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.

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