beam shape analysis of waveguide delivered infrared lasers

Beam shape analysis of waveguide deliveredinfrared lasers

Israel Gannot, MEMBER SPIEM. Ben-DavidA. InbergNathan Croitoru, MEMBER SPIETel Aviv UniversityRamat-AvivIL-69978 Tel AvivIsraelE-mail: [email protected]

R. W. WaynantU.S. Food and Drug AdministrationElectro-optics BranchCenter for Devices and Radiological HealthRockville, Maryland 20857

Abstract. A comprehensive theoretical model is developed to describemid-IR laser radiation propagation in an optical cylindrical waveguide.The effects of various parameters of the beam as well as of the wave-guide on the output beam shape are studied and analyzed. Parameterssuch as beam coupling misalignment, waveguide diameters, and innerwall roughness are studied. The same conditions are applied in the the-oretical calculations as well as in the experiments. Good agreement be-tween the theoretical and experimental results is found. © 2002 Society ofPhoto-Optical Instrumentation Engineers. [DOI: 10.1117/1.1420191]

Subject terms: optical waveguides; lasers; ray tracing; optical waveguide theory;laser applications.

Paper 200501 received Dec. 21, 2000; revised manuscript received June 19,2001; accepted for publication June 28, 2001.

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1 Introduction

One of the methods used to transmit mid-infrared~MIR!radiation from a source~laser, heat, or other IR source! to atarget~tissue, detector!, straight or under bent trajectory,a hollow optical waveguide. Such waveguides were intsively studied and developed in the last decade.1–10 Thesetypes of waveguides are made of plastic or silica tubeswere already used for several applications in medicine.9–13

The practical applications revealed several drawbacwhich limited the extension of utilization into broadefields, such as noninvasive surgery, hard tissue cuttingother procedures needing high power lasers. Thismainly due to the fact that the Teflon waveguides halarge attenuation (A.1 dB/m) and the silica waveguideare not flexible enough~bending radius bigger than 75 mm!for internal diameters of cross section (ID.0.5 mm). Thishas led to studies of the radiation propagation throughbore of the guide~the role of the roughness of the internwall of tube! and to the improvement of the deposited guing layers ~metal and dielectric!, which may give lowerattenuation.14 The analysis of the beam propagation unnow was not accurate enough, since several paramewhich may affect the beam shape and divergence of deered radiation, were not taken into account. These pareters are: the coupling of the IR source to the input, aroughness of the internal wall of the waveguide. Our thretical model was refined to give quantitative representaof the relation between the beam profile and these indicaparameters. The results of calculations based on this mmay contribute to the understanding of the laser radiadelivery in hollow optical waveguides in general, and ouin particular. The results of such a study will lead to tdevelopment of waveguides more suitable for a host of napplications in the fields mentioned before.

2 Experimental Procedure

The plastic and silica waveguides were prepared usingflow chemistry electroless method.1 Before the deposition

244 Opt. Eng. 41(1) 244–250 (January 2002) 0091-3286/2002/$15

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of the guiding~Ag and AgI! layers, the internal wall of theplastic ~Teflon! tube was etched with naphthalene/THF slution, followed by a second etching of sulfochromic acAfter etching the wall, the tube was sensitized and activaby SnCl2 /HCl and PdCl2 /HCl solutions. For silver layerdeposition, we used AgNO3 solution buffered by ammoniaand acetic acid and a hydrazine hydrate solution as aducer. The AgI layer was obtained by reacting the depossilver with iodine solution.15 A similar method13 was ap-plied in the preparation of the silica waveguides.

The attenuation of CO2 laser radiation~wavelengthl510.6mm! transmitted by Teflon and fused silicwaveguides~length L51.0 m and ID51.0 and 0.7 mm!was measured. The measurements were done using a SCO2 laser with maximum power of 15 W. Cutback annondestructive16 methods were used for attenuation mesurements. Beam shape measurements were done witSpiricon beam shape analyzer, which was placed 10after the waveguide’s end. Coupling of the laser beamthe waveguide was done with a ZnSe lens (f550 mm). Thebeam spot size at the waveguide input was 0.3 mm.position of the laser beam at the center of the waveguidinput was determined using a coaligned HeNe visible la

3 Effect of Surface Roughness

The procedure described in the previous section hasgoals: the first is to deposit the thin films, which guides tlaser beam through the hollow waveguide, and the secis to create a smooth and homogenous surface beforepositing the thin layers. This is done by filling the cracand voids beforehand in the hollow tube.

The surface roughness was measured using an atoforce microscope~AFM!. Figure 1~a! shows the surfacetexture of the AgI layer. Analysis of the scan shows thatsurface roughness~s! is between 200 and 450 Å for glaswaveguides and 937 Å for Teflon waveguides.

The distribution of heights was calculated by the AFsoftware and was found to be normally distributed@Fig.

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1~b!#. The distribution of heights is given by

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wherez0 is the mean surface height.The scattering coefficient for such a surface is given

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where w1 is the angle of incidence,w2 is the scatteringangle, L is the length of the scattering surface,T is thecorrelation distance of the surface roughness (T!L) and

nx5k~sinw12sinw2!, ~3!

F~f1 ,f2!5secw1

11cos~w11w2!

cosw11cosw2, ~4!

Ag52ps

l~cosw11cosw2!. ~5!

Fig. 1 Roughness measurement: (a) AgI layer’s surface texture and(b) distribution of heights.

To find the scattering coefficient, we should computeseries in Eq.~2!. The series is calculated numerically unthe last term is less then 0.01%. The scattering coefficwas calculated using the MATLAB program~version 5.2!.Figure 2 shows the scattering coefficient for various surfroughnesses. We can see that as the surface roughnecreases, the normalized scattering coefficient decreaThe scattering coefficient,S, for each ray is the sum of thenormalized scattering coefficients for the positive angdivided by the sum of the normalized scattering coefficiefor all angles@Eq. ~7!#.

4 Theoretical Model

A new ray model was used for calculation of the propagtion of radiation through the waveguide and for the delered beam shape.

According to the ray model,18,19 one can decompose thlaser beam into separate rays. This model may be usince in our casel!d, wherel is the wave length of thecoupled beam andd is the inner diameter of thewaveguide’s cross section. We assume that multiple indences on the metal~e.g., silver! and dielectric~e.g., silveriodine! layers guide the rays by refraction and reflectioThe dielectric layer has a normal distribution of heigh@Eq. ~1!#, which causes scattering.

The propagation of the rays was calculated usingphysical laws of geometrical optics. The following condtions were used:

1. The Fresnel law gives the reflection coefficient afthe incidence with the thin layer.

2. The rays propagate only frontal and not rotation~there are no skew rays!.

3. Two coordinates represent the laser beam crosstion and the point the ray enters into the waveguider~with Gaussian distribution! andu ~with uniform dis-tribution! ~Fig. 3!, where 0<r<R ~R is the laser spotsize! and 0<u<2p. The angleu also determines theplane in which the ray propagates.

Fig. 2 Normalized scattering coefficient versus scattering angle (w580,T/s51000,L5100l).

245Optical Engineering, Vol. 41 No. 1, January 2002

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4. The angle of entrance,w, ~Fig. 3! has Gaussian distribution. This angle determines the angle of propgation,f, by f5902w.

5. The rays have random polarization, TE or TM.

6. The total energy of the laser beam,I, is the sum ofthe energy of all rays, and is given by

I5(i

Ii~sr ,sw ,ri ,wi!, ~6!

wheres r , andsw are the standard deviation of thGaussian beam size and angle, respectively.The new ray model adds the following assumption

7. The surface of the dielectric layer is rough.

8. The roughness centers are distributed randomly.

9. The scattering is produced only on the surface ofincident layer and not in the bulk of it~not inside theAgI layer!, since the AgI layer is more granular thathe Ag layer, hence roughness is higher.

10. The scattered energy is taken only in the positdirection; scattered energy in the negative directis assumed lost. The scattering coefficient~S! isgiven by

S5(w50

90 S~w!

(w529090 S~w!

, ~7!

whereS(w) is given by Eq.~2!.

11. The scattering of the ray changes the ray’s anglepropagation. The new angle is the average anglethe scattered energy.

12. The laser beam is decomposed to a minimum of5

rays.

Using these assumptions, one can calculate the attetion and the beam shape outside the waveguide as a ftion of the waveguide’s parameters~length and inner diam-eter!, and the coupling conditions~focal length of thecoupling lens and off-center movement of the ray!.

When the laser beam hits the waveguide’s inner walundergoes two processes: reflection from a thin layerscattering. According to the previous assumptions, theergy of each ray after one incidence with the inner wall

I i5I i0R~w!S~w!, ~8!

Fig. 3 The ray parameters.

246 Optical Engineering, Vol. 41 No. 1, January 2002

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whereR(w) is the reflection coefficient given by FresneandS(w) is the scattering coefficient.

5 Results and Discussion

The first attenuation and beam shape experiments wmade on silica straight waveguides with internal diameID50.7 mm and lengthL51.0 m. Gaussian beam shapwas measured. Low attenuation~less than 0.4 dB/m! wasachieved. The attenuation as a function of the wavegulength is shown in Fig. 4~a!, the beam shape measureme

Fig. 4 Theoretical and experimental attenuation measurements andbeam shape of straight silica waveguide ID50.7 mm: (a) attenua-tion versus length, (b) measured, and (c) calculated.


Fig. 5 Beam shape of straight silica waveguide ID51.0 mm, L5100 cm: (a) measured and (b) cal-culated. Beam shape of straight silica waveguide ID50.5 mm, L5100 cm: (c) measured and (d)calculated.

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is shown in Fig. 4~b!, and calculated in Fig. 4~c!. As can beseen from the graph, the theoretical results are in agreemwith the theoretical ones.

To compare between the two beam shapes, let us dethe parameterj which is the ratio of theM2 factor of theexperimental beam shape to theM220 of the calculatedbeam shape.

jx5Mx,exp

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~9!

jy5M y,exp

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M y,cal2 .

A good correlation is achieved whenj is close to one.This experimental beam shape is quite similar to tha

the source~not shown, since it was a regular Gaussishape beam! except for a second satellite propagation moof small intensity. A theoretical calculation, for the samcondition, was done. The scattering due to roughness o

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deposited layers~average roughnesss<500 Å! was verysmall. The results of the calculations are shown in F4~b!.

The calculated beam shape is similar to the experimeone (jx51.09,jy50.99). A significant result is that similato the experimental case, a small ring of higher modespropagation is also seen in the theoretical [email protected]~b!#. The cause for the higher modes is the focal lengththe lens. The smaller the focal length, the larger the numof angles that are propagating in the waveguide. This girise to higher modes.

The same measurements and calculations were repefor a ID51.0 mm and ID50.5 mm waveguide. The resultare shown in Figs. 5~a!, 5~b!, 5~c!, and 5~d!. When wecompare the beam shapes shown in Fig. 5 and Fig. 4,notice that with the increase of the ID from 0.5 through 0to 1.0 mm, the number of propagation modes, which is sin the beam profile, has increased, although the fundamtal part remains of Gaussian shape. This result is shoexperimentally and theoretically. The increase in the diaeter caused more emphasized presence of the higher mas shown in Figs. 5~a! and 5~b! in comparison with that of


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Fig. 4. This is due to the coupling between higher modeslower ones, which occurs when the waveguide’s diamedecreases.21 The attenuation,18,19 on the other hand, is decreased.

The correlation for ID51 mm between the experimentaFig. 5~a! and the theoretical Fig. 5~b! results is rather good(jx50.85,jy50.77). The correlation for ID50.5 mm be-tween the experimental Fig. 5~c! and theoretical Fig. 5~d!results is rather good, (jx51.02,jy50.96).

A further increase of the ID drastically spoils the beashape ~result not shown!, where there are much mormodes in the output beam. This drastic change of the ration energy distribution in the propagated beam is badmedical applications. When the higher modes intensgrows, then the energy at the peak is lower, thus we havbeam with hot spots. This beam shape has a lower eftiveness when using it for precise laser cutting of tissuelarger diameter with energy spread over it will cause lowenergy densities, which cause bigger thermal damage.laser spot at the output of a waveguide should be kepsmall as possible, considering reasonable attenuation.

One other factor, which contributes to the deviationthe beam shape from Gaussian, is the off-center couplinwaveguide. This may happen, since there is always a plem in coaligning a laser beam to a small ID waveguidespecially in a medical laser where there are always mo

Fig. 6 Beam shape of straight silica waveguide ID51.0 mm, L5100 cm, and 0.15 mm off-center coupling: (a) measured and (b)calculated.


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ments of the articulated arm and the waveguide whileoperation is performed. For the understanding of bewaveguide aligning problem and its affect on beam shawe carried out the measurements described in the nparagraph.

The laser was first focused at the center of twaveguide’s input. Using the positioners, we moved tbeam from the center toward the edges in both directioWe have taken images of all the output beams at differcenter locations. At each location, we have also measuthe output energy. Out of this series of images, we hachosen to show three off-center couplings at 150, 300,400 mm. For the same locations, we have also appliedray tracing program. Figures 6, 7, and 8 show the resultsthe experiment@~a! in each figure# and theoretical results@~b! in each figure#. It is obviously seen that when the beais further out from the center, the beam is spoiled, symmtry is gone, the main peak is reduced, and higher moappear. We can also see that our model predicts wellexperimental results. The loss of symmetry is due tolarge attenuation of the lower modes, which now propagnear the waveguide’s wall. When the lower modes ahighly attenuated, the higher modes are more emphasiz

These experiments were repeated with a Teflon waguide with internal wall roughness of about 1000 Å~asmeasured with an atomic force microscope!. The results are


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shown in Fig. 9. The theoretical results and the experimtal ones are similar (jx50.84,jy50.87). The effect ofscattering due to the wall roughness on the beam shapthe output of the waveguides is very well pronounceWhen we compare Figs. 5~a! and 9~a!, we can see the effecof the roughness, which iss,500 Å nm in the silica wave-guide ands,1000 Å in the Teflon waveguide. Biggeroughness causes much more scattering, thus a muchordered beam shape. This output beam contains many mhot spots and less pronounced center peak. The theoreresults in Figs. 5~b! and 9~b! confirm these results.

Experiments with the waveguide mentioned before wcarried out at the Vanderbilt Free Electron Laser faciliThe free electron laser wavelength was tuned to 6.45mm.The two types of waveguides were coupled through100-mm lens and the beam shape reading was donethe Spiricon and pyroelectric camera. Figures 10~a! and10~b! show the results for Teflon and fused silicwaveguides, respectively.

The two waveguides are multimode waveguides. A laamount of modes develop and are transmitted in thwaveguides. These modes, of course, cause beam shwhich are far from the Gaussian input beam and havebeam structure of multispots. In the more rougwaveguides, mode coupling processes22 are present~due tothe roughness!, and this causes the smeared structure of


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output beam in the Teflon waveguide. The fused silwaveguide, on the other hand, has much less roughnessthere is a development of modes in it, and together withnot-so-pure Gaussian, like in the case of the CO2 laser,creates the hot spot multimode shape at its output.

6 Conclusions

The ray model described predicts phenomenon in the beshape, for the simple cases shown, quite accurately.have noticed that an increase in the internal diameter ofhollow waveguide decreases the attenuation but increathe deviation of beam shape from Gaussian. Off-center cpling of the Gaussian shape of the laser source decrethe height of the fundamental mode and causes generaof satellites due to the development of additional modRoughness of the internal wall of the waveguide produchigher losses and a noisier beam shape.

In our future plans, we will take into our model morparameters, such as bending, nonGaussian beam shvariation in the angle of the launched beam, introductionthe wavelength to the calculations, and pulse and shpulse treatment~i.e., pulse broadening, micropulses!. Wewill consider various shaped distal tips and eventually wfield interaction~the effect of liquid phase on beam shape!.

Fig. 9 Beam shape of straight Teflon waveguide ID51.0 mm, L5100: (a) measured and (b) calculated.


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Acknowledgment

The authors wish to thank the Ministry of Industrial Affaifor their support through the MAGNET program.

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Fig. 10 Free electron laser radiation transmission: (a) Teflon wave-guide and (b) fused silica waveguide.


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Biographies and photographs of the authors not available.

beam shape analysis of waveguide delivered infrared lasers

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