There is a certain amount of disconnect between the perception and reality of Free Space Optics (FSO), both in the marketplace and in the technical community. In the marketplace, the requirement for FSO technology has not grown to even a fraction of the levels predicted a few years ago. In the technical community, proposed solutions for the limitations of FSO continue to miss the mark. The main commercial limitation for FSO is that light does not propagate very far in dense fog, which occurs a non-negligible amount of the time. There is no known solution for this problem (other than using microwave or other modality backup systems), and therefore FSO equipment has to be priced very competitively to sell in a marketplace dominated by copper wire, fiber optic cabling and increasingly lower cost and higher bandwidth wireless microwave equipment. Expensive technologies such as adaptive optics, which could potentially increase equipment range in clear weather, do not justify the added cost when expected bad weather conditions are taken into account. In this paper we present a simple equation to fit average data for probability of exceeding different atmospheric attenuation values. This average attenuation equation is then used to compare the expected availability performance as a function of link distance for representative FSO systems of different cost.

The use of high-energy laser (HEL) weapon systems in tactical air-to-ground target engagements offers great promise for revolutionizing the USAF's war-fighting capabilities. Laser directed-energy systems will enable ultra-precision strike with minimal collateral damage and significant stand-off range for the aerial platform. The tactical directed energy application differs in many crucial ways from the conventional approach used in missile defense. Tactical missions occur at much lower altitudes and involve look-down to low-contrast ground targets instead of a high-contrast boosting missile. At these lower altitudes, the strength of atmospheric turbulence is greatly enhanced. Although the target slant ranges are much shorter, tactical missions may still involve moderate values of the Rytov number (0.1-0.5), and small isoplanatic angles compared to the diffraction angle. With increased density of air in the propagation path, and the potential for slow-moving or stationary ground targets, HEL-induced thermal blooming will certainly be a concern. In order to minimize the errors induced by tracking through thermal blooming, offset aimpoint tracking can be used. However, this will result in significant tilt anisoplanatism, thus degrading beam stabilization on target. In this paper we investigate the effects of extended turbulence on tracking (or tilt) anisoplanatism using theory and wave optics simulations. The simulations show good agreement with geometric optics predictions at angles larger than about 5 micro-radians (asymptotic regime) while at smaller angles the agreement is poor. We present a theoretical basis for this observation.

The theory is developed for the resolution of a coherent optical synthetic aperture imaging system viewing an object through turbulence. The turbulence induces wave distortions that in turn induce errors in the phase history data collected over the synthetic aperture. The image effects of the phase history errors are space-variant and include broadening of the point spread function as well as geometric distortions. The effect of wave distortions on the intensity image impulse response is related to the usual wave structure function (sum of the log-amplitude and phase structure functions) at the synthetic aperture center frequency. The turbulence-induced limit on resolution is determined for synthetic apertures or any size, without restriction on the size of the real sampling aperture. The results have commonalties to the well-known limit on the resolution of incoherent real aperture imaging systems. A relationship is derived for the resolution of an optical synthetic aperture image forming system relative to the resolution of a passive optical real aperture image forming system viewing through the same inhomogeneous medium.

Atmospheric turbulence is described in terms of a general formulation that does not assume any particular form for the turbulence structure function. The formulation allows for the possibility of Kolmogorov turbulence without bestowing any special favor to this type of turbulence. Expressions are obtained for the two-point correlation function of the complex amplitudes (i.e., Atmospheric MTF) and for the more general function, the two-point two-wavelength correlation function of the complex amplitudes. A cardinal set of measurement procedures naturally derives from these two functions that enables both the integrated strength and the average structure function of the turbulence in a propagation path to be characterized. Kolmogorov and non-Kolmogorov types of turbulence structure are measured impartially by these procedures. The measurement procedures are based on certain key properties of point-object images, properties that carry the essential information about the integrated effects of all mechanisms in the propagation path that affect the wavefronts. These mechanisms can include, but are not limited to, atmospheric turbulence, boundary layer turbulence, telescope aberrations, and the (corrective) effects of adaptive optics. The measurement procedures enable full end-to-end characterization of the entire propagation path between object and image. They take account of amplitude scintillation as well as phase variation in the wavefronts. Once the entire path has been characterized, certain wavelengths can be identified that lead to optimum image resolution. For HEL systems, optimum wavelengths lead to maximum irradiance at the target and maximum target lethality range. Large performance improvements are attained by use of optimum rather than non-optimum wavelengths.

Results are presented for diurnal and seasonal variations in availability for multiple optical ground sites within the Hawaiian Islands. The probability of at least one site available, given one, two and three sites to select from, is modeled. Availability is based on the requirement to simultaneously satisfy constraints on probability of cloud-free line-of-sight and operational thresholds for relative humidity and wind speed. These affect optical coating performance and life, and pointing accuracy, respectively. Modeling techniques are also described for maintaining consistency in the accuracy and fidelity of the atmospheric models in the absence of long-term or site-specific measurements. The results show that availability varies dramatically with time-of-day, and is significantly improved when the number of sites considered increases from only one to two. The analysis also shows that the net effect of wind speed and humidity as a function of time-of-day is not intuitive. The results are applicable to space object imaging, and ground-to-space laser communications and energy projection.

An accurate model for the propagation of infrared and optical frequencies through the atmosphere is a requirement for a number of important communications and surveillance systems. These systems operate over long nearly-horizontal paths that are close to the land or sea surface. There can be strong heat and mass flux gradients near the surface which make accurate transmission predictions difficult. The development and utility of geometrical optics, or ray-trace, methods for the EOSTAR and IRWarp models will be addressed. Both models are driven by bulk meteorological models to provide the environmental fields that can subsequently be used to define the refractivity field. The ray-trace algorithm uses the refractivity field to generate a transfer map. The transfer map provides precise information concerning the number, location, and orientation of the images of a source point. One application of this information is the geometric gain, or the refractive propagation factor, which is an output consisting of a vertical signal intensity profile at a given range. A second application is a passive ranging capability for sub-refractive conditions. The ranging calculation uses the existence of an inferior mirage image to deduce the target range and height.

By using a complex phase screen model for a diffuser located at the transmitter, analytic expressions are developed for the scintillation index of a lowest order Gaussian-beam wave in the pupil plane of the receiver in weak and strong atmospheric conditions. The effect of partial coherence on the scintillation index is analyzed as a function of the propagation distance and the correlation length of the diffuser. The reduction in the scintillation level is shown under all atmospheric conditions. The signal to noise ratio and the bit error rates are discussed.

The propagation problem for partially coherent wave fields in inhomogeneous media is considered in this work. The influence of refraction, inhomogeneity of gain medium properties and refraction parameter fluctuations on target characteristics of radiation are taken into consideration. Such problems arise in the study of laser propagation on atmosphere paths, under investigation of directional radiation pattern forming for lasers which gain media is characterized by strong fluctuation of dielectric constant and for lasers which resonator have an atmosphere area. The ray-tracing technique allows us to make effective algorithms for modeling of a partially coherent wave field propagation through inhomogeneous random media is presented for case when the influecne of an optical wave refraction, the influence of the inhomogeiety of radiaitn amplification or absorption, and also the influence of fluctuations of a refraction parameter on target radiation parameters are basic. Novelty of the technique consists in the account of the additional refraction caused by inhomogeneity of gain, and also in the method of an account of turbulent distortions of a beam with any initial coherence allowing to execute construction of effective numerical algorithms. The technique based on the solution of the equation for coherence function of the second order.

We examine optical beam propagation and scattering in random media using three equations: radiative transfer, Fokker-Planck and Leakeas-Larsen. The Fokker-Planck equation gives a good approximation to the radiative transfer equation for foward peaked scattering phase functions. The Leakeas-Larsen equation gives an even better approximation. The solutions for all three of these equations can be represented as expansions in plane wave modes. Using these plane wave modes, we can compute solutions to these equations in a stable and efficient way.

The intensity of a laser beam after propagation through turbulent media such as the atmosphere may follow different probability density functions (PDFs) depending on the fluctuation regime. For non-coherent receivers the aperture averaging effect reduces the power scintillation leading to a different PDF. Since the analytical approach of deriving the received power PDF knowing the joint-PDF of the intensity at more than just a few points becomes rapidly complex, we review here a much more simplified approach as well as a simulative approach. Both approaches are based on the results of scintillation theory. First, starting from the PDF of the intensity and its spatial correlation, aperture sub-areas can be defined over which the intensity is assumed equal and independent from other sub-areas' intensity. Under those conditions the power PDF is easily worked out. The validity of this method is evaluated according to the level of spatial correlation of the intensity. In a second method, intensity variables are sampled from the Rx-aperture and an approximation of the power PDF is obtained by generating multivariate correlated intensity values. Weak and strong fluctuation regimes are treated separately and the effects of different resolution of the input-intensity-field are discussed. In addition, this paper compares the predicted power characteristics to those deduced from experimental data where the intensity characteristics (PDF, spatial correlation) have been evaluated.

The degrading effects of the atmosphere on a laser communication link can be partially removed with a combination of conventional low-order adaptive optics and other adaptive techniques. Recent experiments performed at UNC Charlotte indicate a measureable reduction in the bit-error rate for a laser communication system by correcting for the phase effects of propagation that are manifested in scintillation at the receiver. Further implementation of an adaptive field-of-view can help to reduce the effect of wide-angle scattering that appears in the extinction ratio. The theory and predictions of the combined adaptive techniques will be discussed along with a description and results of a laboratory experiment replicating a monostatic 1.55 μm laser propagation with a cooperative wavefront beacon at the receiver. The result is scaled to represent an actual propagation of 6 km under moderately high scintillation conditions.

Experimental measurements to investigate the effects of atmospheric turbulence on two major parameters for laser adaptive optic (AO) system design (turbulence coherence length r0 and the atmospheric time constant τ0) were carried out to cover weak, moderate and strong turbulence conditions prevailing in the city of Delhi (India). Diurnal and seasonal variation of atmospheric refractive index structure parameter (C_n²) near the ground was measured with a minimum and maximum recorded values of 2 × 10^-13 m^-2/3 and 10¹¹ m^-2/3 respectively. Estimated values of r0 range from 0.42 mm to 4.4 mm (for 0.6328 μm wavelength of He-Ne laser), 0.8 mm to 8.3 mm (for 1.06 μm wavelength of Nd:YAG laser), 1 mm to 10.5 mm (for 1.3 μm wavelength of Chemical Oxy-Iodine laser), 3.7 mm to 38.2 mm (for 3.8 μm wavelength of DF laser) and 12.5 mm to 131 mm for 10.6 μm CO2 laser wavelength, each for measured Cn2 values of 10¹¹ m^-2/3 to 2×10^-13 m^-2/3. Intensity autocorrelation function measurements of laser scintillations indicate that a bandwidth of ~ 0.5 kHz (corresponding to measured τ0 ~ 2.25 ms) is required for the adaptive optic system to operate effectively in our conditions. Laser beam wander exceeding 100 μrad (both at 0.6328 μm and 1.06 μm wavelengths) at frequencies ranging from 10-20 Hz were observed under strong turbulence conditions. Estimation of number of correction zones for deformable mirror indicate that for the measured turbulence strengths in our atmosphere, the complexity of the AO system at 1.06 μm, 1.3 μm and 3.8 μm wavelengths will be very high as compared to 10.6 μm system where the actuator requirements are much less and within manageable range.

A long-term measurement of the received-power fluctuations caused by atmospheric index-of-refraction turbulence in a near-ground optical free-space laser transmission experiment has been carried out over a eight-months period. Atmospheric index-of-refraction turbulence causes intensity variations in time and space (so called scintillations). These are recorded with differently sized receiver-telescopes, allowing for the calculation of diurnal, seasonal, and meteorological dependences in the received-power statistics. The purpose of this experiment was to gather data for the evaluation of atmospheric optical free-space transmission scenarios. This paper presents statistical evaluations of received-power fluctuations (scintillation-index, fades) over time-of-day and the season. Comparisons with the meteorological circumstances e.g. windspeed and temperature are made.

Recently, new theory governing laser beam scintillation was developed for all regimes of optical turbulence. This theory is based on the Rytov approximation but modified with a filter function that eliminates intermediate scale sizes that do not contribute to the refractive and diffractive effects of propagation. This modification extends the validity of the Rytov approximation into moderate to strong regimes as evidenced by the agreement with simulations and experimental data. In this paper we apply this theory to the phase covariance and new expressions governing phase fluctuations are presented. The phase structure function is then compared with previous experimental data.

Recently, a heuristic model for scintillation in moderate to strong turbulence was developed. It is based on the idea of filter functions that eliminate scale sizes that lose their ability to affect a laser beam as it propagates. This approach allows the validity of the Rytov approximation to be extended into moderate to strong turbulence. In this paper, we investigate applying this theory to second order statistics.

We present the simulations and experimental results on white light generation in the filamentation of high-power femtosecond laser pulse in atmospheric air. We have shown that the strong spatio-temporal localization of the light field in the filament, which provides supercontinuum generation, is sustained due to the dynamic transformation of the field on the whole transverse scale of the beam, including its periphery. Because of the correct consideration of the low-intensity large-scale background of the radiation and high-intensity small-scale filament we obtained the quantitative agreement between the simulated and experimentally obtained conical emission angles of a 250 fs 800 nm 10 mJ pulse. It has been found that the sources of the supercontinuum blue wing are in the rings surrounding the filament as well as at the back of the pulse, where the shock wave formation enhanced by self-steepening takes place. We demonstrated that the conversion efficiency of initially narrow laser pulse spectrum into the supercontinuum depends on the length of filament with high intensity gradients and can be increased by introducing initial chirp into the pulse.

A problem of optical effects in aerosol particles is considered in the tasks of atmospheric femtosecond optics. Based on numerical solution of a problem on diffraction of plane wave of femtosecond duration by a weekly absorbing spherical particle, the spatial-temporal structure of the internal light field is studied. An existence of a multi-mode exciting regime of whispering galler modes is found. It is shown that a decrease of this factor at transition from the monochromatic wave to the femtosecond pulse results in significant decrease of intense internal field in the points of its maxima. A possibility to generate stimulated radiation in a particle at the Stokes frequencies and the third harmonics frequencies is also discussed. The thresholds of nonlinear optical effects under the condition of femtosecond laser pulse action on a dielectric microsphere are considered.

The vectorial and nonparaxial effects of femtosecond laser pulse propagation in gaseous medium are studied by using an order-of-magnitude analysis. A new vector model equation is established, which is valid for an arbitrarily short laser pulse and includes the effects of the coupling between the transverse and the longitudinal components of the electric field in the created plasma channel, e.g., an electrostatic field created longitudinally by the radiation pressure force and/or the ponderomotive force. In addition, we derive an equation governing the time evolution of the plasma current density, which can be used to analyze the mechanism of energy loss during the propagation.

We investigated the frequency spectra and two-dimensional (2-D) distributions of the beam-centroid fluctuation created by spot dancing, which are needed to optimize the design of the tracking system, by using a novel spot-dancing measurement method to suppress the effect of building and/or transmitter vibration. In this method, two laser beams are propagated apart from each other and observed simultaneously using high-speed cameras. The position of each beam centroid is obtained using an image processing system. The effect of transmitter vibration is suppressed by taking the difference between the 2-D coordinate data of the beam-centroid positions. The frequency spectra are calculated using the fast Fourier transform. The beam spots of two HeNe lasers propagated 100 m (indoor) and 750 m (open-air) were observed using a high-speed camera of 10,000 frame/sec. Frequency spectra of the beam-centroid variance of up to 5 kHz could be observed. We also measured the variations of spot dancing in two days when the rates of sunshine were 100% and 0%.

There has been increasing interest in exploiting the pulsed laser rangefinder (LRF) for military electrical-optics systems. With regard to the LRF for military use, it is very important to gain the constant detective probability. However, the effects of atmospherical optical turbulence can degrade the performance. The irradiance fluctuations, one of the effects of atmospherical optical turbulence, can be a limiting factor for pulsed LRF. In this paper, the effects of the refractive index structure parameter C_n, inner scale l₀, laser wavelength λ and receiver aperture size d_r on the received power scintillation and on the detective probability density of 1.06μm LRF were numerical simulated. The results of our numerical simulation can provide the theoretical considerations for reasonable setting, optimal designing and quantitative testing the system performance specifications of the pulsed LRF.

Starting from nonparaxial pulsed-beam propagation equation in free space in temporal frequency domain and making use of spatial Fourier transform, the nonparaxial pulsed-beam solution is derived based on the paraxial pulsed beam solution, where the nonparaxiality is evaluated by a series of expansion. Specifically, the general lowest-order correction field is given in an integral form. Due to the complexity of complex analytical signal (CAS) theory treatment, by using a different initial value from the previous CAS treatment, the lowest-order correction to the paraxial approximation of a fundamental Gaussian beam, uniformly driven by a Gaussian pulse, whose waist plane has a parallel shift from the z=0 plane, are presented. Correspondingly, numerical simulation shows that our lowest-order correction agrees well with the exact paraxial solution(CAS). Apparently, the larger the order is, the more accurate the obtained approximated solution is, and, of course, the more complicated the obtained approximation solution is also.

With the help of the Fast Fourier Transform (FFT) method, a formula is given to study the pulsed spherical beams with the truncated cross section propagating in free space, where the paraxial approximation are also adopted in the derivation. As an application, a theoretical calculation of convergent isodiffracting pulsed beam propagation is presented as an approximation of spherical pulsed beam propagation. Simulation is also shown to illustrate the characteristics of focusing pulsed beam through several kinds of converging lens.

One of the elementary models of molecular band absorption is the quasi-random model. This model is used to study the propagation of a laser beam through vapor media. 1.15μm is one of the many helium-neon lasers operating in the near-IR region; in this region water vapor molecules have five absorption lines. Absorption of this laser beam in a cloud of water vapor, in the frequency interval 8676-8680 cm^-1, is shown in intervals 0.2 cm^-2 wide for two different path lengths. Interaction of a tunable dye laser beam with p-benzoquinone-D₄ lines is studied in the frequecny range 20750-22275 cm-1. Values of transmittance, averaged over intervals of 25 cm^-1, are obtained for two different absorber thicknesses. From these values, intensities of the absorption lines are simulated.

There have been many mature results about reflection and refraction characteristic on medium surface of Gaussian beam, which are verified by practical applications. But, those are limited to regular medium surface such as plane and sphere. When the medium surface is wavy, the reflection and refraction characteristic is greatly different comparing with regular one. In the paper, according to the statistical description of direction distribution on wavy surface by Cox, we have set up a physical model of reflection of laser beam on wavy surface, derived that a beam reflected by wavy surface is also a Gaussian beam when the incident beam is a Gaussian beam, and set up the relationship between Gaussian beam’s light spot size and wind speed over sea surface. According to the wave model on the water surface, the returned laser power expression for the airborne laser bathymetry is derived from. The influence of the wavy water surface, the field of view for the IR received system on returned laser power is discussed.

The coherent wave propagation is affected by the atmosphere in many ways. Several theoretical models for propagation of light through the atmosphere are well known. To predict link availability in different climate zones it is necessary to do field tests for data acquisition. Therefore we have done reliability- and availability-tests on commercial available and also on self-developed optical point-to-point and point-to-multipoint systems. We sent test data at 155 Mbps (STM-1) from one FSO-unit to a distant (2.7 km) FSO-unit. The received data were sent back (loop) to the first unit. Our primary interest in this long-time investigation was the time of link failure, because it turned out that BERs be low in general, less than 10-8 at very bad weather conditions in winter and less than 10-12 at clear sky. In a second measurement campaign we investigated the influence of turbulences in the air. The measurements clearly show variations in the fluctuation of the incoming optical power during a day. In principle there are two periods with strong variations, during the day and during the night, and two periods of rather stable air, these are around sunset and sunrise. The power variations have the highest amplitude and show the fastest changes at noon and they are less distinct and show slower changes in the night. As a medium value we got power variations of 4 dB over the distance of 2.7 km in summer. The duration of fades/scintillations was in the order of 4 to 60 milliseconds at daytime and about 10 to 150 ms in the night.