Nonsequential modeling of laser diode stacks usingZemax:simulation,optimization,and experimentalvalidationNicola ColuccelliIstituto di Fotonica e Nanotecnologie.Consiglio Nazionale delle Ricerche.Dipartimento di Fisica del.Politecnico di Milano,20133 Milano,Italy (nicola.coluccelli@polimi.it)Received 1 March 2010;revised 28 May 2010;accepted 25 June 2010;posted 28 June 2010 (Doc.ID 124900);published 26 July 2010Modeling a real laser diode stack based on Zemax ray tracing software that operates in a nonsequentialmode is reported.The implementation of the model is presented together with the geometric and opticalparameters to be adjusted to calibrate the model and to match the simulated intensity irradiance profileswith the experimental profiles.The calibration of the model is based on a near-field and a far-field measurement.The validation of the model has been accomplished by comparing the simulated and experi-mental transverse irradiance profiles at different positions along the caustic formed by a lens.Spot sizesand waist location are predicted with a maximum error below 6%.2010 Optical Society of America0 CIS code8:080.2740,140.2010.1.Introductiondivergence angles.More reliable and accurate mod-In the past few decades,laser diode stack systems [1]eling of the laser diode,based on an extensive char-have gained increased interest for their successfulacterization,specifically the measured pump beamapplication in a number of different fields such asirradiance profile of the diode source,is requiredsolid-state laser technology,materials processing,to optimize the performance of the laser systemavionics and defense,and biomedicine.Among these,and to predict the effects of the variation of geometrica major application of high-power laser diode stacksand optical parameters on laser performance.is the pumping of solid-state lasers in which tradi-Numerical modeling exploiting commercial opticaltionally used flashlamps have been definitely substi-design software allows for high accuracy,fast andtuted by diode sources,resulting in much highersimple implementation of the model,and short calcu-electrical-to-optical efficiency,lower thermal gradi-lation time.Here I present the numerical modeling ofents induced inside the active materials,higher sys-a real laser diode stack based on the well-knowntem lifetime and reliability,and higher beam quality.Zemax ray tracing software that operates in a non-The pump source and optics are responsible for thesequential mode.Modeling a laser diode by ray tra-pump density distribution in the laser active materi-cing software has been treated in previous studiesal that determines to a large extent the overall[2-8]on the basis of the nominal characteristics de-efficiency of the laser system and influences the uni-clared in the data sheet;however,to the author'sformity,divergence,and opticaldistortions of the out-knowledge,the measured irradiance profiles of theput beam.A first design of the pump optics can belaser diode have never been taken into account.made beginning with the diode source data sheetOur model is implemented and calibrated beginningthat usually provides only synthetic parameters suchwith two simple measurements:a near-field and aas active area dimensions,number of emitters,andfar-field irradiance profile of the laser diode stack.After calibration is performed,the model gives rea-listic and accurate predictions of the pump irradi-0003-6935/10/224237-09315.000ance profiles at any section inside a specified2010 Optical Society of Americaoptical system,with a typical error on spot radius1 August 2010 Vol.49,No.22 APPLIED OPTICS4237and waist position below 6%.Since laser diode stacksare constituted by bars of laser diode emitters,theproposed modeling technique has general validityand can be used to model various laser diode devices.2.Modeling a Laser Diode StackThe numerical model has been implemented usingFig.1(Color online)Detail of the bars of emittersthe Zemax ray tracing software.The whole processof modeling is basically divided into two steps:cali-bration of the model and validation of the model.Thecalibration is performed both in the near-field and inthe far-field regions of the laser diode source;the va-lidation is accomplished by a z-scan measurement.where x and y are the horizontal and vertical posi-The laser diode stack selected for the experimentstions,respectively,referred to the center of the emit-is Model QD-Q1312-B by Quantel,with the mainting surface,wx and wy are the 1/e2 radii of the raycharacteristics (taken from the supplier data sheetbundle,Hx and Hy are the spatial super-Gaussian[9])reported in Table 1;in particular,the laser diodefactors.Other relevant parameters used to defineis provided with an array of fast axis collimating mi-the laser diode object in the Zemax environmentcrolenses,which is the most complicated configura-are the spatial coordinates of the center of the emit-tion for this kind of laser device.ting surface,the total power of the launched ray bun-The laser diode stack is made of a fixed number ofdle,the number of random rays to launch from thestacked bars and each bar consists of a fixed numbersource when performing analysis (see Ref.[10]forof arrays of diode emitters lined along the bar.more details).Figure 1 shows the detail of the bars of emitters.The Zemax model of the laser diode stack hasThe Zemax nonsequential object laser diode repre-been implemented with the following geometricsents a flexible software tool to model each arrayparameters:of emitters in a bar separately.In particular,the la-ser diode object has an angular power distributionthe number of diode bars;I(x,y)given bypitch p between bars;the number of emitters per bar;pitch b between emitters;the dimensions of each emitter.The geometric parameters can be fixed once thewhere x and are the angles formed by thegeometric configuration of the laser diode stacklaunched ray and the normal to the emitting surfacehas been selected.According to the data reportedalong the horizontal and vertical directions,respec-in Table 1,the geometric parameters have beentively,ax and ay are the 1/e2 divergence angles,G.set as follows:12 bars stacked in the vertical direc-and Gy are the angular super-Gaussian factors.Intion with a bar-to-bar distance p of 400um;eachaddition,each laser diode object has a spatial powerbar is composed of 69 emitters with dimensions ofdistribution F(x,y)given by114um x 1 um and pitch b of 140um.It is worth not-ing that what is called emitter in this context,is notTable 1.Characteristics of the Quantel OD-Q1312-Bactually a single emitter but rather an array of singleDiode Stack [9]laser diode emitters.ParameterCharacteristicTo model the beam generated by each emitter inthe Zemax environment,a first simplifying assump-Peak output power"(W)840tion has been made:all the emitters along the stackRepetition frequency (Hz)100have the same geometric configuration and opticalPulse duration(μs)160characteristics,apart from the output power,imply-10×4.4Number of bars per stack12ing that the beams generated by different emittersPitch between bars (um)400±50have the same shape and width of the spatial andNumber of emitters per bar69angular power distributions but different opticalPitch between emitters (um)140powers;in addition,the spatial and angular powerSingle emitter area (um2)114×1distributions of each beam have been assumed toFast axis FWHM divergence (deg)40±23±1.59be Gaussian along the fast axis (FA)and super-Slow axis FWHM divergence (deg)Gaussian along the slow axis (SA)on the basis ofPeak wavelength (nm)808.2the theory reported in Ref.[11].By these assump-FWHM emission bandwidth (nm)s3tions,the real spatial and angular power distribu-“At90 A pump current.tions peculiar to each different emitter are not takenWithout collimating microlenses.into account,which leads to an approximate solution;With collimating microlenses.however,as will be shown,this approach gives quite4238APPLIED OPTICS/Vol.49,No.22/1 August 2010accurate results with modest computational and ex-(b)perimental efforts.Under the above-mentioned as-12sumptions,the following optical parameters havebeen selected to model the beam generated by eachemitter:the 1/e2 beam radius w and wy along the SAand FA,respectively;the 1/e2 beam divergence ax and ay along theSA and FA,respectively;681012681012the spatial H,and angular G,super-Gaussianfactors along the SA;Fig.2.(Color online)(a)Experimental near-field profile of thethe power P generated by the kth emitter inlaser diode stack and (b)computed emitter powers.the jth bar,with=1,...,69 and j=1,...,12.emitter are different (there are even dark emitters)The 1/e2 beam radius along the SA and FA is as-and,as a consequence,the power content of each barsumed to be equal to the half-width of the emitteris variable.The MATLAB routine creates a grid withalong the SA and FA,specifically w=57 um andhorizontal and vertical line distances equal to pitch bwy =0.5um,respectively.The spatialsuper-and p between emitters and bars,respectively.TheGaussian factor H along the SA is assumed to beaverage power content of each pixel in the grid isequal to 10,because each emitter has a nearly rec-evaluated by numerical integration of the powers as-tangular irradiance profile along the SA,whereassociated with the pixels in the original near-field im-the spatial and angular super-Gaussian factors Hage.The output of the MATLAB routine is a matrixand Gy along the FA are assumed to be equal to 1containing the normalized power content of each(Gaussian profiles).The remaining optical para-emitter in the laser diode stack to be used to adjustmeters (i.e.,the 1/e2 beam divergences ax and ay,the powers Pi generated by each emitter and,hence,the angular super-Gaussian factor Gx the powerto calibrate the near field ofthe Zemax model.As canP generated by each emitter)are variables of thebe seen in Fig.2(b),the result ofthis routine providesZemax model to be adjusted to calibrate the simu-a rather good approximation of the measured near-lated near and far fields.As a first step,the calibra-field irradiance profile.tion of the model is accomplished in both theThe parameters to be adjusted to match the mea-near-and the far-field regions of the diode source.sured far field along the SA [see Fig.3(a)]are the 1/e2The measured near and far fields represent the refer-beam divergence a,along the SA and the angularences to calibrate the model.The simulated near-super-Gaussian factor G along the SA.The assump-and far-field profiles must match the measured neartion of super-Gaussian angular distribution alongand far fields.The optimization of the simulated pro-the SA is justified by the physical configuration offiles is done by means of a user-defined Zemax meritthe emitter:as pointed out before,the emitter is ac-function developed for this purpose.As a second step,tually an array of single laser diode emitters,andthe validation of the model is accomplished by meanseach single emitter in the array generates a beamof a z-scan measurement along the propagation caus-with near-Gaussian angular distribution along thetic produced by a focusing lens.In particular,the ir-SA;since there is only partial coherence betweenradiance profiles are measured at different positionsemitters within the same array,the net angular dis-along the caustic and then compared in terms oftribution of the beam generated by an array is wellbeam dimensions(defined according to the ISO stan-approximated by a super-Gaussian function.dard definition of second-order moments [12])to theThe situation is quite different along the FA direc-simulated irradiance profiles produced by the cali-tion.As can be seen in Fig.3(b),in this case,an arraybrated diode stack model.The predicted beam radiiof cylindrical microlenses is employed to collimateand waist position have to be as close as possible tothe strongly divergent beam emitted from eachthe measured ones.bar.The position of each microlens along the verticalThe parameters to be adjusted to match the mea-and axial directions (i.e.,orthogonal to the stacksured near-field irradiance profile are the powers Pemitting surface,see Fig.4)is characterized bygenerated by each emitter in the laser diode stack.Acustomized MATLAB routine has been implemented(b)for this purpose.Figure 2(a)shows the near-field ir-radiance profile measured at the output of the laserdiode stack,that is in the transverse plane locatedjust after the cylindrical FA collimating microlenses.The experimental setup used to measure the near-field irradiance is described in Section 3.The detailsof the emitters and bars can be clearly seen inFig.3.(Color online)(a)SA view and (b)FA view of the beamFig.2(a),in particular,the powers generated by eachgenerated by the laser diode stack1 August 2010 Vol.49,No.22 APPLIED OPTICS4239