for perfect circular polarization and 1 for perfect linear polarization [48]. The mean values of intensity in two typical regions of interest (ROI) (marked as stars in the images of Fig. 6) are obtained for the cases of the azimuthally and 2-order vector polarized beams with SP700nm filters, respectively. The ROI has a size of 20×20 pixels. The intensity variation under different transmission direction angle of the WG polarizer is shown in Fig. 6(a), the intensity of ROI gradually increases as the angle of the WG polarizer varies from 30° to 120° and decreases as the angle varies from 120° to 30°. Based on the extinction intensity Imin and maximum Imax appearing at the angle 30° and 120°, the DOP is calculated to be ∼0.89, which is almost the same as the initial pump laser. The DOP of the initial pump laser is 0.91, whose deviation from the perfect linear polarization may be induced by the optical elements such as the lens [49] and the extinction ratio of the WG polarizer. For the other regions except the selected ROI of the SC beams, the DOPs also have similar values. For the case of the 2-order vector polarized beam, the ROI is located at the horizontal direction on the SC profile, as shown in Fig. 6(b). The maximum Imax appears at 90° and the extinction intensity Imin appears at 0°. In this case, the DOP is also calculated to be 0.89. It indicates that the azimuthally polarized and 2-order vector SC beams approach linear polarization with slightly depolarization. For the perfect linearly polarized femtosecond laser, the SC produced from filamentation can preserve the polarization of the pump laser [50–52]. The initial polarization imperfection is slightly amplified by the phase modulation of two perpendicular components during the nonlinear propagation [52]. Therefore, the SC generated by the vector beams which are quasi-linearly polarized, has almost the same polarization with pump vector laser beam.
Fig. 6. The variation intensity of ROI in the SC beam from (a) azimuthally and (b) 2-order vector polarized beams for the cases of SP700 nm filter by changing the angle of the WG polarizer. ROI is marked by small black star in the right images with the size of 20×20 pixels.
4. Conclusion
In conclusion, we experimentally generate intense vector SC radiation from filamentation in air. The SC generated by the azimuthally, radially, cylindrically and higher-order vector polarized beams is investigated, respectively. We found that the spectral broadening caused by the azimuthally, radially and cylindrically polarized beams is almost identical, and the energy density of SC is greatly enhanced compared with that by linearly polarized Gaussian beam. Furthermore, the spatial polarization distribution of vector SC is measured for different wavelength ranges. It is found that the SC spectra maintain nearly the same polarization distribution of pump pulses due to the linear polarization retention. This paper provides an effective and convenient method to generate powerful SC vector beam by femtosecond filamentation and paves the way to generate sub-fs vector polarized pulses [53,54].
Funding
National Natural Science Foundation of China (12074228, 11874056, 11774038); Natural Science Foundation of Shandong Province (ZR2021MA023); Taishan Scholar Project of Shandong Province (tsqn201812043); Innovation Group of Jinan (2020GXRC039).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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