Measurement of thermally induced changes in therefractive index of glass caused by laser processing

James Sullivan, Jian Zhao, and Ted D. Bennett

The effects of CO2 laser heating of pure fused silica are investigated. Studies show that the laser heatingprocess causes a small volume of glass to be left in an altered microstructural state. To measure therefractive index of this altered region, a process was developed to create a thin film of altered glass.Samples were measured with a prism coupler, and a theoretical model was developed to predictthe intensity values collected during the measurement. A least-squares routine was used to determine therefractive index that results in the best fit between the experimental and predicted intensity data. Therefractive index in the altered glass was found to increase by approximately 0.07%. © 2005 OpticalSociety of America

OCIS codes: 140.3390, 160.4760, 160.6030.

1. Introduction

With the growing use of integrated optics componentsin the fields of communications and computing, thereis an increasing need for the development of fast andlow-cost fabrication techniques for these devices. Onearea that has been the subject of recent research isthe development of alternative methods for creatingplanar optical waveguides. The most commonly usedfabrication technique for silica- �SiO2-� based planarwaveguides is a complex, multistep process involvingphotolithography and several stages of material dep-osition.1,2 In contrast, recent studies of planarwaveguide fabrication have centered on direct-writetechniques, in which focused irradiation is used toform waveguide structures in bulk materials by caus-ing localized changes in the refractive index. For in-stance, index changes as a result of exposure toultraviolet irradiation have been studied for bothpure3 and photosensitive4 silica glasses as well as forpolymer materials.5–7 Other groups of scientists haveinvestigated the use of focused ion beams to affectlocalized index changes in fused silica8–10 and poly-mers.11

In this paper, the refractive-index change inducedin pure fused silica as a result of exposure to CO2laser irradiation is reported. The rapid thermal cycleimposed on the fused silica by the laser results in asmall volume of glass being frozen into a differentmicrostructural state during cooling, leading to theformation of a localized region with an altered refrac-tive index within the glass.

2. Background

Some of the early studies of CO2 laser processing ofglassy materials involved laser nanotexturing of sil-icate glass disks used in computer hard drives.12–14 Asmall region of glass was found to have been left in analtered microstructural state after laser heating. Thechange in microstructure within this small volume(which was due to an average change in the glass’sSi—O bond angles) can be described as a change inthe glass’s fictive temperature within the region,where the fictive temperature is defined as the ther-modynamic temperature at which the liquid struc-ture is frozen into the glassy state.15

To better understand why the fictive temperatureis changed by CO2 laser processing, it is helpful toconsider a qualitative description of the thermal cycleundergone in the glass within this region. This pro-cess is illustrated schematically in the inset of Fig. 1.At the beginning of the cycle, the glass has a fictivetemperature of Tf,1 corresponding to the microstruc-tural state in which the glass was left after its initialfabrication. As the temperature within the glass beginsto rise owing to laser heating, the fictive temperatureremains constant at Tf,1 until the thermodynamic tem-

The authors are with the Department of Mechanical and Envi-ronmental Engineering, University of California, Santa Barbara,Santa Barbara, California 93106. T. D. Bennett’s e-mail address isbennett@engineering.ucsb.edu.

Received 13 January 2005; revised manuscript received 28 June2005; accepted 2 July 2005.

0003-6935/05/337173-08$15.00/0© 2005 Optical Society of America

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perature reaches the glass-transition temperatureTg. The transition temperature is defined as thethermodynamic temperature below which micro-structural relaxation cannot occur. The fictive tem-perature remains constant up to this point becausethe glass’s viscosity is still too large to allow for thematerial to reorganize within the time scale of thethermal cycle. However, once the transition temper-ature is reached, the glass’s microstructure reorga-nizes until it reaches the equilibrium microstructureat the thermodynamic temperature. With furtherheating, the fictive temperature path follows theequilibrium line.

As the material begins to cool, the microstructurecontinues to reorganize to maintain equilibrium.However, as cooling progresses, the glass’s viscositycontinues to get larger, and it becomes increasinglydifficult for the fictive temperature to keep up withthe thermodynamic temperature. Eventually, thetime scale for material relaxation becomes largerthan that of the cooling process, and further materialreorganization is not possible. At this point, the mi-crostructure is frozen into place, and the fictive tem-perature is seen to depart from the equilibrium lineat Tf,2 in Fig. 1. Because the cooling process is sub-stantially more rapid than that experienced duringthe formation of the bulk glass, the glass microstruc-ture becomes frozen into place at a higher transitiontemperature. As a result, the fictive temperature islarger after laser processing than that of untreatedglass.

During laser processing, any location within the glassthat is heated above glass-transition temperature Tg willbe left with a microstructure that is different fromthat of the surrounding (bulk) glass. This microstruc-ture corresponds to a higher fictive temperature thanthat of the bulk glass, and the volume that encom-passes this altered glass is referred to as either thealtered or the treated region. It is believed that thefictive temperature is nearly uniform throughout thisregion because it takes orders-of-magnitude differ-ences in the cooling rate to alter the fictive tempera-ture significantly, as was confirmed by a numerical

calculation of the resultant fictive temperature fieldin silicate glass caused by a rapid thermal cycle.16

Further, it has been shown that the etch rate for CO2laser-processed fused silica in a buffered hydrofluoricacid solution is nearly constant within the treatedregion.17 Because the etch rate is primarily a functionof the glass’s microstructure, a constant etch rateimplies a uniform fictive temperature throughout thetreated region.

The fictive temperature of a glass is important toits physical properties. Its relationship to mechanicalstrength,18,19 chemical stability,20 and optical proper-ties21,22 has been studied. Because the refractive in-dex of a glassy material is determined in part by thematerial’s microstructure, it is suspected that thefictive temperature increase in the glass that is due tothe CO2 laser processing corresponds to a refractiveindex within the treated region that is different fromthat of the surrounding glass. If the index change issufficiently large, the laser can be used for directwriting of waveguide structures into glass.

3. Experiment

To assess whether CO2 laser processing is useful forthe direct-write fabrication of optical waveguides, wewrote simple planar waveguide structures into sam-ples of fused silica. Fused silica was selected ratherthan silicate glass for several reasons, primarily be-cause the treated region in fused silica is mechani-cally stronger than that in silicate glass.23 Theprimary components of the experimental apparatusare a 100 W CO2 laser with a vacuum wavelength of10.6 �m, an acousto-optic modulator, beam-shapingoptics, and a motion-control stage. A two-directionallinear stage is used to provide sample velocities below6.0 cm�s, while a high-speed spindle mounted to alinear stage is capable of providing velocities above1.2 m�s. The sample velocity is a primary variable forlimiting the thermal penetration depth and therebyincreasing the rate of cooling in this experiment.23

The fused-silica sample is mounted onto the desiredstage, which is used to translate the sample acrossthe path of the laser beam. Provided that the stagevelocity and the laser power are kept constant, thisprocess results in a line of treated glass with a con-stant cross section being formed in the fused silica.

A typical cross section of the treated region that isthe result of a single pass of a sample beneath thelaser is illustrated in Fig. 1. The width of the regionis usually of the order of the 1�e beam diameter,whereas the depth is dependent on the laser powerand the sample velocity but generally is of the orderof several micrometers. The shape of the bottom in-terface of the region is due primarily to the Gaussianintensity distribution of the laser beam. In contrast,the profile of the top boundary is the result of threeseparate effects: glass vaporization, hydrodynamicredistribution of material, and compaction. Vaporiza-tion of material is highest toward the center of thebeam. Hydrodynamic material redistribution, drivenby surface tension forces and vapor pressure, is re-sponsible for the bumps seen at the outer edges of the

Fig. 1. Typical shape of the treated region in a fused-silica sam-ple. Inset, fictive temperature map for the treated region duringCO2 laser processing.

7174 APPLIED OPTICS � Vol. 44, No. 33 � 20 November 2005

treated region. Compaction occurs in the treated re-gion because the density of fused silica increases asthe fictive temperature increases.16 Lower laser in-tensities will reduce the final surface topography butalso will reduce the depth of the treated region suit-able to act as a waveguide.

To assess the usefulness of the CO2 laser for the di-rect writing of planar waveguide structures it is nec-essary to quantify the refractive-index changeinduced in the treated region of the fused silica. Anumber of methods exist for measuring the refractiveindices of various types of sample. For instance, theBecke line method24 and interferometry25 are tech-niques for determining the indices of homogeneous(bulk) samples. Prism coupling26 and ellipsometry27

are commonly used to measure the refractive indicesand thicknesses of thin deposited films. Refractednear-field scanning is a technique that yields a two-dimensional index profile of a sample and is usedprimarily in the characterization of optical wave-guides.28,29 However, of these methods, only refractednear-field scanning has the necessary spatial resolu-tion to probe the treated region of the sample. Unfor-tunately, a limited number of attempts to measurethe refractive-index profile of a treated fused silicasample with refracted near-field scanning were un-successful.23

To make the laser treatment amenable to otherindex measurement techniques we exposed samplesto multiple laser passes, with the treated regionsfrom successive passes made to overlap to form a thinfilm of treated glass. Because the fictive temperatureis nearly constant within each treated region, therefractive index within the treated film should beconstant as well. The cooling half of the lasing processcauses glass to be quenched from the liquid state.Therefore there is no influence of the state beforemelting and no effect of multiple passes as long as thecooling rate of each region remains the same. Caremust be taken in selecting the line spacing (i.e., thedistance from centerline to centerline of successivetreated regions), beam diameter, and laser power toensure the best possible uniformity of the treatedregion with suitable depth.23 Following laser process-ing, the top surface of a thin-film sample is observedto be slightly recessed beneath the surrounding un-treated glass surface as a result of cumulative com-paction and evaporative effects and is found todisplay a periodic waviness. Both of these featureswere observed in all the thin-film samples that wereprocessed, regardless of which stage assembly wasused or of the choice of treatment parameters. Toallow for measurement of the thin film by use of aprism coupler, we polished the top surface of eachsample, using diamond lapping films, until the wavysurface texture at the film surface was removed. Us-ing this technique, we could return the top surface ofthe treated region to a rms roughness of approxi-mately 10 nm, compared to a rms roughness of�5 nm for the untreated fused silica. A thin film oftreated glass remains on top of the untreated fused-silica substrate. The profile of the bottom surface of

the film is unknown but is presumed to have somewaviness (similar to the top surface before polishing).

Each thin film sample was measured with a Met-ricon Model 2010 prism coupler. All the measuredrefractive-index values reported in this paper are atthe vacuum wavelength of the He–Ne laser beamused in the prism coupler ��0 � 632.8 nm�. Whereasprism coupling is utilized primarily for measuringthe properties of thin films, it can also be used todetermine the refractive indices of bulk materials.The physical measurement is identical for both thebulk and the thin-film modes, the difference betweenthe two modes is in the model used to determine theoptical properties of the sample from the collecteddata.

A schematic diagram of a prism coupler is shownin Fig. 2(a). The sample is held in place againstthe bottom face of a prism by a small piston. Evenwith the pressure from the piston, a small air gap��100 nm� exists between the prism and the sample.Plane-polarized light from a laser is incident uponone face of the prism, where it is refracted down to theprism–sample interface. For a given incidence angle,the amount of light that is reflected from the interfacedepends on the optical properties of the sample andthe prism. The light that is reflected from the prism–sample interface travels to the exit face of the prism,where it refracts out of the prism and is collected by

Fig. 2. Schematic diagrams for prism coupler measurement: (a)full system, including air gap, (b) interaction at the prism–sampleinterface for the thin film sample (no air gap).

20 November 2005 � Vol. 44, No. 33 � APPLIED OPTICS 7175

a detector. The prism and the sample are mountedonto a rotary table such that the entrance angle of thelaser onto the prism can be varied.

For a bulk material there is 100% reflection fromthe prism–sample interface for incidence angleslarger than the critical angle for the interface, asdefined by Snell’s law:

ns � np sin �p,cr, (1)

where �p,cr is the critical angle and ns and np are therefractive indices of the sample and the prism, re-spectively. Beyond the critical angle, light can tunnelacross the air gap and couple into the bulk material,resulting in less light reaching the detector. Thesharp initial drop in intensity (called the knee) cor-responds to the point at which the incidence angle isequal to the critical angle. One can use the angularlocation of the knee in bulk mode to calculate theindex of a bulk sample, using Eq. (1).

Similar to the case for a bulk sample, light cannotcouple into a thin film for incidence angles largerthan the critical angle. However, even when the crit-ical angle has been passed, light can propagatewithin the film at specific angles (called mode angles)that correspond to conditions of constructive interfer-ence of the reflected light within the film. At each ofthese mode angles, a sharp drop in the measuredintensity occurs. The location of these mode anglesdepends on the film’s index and thickness. In thin-film mode, the prism coupler’s software identifies theposition of the mode angles on the intensity plot anduses this information to calculate the film’s index andthickness. The angular location of the knee is alteredby mode propagation within the film and is no longera useful measure of the sample’s index.

An attempt was made to measure the refractive in-dex of a laser-treated sample by use of the prism cou-pler. Figure 3(a) shows an intensity plot from theprism coupler’s detector for one of these measure-ments. It should be noted that some of the features inthe experimental intensity profiles are due to effectsthat are not accounted for theoretically. For example,the plateau in intensity between points A and B in Fig.3(a) results when light that has coupled into the sub-strate is reflected off the back surface of the sampleand returned to the detector. However, the anticipatedsteep drop at the knee in the profile is readily apparentand is enlarged in Fig. 3(b). A close examination of theregion near the knee, shown in Fig. 3(b), reveals thatthe intensity profile has a slight waviness to it. For abulk material, the falloff in intensity after the criticalangle is smooth, especially in the region close to theknee. In contrast, the intensity profile for our thin-filmsample suggests that there is some effect that is due towaveguiding within the film. The slight dips and peaksin the intensity profile correspond to mode angles forthe film. However, because of the likely waviness of thefilm–substrate interface, each mode is spread over alarger angular range, with the result being shallow,wide modes instead of narrow, deep modes. As a con-sequence, the prism coupler fails to measure accu-

rately the refractive index of the laser-treated surfaceby using the thin-film mode. Furthermore, Fig. 3(b)illustrates that the mode propagation within the filmhas shifted the knee’s location to the right of that ex-pected of a bulk sample (indicated by the dashedcurve), and therefore the bulk mode of the prism cou-pler cannot be used to measure the refractive index.

As a consequence of the weak mode propagationseen in the laser-treated sample, an independentmodel and fitting routine was developed for extract-ing the refractive index from the raw data (detectorintensity and laser incidence angle) collected by theprism coupler.

4. Prism Coupler Model

A precise model for the prism coupler measurementneeds to account for effects such as reflection lossesfrom the prism faces and the attenuation that occurseach time the beam crosses the air gap. However, thedetector intensity at a given incidence angle is deter-mined primarily by the reflectivity of the prism–sample interface at that angle. The prism–sampleinterface (without the air gap) for a thin film is shownin Fig. 2(b). A plane wave of light is incident from theprism onto the film, and multiple reflections withinthe film interfere with the initial reflection from theprism–film interface. Phase difference � betweenpoints A and B is given by30

� �4�nf h cos �2

�0, (2)

Fig. 3. (a) Intensity profile measured by the prism coupler for thethin film sample of fused silica, (b) blowup of the region near theinitial knee.

7176 APPLIED OPTICS � Vol. 44, No. 33 � 20 November 2005

where �0 is the vacuum wavelength of the He–Nebeam and h and �2 are as shown in Fig. 2(b). Using astandard thin-film optics analysis,30 we can expressthe film’s reflectivity for transverse electric polarizedlight as

Rfilm �r12

2 � r232 � 2r12 r23 cos �

1 � r122 r23

2 � 2r12 r23 cos �, (3)

where r12 and r23 are the Fresnel reflection coeffi-cients for the prism–film and film–substrate inter-faces, respectively, defined as

r12 �np cos �1 � nf cos �2

np cos �1 � nf cos �2, (4)

r23 �nf cos �2 � ns cos �3

nf cos �2 � ns cos �3. (5)

For a bulk material, prism–sample interface reflec-tivity R is equal to the square of Fresnel reflectioncoefficient r12:

R � r122. (6)

To elucidate a measurement strategy, we calcu-lated the prism–sample interface reflectivities as afunction of incidence angle for three cases, as shownin Fig. 4. The first case is a calculation, using Eq. (3),of the reflectivity of a thin treated 10 �m glass filmwith index nf � 1.4572 overlying a substrate (un-treated glass) with index ns � 1.4562. The second twocases are calculations, using Eq. (6), of the reflectivi-ties of two bulk material samples, one with thetreated glass index nf and one with untreated glassindex ns. The prism index for all cases is np

� 1.9642. It can be seen from Fig. 4 that the interfacereflectivity for the thin-film case oscillates about thereflectivity profile of a bulk sample with the sameindex as the treated glass nf. Also, the peaks in in-tensity in the thin-film profile coincide with the pro-file of a bulk sample with the same index as the

untreated glass ns. The first observation suggeststhat the treated glass with weak modes can be deter-mined with the prism coupler by use of a bulk mate-rial measurement model. However, instead ofdetermining the location of the knee corresponding tothe critical angle of a bulk material (which can beerroneous), the measurement should utilize a best fitof detector intensity variation as a function of inci-dent angle in the vicinity of the knee.

A detailed prism coupler model was developed forthe system, and it is illustrated schematically inFig. 2(a). A He–Ne beam with TE polarization isincident upon the entrance face of the prism at anangle �i. On reaching the prism, part of the beam isreflected back into the air, while the remainder isrefracted into the prism. The reflection coefficient forthe air-to-prism interface, rap, is given by Eq. (4), andinterface reflectivity Rap is the square of this quan-tity. With the prism’s refractive index np and baseangles �1 and �2 known, incidence angle �p� of thelight transmitted onto the bottom face of the prismcan be expressed in terms of prism entrance angle �i

by use of Snell’s law and basic geometry. The lightincident onto the bottom face of the prism will bepartially reflected and partially transmitted into thesample. However, one cannot determine the amountof light that travels along each path by simply calcu-lating the Fresnel reflection coefficient for the prism–sample interface because of the presence of an airgap, which can be thought of as an imaginary thinfilm. An analysis can be performed to solve for thetransmitted intensity as a function of the gap size, d.Transmission coefficient Tgap, defined as the intensityof light transmitted across the gap divided by theincident intensity, is given by31

1Tgap

� sinh2 y � �, (7)

with

y �2�d�0

�np2 sin2 �p� � nair

2�1�2,

(8)

��N2 � 1��n2N2 � 1�

4 N2 cos �p��N2 sin2 �p� � 1��n2 � sin2 �p��1�2,

(9)

� ���n2 � sin2 �p��1�2 � cos �p��2

4 cos �p��n2 � sin2 �p��1�2 , (10)

n �ns

np, (11)

N �np

nair. (12)

Fig. 4. Thin-film reflectivity plotted alongside reflectivity profilesfor bulk samples at the film and substrate index. The thin-filmprofile is for a film thickness of 10 �m.

20 November 2005 � Vol. 44, No. 33 � APPLIED OPTICS 7177

In Eq. (11), ns is the refractive index of the sample.The corresponding reflected light from the prism–sample interface is

Rgap � 1 � Tgap. (13)

In some cases, optical effects caused by roughness32,33

on the top surface of the sample could affect the re-flectivity from the sample surface. However, becausethe rms roughness of a polished sample is much lessthan the wavelength of the prism coupler’s laser (ofthe order of 1%), these effects can be considered neg-ligible.

The part of the beam that reflects from the prism–sample interface proceeds to the exit face of theprism. Again, Snell’s law and basic geometry can beused to express incidence angle �p� [shown in Fig.2(a)] of the beam onto the exit face of the prism interms of the entrance angle into the prism, �i. Asbefore, both reflection and transmission of the inci-dent beam occur at this interface, and the Fresnelreflection coefficient can be used to determine theratio of the reflected intensity to the incident beampower. The transmitted portion of the beam is thenincident upon the detector; where its intensity ismeasured. Defected intensity Idet is thus the initialbeam intensity (unity) multiplied by the interfacetransmissivities at the entrance and exit faces of theprism and by the reflectivity from the bottom inter-face:

Idet � l�1 � Rap��1 � Rpa�Rgap. (14)

The only unknown parameters in this expression aresample index ns and gap size d. To compare modelpredictions with the measured intensity values fromour samples, we must apply an offset and a gain tothe predicted detector intensity:

Iexp � �Idet � offset� � gain. (15)

A least-squares numerical fit between the predictedintensity values �Iexp� and the experimentally mea-sured data yields the four unknown variables: ns, d,offset, and gain.

Validation testing of the theoretical model and fit-ting scheme was performed with data collected fromprism coupler measurements of bulk samples of fusedsilica and silicate glass. Using the prism coupler soft-ware in bulk mode, we measured the refractive indexof fused silica to be 1.4562 � 0.0001�; while theindex of a silicate glass was measured at 1.5100� 0.0001�. The fitting was made with a variety ofinput angle ranges to determine which ranges re-sulted in the best agreement between the fitted re-sults and the index values measured by the prismcoupler. One must take some care in choosing thedata points used for fitting because of features in theexperimental intensity profiles that are not theoret-ically accounted for.23

A few general trends from the validation testing

are worth noting. First, the quality and accuracy ofthe fit improve as the amount of precritical angle data[points to the right of the knee in Fig. 3(a)] is in-creased. In this region, the offset and the gain are theonly variables that influence the shape of the inten-sity profile. The fitting routine can more accuratelyfix these two parameters when the intensity profilewithin this region displays some curvature. Also, theaccuracy of the fit is improved if the post-critical-angle data included in the fit are limited to thosepoints that occur before the plateau caused by backsurface reflection, i.e., the data to the right of point Bin Fig. 3(a).

The results of the validation testing show that therefractive-index values returned by the fitting rou-tine are accurate to within 0.00015 of the refractiveindex calculated by the prism coupler software inbulk mode, of the same order as the precision of theprism coupler. Figure 5 shows a measured intensityprofile and the corresponding predicted intensity cal-culated by use of the theoretical model for one of thedata sets used in the validation testing. It can be seenfrom this figure that the best-fit least-squares linefrom the model is in good agreement visually with themeasured intensity profile.

5. Fitting Results for the Laser-Treated Samples

In this study results are presented for four thin-film samples of fused silica: two spindle-fabricatedsamples (samples A and B) and two linear stage-fabricated samples (samples C and D). Table 1 liststhe treatment conditions used during the processingof each of these samples. For each sample, data fromexperimentally measured intensity profiles were col-lected from the prism coupler. Measurements weremade at four points within each sample, with twomeasurements being taken at each location, for atotal of eight data sets per sample. For each of thesesets, we used the least-squares program to find thevalues of the unknown parameters—film index nf, airgap thickness d, offset, and gain—that resulted in the

Fig. 5. Experimental intensity plot of a bulk fused-silica sample,along with a best-fit profile from the theoretical model.

7178 APPLIED OPTICS � Vol. 44, No. 33 � 20 November 2005

best fit between the intensity predicted from the the-oretical model and the measured intensity profile.Figure 6 shows an experimental intensity profile withthe corresponding best-fit least-squares curve for oneof the measurements from sample A.

Table 1 also lists the calculated refractive-indexvalues output from the least-squares fitting routinefor samples A–D. The refractive-index value reportedfor each sample is the average of the refractive-indexvalues calculated from the eight measurements ofeach sample. The standard deviation for the data isalso reported and is of the same order as that ob-served during the validation testing (�0.00009).From Table 1, we can see that there is an increase inthe refractive index of the fused silica as a result ofthe CO2 laser heating process that is �0.001, achange of approximately 0.07%. The measuredindex change is similar to those measured in wave-guides fabricated by ion-beam implantation,9,34 al-though the mechanism is quite different. Thisincrease in refractive index is nearly the same forboth the high-velocity (spindle) and low-velocity (lin-ear stage) treatments. This result indicates that it isnot possible to significantly influence the inducedrefractive-index change by altering the linear velocityof the sample beneath the laser beam.

Whereas a refractive-index change of the same or-der as that induced in the fused silica as a result ofCO2 laser writing (�0.001) is sufficient to allow forwaveguiding of light within the treated region, typi-cal waveguide structures employ larger index differ-

ences between the core and cladding regions.29,35

Thus the application of CO2 lasers for the fabricationof waveguide structures in pure fused silica may notbe useful. However, both the overlap process for thin-film fabrication and the index measurement tech-nique described in this paper can be used toinvestigate the effects of CO2 laser processing onother common optical materials, such as doped fusedsilica, silicate glasses, and poly(methyl methacry-late). It may be possible to find a system that yields agreater index change to the laser treatment.

6. Summary and Conclusions

In this paper the effects of CO2 laser heating of purefused silica were investigated. It has been seen thatthe laser heating process causes a small volume ofglass to be left in an altered microstructural state,which results in a change in the refractive indexwithin this region. To measure the refractive index ofthe altered fused silica, a process was developed tocreate a thin film of altered glass. Samples were mea-sured with a commercial prism coupler, and a theo-retical model derived from electromagnetic theorywas used to predict the intensity values collected dur-ing the measurement. A least-squares fitting routinewas employed to determine the refractive-indexvalue of the altered glass that resulted in the best fitbetween the experimentally measured and predictedintensity data. The refractive index in the laser-altered zone was found to be increased by approxi-mately 0.07% compared with that of untreated fusedsilica.

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Table 1. Treatment Conditions and Fitting Results for Thin-Film Fused-Silica Samples

Parameter Sample A (Spindle) Sample B (Spindle) Sample C (Linear stage) Sample D (Linear stage)

Linear velocity (cm�s) 121 121 1.66 1.66Laser power (W) 24.7 20.6 0.3 0.3Beam diameters (�m) 104 104 28 28Line spacing (�m) 10 10 4 4Film index 1.4572 � 0.00012 1.4572 � 0.00011 1.4571 � 0.00010 1.4571 � 0.00011

Fig. 6. Experimental intensity plot and theoretically predictedprofile for a spindle-generated thin-film sample.

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7180 APPLIED OPTICS � Vol. 44, No. 33 � 20 November 2005