1.

Introduction

The brightness potential of a laser is inversely proportional to the square of its wavelength. Short wavelength lasers (SWLs), which I define as having a wavelength ($\lambda$) of less than $2\times {10}^{-6}\mathrm{m}$, or, 2 μm, have an enormous potential for achieving high brightness with an accompanying reduction of power or telescope size. This compactness can lead to weight/volume reductions, which both enhance mission feasibility and reduce costs.

Once a SWL with good beam quality (BQ) is identified, then beam control becomes the key to success. Challenges abound! As the laser wavelength decreases, the phase aberration “bumps” in the beam path: man-made, natural and beam induced—become dramatically more important. In general, energy is scattered from the beam, and the beam itself is deflected. The result is a reduction in far field intensity. This latter parameter is defined as the beam power per unit area that can be projected onto a target. I will refer to this as “flux-in-a-bucket”. Generally, it has units of $\mathrm{W}/{\mathrm{cm}}^2$.

To produce a nearly pristine beam at the target, careful photon management must be accomplished from “A to Z”. Both passive and active beam control are essential. Passive techniques include high quality optics (precise figure, smoothness) and a near diffraction-limited SWL device. Active techniques could include mechanical or nonmechanical adaptive optics (AO). By applying this to the entire photon odyssey, one can achieve high-brightness SWL systems. The path is rough, but the payoff is prodigious! Let us now begin our photon odyssey …in search of short wavelength high brightness laser systems. First we introduce the guides. Freddy the Photon will show us the many obstacles he faces in getting from SWL laser device to the target. His companion, Felix the Flux, represents many SWL photons. Both appear in Fig. 1. These will serve as our animated guides as we trek through the SWL “photon foxholes.” Our quest for high brightness laser systems starts at the source …the laser device. Source brightness is

Fig. 1

Freddy the Photon and Felix the Flux.

Of the several paths to higher source brightness, increasing power is the least attractive! Reasons include:

If a SWL laser, wavelength $\lambda$, is magnified and focused on a target at distance $Z$, then the ideal intensity delivered is

Before leaving this ideal situation, let’s note the potential payoff of SWLs. For example, a reduction in wavelength from $\lambda \sim 4\mu \mathrm{m}$ (deuterium fluoride chemical laser) to $\lambda \sim 0.4\mu \mathrm{m}$ (excimer laser), with all other parameters in Eq. (2) being identical, yields a brightness increase of 100 for the SWL Excimer laser system! This wavelength dependence of $I_{\text{IDEAL}}$ is shown in Fig. 2, and graphically shows the lure of SWL systems!

Fig. 2

Ideal short wavelength lasers (SWLs) far-field peak intensity.

2.

Cost of SWL Systems

Recent data from the Air Force Weapons Laboratory’s (AFWL) Chemical Oxygen-Iodine Laser (COIL) suggests that the cost scaling for telescope aperture is $A^{3/2}$ so that the costs, $C$, of some SWLs should scale as $C\sim p$ $P^{1/2}+a{A}^{3/2}$, where the premultipliers $p$ and $a$ are constants. The SWL system brightness is just source brightness times telescope aperture, or

For example, for constant brightness, a factor of 4 reduction in $\lambda$ results in a 75% cost savings (e.g., 2 μm system versus 0.5 μm). Alternately, given SWL can be scaled an order of magnitude in brightness for a cost growth factor of $\sim 2.4$.

3.

Challenge of Achieving SWL High Brightness

The path to SWLs is paved with phase aberrations or “bumps”. As the laser wavelength decreases, the bumps in the beam path magnify in importance. A real SWL laser system suffers from three classes of aberrations.

As our laser beam conducts its photon odyssey from device to target, it encounters a veritable blizzard of phase “bumps,” each varying in strength and size. The result can be a beam which is jittered, spread, and markedly reduced in peak intensity. While careful photon management can alleviate these effects, ideal performance, Eq. (2), is not achievable.

To understand how these phase aberrations affect the laser beam, we note that “bumps” can be placed in two classes—those small compared with the beam diameter D and those larger than D. Figure 3 shows these two classes. The small phase aberration, size $b$, scatters photons at characteristic angle ${\theta }_b\sim \lambda /b$. The amount of scatter depends on both the strength and dimensions of the bump. This strength scales as the difference in refractive index between the bump and its surroundings. The larger phase bump $B$ acts to steer the entire beam over angle ${\theta }_B$ dependent on refractive index, but not wavelength. Phase bumps sizes between $b$ and $B$ can be expressed as a combination of the two extremes.

Fig. 3

Phase aberration effects on beam.

The result of our SWL photon odyssey is a far-field beam suffering a marked reduction in intensity because of scatter and beam spread. We write this as

Equation (4) consists of three parts. The term in brackets at the end of the equation is just the ideal brightness, $I_{\text{IDEAL}}$ [Eq. (2)]. The exponential term reflects losses due to wide angle scattering (i.e., phase bumps small compared with beam diameter). Finally, the term in front brackets expresses reduction in brightness because of beam jitter (recall this last aberration is driven by bumps larger than the laser beam or by system mechanical vibrations).

Figure 4 compares $I_{\text{IDEAL}}$ and $I_{{\mathrm{REAL}}^{\prime }}$. It shows the quintessential challenge of SWL systems. For convenience, we set $L=1$ (actually, atmospheric absorption/scatter shows a strong wavelength dependence. In practice, for applications requiring propagation through the atmosphere, one picks a laser whose wavelength(s) fall in a transmission “window”). Note the following:

Fig. 4

Far-field intensity scaling with wavelength: real versus ideal.

Figure 5 depicts the major components of a laser system. Figure 6 shows Freddy’s quest for SWL high brightness. To realize the potential of our SWL system, one must meticulously orchestrate the photons to enable a high BQ beam to arrive at the target. Much as a conductor brings harmony to a collection of independent musical instruments, so must the laser system engineer orchestrate Freddy through the system, which includes a mine field of “jitters” and high order phase aberrations. A high quality SWL is the door to very high brightness laser systems. The lock is system phase aberrations—natural, man-made and laser beam produced—that act to dramatically reduce BQ. Beam control is the key, which if used creatively and coherently, can open the door to high brightness SWLs. Note that for a given set of (uncorrected) aberrations, the system Strehl performance actually decreases for $\lambda <{\lambda }^{*}$.

Fig. 5

Major components of laser systems.

Fig. 6

Freddy’s quest for brightness.

The effects of these uncorrected phase aberrations on far field performance are shown in Fig. 7. Our ideal beam is shown for reference. The real beam at the target consists of a central unaffected spot and a “halo” of energy due to aberration-induced beam jitter and spread. The resulting beam is markedly reduced from the ideal in both peak intensity and “flux-in-the- bucket”. Again the challenge of beam control is to bring the real SWL performance close to the ideal.

Fig. 7

Effects of short wavelength lasers (SWLs) phase aberrations on far-field performance.

The remainder of this paper will describe the photon odyssey from device to target. First, some general features of laser systems will be broached. The various sources of optical phase aberrations, man-made, natural, and laser-induced will be examined. Next, effects on the optimum laser wavelength because of wide-angle scatter, beam spread and nonlinear will be plumbed. We will see that each uncorrectable source of phase aberration causes significant reductions in Strehl, or far-field performance. AO techniques have the potential to correct certain system aberrations, and so recover some Strehl. However, today’s mechanical AO systems are cumbersome and costly. Nonlinear optical (NLO) methods will be presented as offering a quantum breakthrough in SWL beam control! How a given SWL laser system scales in brightness will be studied. After noting that monolithic systems (i.e., single laser/telescope) have brightness limitations …because of either engineering or physics constraints …we will examine how lasers and telescopes can be coupled to yield very high brightness systems. If such systems can be rendered highly coherent, their performance will be close to that of a monolith having the same equivalent power and telescope aperture area.

Conclusions drawn in comparing these exciting approaches are based wholly on basic physics and the arguments I will develop in this paper.

4.

General Laser System Features

Lasers have several intrinsic advantages as weapons systems:¹

Some disadvantages of lasers:

In fact, blending lasers and kinetic energy weapons can yield synergy:

Recall the device ideal brightness in Eq. (1) is $B_{\text{IDEAL}}=P/(n^2{\lambda }^2)$. Table 1 summarizes demonstrated performance of several extant lasers.

Table 1

Demonstrated performance of several extant lasers.

5.

Laser Device Scaling

A monolithic laser system consists of a single device and telescope. Such a system has a brightness “ceiling” established via either physics or engineering limitations. I refer to this “biggest monolith with good BQ” as the unit cell. As this single device is power scaled, energy management becomes more difficult, leading eventually to intrinsic loss of BQ or extrinsic optics damage from the increasing beam flux. Thus, a monolithic laser system has a maximum brightness

Attempting to increase power beyond this value can actually cause system brightness to decrease! Figure 8 shows brightness saturation for a single SWL.

Fig. 8

Single device brightness ceiling.

Further power scaling requires coupling lasers together. Such has been demonstrated for ${\mathrm{CO}}_2$ lasers by the Strategic Defense Initiative Organization and the AFWL. We, at the AFWL recently showed coupling for oxygen-iodine (${\mathrm{O}}_2\mathrm{I}$) lasers, and plan near term similar experiments for excimer lasers. As a single laser module grows, three effects combine to degrade BQ per Fig. 9.

Fig. 9

Laser device scaling.

These effects act either individually or in concert to limit the maximum brightness of a unit cell. Now, let’s review the physics that sets the size of the unit cell. The power in the laser cavity (Fig. 9) is just $P\sim LWf$, with $f=\text{nozzle flux}$ ($\mathrm{W}/{\mathrm{cm}}^2$). From Eq. (5), system brightness, $B$, is proportional to $P/n^2$ and $n\propto e^{{(2\pi \varphi /\lambda )}^2}$, where $\varphi$ is the system beam (power)-induced RMS phase aberrations (note that $\varphi \propto L{\mathrm{\Delta }}_{\mathrm{RMS}}$, where ${\mathrm{\Delta }}_{\mathrm{RMS}}$ is the density variance in the lasing direction).

Now observe from the above relation that power scales $\sim$ linearly but n grows exponentially! Thus, beam brightness saturates and eventually decreases! Every monolith or unit cell has scaling limits! At modest powers $B\mathbf{\alpha }P$ because the BQ is approximately constant; however, as the laser cavity volume expands, BQ degrades rapidly. Thus, brightness will eventually be limited by BQ degradation. A second concern is the effects of growing cavity flux on resonator optics.

As an example, consider likely scaling limitations for an ${\mathrm{O}}_2\mathrm{I}$ unit cell. Our 30 kW, in-house ${\mathrm{O}}_2\mathrm{I}$ (COIL) demonstration suggests that if linear scaling is operative, a high quality megawatt-class ${\mathrm{O}}_2\mathrm{I}$ is plausible! BQ degradation will become significant eventually (perhaps in the $\sim 5\mathrm{MW}$ regime); even so, a closed-loop AO system could in principle recover some performance. Low order variations in refractive index, e.g., tilt and focus, can be corrected in the resonator; however, higher order (HO) corrections require a complete AO system. This, then, would leave us with a structures limitation—cavity optics distortion/damage. This threshold might be realized in the 5 to 10 MW range. Thus, based on simple scaling laws and a 30 kW demonstrator, the ${\mathrm{O}}_2\mathrm{I}$ unit cell can probably be scaled to the multi-MW regime while retaining good BQ (via AO corrections). Further power scaling requires coherently lashing together multiple lasers.

6.

Relay Optics: Orchestrating the Beam from the Device to the Atmosphere

Relay optics transport the high power (HP) laser beam from the device to the projecting telescope. For example, windows may be used to accommodate a pressure drop (e.g., device cavity to ambient). A HP beam transmitting such a window will suffer absorption in both the coating and the bulk—and will result in thermal distortion of the window with subsequent phase aberrations imposed on the HP beam. Similarly, reflective optical flats, AO, aperture sharing elements (ASE)—cooled or uncooled—plus a telescope are required. Figure 10 shows an optical suite which, of course, must operate in harmony to deliver a high quality beam to the target. We next plumb performance of these vital components in transporting a HP SWL beam.

Fig. 10

Laser system optics suite.

7.

SWL Windows: a Critical Element

Windows are crucial to SWL systems to either:

Two kinds of windows have been developed for HP lasers—aerodynamic and material. Aerodynamic windows use a high velocity gas sheath across the laser port which is to be “sealed”. A pressure differential $\mathrm{\Delta }p\sim 1/2$ $\rho V^2$ is established to insulate the “inside” from the “outside,” with $\rho$ and $V$ the shear layer density and velocity, respectively.

There are two major disadvantages:

Plan “B” for our SWL system is a material window. This window generally has an antireflective (AR) coating to minimize reflections from the surfaces. Though such coatings are generally only $\sim$ wavelengths thick, laser energy is absorbed in both the coating and bulk material. Figure 11 shows a laser beam incident on our window. This beam generally has a nonuniform intensity profile, as shown by the notch in “Felix the Flux.”

Fig. 11

Short wavelength lasers (SWL) beam/window interaction.

One of five events can occur to each photon:

On a microscopic scale, hot spots are formed within our window due to absorption of a nonuniform incident beam. Each little $\mathrm{\Delta }{T}_i$ temperature causes index of refraction $\mathrm{\Delta }{n}_i$ and window thickness $\mathrm{\Delta }{d}_i$ changes. Each Freddy the Photon, in turn, has a different optical path, resulting in a phase shift across the beam. The emerging beam is complex, with window-induced nonuniformities in both intensity and phase. We estimate the resulting Strehl loss from

Cooling SWL windows will be a tough challenge! Edge cooling is generally ineffective. A novel advanced technique streamed an index-matched coolant through the bulk window. This is promising—but quite untested! Very thin material membranes have been examined as candidate windows, and have been shown to have low absorption under intense laser beam loading. However, these “pellicles” suffer from two disadvantages:

8.

SWL High Power Mirrors: an Important Element

Elements in this suite include device cavity and transfer optics, deformable mirrors (DMs), beam steering mirrors and the telescope. Each mirror generally has applied a highly reflecting (HR) coating, tailored to the laser wavelengths(s). Most HP applications demand reflectivities well above 99%. Figure 12 shows our beam impinging on a mirror. Four outcomes are possible for each photon:

Fig. 12

Short wavelength lasers (SWL) beam/mirror.

Mirrors may be cooled or uncooled; however, because no laser energy is transmitted, heat exchanger (HEX) technology can be effectively used to minimize beam intensity mapping effects. Beam-induced aberrations are generally significantly less than that of windows. However, cooled optics present two principal difficulties:

A quantum advance may be in the offing as a result of low-flow HEX research sponsored by the AFWL over the past two to three years! Traditional HP HEXs use metal (e.g., molybdenum) face sheets with high coolant pressures/flow rates. Distortion coefficients are typically $\sim 40Å/\mathrm{W}/{\mathrm{cm}}^2$. For example, an absorbed laser intensity of $50\mathrm{W}/{\mathrm{cm}}^2$ would result in faceplate distortion of $2000Å\sim \lambda /5$ for a SWL! Corresponding coolant flows are $\sim 4\mathrm{g}/\mathrm{s}/{\mathrm{cm}}^2$. Our low flow HEX concept uses a thin ($\le 0.1\mathrm{mm}$) ULE (glass ceramic) face sheet! The distortion coefficient of ULE is only—$4.5Å/\mathrm{W}/{\mathrm{cm}}^2$! Moreover, the lower flow rate—about $1\mathrm{g}/\mathrm{s}/{\mathrm{cm}}^2$ yields near laminar flow condition. Most importantly for SWL systems, the flow-induced jitter for low flow HEX is $<10\%$ that of “traditional” HP HEXs. Although power handling capabilities of this advanced concept is somewhat less, it is still highly attractive for several potential SWL applications.

9.

SWL Aperture Sharing Elements: a Crisp Challenge

Many high brightness SWL systems require an ASE (material window is an implausible candidate, as noted earlier). This element separates the outgoing (HP) laser beam from the target-return tracking beam (e.g., an active—4 μm laser tracker). Figure 13 shows a simple buried grating. Its task is to efficiently reflect a HP SWL while directing an axial incoming (low power) tracker return to a suitable sensor array. There are strong motivations from all beams sharing the same optical axis—boresiting is automatic, and beam control, in the presence of misalignments, jitter or high order aberrations is greatly simplified.

Fig. 13

A buried grating aperture sharing elements (ASE).

The downside is the knotty optical engineering challenge of developing an ASE. The HP SWL reflects from the HR front surface. The target return laser beam ($\lambda \sim 4$ to 10 μm) is diffracted by the grating to the tracker sensor. The challenge is not building such ASEs—but in managing the thermal energy from the HP SWL that is absorbed at the front surface and/or the bulk (if the uncooled substrate is somewhat translucent to the SWL). This optical engineering challenge is particularly pithy because an ASE is generally composed of several different materials, each having unique thermo-optical properties. As this element is heated by the HP beam, its optical performance must be invariant.

10.

Optical Coatings: Every SWL System Needs Them

Coatings on optics can perform several functions, including

The most important parameter for HP SWL coatings is absorption—this results in thermal-induced optics distortions. Of course, the ideal coating is absorption-free (do not invest in ocean property in New Mexico or “transparentium”). Low absorption coatings [$<200$parts per million (PPM)] for 1.3 μm have been demonstrated in laboratory tests on “coupon” samples (i.e., diameters of order few centimeters). Two essential questions remain:

Neither of the questions have been adequately addressed; both answers are required before building a HP SWL laser system.

11.

Atmospheric Propagation

A HP laser beam propagating from a telescope diameter $D$ to a target at distance $T$ through the atmosphere will experience both absorption and scattering. Absorption can result in nonlinear efforts such as thermal blooming (TB) or stimulated Raman scatter (SRS). Photons can suffer Rayleigh scatter (molecular), aerosol scatter and turbulence-induced scatter or jitter.

Turbulence is a collection of index-of-refraction variances called “eddies”. Local turbulence is due to flow effects and heating around and within the [ground based (GB)] telescope. Atmospheric turbulence is due to natural effects. Both act to degrade a SWL GB system. Eddies are just density fluctuations, in turn, driven by atmospheric temperature and pressure fluctuations. “Old Sol” is the prime mover for natural turbulence! These eddies can be put in two classes (recall Fig. 3): those small compared with the beam diameter ($D$) and those much larger (in fact, there are a nearly continuous spectrum of eddy sizes).

Small eddies (size $b\ll D$) cause the beam to scatter at an angle $\theta \sim \lambda /b$, where $b$ is the eddy size. Note this angle exceeds the SWL laser diffraction angle $\theta \sim \lambda /D$ and so these photons are generally scattered outside the target aim point. Large eddies (size $B\gg D$) tend to deflect or jitter the entire beam. The amount of resulting jitter depends on the strength of turbulence but not on the SWL wavelength. Intermediate eddies can be described as a combination of “big eddy and small eddy”! The effect of turbulence on far-field performance is identical with that of all the other phase bumps or aberrations along our photon odyssey. Jitter spreads the effective spot size on the target while HO aberrations (i.e., wide angle scattering) reduces the Strehl or flux in the bucket, but does not (to first order) effect spot size. Both phenomena, however, serve to decrease far-field performance, and must be successfully broached by an AO subsystem to enable short wavelength ground-based laser (GBL) applications.

Felix the Flux also experiences atmospheric scatter and absorption during his odyssey to the target. Natural or man-made aerosols both scatter and absorb laser energy, as do atmospheric molecular constituents. Rayleigh scattering has a strong wavelength dependence $\sim 1/\lambda$, but above about 1 μm wavelength is negligible. Aerosol scattering dominates for $\lambda >0.8\mu \mathrm{m}$. Figure 14 shows SWL atmospheric absorption/scattering losses for propagation from $\sim$ sea level to space. Note that absorption is dominated by water, and to a lesser extent, by ${\mathrm{CO}}_2$. Clearly, one would not select lasers with wavelengths in the 1.1 to 1.2 μm or 1.35 to 1.5 μm domains!

Fig. 14

Atmospheric scatter/absorption from molecular and aerosol constituents for sea level to space propagation (Ref. 2).

High-power SWL absorption by atmospheric aerosols and molecules can cause a more insidious effect on the beam, e.g., thermal blooming. The absorbed laser energy heats the air, causing both index of refraction and local density changes. The sequel laser beam is then phase aberrated by the heated medium. While slewing and natural winds mollify TB, it can nevertheless have a debilitating effect on SWL far-field performance. Furthermore, the correctibility of this aberration, which is coupled intricately with natural turbulence effects, is today a highly arcane topic! In particular, I know of no experiments that have demonstrated atmospheric compensation for a HP SWL in the presence of both TB and natural turbulence effects! Let’s now turn to sizing the actual potential degradation of TB on our SWL beam.

Gebhardt³ has shown that the Strehl loss for TB scales as

We then apply or “turn on” TB by multiplying $I^{\prime }$ by $I_{\mathrm{TB}}$, or

Note this has the precise form of optical jitter, Eq. (4). Thus, TB effects have the same form in our performance equation as does beam jitter!

A spectrum of other atmospheric nonlinear effects can be induced by a HP SWL. These include SRS and air breakdown. However, SRS has thresholds above—${10}^6\mathrm{W}/{\mathrm{cm}}^2$ and air breakdown intensities are several orders of magnitude higher. In general, TB is the dominant atmospheric nonlinear degradation source for SWL GB systems.

12.

SWL Target Effects: the Omega Point!

The last—and most important—step on our SWL photon odyssey is the target itself! Figure 15 highlights Felix’s meanderings from device to target. Note that many of his photon friends (Freddies) are lost along the way—because of absorption or scattering. Even the remaining flux has aberrations, only some of which can be “ironed out” (removed) by AO (we will broach AO systems next). The beam arriving on target has suffered both a spread and a Strehl loss. In other words, the flux-in-the-bucket is considerably smaller than expected for a “diffraction-limited” system.

Fig. 15

Felix the Flux short wavelength lasers (SWL) photon odyssey: A to Z.

Consider a photon impinging on the target. Three events are possible, two of which are undesirable:

If this absorbed photon flux-in-the-bucket is of sufficient magnitude and duration, then the resulting heating can cause thermal imbalance, melting or burn through of the object …possibly a mission accomplished! Figure 16 presents absorptance wavelength dependence for several surface coating materials. Note that other than black paint, these materials have relatively low absorptance for SWL wavelength in the 1 to 2 μm. At excimer wavelengths ($\sim 0.4\mu \mathrm{m}$), on the other hand, over 80% of the laser energy is absorbed. We see that to achieve the same lethality, an ${\mathrm{O}}_2\mathrm{I}$ system may have to deliver approximately four times the flux-in-the-bucket as its shorter wavelength excimer laser cousin.

Fig. 16

Spectral absorptance for surfaces (Ref. 4).

13.

Adaptive Optics: a Potential Rx for SWL System Brightness

AO can in principle correct the majority of system and atmospheric-induced phase aberrations, and so recover a near-pristine laser beam. Today’s HP laser systems use mechanical DMs for phase correction. These are complex, cumbersome, and generally unreliable, involving up to hundreds of individually reticulated actuators, plus wavefront sensors and sophisticated software. NLOs could provide automatic, nonmechanical HP beam correction. Though this technology is relative nascent, it is the essential enabling technology for SWL beam control! First, let us discuss mechanical AO. Low order aberrations (e.g., Tilt) are best corrected by a beam steering mirror. This unit, in concert with a Tilt sensor has been shown to correct for two-Axis Tilt at bandwidth $\sim 500\mathrm{Hz}$. Our system telescope corrects for focus errors. The DM correct HO phase aberrations for both the optical train and the atmosphere. Figure 17 shows a typical mechanical AO subsystem. Note that this system using a return beam from the target vicinity can compensate for most system phase distortions. The mirror itself may be cooled or uncooled. A number of individually reticulated actuators are pushed and pulled to locally deform the thin mirror surface. Typical strokes required for SWL GBL DM actuators are a few wavelengths. Bandwidths of $\sim 1\mathrm{kHz}$ have been demonstrated for 500 actuator DMs.

Fig. 17

Short wavelength lasers (SWL) adaptive optic (AO) systems.

The number of actuators required is determined by the SWL telescope area, $A$, and the system “coherence length”. For a GBL, this latter parameter is generally dominated by the atmosphere, scaling as

Now the number of DM actuators required is $N\sim A/r_O^2$, with $A$ the area of the telescope. For a 2 m diameter aperture, Table 2 depicts the number of actuators for several laser wavelengths.

Table 2

Number of actuators for several laser wavelengths.

Note for a fixed aperture, the number of DM actuators scales as $N$ $\mathbf{\alpha }$ $1/{\lambda }^{12/5}$ ($N$ can be considered a measure of AO system complexity). Remembering that the inherent brightness of a laser scales as $B$ $\mathbf{\alpha }$ $1/{\lambda }^2$, we see that for a fixed aperture size, the ratio of system brightness achievable to complexity of the AO system is $\sim$ wavelength independent (it actually scales as ${\lambda }^{2/5}$).

A SWL GBL system without a phase compensation system is severely limited in brightness achievable; the maximum aperture for transmission of a high quality beam is $D\sim r_O$, the effective atmospheric coherence length. As noted above, $r_O$ ranges from a few centimeters to $\sim 25\mathrm{cm}$ for SWLs. An AO system can markedly reduce certain phase aberrations and so increase the “effective $r_O$”, defined as $R_O$. A crucial goal is to render $R_O>D$. In fact, if one can sculpt an $R_O$ of several aperture diameters (3 to 4), a corrected atmospheric Strehl of close to unity can be achieved. Remember that two classes of SWL degradations can never be corrected by an AO system:

Even discounting such unrecoverable losses, there are clearly no perfect AO systems. In general, there will be residual tilt and HO losses.

14.

Modularity: the High Tech Trek to Ultra Bright SWL Systems

We noted earlier that as one scales a monolithic laser system in power, device brightness eventually degrades due to loss of BQ. Once the maximum size of this ‘‘unit cell” is known, further scaling can occur via coupling of several unit cells. Let’s estimate the maximum brightness for a monolithic ${\mathrm{O}}_2\mathrm{I}$ laser to be $B^{*}\sim 1.3\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, with $P^{*}=5\times {10}^6\mathrm{W}$ $n=1.5$ (minimum acceptable device BQ) $\lambda =1.3\times {10}^{-4}\mathrm{cm}$.

Next, consider an array of $N$ such coupled lasers; then

Note that the far-field intensity of a perfectly coherent array scales as the square of the number of modules. If this array was totally incoherent, and all lasers pointed to the same spot, it is obvious that

Actual device arrays are partially coherent; their performance falls between these extremes as shown in Fig. 18. In general, coupled device arrays are married with coupled telescope ensembles to yield modular SWL systems.

Fig. 18

Performance scaling of N coupled lasers.

Advantages of modular SWL systems include:

For a modular system, with N mirrors, each with diameter $D/N^{1/2}$,

Modular systems have disadvantages:

We continue by examining the far field performance of a coupled array of N SWL systems. Figure 19 shows such an array. We define ${\sigma }_p$, ${\sigma }_T$ as the RMS piston and tilt errors, respectively. The corresponding phase errors are

Fig. 19

A coherent array of N modules.

And the Strehl loss due to ${\varphi }_p$ and ${\varphi }_T$ is just⁵

Here, we assume no jitter correlations exist among the $N$ beam trains. For comparison, the corresponding Strehl loss for a monolithic system is identical with the above, except with $N^{1/2}=1$.

Several important conclusions follow:

Before departing modular systems, let us pursue the above ${\mathrm{O}}_2\mathrm{I}$ example to show the potential brightness enhancement of an array of coupled devices. Recall for our unit cell, $B^{*}\sim 1.3\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. Suppose the mission requirement is $B\sim {10}^{16}\mathrm{W}/{\mathrm{cm}}^2$. This can be achieved with

15.

Nonlinear Adaptive Optics: the Quintessential Enabling technology for SWL Systems

NLO is the beam control oasis along our path to high brightness SWL systems. Traditional (mechanical) AO systems are cumbersome, costly, complex, and unreliable. While they may suffice for entry level SWL systems, they must “go the way of the albatross” as we “grow the technology”. Conventional AO systems require DMs, wavefront sensors, and reconstructors (analog-to-digital converters). A NLO AO performs all these functions automatically …within the medium. Let’s now “reflect” on a NLO AO system. First, consider an ordinary mirror per Fig. 20. Enroute, Felix the Flux encounters a phase “bump”—any sort of phase aberration. As a result, Felix develops a phase “hump.” After bouncing off the mirror at the specular angle, the hump is still there, but just reversed in phase.

Fig. 20

Conventional mirror and aberrated beam.

Next, consider our NLO mirror in Fig. 21. The NLO materials have two wonderful properties:

Fig. 21

Nonlinear optics (NLOs) mirror and aberrated beam.

Figure 21 shows Felix getting “straightened” out by the NLO medium. Again, he picks up an unwanted phase “hump” as a result of the bump. Now, however, the NLO medium returns the beam along the same path and with the bump now having the conjugate phase. The happy result when Felix passes back through the aberration is a diffraction-limited Felix. In other words, the NLO process has rendered Felix “Antiaberrated” and he becomes ideal after being transmitted back through the inhomogeneity. I have shown the final Felix a little smaller because the efficiency of NLO processes is less than unity; however, efficiencies of 50% to 80% are not unusual.

Albeit with much more difficulty, note that a conventional AO system could have made Felix pristine for completeness. To do so, the hump in Felix would have to be sensed and digitized. Next, several mechanical actuators in the mirror would be pushed against the thin face sheet to create a counterhump. Once finessed, a corrected Felix would reflect at the specular angle. If the mirror could point Felix precisely back through the original atmospheric “bump,” he would emerge nearly diffraction limited.

Next, I will sketch the rudiments of NLO processes. Then we will examine some exciting near-term applications. Optically, nonlinear materials can produce a reflected phase-conjugate beam. Figure 22 aids my explanation. Stimulated Brillouin scattering (SBS) occurs when an intense laser beam is directed into a transparent medium. Threshold laser powers are of order 1 MW. A sound wave results which establishes a “density grating,” is with a spacing of $\sim \lambda /2$. Moreover, this can also be considered an index of refraction “grating,” though the photons are initially reflected weakly; however, this beam interfaces with the continuously arriving incident beam that amplifies the pressure-density variations, which increases the reflected energy etc. The net result can be an efficiently reflected beam that is the phase conjugate of the incident beam. Moreover, each reflected ray precisely retraces its entry path.

Fig. 22

Stimulated brillouin scatter (SBS): an optical nonlinear process.

Four wavelength mixing (FWM) is a NL process in which three beams are input and one is output as shown in Fig. 23. Reference beam A, B, form a density grating. Beam D, the degraded flux, interacts with this pattern. The result again is a back reflected, phase conjugated beam …VOILA! Two features of FWM are particularly attractive for certain applications:

Fig. 23

Four wavelength mixing (FWM): an optical nonlinear process.

Now I’ll discuss several near term applications for nonlinear AO. Supporting research for some of these applications is now underway within my organization at the AFWL.

15.1.

NL AO modular laser systems demonstration

The premier challenge in coupling together laser systems or “unit cells” is to maintain coherence among the several units.This is an essential prerequisite to realize the $N^2$ brightness enhancement from a fully coherent array. Figure 24 shows our setup at the AFWL involving three 10 to 15 J excimer lasers. One laser is used as a master oscillator (MO) to drive two excimer power amplifiers (PA). First, the high quality MO beam is injected into the two PA. An ideal amplifier would not distort the beam; however, the index-of-refraction variance would have to be controlled to at least ${10}^{-6}$ for coherence to be maintained between the PAs. These excimer amplifiers have highly aberrated media. Thus, the emerging beams which enter our SBS (gas) cell are both highly aberrated and partially incoherent. The SBS process “retroreflects” and tailors each beam to its phase conjugate. Thus, the amplified beam emerging from the twin excimer amplifiers at detector D are both good quality and highly coherent …and the system brightness is expected to be $\sim$ four times (i.e., $N^2$ factor) that of either beam line.

Fig. 24

Nonlinear adaptive optics (AO) application: coupled excimer lasers.

15.2.

Correction for thermal blooming and turbulence via NLO techniques

A high quality, repetitively pulsed laser propagates through a cell containing a highly absorbing gas as seen in Fig. 25. Severe TB results. This aberrated beam is phase conjugated back through the cell and imaged at D. Here are some of our recent observations:

• 1. If the TB cell is removed and a conventional flat mirror positioned in front of the SBS cell, the imaged beam is $\sim$ diffraction limited with spot diameter 1.0 units and a Strehl of unity (i.e., good intrinsic system BQ).

• 2. If the TB cell is inserted and the conventional mirror retained, back reflected beam is severely distorted; spot diameter is $\sim 3$ to 5 units and the resulting Strehl is severely reduced.

• 3. If the conventional mirror is removed so the TB and SBS cells are in place, the imaged spot is found to again have a diameter $\sim 1.0$ unit and a Strehl of near unity.

Fig. 25

Nonlinear adaptive optics (AO) application: thermal blooming (TB) correction.

Thus, taking into account slight absorption losses in the TB cell, we conclude that SBS has demonstrated the ability to completely correct for a severe TB environment. This might be extended to the field for propagating a HP short wavelength GBL to space, for example. Figure 26 shows the idea. A low power laser, wavelength $\lambda$, illuminates the object. Some scattered energy is collected, amplified, and SBS processed. Since all distortions from target to SBS cell are imbedded in the entry beam—natural turbulence, TB, amplifier, and optics aberrations, etc., the HP beam arriving at the space target is—diffraction limited. Note that pointing and tracking is “automatic” if within the FOV of our telescopes.

Fig. 26

Nonlinear optics (NLOs) for A-to-Z short wavelength lasers (SWL) beam control.

Though this concept is “MEGA-Exciting”, it has several limitations. For example, the atmospheric relaxation time is about ${10}^{-3}\mathrm{s}$. That is, if a space object is imaged through the atmosphere from a ground site, a new and random realization of the “distorted” image will be seen each millisecond. Though this restricts viewing frame time to $\sim {10}^{-3}\mathrm{s}$, the illuminator could operate continually for extended high fidelity observations. Secondly, due to light’s finite velocity, distant space objects cannot be “sampled” directly by the low power laser as a prelude to HP SWL satellite engagement. Satellite velocities are $\sim 7\mathrm{km}/\mathrm{s}$; in the time required for the laser beam to return from the object (${10}^{-3}\mathrm{s}$ for 300 km range), the satellite has move $\sim 7\mathrm{m}$. Moreover, the HP laser must “lead” by an additional 7 meters. The net result is that the “corrected” HP beam moves through a new and different piece of atmosphere …and so suffers severe distortions. The solution: instead of using the space object as a reference, one must obtain atmospheric optical turbulence information in the lead-ahead direction. Finally, we turn to a FWM application.

15.3.

Imaging via nonlinear adaptive optics techniques

Application of nonlinear techniques offers the prospect of enhanced imaging through distorted media (e.g., atmosphere). Figure 27 shows this scenario. Felix the Flux travel from space through the atmosphere, becomes badly distorted. By using an (FWM) AO, Felix’s image can be recovered after just one way transmission through the atmosphere.

Fig. 27

One way nonlinear imaging.

Figure 28 shows our lab setup. A laser illuminates the object, while the remainder of the beam serves as reference A. The space image passes through the aberrator (simulated atmosphere) and is split into two parts. One part becomes the other (degraded) reference B. The degraded image D interacts with B in the cell a phase conjugated back reflective C is detected as shown—a nearly pristine image.

Fig. 28

One way image reconstruction via nonlinear optics (NLOs).

In summary, system aberrations—optical or atmospheric—can seriously degrade the quality obtained by conventional imaging techniques. One way imaging via nonlinear (FWM) techniques offers significant image enhancement. Resolutions of 20 line pairs/millimeter have been demonstrated at the AFWL …in the presence of strong optical aberrations.

Nonlinear AO offers a quantum jump in SWL beam control and image enhancement capabilities. Conventional AO techniques are complex and unreliable, involving costly mechanical DMs, sensor arrays and sophisticated software. A nonlinear AO accomplishes its task automatically and—all the above functions are done within the medium.

There is a lofty hurdle to overcome to realize the payoff of NL AO techniques …the dearth of available materials. Nonlinear materials that can handle HP SWL beams and offer fast response times are essential …and not available today! This quest must continue—the payoff of NL adaptive technique for SWL is immense—it is indeed the enabling beam control technology for future high brightness laser systems.

16.

Wavelength Scaling: Finding the Optimal SWL for your Application

We have completed our photon odyssey from device to target with our friends Freddy and Felix.We found system aberrations, absorption, and scattering to be rampant. The SWL beam arriving at the target is both spread and reduced in Strehl—that is, the delivered flux-in-the-bucket generally falls well below a diffraction limited system.

AO offer an opportunity to correct certain phase aberrations and recover a portion of this “lost” BQ. Mechanical AO systems are cumbersome and costly. Nonlinear AO techniques offer a chance to leap over the beam control chasm in one jump. Although applications abound, the pace of progress will be limited by the availability of materials, particularly for HP SWL missions.

Suppose we have carefully optically orchestrated our SWL system—BQ, transfer optics, beam path conditioning, etc.,—and have integrated our best AO subsystem. Our SWL system will still have residual phase errors. Net performance is represented by system Strehl Eq. (7):

To examine effects of uncorrected jitter and phase variance on far-field performance, we set $\partial I/\partial \lambda =0.0$ in the above equation, finding

Results are shown in Table 3:

Table 3

Optimal wavelength dependence on system jitter to phase ratio (Δ/ϕ).

Again we see jitter has a relatively weak effect on wavelength selection for optimal system brightness.

An Example: Suppose our goal is to design and field a SWL system for a ground-to-space mission. We are aware of the brightness optimization equation, but do not understand this magnitude of either natural (e.g., turbulence) or beam-induced (e.g., optics heating, TB) effects. We pick $\lambda =1\mu \mathrm{m}$ as our candidate laser wavelength. Our instructions to the SWL system designers include

Now our optimal wavelength considering only HO aberrations is

Equation (9) reflects the residual errors after our AO system has been activated. Suppose we succeed in building our optics such that ${\varphi }_O=0.125\mu \mathrm{m}$ (i.e., ${\lambda }_O/8$) but are surprised to find that the uncorrected contributions from atmospheric turbulence and beam intensity on optics are comparable to ${\varphi }_O$; then

The point is that any uncorrected phase aberrations, either tilt or HO, erode the benefits of SWL systems; moreover, these effects tend to push the system toward longer wavelength if maximum brightness (performance) is the goal.

17.

Conclusion

The trek to high brightness laser system is very difficult …in fact ${(\text{tough})}^N$ …with $N$ a large exponent. Technical thickets and beam control brambles abound! However, the path to success can be traversed and, the payoff is prodigious. HP lasers are essential elements, though emphasis shifts to beam control—careful optical engineering to orchestrate the laser energy from device to target in a pristine manner. No recipe exists for accomplishing this “PHOTON FEAT”; however, I offer these guideposts along our path to high brightness laser systems:

I close with this précis: the journey to high brightness SWL systems is tortuous …but trekkable …and the payoff is immense! Potential pitfalls and pratfalls exist. Guideposts indicate tough optical engineering, with a dollop of physics, is the key. Ordered priorities in developing these exciting SWL systems are:

(No, I did not repeat myself!)

HAPPY PHOTON TRAILS!