Surface High-Energy Laser

Surface High-Energy Laser

RICHARD L. FORK, MEMBER, IEEE, RUSTIN L. LAYCOCK, WESLEY W. WALKER,SPENCER T. COLE, SEAN D. MOULTRIE, DANE J. PHILLIPS, MEMBER, IEEE, AND

JOHN C. REINHARDT

Invited Paper

We describe a design strategy for high-power solid-state laseroscillators using local correction of thermally induced optical dis-tortion. This offers a potential for scaling lowest order Gaussianmode solid-state laser oscillators directly to high average power,e.g. >100 kW, while using a relatively simple near confocal ringresonator. The waste heat is necessarily produced in the gain re-gion; however, the design strategy facilitates scaling by allowingthe laser oscillator to function as though the waste heat was pro-duced in a surface region external to the gain medium.

Keywords—Beam quality, high-power solid-state lasers, thermalmanagement.

I. INTRODUCTION

A. Simple Strategy for Scaling Average Laser Power

A simple, and arguably the preferred, means of generatingcoherent light at high average power and high beam qualityis directly from a near confocal laser oscillator operating inthe lowest order Gaussian mode. The favored spatial distri-bution for the gain for this long slender mode is a regionhaving the similar geometry, dimensions, and orientation asthe lowest order Gaussian mode. The distortions and mate-rial stress, however, produced in removing waste heat fromthis long slender gain region have long hindered use of thissimple strategy for scaling laser power.

B. Fundamental Nature of the Design Problem

The difficulties in removing waste heat from a long slenderlaser gain medium are nontrivial. Basic thermodynamics,

Manuscript received May 23, 2005; revised June 8, 2005. This workwas supported in part by the U.S. Army Research Office under GrantsDAAD19-02-1-0073, DAAD19-03-1-0281, and W911NF-04-1-0097, inpart by AMCOM under Contract DAAH01-01-C-R160, in part by NASAunder Grant NCC8-200, and in part by USRA (NIAC) under Contract07605-003-035.

The authors are with the University of Alabama in Huntsville, Huntsville,AL 35899 USA (e-mail: [email protected]; [email protected];[email protected]; [email protected]; [email protected];[email protected]; [email protected]).

Digital Object Identifier 10.1109/JPROC.2005.853551

Maxwell’s equations, and fundamental material propertiesinform us that the thermally induced optical distortion of thegain medium of a high-power laser becomes unacceptablylarge long before 100 kW of power can be achieved inconventional solid-state materials [1].

The removal of heat in an outward radial direction froma long slender gain region necessarily produces radial tem-perature gradients. These temperature gradients typically re-sult in radial and azimuthal variations in the optical delay insolid-state materials and prevent achievement of good beamquality at high power. Our design seeks to remove this long-standing barrier to scaling lasers by guiding the heat flow inthe gain medium so that while the waste heat is removed in anoutward radial direction, optical distortion is largely absent.

C. Surface High-Energy Laser Design

While one cannot avoid the outward radial flow of heat, itis the accompanying optical distortion, rather than the tem-perature gradients per se, that are the principal barrier toscaling solid-state lasers to high average power. Within theapproximations used here, we identify a strategy based onspecifically configured barriers to heat flow within a gainmodule that leads to optical transmission as if the waste heatwas not produced within the gain medium, but rather on thesurface surrounding the gain medium. Hence the term “sur-face high-energy laser” (SHEL).

D. Differential Correction of Wavefront Distortion

In our model system, where we seek to remove the heat inan outward radial direction from this long slender Gaussianmode, radial thermal gradients are unavoidable. Our concern,however, is with the undesirable radial and azimuthal varia-tions in the transmitted optical wavefront in the presence ofthe outward heat flow that result from these radial tempera-ture gradients, rather than with the radial temperature gradi-ents as such.

We focus here on strategies for correcting the optical dis-tortion caused by these radial temperature gradients in a dif-ferential manner within the gain medium. That is, we allow asmall distortion, but then correct that distortion while it is still

0018-9219/$20.00 © 2005 IEEE

1864 PROCEEDINGS OF THE IEEE, VOL. 93, NO. 10, OCTOBER 2005

Fig. 1. Schematic showing one of a series of gain/cool modules within acontinuous sequence of such modules (region inside dotted line). The se-quence of modules provides axially distributed gain while allowing heat re-moval through radial temperature gradients, but avoiding optical distortion.

small so that the net accumulated distortion never becomeslarge. We repeat this process many times throughout the gainmedium so as to remove heat in an outward radial directionwhile, in effect, avoiding net distortion of the wavefront.

This differential correction of distorting intraresonatormechanisms has been used successfully in managing po-tential sources of temporal distortion of the optical field inmode-locked laser oscillators [2]. The balancing, and hencea neutralizing of two or more potentially distorting mecha-nisms at a differential level throughout a laser medium, is,of course, potentially useful for managing spatial as well astemporal distortion.

II. DISTORTION-FREE GAIN/COOL MODULE

We describe here a basic module composed of a pair of el-ements, one serving primarily a gain function and the secondserving primarily a cooling function. We integrate these twoelements to form a single “distortion free” gain/cool module,Fig. 1 [3]. As a unit, this gain/cool module removes substan-tial quantities of waste heat in an outward radial directionfrom a long slender gain region while introducing, within theframework of our approximations, no net optical distortion.

A. Integrated Series of Gain/Cool Unit Cells

We postulate an extended sequence of these gain/coolmodules contacted with each other so as to produce a longslender continuous gain region, Fig. 1, which is free of op-tical distortion. This long slender gain region is designed toextend over a substantial fraction of the laser intraresonatorregion and to show good spatial overlap with the lowestorder Gaussian mode of the laser oscillator. This extendedgain region provides gain and removal of waste heat andavoids unacceptable wavefront distortion and thermal shock.

We show in Figs. 2 and 3 schematics of the individualgain/cool module in which the temperature variation in the“gain element” is matched by a temperature variation of thesame magnitude, but opposite sign, in the “cool element.”Annular barriers to heat flow in the radial direction in the“gain element” have been introduced that largely prevent ra-dial heat flow in the gain element while allowing specificallycontrolled heat flow from the gain element in an axial direc-tion across the planar interface between the gain and coolingelements.

The goal is thermally induced variations in optical delaythat are equal and opposite in the gain and cool elements at alllocations over the wavefront of the optical field propagatingalong the optical axis . We seek a net optical delay of thewavefront transmitted through the gain/cool module that isindependent of radial and azimuthal position.

Fig. 2. Schematic of the gain/cool element showing pump power P (r),induced temperature change in the gain element �T (r), and induced tem-perature change in the cooling element �T (r) versus radial distance r.

Fig. 3. Axial view of the gain/cool element illustrating the temperaturevariation and the annular barriers in the gain element to radial heat flow.Lighter areas have higher temperature and darker areas lower temperature.An insulating barrier surrounds the outer circumference of the gain element.

We use here as an example a pair of materials for sucha gain/cool module: Ti : sapphire for the “gain element” andundoped sapphire for the “cool element.” The doping of tita-nium into the sapphire transforms the undoped sapphire intoa useful gain medium, while at the same time leaving the ma-terial properties similar to those of the undoped sapphire.

B. Assumptions Regarding Gain/Cool Module

We make major simplifying approximations regarding thematerials and properties of the gain/cool module. We pos-tulate that the thermooptical coefficient dn/dT, the thermalconductivity , the coefficient of thermal expansion, Young’smodulus, and all the other parameters of importance [1] canbe approximated as identical in the gain and cool elementsindependent of the mean temperature of the given elementand also independent of the presence of the specifically struc-tured barriers to heat flow.

We also assume that the substantial radially varying dif-ference in the temperatures of the gain and the cool elementsat the planar interface between the gain and cool elementscan be tolerated, including substantial temperature cycling.This implies, of course, that some relative motion of thesetwo surfaces will be tolerated while maintaining a particularheat transfer coefficient at the interface. We also approximate

FORK et al.: SURFACE HIGH-ENERGY LASER 1865

the discrete changes in radial temperature in the gain moduleby the discrete annular structure as continuous with radialposition. We are exploring models that will address issuesnot included under these approximations. This next stage ofwork is beyond the scope of this current paper.

We assume cylindrical symmetry and insulation of thegain element at the outer circumference from any externalthermal reservoir. The circumference of the cool elementis assumed to be in good thermal contact with a thermalreservoir that receives the waste heat from the cool elementand is maintained at a fixed temperature.

C. Degree and Manner of Control of Heat Flow

We have explored the control that needs to be exerted onthe heat flow through the postulated heat transfer barriers toaccomplish the desired variations in temperature in the gain/cool module. The somewhat counterintuitive finding is thatdespite the net outward flow of a substantial quantity of wasteheat from the gain/cool module the thermally induced op-tical distortion experienced by light transmitted through thegain/cool pair of elements can, within the framework of theapproximations outlined here, be reduced to zero. Also in thismodel, given the local correction of both the thermal lensingand the stress induced birefringence, the thermal shock canbe overcome, in principle, by making the gain region suffi-ciently long.

III. EQUATIONS FOR TEMPERATURE DISTRIBUTION

We develop here equations characterizing the temperaturedistribution in an individual gain/cool module located withinan extended sequence of such modules. We seek in particularto calculate the radial dependence of the heat transfer coef-ficient [4] for the planar interface between the gain andcool elements. We assume annular barriers in the gain ele-ment having a heat transfer rate of zero. We treat the radialand axial equations as separable, as in [3].

We describe the introduction of waste heat by

(1)

Here is the outer radius of the gain region. The differen-tial equation for the temperature in a cylindrical region ofthermal conductivity, under this heat load is

(2)

We assume a temperature change from the unperturbedsystem temperature in the gain element given by

(3)

We assume an identical temperature variation in the coolingmedium of opposite sign

(4)

Solving for the coefficients and , we find

and (5)

We assume that heat enters the gain medium through opticalpumping followed by relaxation and stimulated emission ofthe excited ions. As a representative approximation, let halfthe power introduced by optical pumping be removed viastimulated emission and the other half appear as waste heat inthe gain medium (the quantum defect) as described byin (1). Here is half the total discontinuous temperaturechange at the boundary between the gain and cool elementsat .

The heat transfer coefficient [4] at location r of theinterface between the gain element and the cooling elementthat will yield temperature variations in the gain and coolmedia of equal magnitude, but opposite sign, is

(6)

where is the length of the gain element as measured in thez direction (in the series of gain/cool modules, each coolingelement on the average receives waste heat from half of eachgain module on either side). The magnitude of the discontin-uous temperature change at location r is

(7)

In general, the preferred gain/cool element design willhave a maximum rate of heat transfer across the interface at

with a minimum discontinuous temperature change.Our experimental work suggests that ensuring good contactof optically flat surfaces near helps achieve thiscondition.

The temperature variations in the gain and cooling el-ements will have the same magnitude, but opposite sign.Given our assumptions, these equal but opposite inducedtemperature variations will lead to induced refractive indexchanges that are also equal in magnitude but of oppositesign, producing zero net thermal lensing and zero net thermalstress induced birefringence.

IV. COMPUTER SIMULATION OF GAIN MEDIUM

We have used computer-based simulations to model thesame extended gain medium composed of a sequence of


Fig. 4. Simulation of Ti : sapphire/(undoped sapphire) modules for135 kW of output power (upper image). A schematic (lower image—not toscale) illustrates the relationship of this gain section to the laser resonatorand a tapered duct (shaded gray region) that introduces pump light (yellowarrows).

these gain/cool modules that we described above analyti-cally. Aside from providing gain, these modules are regardedas transparent and supportive of a gain medium that can beincreased in both length and in radius to support scaling inlaser output power.

A. Gain Medium for 135-kW Average OutputLaser Oscillator

We show computer simulations, using the softwareI-DEAS, of the temperature distribution in a series of thesegain/cool modules, Fig. 4. We also show in the lowerschematic (not to scale) in Fig. 4 an illustration of how themodeled segment of ten gain/cool modules is related to alonger gain medium and to a tapered duct used to deliveroptical pump power having relatively low spatial coherence,as from laser diode arrays or sunlight. The pump rate is300 W/cm pump power delivered to the gain medium. Thepower is transformed to produce an average output power inthe lowest order Gaussian mode of 135 kW for an overallgain length of 2 m and a radius of the excited gain regionof 1.2 cm. The medium temperature lies in the range from104 K to 120 K (see the color code on the right of the figure).

The cross-sectional area of the gain region in this sim-ulation is 4.5 cm which corresponds to 30 kW/cm ofoutput power produced per unit cross-sectional area of gainregion. The temperature increase over the radial distancefrom the optical axis to the surface of the gain medium isrelatively small, 8.5 K. For the temperature regime modeledhere 110 K, the sapphire material, and the 2-m length, thelaser is below threshold for thermal shock. We can designsimilar structures that operate slightly less efficiently andallow shorter length of gain material.

B. Spatial Matching of Laser Fields and Gain Medium

Spatial matching of the excited gain medium to the lowestorder Gaussian mode of the laser is helpful in maximizingefficiency and achieving laser oscillator geometry that is op-timally simple. The extended gain region is also valuable in

reducing the heat that must be removed per unit length of thegain region and in avoiding thermal shock.

As a way of expressing this goal in a more quantitativemanner, we borrow from Siegman’s development of normal-ized equations of motion for the cavity mode [5]. In partic-ular, we identify a filling factor of the form

(8)

Here enters as a normalization factor which can be use-fully interpreted as the volume occupied by the electromag-netic fields of the lowest order Gaussian mode. The lowestorder Gaussian eigenmode for the resonator that we describein Section V we denote by . The functions and

describe the spatially dependent population inver-sion and the intensity of the intraresonator optical fields, re-spectively, normalized to yield a filling factor of unity underperfect overlap of the gain and optical fields.

The particular value of the intraresonator intensitychosen to optimize the laser performance is

dictated by the need to balance the goals of efficient extrac-tion of stored power with the need for adequate gain. Theintraresonator fields will preferably be more intense thanthe saturation intensity of the laser transitionas a means of achieving efficient operation [1]. Here isPlanck’s constant, is the optical frequency, is the crosssection for the laser transition, and is the lifetime of theupper laser level. For Ti : sapphire the saturation intensityis 155 kW/cm . We take as a design goal an intraresonatorintensity of twice . The pump power density deliveredper unit volume to the gain medium is given by the meandensity per unit volume of excited ions times the energy ofthe pump quantum or W/cm . (We usedthis number for the computer-based simulation, Fig. 4).

This section is included to assist in developing a moreformal addressing of: 1) the need for good spatial overlap ofthe excited gain medium and optical fields of the lowest orderGaussian mode of the laser resonator; 2) the importance oflarge power density per unit volume as a means of producingmaximum power from a minimum volume of gain material;3) means of scaling to high power by increasing the volumeof the gain medium while avoiding unacceptable levels ofoptical distortion and thermal shock; and 4) a more detailedaddressing of the complexities of actual resonator structuresand actual gain distributions.

V. LARGE AREA LOWEST ORDER GAUSSIAN MODE

A remaining need is selective excitation of the lowest orderTEM Gaussian mode of a near confocal laser resonator.We prefer a near confocal resonator because of the stabilityagainst misalignment [5]. We develop here the reasoning forusing a double confocal ring oscillator, Fig. 4, as a meansof accessing a large area lowest order Gaussian mode in aresonator of practical dimensions.


Fig. 5. Double confocal ring resonator using two paraboloidal mirrorsshowing beam power distribution as modeled using ASAP software. Thediagonal paths satisfy the near confocal condition.

Fig. 6. Double confocal ring resonator with spatially selective gain andloss. The region where the beam is approximately collimated can be length-ened without losing the double confocal character.

A. Area of TEM Mode and Confocal Resonator Length

The well-known symmetrical confocal resonator [5] wedo not consider to be an option. The relationship betweenthe Rayleigh distance , the beam waist , and the wave-length for that resonator is . This implies, forvisible or near infrared light, a resonator length greater thana kilometer for the 1.2-cm radius gain region that we iden-tified above as needed to access the desired average outputpower 100 kW. This appears to be impractical for mostapplications.

B. Need for a Double Confocal Ring Resonator

As regards scaling a laser oscillator to high average powerwith high beam quality, we consider basic requirements forthe resonator to be: 1) a gain area having large cross-sec-tional area; 2) a gain region having a length large comparedto the beam diameter; 3) means for selective excitation ofthe lowest order Gaussian mode of the resonator; and 4) anear confocal resonator. The double confocal ring geometryresonator, derived from a multipass amplifier strategy [7], il-lustrated in Figs. 5 and 6, provides such capabilities.

The four transits of the space between the mirrors providetwo regions where the beam has relatively large cross-sec-tional area (the horizontal beams in Figs. 5 and 6) and two

regions where the beam is focused to a relatively small diam-eter waist (the diagonal beams in Figs. 5 and 6). The confocalmirror spacing is required for these diagonal transits. Thering nature of the resonator provides both regions of largecross-sectional beam area and regions where the small beamdiameter can assist in mode discrimination.

C. Selective Oscillation on the Lowest OrderGaussian Mode

A potential problem with this basic double confocalresonator is that it supports a number of higher orderGaussian modes as well as the lowest order Gaussian modethat we seek. We postulate gain and loss in the resonator in-corporated in ways that will assist in preferentially excitingthis lowest order mode, Fig. 6. Soft Gaussian apertures nearthe foci and a Gaussian gain profile where the beam area isapproximately collimated assist in achieving this selectiveexcitation [5]. The apertures near the foci are challenging torealize because of the high optical intensity at those loca-tions. We do not attempt to address that issue in detail here.We do observe that undoped sapphire at low temperaturetolerates high optical intensities.

In Fig. 6 we have modeled the solid-state gain media ashaving Brewster surfaces and also introduced four soft aper-tures to maintain symmetry while avoiding the complexity ofmultiple physical apertures at the location where the beamscross. The task of specifying the particular geometry, dimen-sions, materials, and other properties of the apertures, gaindistribution, and mirrors required to achieve selective oscil-lation on the lowest order Gaussian mode is beyond the scopeof this current paper.

We outline here a method for addressing the nonlinearcompetition between the different spatial modes using a for-malism developed by W. Lamb and his students [6]. If themean intensity of the lowest order Gaussian mode of the res-onator in the gain region is , then the time-dependent evo-lution of the intensity of that mode is

(9)

Here and denote the unperturbed gain and loss, re-spectively, for the lowest order Gaussian mode, denotesthe reduction of the unperturbed gain caused by self-satura-tion by that lowest order Gaussian mode, anddenotes the reduction of unperturbed gain available to thelowest order Gaussian mode caused by cross saturation ofthe available gain by all of the competing modes (the sumover m).

This mode competition is not trivial to analyze and design;however, given optimal choice of the spatial distribution ofthe gain and the loss [5], and other operating conditions [2],the mode competition can be caused to favor selective oper-ation on the lowest order Gaussian mode. This strategy willbe seen to be related to that used for the free electron laserby the group under G. Neil at Jefferson Laboratory [8].


Fig. 7. Plots of the total power out (solid lines) and limits set by thermalshock for a gain element at 300 K (dotted lines) versus length of the indi-vidual gain element. Examples of one gain element (two lower curves) andeight gain elements (two upper curves) are shown.

VI. POWER SCALING

We consider the case where thermal lensing and stressinduced birefringence are compensated to the degree thatthermal shock alone limits output power. We have computa-tionally simulated the case of laser diode pumped Nd : YAGfor the gain element and undoped sapphire as the cool ele-ment in the gain/cool module (Fig. 2). Composite gain/coolmodules are an option, but require analyses (not given inthis paper) that include the differences in the gain and coolmaterials.

A. Role of Dimensions and Number in the Scaling ofOutput Power

The average power from one continuous sequence of gain/cool modules, of average radius , as shown in Figs. 1 and3, is denoted here as . The power from a laser oscillatorcontaining such continuous sequences of gain/cool mod-ules in our model (we define one such continuous sequenceas a gain rod) is

(10)

The radius is constrained to values whereis the radius of the gain element, for material at temperature

, at which thermal shock becomes the limiting factor. Ourmodel, for the case of Nd : YAG operating at 1.06 m, yieldsfor the power from a gain rod of length 1 m and radius

2 cm, 187.5 kW. We have assumed laser diodepumping at 808 nm and a quantum efficiency of 75%, i.e., nolosses other than the quantum defect. The total output powerfor the case of a resonator containing one gain rod, and alsofor a resonator containing eight such gain rods, is illustratedin Fig. 7. Constraints set by thermal shock for those two casesare also shown. The curves in Fig. 7 only apply to our par-ticular model system and to constraints imposed by thermalshock on that model system.

B. Parameters Characterizing the Laser Power Oscillator

The choice of design parameters is dictated in large part bythe properties of the specific laser transition and well-knownlaser design strategies [1], [2], [5], [6]. The oscillator musthave a moderately large finesse and hence moderate outputcoupling, e.g., 5%–10%, if the intraresonator nonlinear pro-cesses are to exert a strong influence on the beam qualitythrough mode competition [5], [6].

For an intraresonator intensity of 300 kW/cm , we will ex-tract 30 kW of power from the laser oscillator per cm ofmode cross-sectional area. This gives an intraresonator in-tensity that is roughly twice the saturation intensity for theTi : sapphire transition. This will shorten the upper state life-time by a factor of two, but still leave a net gain for the laseroscillator modeled in our simulation, Fig. 4, of 25% pertransit of the gain medium.

This strategy places a substantial burden on maintaininglow intraresonator loss and consequently on the constructionof the laser gain/cool medium and the interfaces that are re-quired to influence heat flow. We recognize the challenges in-herent in the construction of the gain/cool elements; however,a detailed discussion of the development of these gain/coolmodules is beyond the scope of this paper.

VII. COMPARISON WITH OTHER LASER DESIGNS

We compare here the SHEL design strategy with otherlaser design strategies intended to produce high averagepower with high beam quality [9]. It is, in general, difficultto project a variety of design strategies into the future andcompare the various potentials for improvement. We basethis particular comparison on fundamentals of the designstrategies while taking an optimistic view of the potentialof the evolving field of micro- and nanostructured photonicstructures for successfully constructing the interfaces con-trolling heat flow in the gain/cool modules that we havepostulated here.

A. SHEL Versus Thin Disk Laser Designs

The thin disk laser design [10] and the SHEL laserdiffer in that the SHEL is specifically designed to supportscaling to high power by increasing the gain volume in arelatively simple near confocal ring oscillator. The thin disklaser requires multiple reflections from multiple thin disksfor scaling to high power and encounters difficulties withparasitic oscillations in attempting to increase the cross-sec-tional area of the thin disk gain region beyond order of1 cm . The basic gain module for the SHEL is transparentallowing many gain modules to be stacked together to createa relatively long gain path and large gain volume whilekeeping the gain per unit distance in the gain medium smallso as to avoid parasitic oscillations and consequently allowincreasing cross-sectional area as well as increasing thelength of the gain medium.

The thin disk and SHEL designs are similar in that bothremove waste heat from a gain region having a disk-like ge-ometry in a direction normal to the plane of the disk. Thethin disk and SHEL designs differ in that the SHEL designuses a second transparent disk for the cooling function. This


enables the SHEL laser to scale in volume simply by in-creasing the number of gain/cool modules so as to increasethe length of the gain medium. The thin disk laser uses a re-flective cooling region and must reflect the laser beam off ofmultiple reflecting disks to increase gain volume. This leadsto a more complicated scaling process and tends to force theuse of a relatively large gain per unit length that complicatesthe scaling of beam area.

The thin disk laser does lend itself well to dispersion com-pensation and generation of ultrashort optical pulses. TheSHEL laser is also a candidate for dispersion compensationand generation of short optical pulses, e.g. [2], however, typ-ically with a need for compensation of longer material pathsthan are encountered in the thin disk laser.

B. SHEL Versus the Heat Capacity Laser

The SHEL and the heat capacity laser [11] designs are re-lated in that both use a relatively large volume of solid-statematerial as a means of accessing high power. The SHEL andheat capacity laser designs differ in that the heat capacitylaser does not seek continuous operation by steady removalof waste heat, but rather permits a buildup of waste heat fol-lowed by a physical exchange of gain elements during a ces-sation of laser operation.

The heat capacity laser is intended to scale to powers inthe 100 kW and higher range, however, with an upper limiton duration of operation of approximately 1 min. This 1 minof operation is regarded as adequate for some applications.

The SHEL design, as developed here, has the major ad-vantage of offering continuous operation. The SHEL designhas the disadvantage at this writing of requiring substantialdevelopment of a novel micro- and nanostructured photonicgain/cool element as opposed to use of relatively conven-tional gain material allowed by the heat capacity laser design.

C. SHEL Versus Free Electron Lasers

The SHEL laser design is very different from the free elec-tron laser design [8] as regards the physical gain mechanismand the support system. Both designs, however, seek contin-uous high average power, e.g., megawatts, with high beamquality, both use near confocal ring resonators to achieve res-onator stability, both seek large lowest order Gaussian modearea in some regions of the intraresonator beam path, andsmall mode area in other regions of the resonator. Both seekto keep the beam intensity at the laser mirrors at an accept-able level under megawatt average power output.

We have found the work of the free electron laser groupat Jefferson Laboratory particularly helpful in pointing outthe value of the near confocal ring resonator design for usein high-power systems [8]. Major differences occur in thatthe SHEL design lends itself to the simpler solid-state lasertechnology with a corresponding smaller and more readilyportable support system.

D. SHEL Versus Optical Fiber Laser Designs

The SHEL and optical fiber laser designs [12] both use arelatively long gain region as a means of distributing the heat

load and consequently enabling continuous operation at rel-atively high average power while also producing good beamquality. Both approaches, as in the double clad fiber laserand in the tapered duct combined with selective doping in theSHEL design, use confinement of pump light in the vicinityof a doped core region to couple low spatial coherence pumplight into a core region of small cross-sectional area. This ac-cesses relatively high pump intensity over a gain region thatis relatively long in the direction of the propagating opticalfields.

The SHEL design differs from the optical fiber design inthat the optical fiber approach relies on guiding by meansof transverse dimensions of the order of optical wavelengthsto maintain a lowest order Gaussian mode. This limits theability of the optical fiber design to scale in output powerby simply increasing the cross-sectional area of the gainmedium.

E. SHEL Versus Gas Dynamic Laser Designs

Both the SHEL and gas dynamic lasers seek high averagepower through use of a large gain volume. The designs differin that the SHEL design relies on conduction of heat in asolid-state medium to remove waste heat in an outward radialdirection while the gas dynamic laser relies on pump main-tained flow of heated gas out of the gain region [9]. This latterapproach provides a means of removing a relatively largeamount of heat per unit time, but at the price of requiring asubstantial support system of mechanical pumps as well as asupply of the gas used for the laser medium. The gas dynamiclaser approach also often encounters difficulties in handlinghazardous gases. The need for replacement of consumablescan also be a drawback.

The removal of heat via conduction in solid-state materialsgives the SHEL advantages over gas dynamic lasers both inthe compact nature of the laser medium and in the absenceof a need for mechanical pumping and a replacing of gases.An area of particular interest for the SHEL approach is ap-plications in aircraft or mobile platforms, where the compactsolid-state character of the gain medium and absence of needfor consumables and hazardous materials appears particu-larly advantageous.

F. SHEL Versus Master-Oscillator/Power-Amplifier(MOPA) Designs

The SHEL and MOPA designs are related in that bothstrategies seek to use a laser oscillator to generate a lowestorder Gaussian mode and a relatively large volume gainregion to access high output power [9]. The designs differin that the SHEL strategy integrates both the lowest orderGaussian mode of a laser oscillator and the large amplifyingvolume in a single structure and intraoscillator nonlinearoptical shaping mechanisms for directly shaping the highaverage power laser fields.

G. SHEL Versus Combining of Multiple Laser Beams

The SHEL design differs from high-power laser designsthat accumulate power by phase locking or otherwise com-bining multiple laser beams [9] in that the SHEL produces all


the power from one monolithic system. This SHEL approachis dramatically simpler than the difficult task of collectingpower from multiple different laser oscillators and amplifiersand seeking to combine those multiple outputs, often with theadded burden of maintaining interferometrically precise re-lationships between multiple different physical structures.

The SHEL design and the multiple beam combiningdesigns are similar in that both seek high average power.The SHEL design differs in the monolithic nature of thedesign and the emphasis on use of intraresonator nonlinearoptical mode competition to achieve and maintain highbeam quality.

VIII. SUMMARY

The SHEL design offers a novel strategy for use of in-traresonator nonlinear optical shaping mechanisms in a nearconfocal ring laser oscillator to access high average powerwith high beam quality. The goal is to transform powerfrom a relatively large volume solid-state laser gain mediumpumped by light of low spatial coherence, as from laserdiodes or sunlight, into a high quality lowest order Gaussianmode of free space at output powers in excess of 100 kW.

A. Simple Path to High Average Power andHigh Beam Quality

A particularly simple laser system design strategy fortransforming low spatial coherence pump light into highcoherence optical emission at high average power is a nearconfocal ring solid-state laser oscillator operating selectivelyin the lowest order Gaussian mode using an adequately largegain volume. The SHEL design seeks to make this simplestrategy accessible by removing a longstanding barrier topower scaling caused by thermally induced optical distortionproduced in removing waste heat from a solid-state gainmedium.

B. “Apparent” Shift of Heat Load to Surface of the Gain

The SHEL strategy creates temperature profiles in gain/cool module by guiding the heat flow in the gain medium sothat, aside from the mean temperature difference between thegain and cool elements, the temperature profiles in the gainand cooling media are similar, but of opposite sign. Withinthe approximations used here, this leads to compensation ofthe net thermally induced optical distortion. The waste heatis, of course, produced within the gain medium, but the op-tical distortion occurs as if the waste heat was produced ex-terior to the surface of the gain medium.

One way of characterizing the strategy that leads to this ap-parent shift of the waste heat to the surface of the gain regionis in terms of the derivation of Section III. One disk is de-scribed as providing a gain function while the other disk pro-vides a cooling function. Barriers are introduced that causeheat produced in the gain disk to propagate axially out of thegain disk into the cooling disk and then radially outward inthe cooling disk.

The temperature variation with radial position in thecooling disk is the distribution produced for a heat density

of given removal of heat by radialoutward flow to the periphery of the cooling disk. Thetemperature variation with radial position in the gain disk iscaused by the presence of the barriers influencing heat flowto have a distribution which would be produced by “heatgeneration” per unit volume ofand radial inward flow from the outer circumference of thegain disk. This integrated gain/cool module thus has theformal appearance of a module having zero net internal heatgeneration. That is, the temperature distributions in the gainand cool elements of the gain/cool module correspond to thetemperature gradients that would be produced by total heatgeneration having the net value .Thus, as regards the transmission of the laser optical fieldthrough the gain module, during which the influence of thegain element disk and the cool element disk on the opticalfield is integrated, the gain/cool module is formally, and forthe transmitted optical field also in practice, equivalent to asystem generating zero net heat within the gain medium.

There is a difference in mean temperature of the gain andcool disks that is necessary for the removal of waste heatfrom the gain element, but within the approximations we usehere, this difference has no influence on the optical distortion.The heat thus appears within the system, as regards opticaldistortion, as though the heat was produced at the surface ofthe gain/cool module rather than interior to the gain region.Hence the term “surface high-energy laser.”

C. Use of Nonlinear Mode Competition

Within the approximations used here, this SHEL strategymakes the intraresonator nonlinear optical mode competitionavailable as a means of shaping optical fields at high averagepower. This holds for both spatial and temporal shaping ofthe optical fields and potentially opens a powerful new set oftools for shaping optical fields at high average power.

D. Micro- and Nanostructured Photonic Thermal Barriers

The barriers that we postulate as controlling heat flowwill almost certainly prove demanding to construct. Weanticipate that the successful structures will utilize photonicdesign strategies. In particular, given the importance of notintroducing optical loss or distortion while exerting a stronginfluence on the phonon transport we anticipate importantfeatures will be required at a nanostructure and microstruc-ture level. We will need to influence the device properties asregards heat flow while at the same time avoiding damage tothe high optical quality required of intraresonator materials.

IX. CONCLUSION

We have taken a long-term view of the task of scalingsolid-state lasers to high average power while maintaininghigh beam quality. Our goal has been to identify a strategywhich, even if demanding of implementation, shows promiseof enabling major advances in scaling solid-state lasers andlaser oscillators to high average power with high beamquality. The goal at this writing is average power in therange of 100 kW to 1 MW produced in a lowest orderGaussian mode of free space.


In the interest of publishing this design strategy promptly,we have made substantial approximations and used a greatlysimplified description of a complex technical problem. Wehope that this paper stimulates work by others on this inter-esting strategy and that substantial advances in this topic willbe achieved in the near future through efforts by ourselvesand others.

ACKNOWLEDGMENT

The authors acknowledge most helpful conversations withG. Neil of Jefferson Laboratory regarding near confocalring lasers, with J. E. Butler of Naval Research Labora-tory regarding diamond and related materials, and withC.P. Khattak of Crystal Systems, Inc. regarding sapphirematerials. The authors would like to thank Donna Fork foran editorial reading of this manuscript.

REFERENCES

[1] W. Koechner, Solid-State Laser Engineering 5 ed. Berlin, Ger-many: Springer-Verlag, 1999.

[2] J. A. Valdmanis, R. L. Fork, and J. P. Gordon, “Generation of op-tical pulses as short as 27 femtoseconds directly from a laser bal-ancing self phase modulation, group velocity dispersion, saturableabsorption, and saturable gain,” Opt. Lett., vol. 10, pp. 131–133,1985.

[3] R. L. Fork, W. W. Walker, R. L. Laycock, J. J. A. Green, andS. T. Cole, “Integrated diamond sapphire laser,” Opt. Express, vol.11, pp. 2532–2548, 2003.

[4] F. P. Incropera and D. P. DeWitt, Fundamentals of Heat and MassTransfer. New York: Wiley, 1996.

[5] A. E. Siegman, Lasers. Mill Valley, CA: Univ. Sci., 1986.[6] M. Sargent III, M. O. Scully, and W. E. Lamb Jr., Laser

Physics. Reading, MA: Addison-Wesley, 1974.[7] R. L. Fork, F. A. Beisser, and D. K. Fork, “Multipass optical

amplifier using a double confocal resonator geometry,” Revue dePhysique Appliquee, vol. 22, pp. 1665–1671, 1987.

[8] S. Benson, G. Neil, and M. Shinn, “Lasing with a near-confocalcavity in a high power FEL,” Proc. SPIE, vol. 4632, pp. 115–121,2002.

[9] D. L. Lamberson, E. Duff, D. Washburn, and C. Holmberg,“Whither high energy lasers,” Air Space Power J., vol. 18, no. 1,Spring 2004.

[10] A. VossU. BrauchK. WittigA. Giesen, “Efficient high-power-diode-pumped thin-disk Yb : YAG-laser,” Proc. SPIE, vol. 2426,pp. 501–508, 1995.

[11] W. Hardin, “Livermore’s new military laser sets new solid-stateaverage power record,” OE Mag., vol. 4, p. 6, Jun. 2004.

[12] Y. Wang, C.-Q. Xu, and H. Po, “Thermal effects in kilowatt fiberlasers,” IEEE Photon. Technol. Lett., vol. 16, no. 1, pp. 63–65, Jan.2004.

Richard L. Fork (Member, IEEE) was bornin Dearborn, MI, He received the B.S. degreein physics from Principia College, Elsah, IL,in 1957 and the Ph.D. degree in physics fromMassachusetts Institute of Technology (MIT),Cambridge, in 1962 for work in optical andatomic physics.

He was a Research Assistant at the Naval Re-search Laboratory, Washington, DC, in Summer1956, a Member of Technical Staff, AT&T BellLabs, Murray Hill, NJ, from 1962 to 1970, a

Member of Technical Staff, AT&T Bell Labs, Holmdel, NJ, from 1970to 1990, and Professor of Physics at Rensselaer Polytechnic Institute,Troy, NY, from 1990 to 1994. He is currently Professor of Electricaland Computer Engineering, University of Alabama in Huntsville (UAH),Huntsville. He was also with the Air Force Research Laboratory (AFRL),Rome, NY, in the summer visiting faculty program in 1991, workingon mode-locked optical fiber and solid-state lasers. He worked in thesummer Visiting Fellow program at NASA Marshall in 1995, addressingthe problem of use of optical amplifiers to optimize signal to noise ratio in

coherent LADAR for wind sensing. He worked for AFRL, Rome, NY onharmonically mode-locked fiber lasers during 1994–1995. He consulted forSpace and Missile Defense Command on Advanced Discriminating LaserTechnology and laser diode technology for missile defense systems. Hewas, and currently is, supported by numerous NASA contracts addressingspace solar power and multiple Army Research Office and Joint TechnologyOffice contracts addressing advanced laser technology. He has almost 100refereed publications. Most recent publications are in Optics Express. Pre-vious research interests addressed ultrashort laser technology and research.Recent interests address high-power lasers having high beam quality.

Prof. Fork is a Fellow of the Optical Society of America, a Fellow of theAmerican Physics Society, and a Member of SPIE and the Directed EnergyProfessional Society. He is a recipient of the Laser Focus Invention of theYear 1983 for the colliding pulse laser; he had the most cited technical paperof 1964 in any journal. He was named UAH Outstanding Engineering Pro-fessor in 1995. He was part of a team that held the world record for theshortest optical pulse, 6 fs, from 1987 to 1997.

Rustin L. Laycock was born in Dallas, TX,in 1980. He received the B.S. degree in opticalengineering from the University of Alabama inHuntsville (UAH), Huntsville, in 2003.

He has been working in the Laser Science andEngineering group at UAH for two years. Hiswork primarily deals with simulating heat flowand optical properties of high energy laser gainmaterial with I-deas and ASAP.

Mr. Laycock has been a member of the Di-rected Energy Professional Society (DEPS).

Wesley W. Walker was born in Tullahoma, TN,in 1977. He received the B.S. degree cum laude inoptical engineering at the University of Alabamain Huntsville (UAH), Huntsville, in May 1999.He is currently working toward the Ph.D. degreein optical science and engineering at UAH.

He is a Senior Engineering Assistant for Prof.R. Fork in the Laser Science and EngineeringGroup at UAH. His dissertation research involvesa time-resolved interferometric method to createtemperature maps and measure heat flow at the

interface of two transparent dielectric materials. He is the primary authoron two conference proceedings and a secondary author on several more. Heis a secondary author on one peer-reviewed journal article.

Mr. Walker has been a member of the Directed Energy Professional So-ciety (DEPS) and won the award for Best Student Presentation at the 4thAnnual DEPS Symposium in Huntsville, AL, in October 2001.

Spencer T. Cole was born in Alabama in1973. He received the B.S. degree in electricalengineering (EE), with an emphasis in controlsystems, from the University of Alabama, Birm-ingham, in 1996 and the M.S. degree in EE, witha specialization in optics and minors in bothcommunications and math, from the Universityof Alabama in Huntsville (UAH), Huntsville, in2003. He is currently working toward the Ph.D.degree in EE at UAH.

His work experience includes five summers asan engineering intern at the Weapons Sciences Directorate of the US ArmyAMCOM, plus two years experience in land surveying and civil engineering.He is currently a Senior Engineering Assistant at UAH under Dr. Fork. Herecently received a National Defense Industrial Association graduate fel-lowship. Under Dr. Fork, he has worked extensively in the development ofhigh-energy lasers. He is coinventor of a patent on a thin disk laser designand a free-space optical gyroscope. He is first author of one refereed paperand appears as a secondary author on four other refereed papers.

Mr. Cole is a member of the National Defense Industrial Association,Mortar Board (national honor society), Eta Kappa Nu (electrical engineeringhonor society), and Tau Beta Pi (national engineering honor society).


Sean D. Moultrie was born in Huntsville, AL,in 1980. He received the B.S. degree magna cumlaude in optical engineering from the Universityof Alabama in Huntsville (UAH), Huntsville, in2004. He is currently working toward the M.S.degree in electrical engineering at UAH with em-phasis in optics and photonics technology and en-gineering management.

He is currently working for Dr. Fork in theLaser Science and Engineering Group at UAH.He has constructed a feedback system for stabi-

lizing interferometric fringes in the lab. He is also involved with assistingDr. Fork in his classes and optical laboratories.

Mr. Moultrie is a Member of the Huntsville Electro-Optical Society(HEOS) and SPIE and is the President of UAH’s SPIE Student Chapter.

Dane J. Phillips (Member, IEEE) was born inHouston, TX, in 1979. He received the B.S.degree in electrical engineering, with emphasesin digital logic and physical phenomena, fromTennessee Technological University, Cookeville,TN, in 2002 and the M.S. degree in electricalengineering, with focuses in optics and elec-tromagnetics, from the University of Alabamain Huntsville (UAH), Huntsville, in 2004. Heis currently working toward the Ph.D. degreein electrical engineering from UAH under

Dr. R. Fork.

He is researching the utilization of photovoltaics optimized formonochromatic laser illumination in a laser power beaming infrastructure.He is heavily involved in the undergraduate optical engineering curriculumthrough instructing labs, creating laboratory manuals, equipping labs, andassisting in senior design course work.

Mr. Phillips is a Member of SPIE, Eta Kappa Nu (the electrical engi-neering honor society), and the Huntsville Electro-Optical Society (HEOS).

John C. Reinhardt was born in Austin, TX, in1980. He received the B.S. degree in mechanicalengineering in machine design from TennesseeTechnological University, Cookeville, in 2004.He is currently working toward the M.S. degreein optics from the University of Alabama inHuntsville (UAH), Huntsville, focusing on lensdesign and vibrations.

He was a Mechanical Contractor with CarwileMechanical in 2003. In the Summer of 2004, hewas a Design Engineer with Des Case. Currently,

he works for the Laser Science and Engineering Group, UAH. He is cur-rently researching the mining of ice on the lunar surface.


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Surface High-Energy Laser