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Abstract
Multi-filament structures produced by vortical high-power femtosecond pulses propagating through clouds and fog can simultaneously clear two channels with cylindrical and annular profile. We present a method to achieve Free Space Optical (FSO) communications through such highly scattering media by propagating appropriately shaped laser modes through these channels. As a proof of concept, we implemented a Laguerre-Gaussian beam as information signal carrier to demonstrate transmission of 543-nm CW laser beam through a 1-m long cloud chamber using both channels. The low power of the information signal in this experiment allows considering applications in Earth–satellite FSO communication.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Free-space optical communications (FSO) is a line of sight communication method that provides unguided wireless optical data in free space. The establishment of a robust FSO network is garnering significant interest using both classical [1–4] and quantum light [5–9]. FSO is growing rapidly to meet the widespread wireless demand within the network of satellites [10] and among the Earth, satellites, and drones [5,9,11–13]. A free-space quantum communication satellite has already demonstrated quantum key distribution over 1200 km between the satellite and the Earth [8,14]. Laser telecommunication programs [15,16] aiming at significantly increasing the data rates when compared to those available with radio frequencies (RF) are supported by several space agencies [17,18]. FSO faces a persistent challenge in the form of adverse atmospheric conditions that obstruct light propagation, including clouds and fog. The randomness in size and distribution of water droplets that make up a rain cloud leads to substantial scattering of the optical energy and rapid scrambling of the information signal encoded in small-diameter laser beams. The amplitude fluctuation and wavefront distortion caused by atmospheric turbulence can additionally severely degrade the transmission efficiency and increase the bit error rate. The current strategy to surmount this barrier to FSO is to increase the number of networked ground stations, which is a complex and expensive solution.
High-power continuous wave (CW) CO$_2$ lasers have been successfully used to improve line-of-sight visibility [18]. However, a high laser intensity is required to vaporize and shatter water droplets – typically 10$-$1000 MW cm$^{-2}$ [19,20]. Other methods use an aperture averaging technique to attenuate the amplitude fluctuation with adaptive optics (AO), which compensates for the wavefront distortion caused by atmospheric turbulence [21–26]. The technological maturation of femtosecond (fs) terawatt-class lasers is an opportunity to reconsider practical FSO through dense clouds or fog with a fundamentally different approach – nonlinear propagation that leads to laser filamentation in the atmosphere [10,18,27–32]. Compared to RF communications, FSO operates at higher frequencies with wide-open bandwidth, resulting in a significantly higher capacity of communication links [36]. One promising scheme to tackle signal losses in FSO is to couple a laser filament to the beam path traversed by the information signal. The filament displaces water droplets in its immediate vicinity to create a more transparent channel, within which the information signal beam can travel unobstructed [18]. The hydrodynamic expansion of the plasma produces a shock wave, which expels water droplets in the region that surrounds the beam. Experiments with a single filament generated by a Gaussian beam through fog have demonstrated this effect [18]. However, the information signal in a form of Gaussian beam embedded in a single filament channel experiences rapid divergence. This is because the intense, rapid, and localized heating of air by the filament leaves behind a local air density hole that acts as a negative lens.
Approaches that employ multi-filamentation provide an alternative to guide the information signal beams through the air. Multiple filaments generated by structured light [37] can form a waveguide structure in the air, where an axial increase in refractive index is surrounded by a region of relative drop in refractive index. This mimics the core-cladding structure of an optical waveguide [34]. Thermal air waveguides with a lifetime in the millisecond range have been demonstrated in previously reported experiments [33]. These waveguide structures provide a clear channel for a Gaussian signal to propagate through the cloud.
Several approaches to produce multi-filaments have been demonstrated. One such approach involves using pulses of light with peak powers exceeding the critical power ($\mathscr {P}_{cr}$) by a factor of 10$-$100 [38]. While multi-filaments are produced using this method, the power requirement is a major issue. Another approach focuses a four-lobe femtosecond beam produced by an orthogonal half-pellicle setup [33]. Each lobe produces a filament forming a multi-filament structure. In the first approach, high-power ultrashort pulses carrying orbital angular momentum undergo azimuthal fragmentation into many filaments when focused by a lens [34]. Recent findings demonstrate the possibility to optimize the spatial structure of these multi-filament waveguides through iterative wavefront control [35].
Vortical femtosecond pulses generate a circular distribution of filaments. Figure 1.(a–c) illustrates the mechanism by which the dual channels are created through the cloud. The azimuthal fragmentation of a single Laguerre-Gaussian (LG) pulse produces many filaments [34,35]. Following the lifetime of the plasma, each filament leaves behind an area of high pressure due to the deposited energy. The hydrodynamic expansion of these regions releases shock waves. As shown in Fig. 1(a), the superimposed shock waves increase the index of refraction in the region between the filaments. A guiding structure is created with a region of relatively high refractive index surrounded by a ring of lower refractive index; this is referred to Channel 1 (CH1). The outward propagating shock wave clears a transparent channel by expelling the water droplets, creating Channel 2 (CH2). The timescale of this process is on the order of several hundreds of nanoseconds [33]. Residual heat sustains CH1 well past the lifetime of the acoustic waves, as shown in Fig. 1(b). The last stage of the structure evolution is illustrated in Fig. 1(c), where the transverse refractive index profile of CH1 smoothens out as the heat dissipates. The transition from the second stage to the third stage of evolution can last well into the millisecond range. CH2 has a typical decay lifetime on the order of several milliseconds before collapse as well [18]. Given the lifetime of each channel, it can be assumed a quasi-steady state resembling Fig. 1(c) can be reached if a high repetition pulse train is used.
Fig. 1. Transparent channels created by the multi-filament structure allow the information signal to propagate through cloud or fog. The main figure illustrates the filaments clearing two channels as it propagates through the cloud; the information signal is transmitted through these channels. The inset (a–c) is a conceptual illustration of the evolution of the refractive index change induced in the cloud by a single LG femtosecond pulse, based on work in Ref. [18,33–35]. The water droplets that form the cloud are illustrated in the area surrounding the filament as short yellow strips. (a) The generated shock waves clear the water droplets from the region surrounding the filaments, creating a transparent Channel2 (CH2). The boundary of CH2 is marked by the dashed circle. The shock waves also interact at the center of the structure, increasing the local index of refraction and creating Channel1 (CH1). (b) The acoustic waves dissipate, but localized heating of air causes a drop in density creating a ring of lower refractive index. This ring surrounds a higher density central region. (c) Dissipation of heat after several hundred microseconds leads to a smoother refractive index profile of CH1. CH2 created by the shock waves has a typical lifetime on the order of several milliseconds [18]. The order of magnitude timescales at each stage of channel evolution is provided. The inset (d–f) illustrates the information signals LG$_{0,1}$, LG$_{4,0}$ and LG$_{6,0}$ respectively. The inset (g–i) illustrates the spatial profile of each information signal coupled with a multi-filament structure. The inset (g) illustrates the arrangement of filaments between the Gaussian center and the annular beam.
In this paper, we demonstrate a new approach that could allow effective FSO through air obstructed by cloud and fog. The approach is based on the use of optimized multi-filament structures to clear a dual channel in the air and guide a LG information signal beam. Figure 1 illustrates the principle of this guiding method. As a proof of concept, we guide a 543-nm CW information signal carried by LG$_{0,1}$, LG$_{4,0}$, and LG$_{6,0}$ [Fig. 1(d–e), respectively] beams generated by a spatial light modulator (SLM) through a 1-m long cloud chamber (1.0$\times$0.3$\times$0.3 m$^3$) using a high-power femtosecond pulse modulated with a spiral phase plate (SPP) to generate multi-filaments. The multi-filaments are embedded with the information signal. The spatial profile of coupled multi-filament structure and the information signal is shown in Fig. 1(g–i). By utilizing information signals of different dimensions and shapes, the size and structure of each transparent channel can be inferred.
2. Experimental procedure
The laser source used in our experiments is a custom-built Ti:sapphire chirped-pulse amplification system operating at 480-Hz repetition rate and generating pulses of $\sim$40-fs duration at a $\sim$800-nm center wavelength. The system is capable of delivering a pulse energy of $\sim$20 mJ.
Vortical beams of topological charge $\ell =$1 and $\ell =$5 are produced by passing a femtosecond Gaussian beam through appropriate fused silica SPPs, which are 1-mm thick and 46-mm wide. Both SPPs have a radial index of zero. The diameter of the filament driver beam before passing through the SPP is set by an iris, and the beam is then weakly focused using a lens with a focal length $f=$2.5 m (Fig. 2). The SPP used to generate the vortex beam of order $\ell$ imposes a modulation in the form of $\exp (i\ell \Phi )$, modulo 2$\pi$, onto the flat phase front of the filament driver, where $\Phi$ represents the azimuthal angle.
Fig. 2. Schematic of the experimental setup. The Gaussian beam generated by the laser is converted to a Laguerre-Gaussian (LG) beam using a fused silica spiral phase plate (SPP) and focused by a lens with focal length $f=$2.5 m. An information signal emitted at 543 nm is shaped by an LG phase mask applied with an spatial light modulator (SLM). The filament driver and the information signal are combined using a dichroic mirror (DM1) and co-propagate through the cloud chamber. After filtering out the residual filament driver beam with DM2 and a series of bandpass filters, the information signal is imaged by an sCMOS camera. The inset shows a side image of the multi-filament beam propagating through the cloud chamber.
The information signal is carried by the LG beam generated with the SLM illuminated by a continuous wave (CW) laser operating at 543 nm. LG phase masks are applied to the SLM to generate vortex beams. Ample spectral separation was achieved from the filament driver by using this wavelength.
In the experiment, we generated three different LG$_{\ell,p}$ beams with azimuthal order (topological charge) $\ell =$0, 4, and 6 and radial order $p =$1, 0, and 0 [39–41], as shown in Fig. 3. A dichroic mirror (DM1) is used to couple the information signal with the filament driver (Fig. 2). A meter-long chamber containing an ultrasonic nebulizer (modified Honeywell HUL532B ultrasonic mist maker) is used to simulate cloudy atmospheric conditions. This mist maker produces water droplets with a median diameter of 5.6 µm. A pressure equalization valve is used to keep the chamber at an atmospheric pressure at all times. An air pump is used to create a homogeneous mixture by vacuuming out the top layer of dry air before making a measurement. A hole was drilled on both end of the cloud chamber to allow the filament and signal to pass. The cloud chamber was placed such that the filament exceeded the boundary of the cloud chamber at its entrance and exit. The cloud drastically attenuated the information signal, resulting in a power drop from $\sim$1.6 µW to $\sim$ 60 nW. The measured attenuation coefficient for the cloud at a wavelength $\lambda =$543 nm is 14.26 dB/m. The information signal is collected with a $f=$15-cm lens and imaged using a Thorlabs sCMOS camera. For each measurement, the information signal is imaged before and after the filament is introduced into the cloud chamber. The camera uses an exposure time of 30 ms, capturing multi-shot images of the information signal. Given the lifetime of the channels as illustrated in Fig. 1, the images represent the time-averaged state of both channels.
Fig. 3. Beam profile of the information signal beam generated by the SLM: (a) LG$_{0,1}$, (b) LG$_{4,0}$, and (c) LG$_{6,0}$
2.1 Beam alignment
While a single filament can clear a channel through cloud, it has been demonstrated [33–35] that by judiciously arranging multiple filaments, one can built an annular channel (CH1 in Fig. 1). In this experiment we use the guiding structure created by a vortical filament driver beam to guide the LG$_{0,1}$ information signal with a “bullseye” intensity profile. A screen is set in front of the DM1 to align the center of the information signal with the phase singularity of the filament driver. Fine adjustments are then made with the camera. Finally, the focusing of the multi-filament structure is adjusted with the iris. The radius of the multi-filament structure increases, with the trade-off being the reduction of pulse energy. This allows the Gaussian spot in the center of the information signal carrier LG$_{0,1}$ to propagate through the CH1 structure without interacting with the filament. This is especially true when the LG$_{1,0}$ SPP is used, owing to the smaller diameter of the filament driver beam. This process is shown in [Visualization 1].
3. Results and discussion
In the present work, we do not quantify self-focusing thresholds for vortex beams or image CH2 and/or CH1 between the filaments. We assume that the onset of plasma production is an indicator of self-focusing.
3.1 Single filament through the cloud
Single filaments created by a driver beam with near-Gaussian profile can clear a quasi-transparent channel through which, an information signal can be transmitted. However, due to the evolution of the refractive index profile of air after a single-filament propagation, which is thermal in nature, an information signal carried by a Gaussian beam that propagates symmetrically around the filament axis undergoes lensing. This is due to the creation of a density hole in the air, causing that region to act as a diverging lens. This scenario is presented in Fig. 4, where a LG$_{0,1}$ signal is coupled directly on top of a single filament. Figure 4(a) shows the LG$_{0,1}$ beam in the cloud before the filament is introduced, while Fig. 4(b) shows the information signal in the cloud with the filament present.
Fig. 4. The LG$_{0,1}$ information signal embedded with a single filament in the cloud. (a) LG$_{0,1}$ beam in the cloud before the filament is introduced; (b) LG$_{0,1}$ beam after a single filament is introduced; and (c) enhancement factor calculated from (a) and (b). The density hole left by the filament can be seen in the center of the LG$_{0,1}$ beam.
When propagating through the filament-produced channel, the information signal is defocused. Figure 4(c) shows the enhancement factor, $\Gamma = I/I_0$, defined as the ratio of the intensity of the information signal propagated through the cloud with the filament present ($I$) and the intensity of the information signal propagated through the cloud without the filament-produced channel ($I_0$). The density hole left in the wake of the filament can be seen in Fig. 4(c).
3.2 LG $_{1,0}$ filament
In order to investigate the transmission of information signal carried by an LG beam through a cloud, we generated multi-filament structure longer than 1 m (Fig. 2). The filaments are generated by a vortex beam of order $\ell =$1 after passing the SPP. We first generate the information signal LG$_{0,1}$ and transmit the vortical filament driver beam and the information signal through the chamber. The results of the experiment are shown in Fig. 5. Fig. 5(a), (d) & (g) shows the normalized intensity profile of the information signal carriers (LG$_{0,1}$, LG$_{4,0}$, and LG$_{6,0}$, respectively), after propagating through the cloud alone. The information signal with filament present is shown in Fig. 5(b), (d) & (h). The information signal is imaged by the same detector at the same position, with identical exposure time. For each vortex beam, the enhancement factor is obtained by taking the ratio of the intensity profiles with filament present and that without the filament.
Fig. 5. Experimental results with the multi-filament structure generated by the LG$_{1,0}$ SPP. The images in the left column (a, d & g) show each information signal (LG$_{0,1}$, LG$_{4,0}$, and LG$_{6,0}$, respectively) before the filament is introduced. The middle column (b, e & h) shows the information signal after the filament is introduced. The right column (c, f, & i) shows the enhancement factor calculated for each pair of information signals in the respective row.
The results are visualized in Fig. 5(c), (f) & (i). It is evident from Fig. 5 that the intensity of information signal is significantly increased. The information signal carried by LG$_{4,0}$ and LG$_{6,0}$ beams propagates through the quasi-transparent CH2 without any apparent defocusing. The LG$_{0,1}$ beam utilizes the CH1 structure between the filaments. Figure 5(b) & (c) demonstrates that the Gaussian center is not defocused. This is a significant improvement over using a single filament.
3.3 LG $_{5,0}$ filament
We repeated these measurements by replacing the vortex beam of order $\ell =$1 (SPP$-$1) by a vortical beam of $\ell =$5 (SPP$-$5). The choice of $\ell =$5 is not due to specific characteristics of the vortical beam but due to availability of the SPP. The results are shown in Fig. 6. The left column [Fig. 6(a), (d) & (g)] shows the transmitted information signal carrier through the cloud in the absence of the filaments; the middle column [Fig. 6(b), (d) & (h)] shows the transmitted information signal in the presence of the filaments; and the right column [Fig. 6(c), (f) & (i)] shows the enhancement of the transmission through the cloud by information signal carriers LG$_{0,1}$, LG$_{4,0}$ and LG$_{6,0}$. One can observe that the information signal carried by LG$_{4,0}$ is transmitted without significant distortion, while the LG$_{6,0}$ and LG$_{0,1}$ show a scattering pattern. The Gaussian spot at the center of the LG$_{0,1}$ beam shows a clear enhancement.
Fig. 6. Experimental results with the multi-filament structures generated by the LG$_{5,0}$ SPP. The images in the left column (a, d & g) show each information signal (LG$_{0,1}$, LG$_{4,0}$, and LG$_{6,0}$, respectively) before the filament is introduced in the cloud. The middle column (b, e & h) shows each information signal after the filament is introduced in the cloud chamber. The right column (c, f & i) maps the enhancement factor achieved for each information signal.
In both vortical filaments of order $\ell =$1 and $\ell =$5, the information signal carried by LG$_{4,0}$ is clearly transmitted. We have not achieved the same level of transmission for the Gaussian spot at the center of LG$_{0,1}$. In both cases, we can conclude that CH2 and CH1 are sufficiently large to allow their transmission. Therefore, we can estimate the size of CH2 and CH1 to be wider than the external diameter of the LG$_{4,0}$ and that of the Gaussian spot at the center of LG$_{0,1}$, respectively. In the case of the LG$_{0,1}$ beam shown in Fig. 6(c), the Gaussian center shows clear enhancement, but the ring-shaped beam is scattered. Given the dimensions of the water droplets, it can be assumed that Mie scattering is the dominant form of scattering. The LG$_{6,0}$ beam also shows clear signs of Mie scattering.
The information signal LG$_{6,0}$ is transmitted with little distortion through the cloud using CH2 cleared by the LG$_{1,0}$ filament driver [Fig. 5(i)], while it is weakly scattered through the CH2 cleared by LG$_{5,0}$ [Fig. 6(i)]. Likewise, the ring of LG$_{0,1}$ is completely blocked when propagating through the CH2 cleared by LG$_{1,0}$, but it is transmitted with a slight occurrence of scattering when using LG$_{5,0}$. The critical power $\mathscr {P}_{cr}$ increases to form multi-filaments with increasing topological charge [34], resulting in shorter filaments. This effect may cause the tail end of the multi-filament to be ineffective in sustaining the quasi-transparent CH2. In the experiment, this affected the larger diameter beams, while the smaller LG$_{4,0}$ beam was unaffected. Ultimately, it can be concluded that CH2 and CH1 cleared by LG$_{5,0}$ beam is wider than that created by LG$_{1,0}$.
3.4 Multi-filament vs single filament
In order to compare the performance of a single filament to the multi-filaments channel in cloud clearing, we compared the enhancement factor of the information signals through the cloud. In our experiments, we tested different filament structures that arise from Gaussian beam (LG$_{0,0}$) or structured light beams such as LG$_{1,0}$ and LG$_{5,0}$ as the filament drivers. The average enhancement of the information signal (LG$_{0,1}$, LG$_{4,0}$ and LG$_{6,0}$) transmitted through the cloud via channel(s) cleared by LG$_{0,0}$, LG$_{1,0}$, and LG$_{5,0}$ filament(s) is plotted in Fig. 7. The average enhancement is calculated from the enhancements mapped in Figs. 4, 5, and 6. The error bars show one standard deviation of the average enhancement factor. In the context of data transmission through a dynamic system such as the cloud, it is evident that multi-filaments outperform single-filament structures. Between two vortex beams with the same input energy, LG$_{1,0}$ has demonstrated better performance in terms of enhancement of the information signal.
Fig. 7. Average enhancement of each information signal coupled to different filament driver beams. The information signals are (Blue): LG$_{0,1}$ (Red): LG$_{4,0}$ and (Yellow): LG$_{6,0}$.
The LG$_{0,1}$ information signal that utilizes CH1 shows a clear improvements over the single filament created by a Gaussian beam (Fig. 4). This improvement is mainly due to avoidance of thermal lensing of the information signal beam by the density holes created by the filament. As discussed earlier, the intense, rapid and localized heating of air by the plasma leaves a region of low density in the air as shown in Fig. 4(c). The resulting drop in refractive index defocuses the light incident on it. The vortical multi-filament structure is designed to have these density holes outside the zone of influence of the information signal; thus, the information signal is not scattered by this mechanism. Therefore, CH1 is suitable for transmitting beams with Gaussian profile through the scattering medium.
The LG$_{1,0}$ filament driver performed the best in all experiments. This is attributed to the fact that the multi-filament structure is both relatively wide and long. Although a point to note is that the outer ring of the LG${_{0,1}}$ information signal is not recovered with the LG$_{1,0}$ filament driver. It can be deduced that the ring of the LG$_{0,1}$ beam was larger than CH2 as it is completely scattered by this very dense cloud.
The shorter multi-filament structure created by the LG$_{5,0}$ beam is a limiting factor due to the reduction of size of the quasi-transparent CH2. This is primarily down to the instability of the filaments at the tail ends of the cloud. As the filaments are shorter, the tail ends are not as spaced away from the cloud as the in cases for the gaussian and LG$_{1,0}$ filament drivers. The lower intensity of the filaments at the edges of the cloud, leads to significant tapering of the CH2. The narrowing affects the wider information signals with larger topological charges such as the LG$_{6,0}$.
These results demonstrate the feasibility of the use of this method to enhance FSO in cloudy environments. It is expected that high data rates can be achieved with a high-frequency modulator operating at the standard telecom wavelength (1.55 µm). This wavelength also suffers less Mie scattering when compared to the visible light.
4. Conclusion
We have experimentally demonstrated for the first time an improved approach for FSO in cloudy environments by embedding vortical multi-filament structures generated by a high-power femtosecond laser within Laguerre-Gaussian information signal beams. We have used CH1 and the quasi-transparent CH2 generated by the multi-filament structure to transmit the information signal carried by LG$_{0,1}$, LG$_{4,0}$, and LG$_{6,0}$ beams. By comparing the enhancement factor, we have shown that the channels generated by LG$_{1,0}$ beam perform better than that generated by a Gaussian beam and the LG$_{5,0}$ beam. Further investigation via time-resolved imaging will be necessary to compare the channel size generated by each beam. The improvements in transmission of information signal based on this approach could aid in the design of advanced FSO communication systems that reduce the transmission losses that are common in challenging weather conditions.
Funding
Defense Threat Reduction Agency (HDTRA1-20-2-0002); National Nuclear Security Administration (DE-NA0003920); National Geospatial-Intelligence Agency (HM0476-20-1-0012).
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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