Dynamic media such as atmospheric clouds and fog form a formidable barrier to light propagation for free-space optical communication (FSO). To overcome such an obstacle, we propose to make use of the acoustic properties of a laser filament coupled together with a donut-shaped signal beam. A filament generated by an ultrafast laser is accompanied by an acoustic wave that clears a cylindrical chamber around the filament’s plasma column that can mimic a transmission channel. We present a method to couple a Laguerre–Gauss beam through the obstacle-free channel. We image and measure the transmitted signal carried by the structured beam to demonstrate an efficient method for FSO through cloudy conditions, which requires low energy, is resilient to noise, and is unaffected by the filament.

The light-based communication between orbiting satellites and the Earth’s surface offers the prospect of significantly increasing space to ground data rates and constitutes a key element in the future for secure worldwide quantum communication networks.1–3 Free space optical links between the Earth and space referred to as free-space optical communication (FSO) face a persistent nemesis in the form of atmospheric clouds. Compared to radio frequency (RF) communication, FSO operates at higher frequencies with wide-open bandwidth, resulting in significantly higher capacity communication links.4 The randomness in size and position of water droplets leads to substantial scattering of the optical energy and quickly scrambling the signal encoded in laser beams. The amplitude fluctuation and wavefront distortion caused by atmospheric turbulence can also severely degrade coupling efficiency and increase the bit error rate. This barrier is currently surmounted by increasing the number of networked ground stations, a very complex and expensive solution. Early attempts to clear the sky from fog and clouds involved CO2 lasers to increase visibility have been realized. However, high energy is required to vaporize and shatter water drops (typically [10, 1000] MW cm2/pulse).5,6 Other methods use an aperture averaging technique to attenuate the amplitude fluctuation utilizing adaptive optics (AO) methods to compensate for wavefront distortion caused by atmospheric turbulence.7,8 The emergence of femtosecond (fs) terawatt class lasers is an opportunity to reconsider FSO through dense clouds or fog with a fundamentally different approach: laser filamentation.2,9,10 Filamentation is a phenomenon describing a long thin plasma string (the filament), produced by a balance between the optical Kerr effect and plasma defocusing.11–16 Laser filaments are self-sustained of around a dozen micrometers in diameter and up to hundreds of meters in length, greatly extending the traditional linear diffraction limit.17–21 Properties of filaments such as their stability under air turbulence and their interaction with water droplets have been studied.22–24 The creation of the filament is accompanied by an expanding shock wave that displaces water droplets in its immediate vicinity to create a cylindrical channel within which the signal beam can travel unobstructed.10,25 Schimmel et al. used a high repetition rate laser (1 kHz) to demonstrate that the cleared channel can become stable and quasi-transparent with a millisecond ranged window waveguide. A Gaussian beam coupled in counter-propagation to a filament has been used as signal carriers.10 However, the spatial overlap between the signal carried by the Gaussian beam and the filament is of critical importance both for transmission enhancement and for the reduction in thermal lensing induced by the filament. The interaction between the filament and the signal can cause the signal to be degraded10 [and references therein]. A new method that avoids signal losses due to thermal lensing is to couple the laser filament together with a structured light beam. Structured light generally refers to an optical beam with a tailored spatial amplitude and phase distribution with unique properties.26 One type of structured light involves orbital angular momentum (OAM) beams that are also known as vortex beams because of their donut-shaped intensity profiles with a null at the center; they are perfectly suited to propagate around the filament.27–29 The signal carried by the Laguerre-Gauss (LG) beam is generated dynamically by a spatial light modulator (SLM), which allows the creation and control of a plethora of structured light.30 

In this paper, we utilize the channel cleared by a high-repetition-rate laser filament in the cloud to demonstrate unobstructed transmission of LG,0 beams. The donut-shaped intensity distribution of LG,0 light allows co-propagation with the filament without interference between the two beams. The LG beam as an information carrier can be modulated in amplitude and phase, and information can also be encoded in its OAM states for increased secure communication.31 The dimensions of the cleared channel ranging greater than 1 mm10 in diameter allows transmission of various donut-shaped beams. Hence, one can transmit any LG beam with a diameter smaller than that of the cleared channel. In this experiment, we have selected LG12,0, to be the upper threshold.

Our experimental methodology is based on using the channel generated by the femtosecond pulse through a cloud chamber to transmit a signal carried by an LG beam. The experimental setup is shown in Fig. 1. A Ti:Sapphire (wavelength centered at 810-nm) pulsed laser with a pulse duration of 52-fs, 1.67-mJ energy/pulse, and 3-kHz repetition rate is focused by a 2-m focal length anti-reflection (AR) coated lens. The signal is generated from a continuous wave (CW), single longitudinal mode diode laser with 635-nm wavelength. The signal beam is collimated and expanded using a beam expander (BE). The diameter of the beam is chosen so that it covers the entire face of the spatial light modulator (SLM), which is a Santec SLM-200 phase-only modulator. We display various holographic masks on the SLM to generate the desired structured light beams.32 An iris (I) is used to block the undesired part of the signal. To allow extra flexibility and ensure that the annular beam fits well within the cleared channel, the generated beam is expanded and collimated using a collimator consisting of two spherical lenses. The filament and the signal are coupled using a homemade mirror coupler (MC) as shown in Fig. 1(c). The MC is a gold plane mirror built on the fused silica substrate (Thorlabs PF20-03-M01). It is 2-in. (50.8-mm) in diameter. In the center, we drilled a hole of 2.65-mm in radius. This MC is used to couple the signal and the femtosecond pump through the air. The information beam was widened to increase the inner diameter of the LG beam. The MC is placed in a position where the entire femtosecond beam passes through the hole. The advantage of using an MC as opposed to a traditional beam combiner is that the femtosecond beam in its entirety is utilized to produce the filament. Generally, the increase in the pump power will result in a filament with higher plasma density.33 The pump generates a filament >50-cm length in air. The white glowing line shown in Fig. 1(a) illustrates a side view of the generated filament imaged using a Sony α a5000 camera. A ruler is placed behind the filament as a reference. To couple the signal with the filament through the cloud, a dichroic mirror (DM2) was used instead of the MC, since the channel size is 1-mm according to the pump wavelength and the pulse energy.10 The spatial dimensions of the cleared channel for our experiment dictated this choice. However, it has been shown that mid-IR filaments will clear a channel with a much larger diameter (about 4-cm at 10-μm34) and are expected to propagate over considerable distances.34–39 The mitigation of pulse energy losses before filament formation is crucial and the MC is perfect for this scenario. Both the filament and the LG beam propagate through a homemade cloud chamber of dimensions 40×30×15-cm3. The length of the chamber is chosen to have at most 5-cm of the filament on either side of the cloud chamber [see Fig. 1(b)] to avoid the signal being scattered by the outflow mist. Two holes of 1-cm in diameter are made on either side of the chamber to let the light in and out. The chamber is made using Acrylic Plexiglass, a transparent material. The cloud is generated using an ultrasonic nebulizer. A pressure equalization valve keeps the chamber at atmospheric pressure. One meter after the cloud chamber, the LG beam signal coupled with the femtosecond beam (no longer a filament) is filtered by a dichroic mirror (DM) and two interference filters (IF). A variable neutral density (ND) filter is positioned before the sCMOS to attenuate the signal and avoid damaging the camera. To measure the transmitted signal, we replaced the sCMOS camera by a Thorlabs Photomultiplier Module (PMTs) and added (behind the ND filter) a lens (f=5-cm) to fit the beam in the PMT aperture.

FIG. 1.

(a) Schematic of the experimental setup. L, lens f=2-m; BE, beam expander; SLM, spatial light modulator; I, Iris; DM, dichroic mirror; IF, interference filters; ND, neutral density filters; and MC, mirror coupler. The structured light beam generated by the SLM is coupled with the filament by the MC before entering the cloud chamber. After filtering out the femtosecond pulse with DM, IF, and ND, the structured light is imaged by an sCMOS camera. (b) Side view picture of the filament (glowing line) in the air with a yellow line as a guide. (c) Filament propagates through the chamber containing a sparse cloud. (d) Image of the in-house developed MC.

FIG. 1.

(a) Schematic of the experimental setup. L, lens f=2-m; BE, beam expander; SLM, spatial light modulator; I, Iris; DM, dichroic mirror; IF, interference filters; ND, neutral density filters; and MC, mirror coupler. The structured light beam generated by the SLM is coupled with the filament by the MC before entering the cloud chamber. After filtering out the femtosecond pulse with DM, IF, and ND, the structured light is imaged by an sCMOS camera. (b) Side view picture of the filament (glowing line) in the air with a yellow line as a guide. (c) Filament propagates through the chamber containing a sparse cloud. (d) Image of the in-house developed MC.

Close modal

The filament length is limited by the pulse energy. We produced filaments of >50-cm in length. The critical power (Pcr) for filamentation to occur is governed by

Pcr=λ28πCn0n2,
(1)

where λ is the wavelength of the laser, C is the numerical factor defined by the beam profile, n0 is the refractive index of the medium (air), and n2 is the nonlinear refractive index due to the optical Kerr effect.16 The critical power for a Gaussian beam centered at 800 nm is 3.19 GW. Our laser produces pulses with a peak power of 33.4 GW. This significantly large peak power allows us to form a long filament. Adjustments to pulse compression and energy can be used to vary the length of the filament. The Laguerre–Gaussian beam is the first solution to the paraxial wave equation in cylindrical coordinates (ρ,ϕ,z). The general expression of its amplitude distribution is given by40 

LG(ρ,ϕ)=A,p×eiϕ×eiψ,p(ρ,z),A,p=N,pw×(2ρ)||×Lp||(2ρ2)×eρ2,ψ,p(ρ,z)=kρ2R+(||+2p+1)arctan(z/z0),ρ=rw(z).
(2)

The parameters are as follows: k, wave-number; z0, Rayleigh range; p, radial order integer; , topological charge; Lp||, generalized Laguerre polynomials; w(z), beam waist; w(z)=wo1+(z/zR)2; R, wave-front radius; and N,p, normalization constant. eiϕ describes the helical phase structure of the light, which carries orbital angular momentum per photon. The phase singularity at the center of a vortex beam along its propagation axis gives the beam a spatial intensity profile that ensures no light is directly interacting with the filament. The LG beam is produced by illuminating a phase mask displayed on the SLM;32 the phase mask or the hologram is computer generated. The inner diameter of the intensity profile of the LG beam is related to its topological charge () and the beam waist (w) by w2. By using DM2, we have chosen to couple the filament and the signal carried by the LG beam with =12 (noted LG12,0) through the cloud. To have an intense signal, the signal needs to be shrunk down. The center of the donut beam needs to match the axis of the filament. And the diameter of the shrunk beam needs to be smaller than 1-cm, the chamber side holes. In Fig. 2, we capture the procedures to demonstrate that the signal beam is transmitted virtually unobstructed in the cloud chamber when coupled with the filament. For all the measurements, the exposure time of the sCMOS camera was fixed and remained unchanged. Figure 2(a) shows the femtosecond filament after it is transmitted alone through the cloud filled chamber. We used neutral density filters to ensure that the filament intensity is attenuated by several orders of magnitude before it is imaged. While the chamber is still cloud-filled, we block the femtosecond beam and turn on the signal beam. As expected, most of the signals are scattered as shown in Fig. 2(b). The signal beam when transmitted in free space is captured in Fig. 2(c). Next, we have both the filament and signal beam propagate through the cloud-filled chamber. In Fig. 2(d), we imaged the resulting intensity distribution of the coupled signals. It is clear that the signal is transmitted unobstructed through the transmission channel created by the filament. The intensity profile of the signal in free-space is plotted in Fig. 2(e), and in Fig. 2(f), we plot the signal coupled with the filament transmitted through the cloud. The transmission of the signal through the cloud chamber is further characterized by replacing the sCMOS by a photomultiplier module (PMT). We connect the PMT to an oscilloscope to monitor the variation of the signal beam. The signal intensity is read in voltage: the minimum transmission is 4.4-V and the maximum is 5.8-V. This is equivalently measured by a power meter to correspond to 68-nW for the minimum signal transmitted and 130-nW for the maximum. The presence of the filament increases the transmitted signal by over 90%. To characterize the cleared channel time, we manually block and unblock the pump beam (femtosecond beam) in 3 s intervals. The pink shaded area in Fig. 2(g) highlights the time that the filament is unblocked. It is clear in Fig. 2(g) that when the filament is blocked, the signal beam is completely obstructed. When the pump is unblocked, the intensity of the signal increases before reaching a maximum. Likewise, when the pump is off, the intensity of the signal drops down before it reaches the background level. The time interval that the signal intensity requires to reach the maximum when the pump is unblocked is close to that necessary to reach the ground when the pump is blocked. In other words, Fig. 2(g) shows that the rise time for the transmitted signal to reach its maximum is comparable to the fall time at which the signal vanishes. We estimated the rise and fall time to be equivalent to the cleared channel lifetime, which we have measured it to be 12-ms. This estimation is close to that made by Schimmel et al.10 This transmission plot also highlights that the significant drops in transmission are not present in the case of a donut-shaped beam compared to a gaussian information carrier. Right after the channel is established, we observe a fast, short, and small transmission drop. These short fluctuations are due to the dynamic nature of the cleared channel. We expect these fluctuations to be much lower in clouds found in the atmosphere, which are significantly lower in density than the ones produced in the cloud chamber. The high repetition rate of the laser makes those fluctuations short and small. It is known that most of the energy deposited by the femtosecond pulse in the plasma is used to generate the shock waves.10 We also characterized the signal-to-noise ratio (SNR) to estimate the density of the cleared channel,

SNR=20×log10(SignalNoise).
(3)

The SNR is defined as a ratio between the signal intensity coupled to the pump that generates the filament and the intensity of the noise when the signal is blocked and the pump is left on. Across all measurements, the signal power is kept constant. When the channel is well established, the SNR defined by Eq. (3) is 1.7-dB. By scanning across the diameter of the intensity profile of the signal (LG12,0) alone [Fig. 2(e)] and then coupled to the pump [Fig. 2(f)], we noted no crosstalk. The density of the cloud is such that it does not allow signal transmission without the filament. When the transmission channel is established, we estimated an 90% increase signal in transmission through the cloud. We demonstrated the ability to transmit data carried by an LG beam with an adjustable repetition rate through a dense cloud with nearly zero initial transmission. There are further advantages in using light-carrying OAM and signal beam, one of which is to encode information within the OAM degree of freedom of the signal beam higher dimensional telecommunication.26,41 Therefore, maintaining the OAM of the light as signal is crucial for our proposed scheme. To demonstrate the conservation of the OAM through the cloud, the topological charge () of the signal beam is measured using the tilted spherical lens.42,43 We use a spherical lens to transform an LG,p mode into a Hermite–Gaussian (HGm,n) mode.42, is determined by counting the bright fringes (N) of the HGm,n: =N1. Figure 3 shows the mode conversion between the LG mode and the HG mode. Figure 3(a) shows the LG12,0 light signal in air and its corresponding HG mode is shown in Fig. 3(c). The light signal couple with the filament after it has traveled through the cloud chamber is shown in Fig. 3(b); its corresponding HG beam after mode conversion is displayed in Fig. 3(d). We, therefore, show that the OAM state of the signal beam is not affected in cloudy conditions when propagated together with the filament. For the implementation of this proof of concept we propose, it is necessary to demonstrate a cleared channel over a long distance. Previously, transmission of LG beams over long distances in the atmosphere have been demonstrated.44 Recently, multi-filaments have been demonstrated45 over a short distance using structured light beams and over hundreds of meters17,46 with Gaussian beams. In our experiment, the channel diameter estimated using the signal carrier is >1-mm. It has been established that the channel diameter depends on the energy deposited in the plasma, thusin the laser pulse energy. For satellite-to-earth or satellite-to-satellite telecommunication, filaments generated by mid-infrared lasers might have to be considered. It is expected that at 10-μm, a filament diameter of 4-cm can be produced and can propagate for several kilometers in the atmosphere.34 

FIG. 2.

Transmission of the signal through the chamber full of air and of cloud. (a) Filament alone was imaged after it propagated through the chamber. (b) Signal alone through the cloud chamber. (c) Signal (LG12,0) through the chamber full of air. (d) Signal coupled with the filament through the cloud chamber. The filters were removed for this measurement. (e) and (f) Intensity profile across the diameter of the signal alone in air and coupled with the filament through the cloud chamber, respectively. (g) The transmission of the signal through the cloud chamber taken by the PMT. The pink slice shows the pump (filament) “on” and the white slices show the pump “off.”

FIG. 2.

Transmission of the signal through the chamber full of air and of cloud. (a) Filament alone was imaged after it propagated through the chamber. (b) Signal alone through the cloud chamber. (c) Signal (LG12,0) through the chamber full of air. (d) Signal coupled with the filament through the cloud chamber. The filters were removed for this measurement. (e) and (f) Intensity profile across the diameter of the signal alone in air and coupled with the filament through the cloud chamber, respectively. (g) The transmission of the signal through the cloud chamber taken by the PMT. The pink slice shows the pump (filament) “on” and the white slices show the pump “off.”

Close modal
FIG. 3.

Mode conversion to demonstrate OAM conservation: (a) LG12,0; signal beam transmitted in air; (b) signal beam coupled with the filament through the cloud chamber. (c) Using the tilted lens method, the initial signal is converted to its corresponding HG45° mode. (d) The same mode conversion is done for the signal beam transmitted through the cloud chamber. For the last conversion, the filament was completely block.

FIG. 3.

Mode conversion to demonstrate OAM conservation: (a) LG12,0; signal beam transmitted in air; (b) signal beam coupled with the filament through the cloud chamber. (c) Using the tilted lens method, the initial signal is converted to its corresponding HG45° mode. (d) The same mode conversion is done for the signal beam transmitted through the cloud chamber. For the last conversion, the filament was completely block.

Close modal

We have demonstrated a method to couple light through a cloud via a stationary high-speed communication channel generated by a 3-kHz repetition rate laser. Our experiment has been driven on a laboratory scale, with dense clouds. We have coupled the filament with LG-like intensity distribution to show that the implementation of this method will lead to no interference with the filament. By measuring the topological charge in the air and through the cloud, we have shown that the orbital angular momentum of the structured light carrying the signal is conserved. We believe that the method of communication we have presented will result in robust FSO communication systems, which can be implemented to compensate for losses induced by difficult weather conditions.

This work was funded in part by the National Geospatial Intelligent Agency under Grant No. #HM04762010012.

The authors have no conflicts to disclose.

Tianhong Wang and Saad Bin Ali Reza contributed equally to this work.

Tianhong Wang: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Saad Bin ali Reza: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Finn Buldt: Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (lead); Visualization (lead); Writing – review & editing (equal). Pascal Bassène: Formal analysis (equal); Methodology (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Moussa N’Gom: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

Tianhong Wang: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Saad Bin Ali Reza: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Finn Buldt: Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (lead); Visualization (lead); Writing – review & editing (equal). Pascal Bassène: Formal analysis (equal); Methodology (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Moussa N’Gom: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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