Effect of Water and Aerosols Absorption on Laser Beam Propagation in Moist Atmosphere at Eye-Safe Wavelength of 1.57 µm

: To realize optical wireless power transmission, atmospheric propagation of eye-safe wavelength (1.57µm) laser beams was theoretically investigated. Laser beams are affected by the presence of water vapor and aerosols which absorb and scatter the laser energy. The scattering coefficients of water molecules and aerosols were estimated to be about 6.3 × 10 -7 and 5.6 × 10 -5 m -1 , respectively, at wavelength (λ 0 ) of 1.57µm. Furthermore, the absorption coefficients of moist air at 30% relative humidity and aerosols were estimated to be about 6.16 × 10 -3 and 2.52 × 10 -5 m -1 , respectively, at λ 0 = 1.57µm. Then simulation of laser beam propagation in the moist atmosphere at λ 0 = 1.57µm was performed using these coefficients. Under the condition of no wind, the beam intensity decreases rapidly with increasing the length z and the rate of decrease slows down as the beam radius (ω) increases. When z h is defined as the z where the normalized intensity is halved, the z h (= 25 m) at ω = 20 mm when input power P = 10 W is about three times longer than that (= 8 m) when P = 100 W. This result indicates that the thermal distortion of laser beams due to accumulated heat around the z axis becomes more conspicuous as the optical power increases. The effect of this thermal beam distortion can be weakened when the laser beam is subject to crosswinds. Under the condition of gentle uniform wind with wind velocity v = 5 m/s, propagation of laser beams with ω = 20 mm was studied when P = 100 W. The z h (= 105 m) when v = 5 m/s is about 13 times longer than that (= 8 m) when v = 0 m/s. Thus, under conditions of v = 5 m/s and 30% relative humidity, laser beams with P = 100 W and ω = 20 mm can propagate over 100 m without damaging the initial beam shape at λ 0 = 1.57µm.


Introduction
Wireless power transmission (WPT) is an important technology to transmit energy remotely from a power source to an electrical apparatus [1].WPT technology relies on electromagnetic radiation, such as microwaves and/or optical beams, to enable long-distance energy transfer.
As for microwave WPT (MWPT), a large-sized phased-array antenna is necessary for increasing the directivity and transmission efficiency owing to large diffraction effect of microwaves.In addition, high power electromagnetic radiation results in the serious issue of electromagnetic interference (EMI) to the target apparatus and surrounding electrical devices.On the other hand, optical WPT (OWPT) is the only WPT technology with the advantages of long transmission distance, high directivity, and no EMI noise [2].Even compared with MWPT, OWPT has the potential to maintain high efficiency over long transmission distances due to small diffraction effect of light.Figure 1 shows basic concept of OWPT.
The light source (laser or light emitting diode) and the O/E converter (solar cell, etc.) are basic devices of OWPT.Solar cell has advantages of high O/E conversion efficiency and thin thickness.Figure 2 shows the absorption spectra of several commercially available solar cells and semiconductors.As shown in Figure 2, GaAs and hydrogenated amorphous silicon (a-Si:H) exhibit large absorption coefficients (αs) of > 10 6 m -1 at the wavelength of < 0.8 and < 0.65µm, respectively.These αs are larger than that of crystalline silicon (c-Si).On the other hand, GaSb exhibits large α of > 10 5 m -1 at the wavelength range from 1.4 to 1.7µm.
Increasing the laser power raises the issue of safety to the human body.Laser safety is governed by the IEC 60825-1 standard [7].This standard gives safety limits for exposure to laser light.Safety limits vary by wavelength and duration of exposure.Generally speaking, the longer the wavelength and the shorter the irradiation time, the higher the safety [8].
Sahai and Graham proposed laser diode array based OWPT systems using a commercially available GaSb semiconductor as an O/E converter [9].In their system, a commercially available multi-mode InGaAsP/InP edge-emitting laser diode array was used as a light source and the oscillation wavelength of the semiconductor laser was set to 1.40µm considering laser safety.
Furthermore, Mukherjee and coworkers reported laser power transfer experiments across a distance of 30 m at an eye-safe wavelength of 1.55µm [10].In their system, a diode pumped high power fiber laser and lattice-matched InGaAsP/InP were used as a light source and O/E converter.A maximum O/E conversion efficiency of about 45% was achieved at an incident laser power density of about 1 kW/m 2 and above [10][11][12].
In order to transfer high-power laser beam to a distant O/E converter, the laser beam must propagate through the moist atmosphere.Atmospheric propagation of laser beams at eye-safe wavelength of 1.57µm is affected by the presence of water molecules and aerosols which absorb and/or scatter the laser energy.
In this article, we investigated the effect of water molecules and aerosol on high-power laser beam propagation in the moist atmosphere at λ 0 = 1.57µm.

Extinction Coefficients of Water and Aerosols
The relationship between the extinction coefficient (α ext ), the absorption coefficient (α abs ), and the scattering coefficient (α sca ) is given by (1)

Scattering Coefficients
Scattering of laser beams in the atmosphere is caused by gaseous molecules and aerosols.The molecular scattering is appreciable only for the shorter visible wavelengths while beyond about 1µm the scattering can be attributed to the atmospheric aerosols [24].
On the other hand, the α sca values of aerosols vary greatly depending on weather conditions, especially the absolute or the relative humidity, and seasons [26].If the aerosol size distribution is known, as well at the effective index of refraction of the aerosol, the α sca can be calculated using the Mie scattering theory [27][28][29].
Barnhardt and Streete estimated the α sca values at various relative humidity using a two-component composite of continental and maritime size distributions of aerosols [24].Their estimated α sca value for a 2.5:1.0 continental: maritime mixing for 50% relative humidity was about 5.6 × 10 -5 m -1 at λ 0 = 1.57µm [24].

Water
In the atmospheric absorption at λ 0 = 1.57µm, the dominant molecular absorber is water vapor.Figure 3 shows the absorption coefficients of water at 293 K for the spectral region from 0.2 to 1.8µm [31,32].
As shown in Figure 3, water molecules exhibit a strong absorption peak at 1.45µm and an absorption coefficient α w of liquid water is about 8.0 × 10 2 m -1 at λ 0 = 1.57µm [31].
On the other hand, the relationship between the water vapor density ρ v (unit: kg m -3 ) at 300 K and relative humidity h is given by the following equation [33].
0.02557 • When relative humidity h is 30%, the ρ v value at 300 K was estimated to be about 7.67 × 10 -3 kg m -3 by using Eq.(2).
By comparing this water vapor density with the density ρ (= 996.62 kg m -3 [34]) of the saturated water at 300 K, the water content c w per 1 m 3 of moist air at 30% relative humidity was estimated to be about 7.7 × 10 -6 .
By using c w and α w , the absorption coefficient α abs of moist air at 30% relative humidity is given by • By using Eq. ( 3), the α abs of moist air at 30% relative humidity was estimated to be 6.16 × 10 -3 m -1 at λ 0 = 1.57µm.
In this subsubsection, the α abs value of aerosols (BC, BrC, and MD) at λ 0 = 1.57µm were estimated as follows.
Parameters related to aerosol absorption are shown in Table 1.In this table, the subscripts VIS and NIR indicate that the physical properties were identified at wavelengths (λ) of 0.55 and 1.57µm, respectively.
k and β are the imaginary part of the refractive index and the absorption coefficient of an aerosol material.
β VIS is related to k VIS as where λ VIS = 0.55µm.On the other hand, β NIR is related to β VIS as where λ NIR = 1.57µm and AAC is the absorption Ångström coefficient [48].AAC close to 1 is expected in spectral regions where the refractive index of the aerosol material has a weak spectral dependence, just like BC [36,41] and MD, whereas AAC = 1.5 is assumed to BrC [41].By using the mass concentration c, mass density ρ, and β NIR , the absorption coefficient α NIR of the aerosol material is given by As shown in Table 1, the α NIR value of BC is larger than those of BrC and MD.The sum of α NIR values of BC, BrC, and MD is defined as the absorption coefficient α abc of aerosols.
Scattering and absorption coefficients of water vapor and aerosols estimated at λ 0 = 1.57µm are listed in Table 2.In the following calculation, the sum (= 6.19 × 10 -3 m -1 ) of α abs values of water vapor and aerosols was used as the absorption coefficient α abs of the moist atmosphere.On the other hand, the extinction coefficient α ext (= α abs + α sca ) was used as α.

Simulation of Gaussian Laser Beam Propagation
Propagation of Gaussian laser beams in the moist atmosphere was investigated theoretically.

Laser Beam Propagation with No Crosswind
In this subsection, for the sake of analysis, we assumed that there is no relative motion (no wind) between the laser beam and the moist air.Laser beam propagates along the z direction at λ 0 = 1.57µm.
When laser beams propagate in the moist atmosphere, thermal distortion of laser beams arises because the absorbed laser power in the atmosphere changes the index of refraction and therefore changes the beam intensity itself [49].A stable state is created by balancing the dissipation of heat due to heat conduction in the xy-plane orthogonal to the traveling z-direction of light and the increase in heat due to absorption of laser power by water vapor and aerosols in the atmosphere.
The steady state solution for an initially collimated Gaussian laser beam propagating through the atmosphere at a point z away from the output end (z = 0) of laser was derived as follows: [49,50].
Let z h be the z where the normalized intensity is halved, then the z h (= 25 m) at ω = 20 mm when P = 10 W is about three times longer than that (= 8 m) when P = 100 W.
This result indicates that the thermal distortion of laser beams due to accumulated heat around the z axis becomes more conspicuous as the optical power increases.
The effect of this thermal beam distortion can be weakened when the laser beam is subject to crosswinds [51].
In the following subsection, we described the calculation results of Gaussian laser beam propagation in moist atmosphere with gentle uniform crosswind at λ 0 = 1.57µm.

Laser Beam Propagation with Gentle Uniform Crosswind
When an initially collimated Gaussian laser beam propagates in the moist atmosphere with transverse air flow, thermal distortion of the beam is not symmetrical around the z axis because of the asymmetry introduced by the one-dimensional wind velocity.
For the sake of analysis, we assumed that there is a uniform wind with the velocity v in the x direction.
Taking into account this problem, the steady state solution for the initially Gaussian laser beam was derived by Gebhardt and Smith [52].The solution is as follows: where Here ρ (= 1176.3 kg m -3 [34]) and C p (= 1007 J kg -1 K -1 [34]) are the density and specific heat of the moist atmosphere at 300 K, respectively.erf (x) is the error function with respect to x.
As shown in Figures 7 and 8, the beam intensity decreases with increasing z without damaging the initial beam shape.At z = 100 m, the intensity of laser beam is about half of the initial intensity at z = 0 m.When x = y = 0, the normalized intensity distributions of laser beam with P = 100 W and ω = 20 mm were calculated using Eq. ( 10) when v = 5 m/s, 30% relative humidity, and λ 0 = 1.57µm.The calculated results are shown in Figure 9.For reference, this figure also shows the calculation results when v = 0 m/s.
As shown in Figure 9, the z h (= 105 m) when v = 5 m/s is about 13 times longer than that (= 8 m) when v = 0 m/s.
When a lattice-matched InGaAsP/InP is used as an O/E converter for 1.57µm laser beams, a maximum O/E conversion efficiency (about 45%) was achieved at an incident laser power density of about 1 kW/m 2 and above [10][11][12].
If P = 100 W and ω = 20 mm is assumed, an incident laser power density of about 1 kW/m 2 and above is achieved when the normalized intensity I / I 0 is larger than 0.0126.This minimum I / I 0 (0.0126) is realized at z ∼ 610 m when v = 5 m/s, 30% relative humidity, and λ 0 = 1.57µm.
The intensity distribution of laser beam at z = 610 m were calculated using Eq. ( 10) when v = 5 m/s, P = 100 W, ω = 20 mm, 30% relative humidity, and λ 0 = 1.57µm.The calculated result is shown in Figure 10.As shown in Figure 10, the laser beam is shifted into the direction of the flow and the distorted crescent shape of the laser beam appears.This is a self-induced thermal lens effect caused by thermal distortion of laser beam [52].
Thus, under conditions of v = 5 m/s and 30% relative humidity, laser beams with P = 100 W and ω = 20 mm can propagate over 100 m without damaging the initial beam shape at λ 0 = 1.57µm.

Conclusion
Atmospheric propagation of eye-safe wavelength (1.57µm) laser beams is affected by the presence of water vapor and aerosols which absorb and scatter the laser energy.The scattering coefficients of water molecules and aerosols were estimated at wavelength (λ 0 ) of 1.57µm.Furthermore, the absorption coefficients of moist air at 30% relative humidity and aerosols were estimated to be about 6.16 × 10 -3 and 2.52 × 10 -5 m -1 , respectively, at λ 0 = 1.57µm.Then laser beam propagation in the moist atmosphere at λ 0 = 1.57µm was theoretically investigated using these coefficients.Under the condition of no wind, the beam intensity decreases rapidly with increasing the length z and the rate of decrease slows down as the beam radius (ω) increases.When z h is defined as the z where the normalized intensity is halved, the z h (= 25 m) at ω = 20 mm when input power P = 10 W is about three times longer than that (= 8 m) when P = 100 W.This result indicates that the thermal distortion of laser beams due to accumulated heat around the z axis becomes more conspicuous as the optical power increases.The effect of this thermal beam distortion can be weakened when the laser beam is subject to crosswinds.Under the condition of gentle uniform wind with wind velocity v = 5 m/s, propagation of laser beams with ω = 20 mm was studied when P = 100 W. The z h (= 105 m) when v = 5 m/s is about 13 times longer than that (= 8 m) when v = 0 m/s.Thus, under conditions of v = 5 m/s and 30% relative humidity, laser beams with P = 100 W and ω = 20 mm can propagate over 100 m without damaging the initial beam shape at λ 0 = 1.57µm.
The eye-safe wavelength of 1.57µm is very close to the lowest loss wavelength (1.55µm) of optical fibers.For this reason, the optical power generated from the light source at 1.57µm can be carried through the optical fiber with almost no loss.So it is possible to bring the optical power close to the target through the optical fiber and then emit the light beam toward the target from there.
It is a great advantage of using a light source with an eye-safe wavelength of 1.57µm that an optical wireless power transmission system can be constructed flexibly by incorporating optical fiber in some suitable section.

Figure 2 .
Figure 2. Absorption spectra of commercially available solar cells and semiconductors.

Figure 6 .
Figure 6.Normalized intensity distribution of laser beam at z = 0 m with v = 5 m/s and 30% relative humidity.

Figure 7 .
Figure 7. Normalized intensity distribution of laser beam at z = 50 m with v = 5 m/s and 30% relative humidity.

Figure 8 .
Figure 8. Normalized intensity distribution of laser beam at z = 100 m with v = 5 m/s and 30% relative humidity.

Figure 10 .
Figure 10.Normalized intensity distribution of laser beam at z = 610 m with v = 5 m/s and 30% relative humidity.

Table 1 .
Parameters of aerosol absorption.

Table 2 .
Scattering and absorption coefficients at 1.57µm.