Nonlinear polarizability of alphaiodic acidG. R. Crane Citation: The Journal of Chemical Physics 62, 3571 (1975); doi: 10.1063/1.430950 View online: http://dx.doi.org/10.1063/1.430950 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/62/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Nonlinear electrophoresis of ideally polarizable particles Phys. Fluids 26, 102002 (2014); 10.1063/1.4897262 Nonlinear piezoelectricity and electrostriction of alpha quartz J. Appl. Phys. 60, 1465 (1986); 10.1063/1.337787 ALPHAIODIC ACID: A SOLUTIONGROWN CRYSTAL WITH A HIGH FIGURE OF MERIT FOR ACOUSTOOPTIC DEVICE APPLICATIONS Appl. Phys. Lett. 13, 156 (1968); 10.1063/1.1652551 ALPHAIODIC ACID: A SOLUTIONGROWN CRYSTAL FOR NONLINEAR OPTICAL STUDIES ANDAPPLICATIONS Appl. Phys. Lett. 12, 186 (1968); 10.1063/1.1651945 Zeeman Effect on the Quadrupole Spectrum of Iodic Acid J. Chem. Phys. 26, 351 (1957); 10.1063/1.1743297

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Nonlinear polarizability of alpha-iodic acid G. R. Crane

Bell Telephone Laboratories. Incorporated. Holmdel. New Jersey 07733 (Received 13 January 1975)

The nonlinear optical coefficient d \4 of HI03 has been remeasured by the wedge technique. The new value d r~o, = 13.1 ± I d ~fP substantially agrees with values previously determined via phase matched experiments. A probable reason for failure of a simple bond polarizability scheme to predict this coefficient is discussed.

INTRODUCTION

Recent papers1•2 have successfully predicted the non­linear optical coefficients of several iodate compounds by use of a bond additivity model. With the exception of d14 for HI03 , the observed and calculated values agree within one standard deviation. The apparent misfit for this one coefficient (about three standard deviations) could be attributed to either inaccurate measurements or additional interactions not present in the other iodates. This paper reports an additional measurement of du for" HIOs which eliminates the former possibility. A Simple argument is given which shows that the latter possibility is indeed reasonable.

Previously reported values of 10.2 ± 1. 93 and 16 ± 44 (times d36 for KH2 P04 (KDP)] were obtained by phase matched second harmonic generation measurements. The present investigation was carried out using the wedge technique. 5,6

EXPERIMENTAL

A wedge of angle (J = 2 0 was made as shown in Figure 10 The second harmonic signal was then measured as shown in Fig. 2. The measured coherence length 114 was 3. 15 /-Lm in close agreement with the value 3.16 cal­culated from the known indices of refraction. 4 The ob­served signal was compared with the second harmonic signals from dll of a-quartz and dss of lithium iodate. Since corrections for absorption were negligible for these materials, the coefficient dHl40s was calculated from6

(1)

where SUbscript A refers to HIOs and B refers to the ref­erence material (a - Si02 or LiIOs), P is the peak power at 2w, I is the coherence length, nlA and n2A are the in­dices of refraction for material A at wand 2w, respec­tively. C(r/) is the wedge correction factorS given by

(2)

where 1J=w tan(e/I) and w is the laser beam width (38 /-Lm in this case). For these measurements, C{1j) was es­sentially unity for a - 8102 and LilOs• For H10s. C(1J) calculated from (2) was 0.92 in close agreement with the observed value of

C( )H10S _ P JDIiI (Zw) TJ abe -P (2w)+P (Zw)

IDIl% mtn (3)

The Journal of Chemical Physics, Vol. 62, No.9, 1 May 1975

The experimental results were

and

dnIOS = (1. 08 ± O.1)d~~I03

This pair of determinations then gives a ratio

dhuos / drl-SlO2 = 14. 9 ± O. 5

in agreement with previous measurements. 7 Taking the known ratios of these two coefficients to dFsPand averag­ing, a best value of

d~!03 = (13.1 ± l)d~P

is obtained.

DISCUSSION

The bond additivity model applied to the iodates de­scribes the observed nonlinearities in terms of the io­dine-oxygen interactions. 1 Specifically, "bonds" with lengths approximately 1. 9 and 2.9 A and the lone pair of electrons each are assumed to have second order polar­izability tensors with two independent elements, f3" and {3J., respectively. 1 The macroscopic polarizability of the crystal is derived from the bond polarizabilities by the relation

(4)

or in expanded form,

where the sum is over bonds, s, with direction cosines .a, V is the volume of the unit cell, and 61J is the Kro­necker delta.

011

/Z

011

FIG. 1. Orientation of wedge used to measure d 14 for mo3•

Laser beam is along [0111. E'" is along (0111 and E 2w is along £.

Copyright © 1975 American Institute of PhYSics 3571

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3572 G. R. Crane: Nonlinear polarizability of alpha·iodic acid

TRANSLATION DIRECTION

LEr i FILrR

1'7+~-i~~~~~~C? LASER! CRYSTAL I DETECTOR

POLARIZER ANAL YZ ER

FIG. 2. Schematic of experimental setup.

For the particular coefficient d 14(=d12S ), only the quan­tity (30 = (311 - 3(31 contributes to the macroscopic polar­izability. Bergman and Crane l (BC) have shown that for LiIOs Ca(IOs)a' 6H20, and KIOaFa, (3"'?'.3(31 for the three interactions considered. If the same set of interactions are the principle source of nonlinearity in HIOs, then Eq. (5) predicts a small du for HIOs•

The large observed value of 13.1 xdfe>P indicates that some interaction peculiar to the HI03 molecule (as con­trasted to the 10; ion) contributes either directly or in­directly to the nonlinear polarizability -of crystaline HIOs' A direct contribution might be the nonlinear polar­izability of the O-H covalent bond. For this interaction to be the major part of d~los however is inconsistent with the observed nonlinear coefficient of KzH(IOs)zCl = KIOs • HIOs ' KCI) which are in good agreement with the values calculated using the polarizabilities of BC.

On the other hand, an indirect contribution might be the distortion of the 1-0 bonds and the lone pair due to the interaction with the O-H covalent bond and perhaps due also to the hydrogen bond joining adjacent molecules.

This could result in relatively small changes for /3"

and (31 for each 1-0 bond and for the lone pair. Since Eq. (5) gives dHl~03 as proportional to the difference be­tween two nearly equal numbers, the small changes in the polarizabilities of the bonds could cause an enormous change in d~lo3 without perhaps significantly changing to nonlinear coefficients of KzH(I03)2Cl. Unfortunately there is insufficient experimental data to really deter­mine the polarizability of the HI03 molecule so the so­lution of this problem must be deferred until more ma­terials (possibly the acid-alkali iodates) have been studied.

CONCLUSION

The previously reported values3•4 for dHl~03 are found

to be substantially correct. The most probable explana­tion for the poor fit for this coefficient in the bond ad­divitity scheme is the difference between the HI03 mol­ecule and the 10; ion.

ACKNOWLEDGMENTS

The author is deeply indebted to his colleagues J. G. Bergman, J. H. McFee, and B. C. Tofield for their advice and encouragement in preparation of this paper.

lJ. G. Bergman and G. R. Crane, Chern. Phys. 60, 2470 (1974). 2B . C. Tofield, G. R. Crane, and J. G. Bergman, J. Chem.

Soc., Faraday Trans. II 70, 1488 (1974). 3 J. E. Bjorkholm, IEEE J. Quant. Electron QE4, 970 (1968);

aad QE5, 260 (1969).

4S. K. Kurtz, T. T. Perry, and J. G. Bergman, Appl. Phys. Lett. 12, 186 (1968).

5J . J. Wynne and N. Bloembergen, Phys. Rev. 188, 1211 (1969).

6G . D. Boyd, H. Kasper, and J. H. McFee, IEEE J. Quant. Electron. QE7, 563 (1971).

7J. Jerphagnon, Appl. Phys. Lett. 16, 298 (1970).

J. Chern. Phys., Vol. 62, No.9, 1 May 1975

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