Propagation of High-Energy Lasers in a Maritime Atmosphere

P. Sprangle, J.R. Peñano, and A. Ting
Plasma Physics Division
B. Hafizi
Icarus Research, Inc.

Introduction

One of the Navy's primary interests in a laser-based directed energy weapon (DEW) system arises from the need for antiship cruise missile and tactical air defense. The Navy is currently considering two main classes of laser systems for DEW applications. These are the free electron laser (FEL) and the solid-state diode pumped laser. The FEL can be designed to operate over a wide range of wavelengths and is capable of generating high average power at high efficiency.1 Diode pumped solid-state lasers can operate at a limited number of discrete wavelengths and, in principle, can be compact and efficient. The Navy's future all-electric-ship can make available a significant amount of electrical power for a laser-based system. The major elements of this system, which are presently being studied and evaluated, include the high average power laser source, beam control, atmospheric propagation, and lethality.

This article addresses key physical processes associated with the propagation of high-average power laser beams in a maritime environment. A number of physical processes affect and limit the amount of laser energy that can be delivered to a target. These effects are interrelated and include thermal blooming, turbulence, and molecular/aerosol absorption and scattering. These processes affect the laser intensity profile by modifying the refractive index of the air, which causes the laser beam wavefront to distort. Wavefront distortion results in enhanced transverse laser beam spreading, and can severely limit the amount of energy that can be propagated. The maritime environment is particularly challenging for high energy-laser (HEL) propagation because of its relatively high water vapor and aerosol content. In the infrared regime, water molecules and aerosols constitute the dominant source of absorption and scattering of laser energy, and represent a limitation for HELs propagating in a maritime atmosphere.

Absorption and scattering of laser energy by molecules, water vapor, and aerosols is a strong function of wavelength.2 Therefore, the choice of laser wavelength is critical for maximizing the laser energy that can be delivered to a target. One of the major advantages of using an FEL for the DEW system, besides its potential for high average power and efficiency, is its ability to operate at a predetermined wavelength. Absorption of laser energy causes local heating of the air. The resulting local reduction in both the air density and refractive index causes the laser beam to undergo thermal blooming, i.e., defocusing. This deleterious process can be significantly reduced by choosing an operating wavelength in an atmospheric window where the absorption is low. Figure 1 shows the extinction coefficient, i.e., sum of scattering and absorption, as a function of wavelength. As shown in Fig. 1, there are several molecular transmission windows in the infrared wavelength range near 1, 1.6, and 2.2 μm.

FIGURE 1
Extinction coefficient of air with (red) and without (black) aerosols vs wavelength for a midlatitude summer (MLS) Navy maritime environment with 50-km visibility. The extinction coefficient was generated using MODTRAN.

In a maritime environment, water vapor absorption plays a major role in determining optimal wavelength. Water vapor has a transmission window centered at 1.045 μm, which is sufficiently broad to permit the propagation of a train of ultrashort pulses characteristic of FELs (Fig. 2). That is, the spectral width associated with the FEL pulses lies well within the water vapor window at 1.045 μm ± 0.004 μm, as shown in Fig. 3. The detailed line structure within the atmospheric windows at 1.6 μm and 2.2 μm results in a higher effective absorption for ultrashort FEL pulses. It should be noted that there are diode-pumped solid-state lasers based on neodymium-doped lithium yttrium fluoride (Nd:YLF) crystals that lase at 1.047 μm and, in principle, can also operate within the water vapor window.

FIGURE 2
Schematic diarame of a pulse train characteristic of an FEL. The duty factor of the pulse train is t₁/t₀.

The physical processes described above are modeled using the propagation code HELCAP (High Energy Laser Code for Atmospheric Propagation). HELCAP is a 4-D (3-D space + time) computer simulation developed at NRL that models the propagation of HEL beams through air affected by a variety of linear and nonlinear processes. The code self-consistently solves a set of coupled nonlinear equations for the laser beam and surrounding air medium. The present version of HELCAP includes thermal blooming, molecular and aerosol absorption/scattering, turbulence, Kerr focusing, ionization, stimulated rotational Raman scattering, laser energy depletion due to ionization, collisions, and quantum saturation effects. Not all of these processes are important in the parameter regime of interest here. However, the capability exists to model the propagation of laser pulses with much higher intensities for a number of other applications.

Atmospheric HEL Propagation

In this section we discuss key processes that affect atmospheric propagation of FELs in general, and present the physical model that forms the basis for the HELCAP propagation code. For the parameter regime considered here, key physical processes are thermal blooming, turbulence, and molecular/aerosol absorption and scattering. HELCAP models all of these processes in a fully time-dependent manner. In addition, it has the capability to model transient thermal blooming effects and propagation through stagnation points, i.e., regions of vanishing wind velocity where thermal blooming is enhanced.

In the HELCAP model, the laser electric field E(x, y, z, t) is written as E(x, y, z, t) = A(x, y, z, t) exp(i( k₀z - ω₀t)) ê_x/2 + c.c., where A is the complex laser amplitude, i.e., amplitude and phase, k₀ is the carrier wavenumber, ω₀ is the carrier frequency, z is the propagation coordinate, ê_x is a transverse unit vector in the direction of polarization, and c.c. denotes the complex conjugate. The spatial rate of change of the complex laser amplitude is found to be3,4

where k₀ = n₀ω₀/c, n₀, is the ambient refractive index of air; c is the vacuum speed of light; δn_TB, δn_T, and δn_A represent the change in the refractive index due to thermal blooming, turbulence, and aerosols, respectively; α is the molecular/aerosol absorption coefficient; and β is the molecular/aerosol scattering coefficient. In calculating the aerosol contributions to α and β, the size distribution and type of aerosol must be considered. Here, we use absorption and scattering coefficients generated using the "maritime" aerosol model of the atmospheric transmission codes MODTRAN and FASCODE. The extinction coefficient refers to the sum α + β.

Equation (1) for the laser amplitude is self-consistently coupled to models for the atmospheric medium through various source terms appearing on the right-hand side of the equation. In what follows, we describe the models for the various terms.

Thermal Blooming

Propagation of a laser beam in the atmosphere results in a small fraction of the energy being absorbed by the air. The absorbed energy locally heats the air and leads to a decrease in the air density. The resulting change in the refractive index is given by δn_TB = (n₀ - 1)δρ/ρ₀ where ρ₀ and δρ are the ambient and perturbed air mass density, respectively. This refractive index variation caused by the local heating of the air leads to a defocusing or spreading of the laser beam known as thermal blooming.

The perturbed air mass density may be calculated by using a hydrodynamic description of air. Analysis of thermal blooming starts with the fluid equations for continuity, momentum, and energy, as well as the ideal gas law. The HELCAP code solves a general set of coupled, linearized fluid equations for the perturbed air density and temperature change caused by the laser. The source term for the perturbed air mass density is the rate at which laser energy density is absorbed, α<I>, where α is the total effective absorption coefficient and <I> = (c/8π)<|A|2> is the average laser intensity. Thermal blooming is a sensitive function of the heating mechanisms present in air. Aerosol heating also affects thermal blooming by heating the surrounding air by a number of mechanisms.

Molecular Absorption

Molecular absorption of laser energy occurs at discrete but closely spaced lines (wavelengths). For example, Fig. 3 shows the absorption of air near the 1-μm transmission window. The absorbed laser energy goes into exciting the rotational and vibrational modes of the air molecules. The rotational/vibrational energy goes into heating the air through collisional processes that take place on a molecular collision time scale of ~ 100 ps - 200 ps. Thermal blooming occurs on a much longer, hydrodynamic, millisecond time scale.

FIGURE 3
Extinction coefficient vs wavelength with (red) and withoug (solid black) aerosols showing in detail the transmission window near ~1 μm. The extinction coefficint was generated using PLEXUS/FASCODE 3 for the same maritime environment as Fig. 1. The dashed curve is a sketch of the spectrum of an ultrashort laser pulse. Note that the continuum absorption at ~ 1.045 μm is ~ 6 X 10^-3 km^-1, which is somewhat highter than the absorption coefficient calculated using MODTRAN 4.

Although nitrogen and oxygen are by far the most abundant molecules comprising air, they have no permanent electric dipole moments and are, therefore, relatively free of absorption lines in the infrared. Polar molecules such as H₂O, on the other hand, have permanent dipole moments and are typically strong absorbers in the infrared (IR) regime. The vibrational-rotational transitions in these molecules absorb in the mid-IR, while their rotational transitions lie in the far-IR. For HEL propagation in the maritime environment, water molecules are by far the most important IR absorbers at low altitudes. Ultrashort laser pulses have spectral widths sufficiently broad to generally overlap a number of absorption lines. The effective absorption coefficient α_M is obtained by taking the appropriate overlap integral of the laser pulse spectrum and the absorption spectrum.

In the atmospheric window near 1 μm, the molecular absorption for an ultrashort laser pulse is determined mainly by the continuum absorption, as shown in Fig. 3. However, there is still a need for experiments to accurately determine the continuum absorption coefficient.

Turbulence

Turbulence affects the propagation of a laser beam through fluctuations in the refractive index caused by thermal fluctuations in the air. These fluctuations are inherent in the air and are not induced by the laser. Hence, unlike thermal blooming, the effect of turbulence on the laser propagation is independent of laser intensity. Modeling of turbulence is implemented by introducing fictitious phase screens at regular intervals along the propagation path. The screens randomize the phase of the laser field and represent the cumulative effect of turbulence on propagation between the two phase screens.

The Fourier transform of the fluctuating part of the refractive index due to turbulence can be expressed in terms of the spectral density function Φ_n (k⊥, z), where k⊥ = (k2_x + k2_y)1/2 is transverse wavenumber. The modified von Karman spectral density function is given by Φ_n (k⊥, z) = 0.033C2_n ((2π/L₀)2 + k2⊥)-11/16 exp[-k2⊥ l2₀/35], where C2_n is the refractive index structure constant, L₀ is the outer scale length, and l₀ is the inner scale length. Typical values for the inner and outer scale lengths are 1 and 100 m, respectively.

Turbulence can lead to both spreading and wandering of the laser beam. For an initially collimated beam with spot size (radius) w₀ propagating over a distance L, the increase in the laser spot size due to turbulence is given by ρ_spread = (λ/π ρ_c)L, where the transverse coherence length is given by ρ_c ≈ 0.158 λ (λ1/3 / C2_n L)3/5. Turbulence also causes the collimated beam centroid to wander transversely by the average amount, ρ_wander ≈ 1.14[C2_nL3/(2w₀)1/3]1/2. The ratio of the beam wander to the beam spread is ρ_wander /ρ_spread ≈ 0.5 and is relatively insensitive to laser and atmospheric parameters.

Adaptive optics can be used to correct for wavefront distortions due to turbulence, which is a process independent of intensity. Thermal blooming, however, is a highly nonlinear process and can only be modestly mitigated by conventional adaptive optics techniques. To correct for thermal blooming distortions, both the wavefront as well as the intensity of the transmitted laser beam must be compensated.

Maritime Aerosols

Aerosol scattering and absorption can play a significant role in limiting the laser energy that can be delivered to a target. Maritime aerosols consist of water droplets distributed over a wide range of radii (R_A ~ 0.01 to 10 μm) and densities (n_A ≤ 103 cm-3). The average water content of aerosols is typically far less than that of humid air. For example, at a temperature of 30°C and relative humidity of 50%, the water vapor mass density is ρ_WV ~ 1.5 X 10-5 g/cm3, while the average mass density of maritime aerosols is typically far less, ≤ 10-9 g/cm3. For oceanic water, the absorption coefficients are α_W ~ 7, 20, and 50 cm-1 at the wavelengths λ ~ 1.045, 1.625, and 2.264 μm, respectively. For pure water, note that the absorption coefficients are somewhat less than for oceanic water. Unlike water vapor, there are no absorption windows for liquid water since the molecular collision frequency is ~103 higher in liquids.

Although the average water mass density of maritime aerosols is small, it can have a large effect on the scattering of laser radiation. In the Rayleigh limit, the laser wavelength is large compared to the aerosol radius λ >> R_A, and the scattering coefficient is pro-portional to R6_A ~ N2_W, where N_W is the number of water molecules in the aerosol. This is a factor of N_W larger than molecular Rayleigh scattering for the same number of water molecules. In the Mie limit, the laser wavelength is small compared to the aerosol radius λ >> R_A, and the scattering coefficient is proportional to R2_A ~ N_W2/3 . The number of water molecules in an aerosol is large, e.g., for R_A = 0.1 μm, N_W ~ 108 water molecules. The aerosol scattering coefficient in the wavelength range of interest can be as large as β_A ~ 0.2 km-1.

The rate at which laser energy is absorbed determines the degree of thermal blooming. The thermal blooming source term can be written as α <I> = α_M <I> + ϒ_AC. The molecular absorption coefficient α_M is given by an overlap integral of the molecular absorption coefficient and the laser pulse spectrum, and is a sensitive function of the laser wavelength and pulse length. The aerosols absorb laser energy. The heated aerosols transfer part of their thermal energy to the surrounding air through con-duction; this contribution is contained in ϒ_AC. The time scale for heat conduction from the aerosol into the surrounding air is given by τ_c ~ l2 / D, where D is the diffusion coefficient and l is on the order of the interaerosol spacing.

Simulations of HEL Propagation in a Maritime Atmosphere

In this section we present results of numerical simulations of the propagation of a high-energy laser beam through a maritime environment. For the present study, the HELCAP simulation solves Eq. (1) for the laser envelope and self-consistently tracks the nonlinear response of air. We consider the propagation of FEL pulse trains with wavelengths in the 1.045, 1.625, and 2.264-μm transmission windows. The pulse trains used in the HELCAP simulations are composed of Gaussian pulses with intensity I = I_peak exp[-(t - z/c)2 / τ2_L]exp(-2r2 /w2₀), pulse duration τ_L, pulse separation τ₀, and initial spot size w₀. The average intensity associated with this pulse train is given by <I> = √ π I_peak τ_L/τ₀. The focusing geometry is illustrated in Fig. 4(a).

FIGURE 4
(a) Schematic illustration of the focusing geometry used in the simulations. The atmosphere is characterized by an average aerosol mass density of 10^-1 g/cm³, turbulence with index C²_n = 10^-16m^-2/3, and scale lengths l₀ = 1 cm and L₀ = 100 m, and a uniform wind. The absorption and scattering coefficients used in the sumulations are listed in Table 1. (b) Simulation results showing average power in the arbitrary units within the target area for laser wavelengths λ = 1.045, 1.625, and 2.264 μm.

We consider a specific maritime atmosphere that is representative of moderate propagation conditions. The atmosphere is characterized by an average aerosol mass density of 10-9 g/cm3 and a uniform wind. Table 1 lists the absorption and scattering coefficients used in the simulations. These coefficients are consistent with the "maritime" atmospheric model used in FASCODE. The ambient air temperature is assumed to be 296 K. The turbulence is characterized by index C2_n = 10-16 m-2/3, inner scale length l₀ = 1 cm, and outer scale length L₀ = 100 m.

Figure 4(b) shows the results of several simulations for propagation of a high average power FEL beam in the 1.045, 1.625, and 2.264-μm transmission windows. The figure plots P_target vs laser wavelength, where the quantity P_target is a figure of merit representing the average power at the target range within a given area centered about the peak. The results indicate that the power delivered to the target is highest when propagating in the 1.625-μm transmission window compared to the 1.045 and 2.264-μm windows. In the 2.264-μm transmission window, the large molecular absorption severely limits the power delivered.

Figure 5 plots the normalized average power on the target vs power at the transmitter for the 1.045 and 1.625-μm wavelengths. For lower transmitted powers, the power delivered on target at 1.625-μm is slightly greater than for 1.045-μm because of the lower scattering coefficient at 1.625-μm. However, because of the higher molecular absorption at 1.625-μm, thermal blooming significantly decreases the efficiency of this wavelength at higher power levels.

FIGURE 5
Average power on target vs normalized laser power at the transmitter P₀ for wavelengths λ = 1.045 μm (filled circles) and λ = 1.625 mm (open circles).

Figure 6 plots laser intensity vs time and transverse coordinate x at the target range for 1.045 and 1.625-μm wavelengths. Note the deflection of the trailing parts of the beam into the wind due to the time-dependent nature of the thermal blooming process.

FIGURE 6
Average laser intensity on target vs time and transverse position x for λ = 1.625 μm and initial (z=0) normalized power. Other parameters are indentical to those of Fig. 5.

Figure 7 shows the cross-sectional plots of average laser intensity on target for the three wavelengths of interest. The beam cross sections for the 1.045 and 1.625-μm wavelengths show a relatively well-focused beam with little deflection. However, the 2.264-μm wavelength beam shows severe distortion due to thermal blooming and a much lower intensity on target. The characteristic crescent shaped caused by blooming is not discernible because of the turbulence present in these examples.

FIGURE 7
Corss sectional plots of average laser intensity on the target, corresponding to the simulations discussed in Fig. 4.

Discussion and Conclusions

Laser-based directed energy weapons are envisioned to be an integral part of future Navy vessels. The free electron laser, in particular, is especially suited for maritime applications. It can be designed to operate over a wide range of wavelengths and is capable of generating high average power at high efficiency.

In this article we discussed and analyzed the key physical processes that affect the propagation of high-energy lasers in a maritime environment. These processes include thermal blooming, turbulence, and molecular/aerosol absorption and scattering. Aerosol scattering and absorption as well as water vapor absorption can be a major limitation for HEL propagation in a maritime environment.

Using the HELCAP code, we performed full-scale simulations of propagation in the atmospheric transmission windows near 1.045, 1.625, and 2.264-μm.

Acknowledgments

The authors thank John Albertine and Wallace Manheimer for useful discussions.

[Sponsored by NAVSEA, JTO, and ONR]

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