microscopic single-crystal refractometry as a function of wavelength

$: Microscopic single-crystal refractometry as a function of wavelength$
1186 J. Opt. Soc. Am. B/Vol. 11, No. 7/July 1994 Laura D. DeLoach

Microscopic single-crystal refractometryas a function of wavelength

Laura D. DeLoach

Lawrence Livermore National Laboratory, P.O. Box 5508, L-493, Livermore, California 94550

Received October 4, 1993

The refractive indices of crystal fragments 50-200 Am in size can be measured for light wavelengths between365 and 1100 nm with a spindle-stage refractometer. Established methods from optical crystallograpy areused to orient a crystal on the microscope spindle stage and then to match its refractive index to an immersionfluid. The refractive index of the fluid for the wavelength of light and matching temperature is determinedby comparison of a reference crystal on a second spindle axis with the fluid under the match conditions.Investigations of new nonlinear-optical crystals admirably demonstrate the advantages of measuring therefractive index to ±0.0004 in small single crystals.

1. INTRODUCTION

Accurate refractive-index determinations are an essen-tial part of the investigation of new optical materials.However, in the early stages of development, a new mate-rial's available size and quality often preclude the use ofsome measuring techniques. The high-precision meth-ods for determining the refractive index to 10-5 10-4include minimum-deviation spectrometry,l critical-anglerefractometry, 2 and interferometry, 3 among others.4 Butthese methods have strict sample requirements: highlypolished surfaces are necessary, and anisotropic crys-tals may require precisely oriented geometries. Theyare generally suited to single crystals at least severalcubic millimeters in volume. By contrast, refractive-index measuring techniques that are applicable to smallsamples and for which minimal sample preparation isnecessary typically are accurate to only a few parts in thethird decimal place. These are the various oil immersionmethods employed with a polarizing microscope.5

Although progressive levels of sophistication amongthe oil immersion techniques have been developed, allthese techniques work on the principle of refractive-indexmatching. The refractive index of a transparent solidis compared with those of a series of immersion liquids.A match is achieved when the crystal's refractive indexequals that of one of the liquids or lies between those oftwo consecutive liquids. Equal refractive indices are rec-ognized by the distinctive loss of relief between the grainand the oil when observed in transmitted light.

In practice, immersion studies require at a minimumcrushed grains dispersed in an oil mount. First, therandomly oriented grains of optically anisotropic crystalsare examined with a light-polarizing microscope to iden-tify suitably oriented fragments. These oriented grainsare then compared and are determined to be higher,lower, or equal in value to the refractive index of thesurrounding fluid. Accordingly, a now oil/grain slide isprepared with an appropriate fluid, and the process isrepeated until the principal refractive indices are allmeasured, typically within ±0.005. Unfortunately these

crushed-grain immersion studies may be plagued by po-tentially significant errors. These can include measuringa nonprincipal refractive index because of grain misorien-tation, compiling a composite of optical properties from aninhomogeneous sample, and finally, inaccurately assess-ing the matching oil's refractive index because of uncer-tainties in its optical properties. As a consequence thecrushed grain/oil slides often are inadequate for purposesother than some grain identifications.

An advanced oil immersion method that enables re-fractive indices to be measured easily to ±0.001 from asingle crystal fragment is spindle-stage microscopy.6

The spindle stage is a single-axis rotation device mountedto the stage of a polarizing microscope. A needle holdinga crystal fragment mounts to the spindle-stage appara-tus. Rotations of the spindle and the microscope stageare mutually perpendicular such that grains may be ori-ented with their privileged vibration directions parallel tothe polarizer and the microscope stage. An oil cell sur-rounds the crystal with fluid and is removable for easychanges of oil without affecting the crystal's placement.Spindle-stage studies minimize the potential errors in oilimmersion methods that are due to grain misorientation,so that the accuracy of the method is determined by theaccuracy with which the refractive index of the matchingoil is known. Moreover, because refractive indices aremeasured from a single grain, the uncertainty that is dueto sample inhomogeneity can be avoided. Tightly con-trolled experimental conditions and the use of calibratedimmersion fluids can reduce the uncertainties to ±0.0005.

The refractive index, its wavelength dependence, andits temperature dependence are a function of the oil'scomposition. Thus loss of volatile components, contam-ination, and unavoidable aging processes7 mean that n,dn/dT, and dn/dA must be verified for accurate determi-nations. One typically performs calibrations by makingminimum-deviation measurements with hollow prismsfilled with the index-matching fluid8 or by employing ahigh-accuracy Abbe refractometer. 2 Both techniques aretime consuming and may prove objectionable for routineuse. Furthermore, the determination of accurate refrac-

0740-3224/94/071186-11$06.00 ©1994 Optical Society of America

Vol. 11, No. 7/July 1994/J. Opt. Soc. Am. B 1187

tive indices during spindle-stage studies may continue tobe plagued by undetected contamination of the fluid in theoil cell. As a consequence of such instabilities suffered bythe optical properties of fluids, a number of authors haveproposed techniques for calibrating the oil's refractive in-dex in situ. 6 "9-11

One method of in situ refractometry was initiated byFeklichev and Florinskii9 "10 and permits the oil's refrac-tive index to be matched to that of a reference crystal.A well-characterized, birefringent crystal on a secondspindle axis and in proximity to the unknown is rotateduntil a refractive-index match is observed with the oil.The true index of the liquid in the cell can be obtainedat the time of the match and without concern for thepresence of possible contaminants. Medanbach" furtherrefined the design and the technique and has describedthe most elegant version of the microrefractometer spin-dle stage previously reported. However, the Medanbachdevice and other versions have been limited to measure-ments in the visible spectrum. Recent and strong mo-tivation exists for measurements extending outside thevisible spectrum. At Lawrence Livermore National Lab-oratory a search for new frequency-conversion crystalsled to developing a more progressive spindle-stage refrac-tometer that permits refractive-index measurements from365 to 1100 nm.

A new spindle-stage refractometer is being reportedhere. The methods for measuring dispersion of the re-fractive indices between 365 and 1100 nm are describedfor small-single-crystal fragments. In Section 2 a de-scription of the instrument design and principles ofspindle-stage refractometry are presented with referencesto Bloss's thorough treatment of the more traditionalsubject.6 Section 3 is a discussion of the accuraciesattainable and corroborates these with measurementsof known materials. Section 4 presents experimentalresults. Dispersion measurements were completed onnew nonlinear-optical crystals, and the data are used todemonstrate the advantages of this new capability forpredicting phase-matching (PM) properties in harmonic-generating crystals.

2. SPINDLE-STAGE REFRACTOMETRY

A. Principles of DesignFigure 1 is a photo of two spindle stages arranged formicrocrystal refractometry. Goniometer heads6 are at-tached to the spindle-stage barrels and hold fibers onwhich the crystals are mounted. The sample spindleholds a fragment of the crystal to be investigated, whereasthe reference spindle accommodates a standard for whichthe optical properties are well known. The samplespindle, attached to the microscope stage, is free to rotate-.140° about the microscope axis and 3600 about the spin-dle axis so that the principal vibration directions may beoriented. The optical orientation of anisotropic crystalsproceeds rapidly by observation of their conoscopicallyproduced interference figures.5 (For detailed descrip-tions of orientation procedures for uniaxial and biaxialcrystals, the reader is directed to Ref. 5 or 7. Commer-cial computer codes are also available6"12 for determiningcrystal orientations through data reduction of extinctionmeasurements. The use of software for orienting biaxial

crystals may be particularly useful when dispersion of theoptical directions is significant.) The reference spindle isfixed with respect to the microscope vertical axis, but thespindle axis is free to turn 360°. The additional motionof the sample spindle about the microscope axis is notnecessary for the reference spindle because the standardcrystal has been preferentially mounted with respect toits optical directions.

The reference crystal is optically uniaxial and birefrin-gent (see Subsection 2.B below). The sketch presentedin Fig. 2 is of a uniaxial optical indicatrix representingthe reference crystal on the refractometer spindle axis.The crystal is mounted on a goniometer head with itsunique optic axis perpendicular to the spindle axis, anorientation that may be refined by small adjustments ofthe goniometer-head arcs. When the goniometer head isscrewed onto the reference spindle stage, the crystal's op-tic axis is located in the vertical plane parallel to the mi-croscope's polarizing direction. On microscopes of recentmanufacture the polarizing direction has been standard-ized to an east-west orientation; consequently the ref-erence spindle is pointing north or south, and rotationof the spindle causes the crystal's optic axis to rotate inthe east-west vertical plane. (Here it is assumed thatthe observer, looking routinely down the eyepiece, facesnorth, and the field of view is oriented with north as-signed to the top.)

A reference crystal that has been accurately mountedmay be rotated to vary its refractive indices continuouslybetween ne, for light vibrating parallel to the optic axis,and n0 , for light vibrating perpendicular to the optic axis.Thus the refractive index of a fluid in the cell may bedetermined by rotation of the spindle through some angleo until a match with the oil is observed. The mutualrefractive indices of the reference crystal and the oil, andultimately of the unknown, are then determined fromEq. (1):

Fig. 1. Spindle-stage refractometer developed at Lawrence Liv-ermore National Laboratory. Two spindle stages are shownattached to the stage of a polarizing microscope. The referencespindle is indicated and holds a standard or refractometer crys-tal. The spindle in front holds the sample under investigation.A heating oil cell in the background accommodates both crystalsfor immersion studies.

Laura D. DeLoach

Laura D. DeLoach1188 J. Opt. Soc. Am. B/Vol. 11, No. 7/July 1994

Reference

2 no2 n n

nO=n2 . COS2 + n2 sin2

Polarizer

Fig. 2. Uniaxial refractometer crystal schematically repre-sented by an optical indicatrix on the reference spindle. Asthe standard crystal is rotated, the vibration direction parallelto the microscope's polarizer varies continuously between ne,for light polarized parallel to the optic axis, and no, for lightpolarized perpendicular to the optic axis. is the position atwhich the crystal's vibration direction is observed to match thesurrounding fluid. This nonprincipal refractive index no of therefractometer crystal is then determined according to the givenequation. On rotation of the spindle through 3600, one shouldobserve four different spindle settings that have a refractiveindex no corresponding to a match.

2 n,2 n, 2

n92 = n, 2 cos2 0 + ne2 sin20 (1)

Here 0 is the angle between the reference crystal's op-tic axis and the vibration direction of the refractive-indexmatch (see Fig. 2). The reference spindle is capable of360° of rotation; consequently there are four angular set-tings, two about each end of the optic axis, with equivalentrefractive indices. All four matching positions shouldbe recorded such that four independent determinationsare made.

The refractive-index match is evaluated for a dis-crete temperature and wavelength of light by eitherthe double-variation' 3 or the single-variation method.6

Double-variation methods, as the name suggests, allowthe operator to vary wavelength and temperature andare achieved with a wedge interference filter6 for con-tinuously tunable visible light and a thermally variableoil cell. Single-variation methods utilize a temperature-controlled oil cell and discrete narrow-bandpass filters.The temperature-variable cell required by either tech-nique may be as simple as a heating element carryingcurrent from a standard dc power supply6 or a moresophisticated design that also provides cooling capabili-ties such as those described by Medanbach."1 A thermo-couple should be located in proximity to the crystals in thecell for monitoring the temperature. Moderate tempera-ture changes (20-60'C) can be accommodated, althoughexcessively high temperatures have practical implica-tions, owing to the volatile nature of standard index-matching fluids and because lowered viscosities are moredifficult to contain. Moreover, corrections to the refer-ence crystal's refractive index should be considered athigher-temperature matches. For refractive-index mea-surements in this study, we employed single-variationmethods by holding the wavelength constant and by tun-ing the temperature between 20 and 350C.

To permit measurements outside the visible spectrum,a CCD solid-state camera is attached to one port of themicroscope. The camera's silicon detector has a broadspectral response that makes it possible to image lightfrom 350 to 1200 nm in wavelength on a television moni-tor. The CCD camera has exceptional resolution in theUV-visible regions, which justifies its use even for vis-ible wavelengths of light. In fact, subtle light-level dif-ferences that result from refractive-index differences andthat are otherwise undetected by the human eye are vis-ible with the CCD.

The CCD detector responds to light in the UV andthe IR regions, but a standard polarizing microscope,as equipped, requires some modification before these ex-tended light studies are possible. Manufacturers installfactory cutoff UV filters and heat filters that must beremoved from the light path for transmittance in thesespectral ranges. Additionally, the use of standard glassoptics restricts the light intensity and range in the UV,with the lower-wavelength limit of transmittance ulti-mately being defined by the glass. If one uses an intenseUV light source such as a high-pressure Hg arc burnerand/or equips the camera with an image intensifier, thelower wavelength sufficiently visible to the camera's de-tector is approximately 365 nm. The polarizers of thestandard microscope also restrict the operational range.Wavelengths of 400 nm or less are absorbed by the polar-izing element on standard microscopes, and wavelengthslonger than approximately 800 nm are transmitted unpo-larized. Calcite and/or film polarizers can be purchasedthat operate satisfactorily in either of these two regions.

B. Refractometer CrystalsNumerous crystals are suitable for refractometry, and aset of readily available crystals is desirable. An idealrefractometer is uniaxial, transparent over a wide rangeof wavelengths, optically well characterized for the regionof 365-1100 nm, and thermally and chemically stable forthe operating conditions. The crystal should be suffi-ciently birefringent to bracket the lowest and the highestrefractive-index values of the sample crystals being in-vestigated. If the sample crystal is an unknown, theprobability that a reference crystal covers the range ofrefractive indices increases with increasing birefringence.A set of uniaxial crystals, spanning the range from 1.335to 1.908, is presented in Table 1, along with references touseful optical data for these materials.14- 9 Other crys-tals will serve satisfactorily if adequate dispersion dataare available or can be measured either by minimum

Table L Possible Reference Crystalsfor Spindle-Stage Refractometry

Compound ne no Reference

NaNO3a 1.335 1.585 14

KDP 1.471 1.513 15

CaCO3 1.486 1.658 16, 17

MgCO3 1.512 1.703 Appendix A

BaB 2 0 4 1.553 1.670 18

ZnCO3a 1.621 1.849 11

LiUO3 1.754 1.908 19

a Optical data were available for only a limited range of visible wave-lengths.


deviation or by some other high-precision technique.Materials with lower birefringence will work as referencecrystals, and in fact these crystals offer the advantageof decreased angular sensitivity and hence more pre-cise refractive-index determinations (see Subsection 3.B).Although optically uniaxial crystals are preferred, biax-ial crystals may be utilized if they are orthorhombic insymmetry or if no significant dispersion of the principaloptical directions occurs.

C. OilsAlthough the measurable range of refractive indices islimited by the availability of refractometer crystals, inpractice the limiting factor is more often the availabilityof suitable fluids. Index-matching fluids are particularlyvolatile and have low viscosity at refractive indices of 1.4or less. On the other hand, fluid compositions that arecorrosive to the optics and the crystals are a problem forliquids with refractive indices greater than -1.8. Basedon experience with the commercially available sets of oils,we note that refractive indices between approximately 1.3and 1.8 are accessible for measurement by oil immersiontechniques.

The spectroscopic properties of the fluids must be con-sidered for measurement at nonvisible wavelengths. Ab-sorption was investigated for a selection of oils fromCargille Laboratories'2 0 standard index-matching fluidsets. Their absorbances were determined in a 1-cm path-length cell on a Perkin-Elmer Lambda 9 spectrophotome-ter. The findings reveal that fluids with a refractiveindex of -1.6 and higher absorb UV and short-wavelengthvisible light to a significant degree. Furthermore, theoils fluoresce at these short wavelengths of light, emit-ting a visible blue light. The fluorescence may be at-tributed to organic components and fortunately appearsto be insufficient to compete with the impinging wave-length of light. In the near IR, small absorption peaksare observed near 850-880 nm and near 1080 nm formany of the oils. The small, near-IR absorption peaks,most likely weak overtones of molecular vibrations inthe IR, have not been found to interfere with measure-ments. In fact, with adequate illumination, sufficienttransmission is produced through the 2-mm path lengthof the oil cell for measurements between 365 and 1100 nmfrom Cargille Laboratories' refractive-index liquids be-tween approximately 1.3 and 1.7. The higher-refractive-index fluids may also be used but are restricted to themidvisible and longer wavelengths.

3. ACCURACY OF SPINDLE-STAGEREFRACTOMETRY

The sources of error for the traditional oil immersionmethods arise predominantly from uncertainties in thefluid's optical properties. This is a moot issue when oneis measuring the refractive index of the oil in situ on thespindle-stage refractometer, yet a number of other sourcesof error remain. The most severe uncertainties can arisefrom ambiguities in the match determination that resultfrom sample morphology. Fortunately a simple screen-ing test to eliminate grains that have this problem canbe utilized. Next in importance are uncertainties in theangle of the refractometer crystal and in determining the

incident wavelength of light. These too can be reducedby specific measures. Less important is the uncertaintyin crystal orientation of the sample and, finally, in thesample temperature. In this section contributions to theerrors are discussed in more detail, and an experimentalstudy of the accuracy of these methods is reviewed.

A. Match Criteria and Grain MorphologyThe error that is introduced as a result of the match cri-terion can be quite significant. Refractive-index matchesare twice judged: once between the sample crystal andthe surrounding oil and once for the oil with the immersedrefractometer crystal. To minimize errors in judging arefractive-index match with the refractometer crystals,grains were all ground to be approximately spherical withdiameters between 100 and 200 pum. The sphere sur-faces were then chemically etched with an appropriatesolvent to reduce scattering sites. The spherical grindingreduces the refraction of the light rays by eliminating theangular edges so that more sensitive matches may be de-termined. In contrast, the sample crystal is not treated,and its morphology can still lead to uncertainty in matchidentification. Using the Becke lines match test, 5 someresearchers have reported6 ' 2 ' unfavorable grain shapesgiving false readings, and statements in the literaturesuggest that ideal Becke line conditions may exist for cer-tain grain morphologies. Alternative match criteria toBecke lines may be less sensitive to grain morphologies,for example, oblique illumination, double diaphragm, andphase contrast,21 but are not necessarily more accurate orwithout their own potential difficulties.

In this investigation, ambiguous index matches havebeen observed from irregular-shaped glass grains im-mersed at match conditions. An isotropic fragment ro-tated on the spindle axis may reveal certain orientationsfor which matches with the fluid are not observable or areerroneous. For the high dispersion of the blue spectralregion, these errors can be particularly significant. Mostcrystals of interest to mineralogists and materials scien-tists are optically anisotropic; thus a fragmented grain isunlikely to have an ideal morphology for each orientationrequired for measurement of a principal vibration direc-tion. Nonetheless, a useful test for eliminating grainsthat have poor morphologies can be performed. An ori-ented grain can be observed under any set of near-matchimmersion conditions, and the oil can be heated throughthe apparent match temperature. A well-defined tem-perature match should be observed if the grain is suit-able. If no distinct match can be cited through a rangeof temperatures that is adequate for observation of thereversal of Becke line movement, the grain should be re-jected. In practice, only a small fraction of single crystalmounts is rejected.

B. 0, Orientation of the Refractometer CrystalErrors result from misorientation of the refractometercrystals and are greatest near a match angle of = 450.This is because angular sensitivity of the refractive in-dex, dn/dO, increases as the angle to a principal vibra-tion direction increases. The effect is greater in crystalswith higher birefringence. Thus the angular sensitivi-ties of sodium nitrate and KDP, for example (Table 1), willbe dramatically different. To minimize errors resulting

Laura D. DeLoach

1190 J. Opt. Soc. Am. B/Vol. 11, No. 7/July 1994

from the measure of 0, the basis for selecting a refrac-tometer crystal would be to choose the least birefringentstandard that suits the need.

The refractometer crystal is rotated through 3600, anda match is observed for four unique settings of the refrac-tometer spindle axis. The difference between the anglesdetermined from the four values will approximately de-termine the precision of these angular readings. Withthe setup currently described, the routine precision of 0 m

is better than ±7 arcmin. This angular uncertainty cor-responds to a maximum refractive-index uncertainty atA ' 405 nm of ±0.0004 for the carbonates (CaCO3 andMgCO3) and ±0.0006 for NaNO3. It is possible to readthe spindle-stage barrel to ±5 arcmin with the CharlesSupper2 spindle stages currently in use.

C. A, Wavelength of MatchThere are two distinct effects associated with the finitebandpass of a filter that contribute to errors in calculat-ing n. The spectrum of the light passed by a filter has acharacteristic central wavelength and a spectral width.For a graded interference filter, an uncertainty in thecentral wavelength as large as ±5 nm can result. Thecentral wavelength transmitted by a narrow-bandpass fil-ter, however, can be ascertained with very high accuracy,±1 nm. Of course, transmission through both types offilter depends on the spectral distribution of the lightsource. The spectral width of the light transmitted byboth the wedge and the narrow-bandpass filters, approxi-mately 10 nm, could also lead to uncertainties by makingit more difficult to distinguish a good match in a given oil.Both these issues are significant in the UV, in which thedispersion is high but can be effectively neglected at thevisible and the near-IR regions. To minimize these er-rors at short wavelengths, a high-pressure Hg arc lampwith sharp spectral lines in the UV-visible regions wasemployed. Appropriate bandpass filters were chosen forfurther reduction of the background light near these se-lected lines.

D. Sample Orientation and TemperatureThe spindle-stage refractometer is subject to random er-rors from two main sources: (1) misorientation of thesample crystal and (2) the sample temperature. Theuncertainty arising from misorientations of the samplecrystal is generally insignificant with respect to therefractive-index determination because crystals are al-ways approximately oriented for measurement along aprincipal vibration direction. These are the least an-gularly sensitive directions in anisotropic crystals. Asreported by Bloss,6 even for highly birefringent crystalsorientation errors of a couple of degrees may result in dif-ferences within 0.0002 of the principal refractive index.

The match temperature is important to the extent thatthe crystal has a high dn/dT. Experimental tempera-tures for these studies were maintained between 20 and35°C, as determined from a thermocouple mounted inproximity to the crystals submersed in oil. Tempera-tures were monitored only to ensure stability during mea-suromont and to maintain them near room temperature,for which the standard's refractive indices have gener-ally been reported. The typical temperature coefficientscited for oxide and fluoride crystals are of the order of

10- 10-5 i C-' and therefore suggest that measurementsover a wider range of temperatures would be affecting therefractive indices of both the refractometer crystals andthe sample crystal.

The sources of error investigated during this study re-veal that the uncertainty of the rotation angle 0 for therefractometer crystal is the most significant. This con-tribution to the calculated index of refraction is ±0.0004but depends on the choice of refractometer crystal and, tosome extent, on the wavelength of light. For this level ofaccuracy to be attained over the range of 365-1100 nm,however, the wavelength uncertainties in the blue mustbe minimized, the temperature must be maintained be-tween 20 and 35 0C, and the grain's morphology must besuitable for the index-matching criterion. A summary ofthe sources of error and their magnitudes is presented inTable 2.

E. Experimental Determination of AccuracyTo confirm the experimental accuracy attainable byspindle-stage refractometry, measurements of someknown glasses and crystals were completed over the rangeof wavelengths of interest. In most cases refractive in-dices were determined between 365 and 1050 nm for sixto eight discrete wavelengths and were then least-squaresfitted to the Sellmeier dispersion equation

(2)n =A+ A+C + DA2,

where A is the wavelength in micrometers and n is theprincipal refractive index of interest. This particularSellmeier form has been found to provide a reasonable fitto the dispersion characteristics of transparent solids be-tween their UV and IR absorption bands. The equationsgenerated from the spindle-stage data typically reproducethe measured values to better than n ± 0.0003.

Refractive-index values of the known materials investi-gated are presented in Table 3 and include optical glassesavailable from the Cargille Laboratories' reference set2 0

and optical crystals previously studied in the labora-tory. In all the cases the optical properties are known by

Table 2. Sources of Error in Spindle-StageRefractometry

Maximum EstimatedSource of Error An Comments

Grain morphology Significant Eliminate unsuitablegrains withtemperature-matchtest

Rotation angle (30) < ±0.0004 Use crystal withof refractometer lowest adequatecrystal birefringence to

reduce angularsensitivity

Wavelength An = (dn/dA)3A Use line sourcesuncertainty (3A) ±0.001 (UV) and/or narrow-

±0.0001 (IR) bandpass filtersin the near UV

Angular ±0.0001 ±2' Orientationuncertainty of acceptablesample crystal

Laura D. DeLoach


Table 3. Comparison of Refractive Indices Measured for Several Solids by Different MethodsaA (nm)

Solid Methodb 365.5 404.7 487.2 546.1 647.6 750.0 850.0 1050.0

Cargille glass 1.51c S.S. 1.5239 1.5155 1.5120 1.5083Co. 1.5234 1.5157 1.5120 1.5079



LiBO3 (n = /3) S.S. 1.6252 1.6184 1.6095 1.6056 1.6010 1.5978 1.5953 1.5912M.D. 1.6251 1.6181 1.6096 1.6056 1.6008 1.5875 1.5950 1.5911

BaB2 04 (n = E) S.S. 1.5754 1.5690 1.5587 1.5544 1.5499 1.5473 1.5456M.D. 1.5750 1.5686 1.5587 1.5547 1.5502 1.5475 1.5455

Deuterated L-Arginine phosphate S.S. 1.5894 1.5835 1.5771 1.5731 1.5702 1.5659(n = y) M.D. 1.5893 1.5835 1.5770 1.5728 1.5699 1.5658

'All wavelengths were not available for all solids at the time of this study.bMethod: S.S., spindle stage; Co., company supplied; M.D., minimum deviation.c Cargille glasses: supplied refractive-index data are limited to the visible region between 435.8 and 656.3 nm.

Table 4. Sellmeier Coefficients [Eq. (2)] Determined from Refractive-Index Data of NewNonlinear-Optical Crystalsa

Compund n A B C D

L-Arginine chloride monohydrate a 2.35693 0.01673 -0.01375 -0.00553/3 2.56983 0.02473 -0.00761 -0.00570y 2.64700 0.02357 -0.01656 -0.01459

L-Arginine bromide monohydrate a 2.42018 0.01712 -0.02117 -0.01294,B 2.60613 0.03251 0.00318 0.00518y 2.68036 0.02281 -0.03029 -0.01299

L-Arginine fluoride a 2.21633 0.01445 -0.00972 -0.01098,B 2.41384 0.01425 -0.03726 -0.02328y 2.48299 0.01868 -0.01612 -0.01855

L-Arginine acetate a 2.31685 0.01606 -0.02124 -0.01105/3 2.35076 0.01555 -0.02464 -0.01214y 2.45789 0.01824 -0.02463 -0.01347

L-Arginine diarsenate a 2.35711 0.01426 -0.01995 -0.01861/3 2.45055 0.01487 -0.02927 -0.01912y 2.53786 0.02245 -0.01068 -0.01564

K2La(NO3)5 2H2 0 a 2.20094 0.01426 -0.03134 -0.00618/3 2.31901 0.02001 -0.02474 -0.00586y 2.38504 0.02085 -0.02694 -0.00873

K2Ce(NO3)5 . 2H 20 a 2.21109 0.01410 -0.03458 -0.00639/ 2.33882 0.01934 -0.03335 -0.00793y 2.40514 0.01941 -0.03715 -0.01357

aRefractive-index data are tabulated in Appendix B.

use of high-accuracy methods. The crystals are samplesfor which n is known to ±5 X 10-5 from minimum-deviation spectrometry over the range of 365-1200 nm.The glasses also have refractive indices known to ±5 i0-5, although the actual data are restricted to wave-lengths between 435.8 and 656.3 nm. The spindle-stagerefractometer was used to obtain the refractive indices ofglasses at four wavelengths from 404.7 and 647.6 nm. Asingle principal vibration direction was arbitrarily chosenfor study among the optical crystals, and the full extendedrange of wavelengths was utilized.

The refractometer crystal employed in each instanceis the calcite sample, and therefore a maximum un-certainty of ±0.0004 is expected per data point. Therefractive indices measured with spindle-stage refrac-tometry and minimum-deviation spectrometry are bothtabulated, and the agreement is within the expected error

bars in almost every case. The exceptions are the opticalglasses at 404.7 nm, for which the measured refractiveindex was compared with an extrapolated value. It wassuggested23 that uncertainties of n ± 0.0005 would beexpected for extrapolated values calculated from their re-ported Cauchy dispersion equations, and this factor mayexplain the discrepancy.

4. EXPERIMENTAL STUDIES OF NEWFREQUENCY-CONVERSION CRYSTALSThe spindle-stage refractometer described in this paperwas used extensively to study new crystals that are po-tentially useful as optical harmonic generators. It haslong been understood that efficient harmonic generationin crystals requires that the PM velocities of the funda-mental and the harmonic waves in the crystal be equal.

Laura D. DeLoach


This condition of PM can be achieved in birefringent crys-tals when the fundamental and the harmonic waves travelwith different polarizations. The crystal orientations forwhich the PM conditions are met may be calculated ifaccurate refractive-index values for each of the wave-lengths of interacting optical waves are known.2 4 Forthe Nd:YAG laser, for example, the sum-frequency gen-eration of the second and the third harmonics requiresrefractive-index data at 1064.2, 532.6, and 354.7 nm.

In the course of these studies the dispersion of severalnew nonlinear crystals, most of which are biaxial, wasmeasured for wavelengths between 1050 and 365 nm,nearly the full range between the fundamental and thethird harmonic of Nd:YAG. Table 4 reports Sellmeier co-

efficients for seven of these crystals; Appendix B gives therefractive-index data from which these fits were obtained.These determinations were carried out on samples whosecrystal sizes were between 50 and 200 am. These crys-tals were subsequently grown to sizes sufficient to havetheir PM angles directly measured according to thetechniques described in Ref. 25. A comparison of thesedirectly measured PM angles and the predicted angles ob-tained from the Sellmeier equations should thus providea means of assessing the accuracy of our refractive-indexdata.

A summary of PM angles is presented in Table 5 asa means of demonstrating the advantages of spindle-stage refractometry in the study of new nonlinear-optical

Table 5. Comparison of Measured and Calculated PM Angles (0) in New Nonlinear-Optical Crystals

Compound Processa Plane Omeas Opred Axis/Locusb

- 9 M m av 43.5 41.3 a (B)

2w(II)

3w(I)

3w(II)

L-Arginine bromide monohydrate 2w(I)

2w(II)

3U(I)

3w(II)

L-Arginine fluoride 2@(I)

2w(II)

3w(I)

3w(II)

L-Arginine acetate 2X(I)

2cw(II)

3w(I)

K2La(NO3)5 2H 2 0' 2w(I)

2w(II)

3X(I)

3&o(II)

K2 Ce(NO3)5 2H20C 2w(I)

2w(II)

a/3aya/3aya,3aya,8aya/3

aya/3

aya/3

aya/3

ayayaya/3aya/3aya/3

ay

a/3

a,/3a/3a/3a,6aya/3

ay

Af'

aya'3aya/3ay

Aas

a/3a,)'

3.853.832.4

40.221.553.640.852.539.465.254.414.046.056.828.654.726.564.641.154.327.5

60.1

51.30.8

70.239.672.142.668.540.450.920.268.540.4

9.052.732.351.330.061.342.640.221.554.240.853.039.565.753.312.444.656.528.453.025.762.939.853.528.723.960.54.9

57.752.0

4.069.839.971.641.767.741.050.721.867.741.0

a (B)

a (B)

a (B)

a (B)

a (B)

a (B)

a (B)

a (A)

a (B)

a (B)

a (B)

y (B)

aaa7a

(C)

(C)

(B)

a (B)

a (B)

a (C)

a (B)

a (B)

a Process: 2 = second-harmonic generation; 3w = third-harmonic generation; and types I and II refer to the mixing schemes, where type I refers to

the case i wllih two input waves travel polarized along a slow vibration direction and the resultant wave travels polarized along a fast vibration direction

(S + S - F) and type II refers to the case in which two input waves travel polarized along a slow and a fast vibration direction and the resultant wave

travels polarized along a fast vibration direction. For mixed input frequencies, the higher-energy input wave is the slow polarized wave (F + S - F).

b Axis is the reference direction from which 0 is measured in the reported plane. The (A), (B), and (C) loci correspond to Fig. 3.

c Ref 26.

\.,J-tiXglinjau tanuil..


(A) l l(or c)

(B) y r(or a)

(C) v--t-xl-t- l----1 } (ora)

. I

Fig. 3. Three stereonets depicting different PM curve topolo-gies. The stereonet is drawn with reference directions cor-responding to a biaxial crystal's dielectric axes, a , and .The equatorial plane corresponds to the crystal's optic plane,containing the two optic axes shown emerging at the x locationsand with the acute bisectrix a (or y) at the origin and the obtusebisectrix y (or a) at the perimeter. The optic normal ,G is 90°away at the poles. The PM curves are continuous equivibrationdirections. These loci geometries (A, B and C) can be used inconjunction with the PM information in Table 5 to evaluate thecurves. Angles reported in the optic plane (a, y) are measuredfrom the acute bisectrix, and angles reported in one of the othertwo principal planes are measured from their indicated axes.

crystals. Here materials for which PM-angle determina-tions were made both directly and by calculations fromrefractive-index data are listed with their allowable PM

processes. The angles are reported for the principal op-tic planes and according to the conventions sketched inFig. 3. In Fig. 3, generic PM curves are represented onstereographic projections, with the reference dielectricaxes emerging at the three possible locations indicated.The PM curve is a locus of points defined by the contin-uous equivibration curve that connects all the PM orien-tations together where they intersect with the plane ofthe stereonet. Three types of loci are drawn in Fig. 3to demonstrate how the PM angles given in Table 5 arereferenced to the reported axes. Each stereonet is ori-ented with the optic plane (ay) normal to the page andthe trace of which marks the equatorial plane of the stere-onet. The acute bisectrix is at the origin, and the ob-tuse bisectrix is 900 away at the perimeter. Optic axesare represented by an X where they would emerge in theplane of the stereonet. The PM processes that are consid-ered include the two possible second-harmonic-generation(SHG) schemes and the three possible third-harmonic-generation (THG) schemes. These processes are definedaccording to whether the input waves travel with thesame polarization (type I) or with different polarizations(types II and III).

The results given in Table 5 confirm that the accura-cies with which refractive indices are determined withthe spindle-stage refractometer are sufficient to predictPM angles in nonlinear crystals. In particular, phase-matched orientations for SHG from Nd:YAG are deter-mined with an accuracy of ±2°, and for THG agreementis usually better than ±5°. The greater uncertainty inthe PM angle for THG results from the need to extrapo-late the dispersion curves to 354.7 nm. On the otherhand, for cases in which the angle differences are signif-icantly greater, for example, KLN 2(I) and LAC 2(I),the error in the predicted angle results from the extremesensitivity of the PM calculation for propagation along ornear a principal dielectric axis (a condition known as non-critical PM). In this case the experimental uncertaintiesin the refractive indices of - 4 10-4 are sufficient toexplain the observed discrepancy.

5. CONCLUSIONSAccurate optical properties can be obtained from smallcrystalline samples with the spindle-stage refractome-ter designed for extended-wavelength studies. The in-strument attaches to a polarizing light microscope andis suitable for the study of grains 50-200 m in size.Refractive indices can be determined with an accuracyof ±0.0004 for wavelengths between 365 and 1100 nm.The extended spectral range and the high level of ac-curacy are expected to have diverse applications in theresearch of new optical materials. One application innew materials has been admirably demonstrated. Dis-persion data obtained from the spindle-stage refractome-terare sufficiently accurate over the required wavelengthregions to predict less readily attainable PM orientationsin nonlinear-optical crystals. In particular, for frequencydoubling of light in the IR (e.g., Nd:YAG), PM angles maygenerally be calculated within ±2°. For frequency mix-ing of light to blue or near-UV wavelengths, the PM anglemay be calculated within ±5°.

Laura D. DeLoach


Table 6. Refractive Indices of MgCO3Measured by Minimum Deviation at 25°C

A (nm) ne no

1130 1.50629 1.68526

1064 1.50673 1.68665900 1.50722 1.68805

800 1.50809 1.69051700 1.51073 1.69718600 1.51297 1.70254

565 1.51404 1.70483532 1.51523 1.70760500 1.51663 1.71081

450 1.51943 1.71722400 1.52342 -

365 1.52730 1.73561

Table 7. Sellmeier Coefficients [Eq. (2)]for MgCO3 Data Given in Table 6

n A B C D

ne 2.267040 0.0081835 -0.0093924 -0.0036005no 2.849137 0.0191492 -0.0176812 -0.0190330

APPENDIX A

The crystal of magnesite, MgCO3, which is listed inTable 1, was characterized for the specific purpose ofproviding a new standard for reference research. TheBrazilian magnesite (catalog NMNH# 103615-3), waskindly provided by the Smithsonian Institution's Divisionof Mineral Sciences, and, to my knowledge, this is the firstknown report of detailed optical properties on the mate-rial. Table 6 lists the refractive indices measured on a1-cm prism cut from a large single crystal. The indiceswere determined by minimum-deviation measurementson a prism spectroscope equipped for studies between365 and 1100 nm. The refractive indices measured at acontrolled room temperature of 25°C are determined tohave an accuracy of ±0.00005 for the instrument and themethods utilized. These data were least-squares fitted tothe Sellmeier dispersion equation to yield the coefficientspresented in Table 7. The obtained fitting accuracy is±0.00001, which is much better than the experimentalaccuracy.

Table 8. Refractive Indices Measured by Spindle-Stage Refractometry for New Nonlinear-Optical Crystalsn

Compound A (Ium) a /3 Y

L-Arginine chloride monohydrate

L-Arginine bromide monohydrate

L-Arginine fluoride

L-Arginine acetate

0.36500.40050.48720.54610.64760.75000.85001.0500

0.36500.40050.48720.54610.64760.75000.85000.95001.0088

0.40050.48720.54610.64760.75000.85000.95001.0088

0.36500.40050.48720.54610.64760.75000.8500

0.95001.0500

1.6631

1.63601.62851.62141.61581.61241.6082

1.58001.57151.55901.55411.54731.54431.54171.5382

1.60501.59431.58031.57391.56741.56411.56061.55821.5568

1.52001.50921.50431.49881.49551.49311.49071.4898

1.56811.55851.54561.53921.53351.53051.5266

1.52491.5227

1.67501.65611.64801.63841.63291.6296

1.6257

1.58931.57441.56931.56231.55811.55511.55201.5508

1.57881.56921.55601.55081.54411.54041.53761.63541.5336

1.68761.67531.65881.65141.64271.63751.63411.6287

1.68931.66931.6621

1.64811.6441

1.6403

1.61531.60141.59461.58751.58351.57981.57801.5750

1.61991.60951.59321.58811.58111.57621.57261.57001.5689

(Table Continued)


Table 8. Continued

nCompound A (m) a /3 y

L-Arginine diarsenate 0.3650 1.5749 1.6098 1.64910.4005 1.5672 1.6000 1.63830.4872 1.5551 1.5868 1.62290.5461 1.5499 1.5813 1.61610.6476 1.5444 - 1.60820.7500 1.5405 1.5709 1.60260.8500 1.5376 1.5675 1.59980.9500 1.5350 1.5656 1.59631.0500 1.5329 1.5631 1.5942

K2 La(NO3)5 2H 2 0 0.3650 1.5297 1.5820 1.60630.4005 1.5201 1.5702 1.59360.4872 1.5062 1.5530 1.57560.5461 1.5008 1.5460 1.56820.6476 1.4950 1.5387 1.56010.7500 1.4915 1.5341 1.55560.8500 1.4891 1.5306 1.55180.9500 1.4872 1.5285 1.54961.0500 1.4857 1.5269 1.5475

K2 Ce(NO3) 5 * 2H 2 0 0.3650 1.5340 1.5912 1.61420.4005 1.5238 1.5775 1.59990.4872 1.5098 1.5597 1.58110.5461 1.5041 1.5524 1.57320.6476 1.4983 1.5443 1.56530.7500 1.4947 1.5398 1.56030.8500 1.4924 1.5365 1.55670.9500 1.4905 1.5343 1.55421.0500 1.4890 1.5324 1.5519

APPENDIX B

The Sellmeier coefficients presented in Table 4 andutilized for calculating refractive indices according toEq. (2) are derived from a nonlinear least-squares fitof refractive-index data obtained with the spindle-stagerefractometer. The refractive indices measured for thenonlinear-optical crystals are given in Table 8.

ACKNOWLEDGMENTS

The author thanks David Eimerl, group leader of theNonlinear Optical Materials Group at Lawrence Liver-more National Laboratory, for providing the opportunityand the time to develop the spindle-stage refractome-ter and technique. Other members of the group whowere instrumental include Victor Sperry, who machinedand fabricated the parts; Steve Velsko, who made pos-sible the small-crystal phase-matching measurementsand who provided useful advice in the preparation ofthis manuscript; Mark Webb, who made many of thephase-matching measurements; and Francis Wang andChris Ebbers, who grew crystals of the nonlinear-opticalmaterials reported. Finally, the author is indebted toF. Donald Bloss of Virginia Polytechnic Institute andState University, Blacksburg, Virginia, for his role inadvancing crystal optics and light microscopy education.This research was performed under the auspices of theU.S. Department of Energy by Lawrence Livermore Na-tional Laboratory under contract W-7405-ENG-48.

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8. R. S. Longhurst, Geometrical and Physical Optics, 3rd ed.(Longman, New York, 1973), p. 89.

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Laura D. DeLoach

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16. F. A. Jenkins and H. E. White, Fundamentals of Optics(McGraw-Hill, New York, 1976).

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19. S. Umegaki, S. I. Tanaka, T. Uchiyama, and S. Yabumoto,"Refractive indices of lithium iodate between 0.4 and2.2 /im," Opt. Commun. 3, 244-245 (1971).

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Laura D. DeLoach

22. Charles Supper Company, Inc., 15 Tech Circle, Natick, Mass.01760-1026.

23. Bob Sacher, R. P. Cargille Laboratories, Cedar Grove, N.J.07009 (personal communication, 1990).

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26. C. A. Ebbers, L. D. DeLoach, M. Webb, D. Eimerl, S. P.Velsko, and D. Keszler, "Nonlinear optical properties ofK2La(NO3)s 2H20 and K2Ce(NO3)5s 2H2 0," IEEE J.Quantum Electron. 29, 497-507 (1993).

microscopic single-crystal refractometry as a function of wavelength

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