Lithium Niobate (LiNbO3)

Lithium Niobate (LiNbO.) EDWARD D, PALIK Naval Research Laboratory Washington, D.C.

Lithium niobate is a uniaxial, trigonal crystal useful for second-harmonicgeneration applications of laser radiation. Index matching at co and 209 in the near IR-visible region is accomplished by temperature tuning of the ordinary (o) refractive index no(CO)(E 2_c axis) and the extraordinary (e) refractive index ne(2CO)(E II c axis). Two types of material are considered stoichiometric and congruent. A mole ratio of LizO/(LiO 2 + Nb2Os) = 0.500 corresponds to stoichiometric material. This is grown from a melt containing excess Li. A congruently melting composition crystal grows from a melt of the s a m e composition, corresponding to a mole ration of Li20/(LiO 2 + Nb2Os)= 0.486. This material is used in most applications. The UV data are taken from the reflection data of Wiesendanger and Giintherodt [1] obtained at 293 K on cleaved surfaces; stoichiometry was not specified. Kramers-Kronig (KK) analyses for both polarizations (Ell and 2_ to the c axis) were performed. Above ~ 7 eV, the difference in Rii and R• is negligible. An analysis by Barner et al. I-2] from 4 to 14.5 eV with unpolarized light and their subsequent KK analysis is not used here because of the large differences with Wiesendanger and Giintherodt [1]. It is not obvious that n, k (unpolarized) are indeed averages of no, ne and ko, k~. Since no,e and ko,e were calculated from values of el and e2 as read from a graph, the numbers are probably good to two figures, although three figures are listed in Table VII. Table VII is plotted in Fig. 7 for both o and e rays. The absorption edge of congruent material has been studied by Redfield and Burke [-3] over a wide temperature range. A series of samples were mechanically polished. This produced spurious absorption in the smallabsorption region when compared to the transmission of the next thicker sample. The c axis was in the plane of the sample, so that dichroism might be measured. However, very little difference was observed, so that only E 11c data are given. The tabulated data are for 300 K. The refractive index in the transparent region has been measured for various materials, MgO doped [4], stoichiometric [5], and congruent [6]. Generally, the minimum-deviation technique has been used with the optic axis 695 HANDBOOK OF OPTICAL CONSTANTS OF SOLIDS

ISBN 0-12-544420-6

696

Edward D. Palik

parallel to both faces of the prism. We tabulate the data from Boyd et al. [-5] and Nelson and Mikulyak [6]. Boyd et al. [5] do not state room temperature explicitly. Nelson and Mikulyak [6] used 24.5~ and state an accuracy of _ 0.0002. Differences in n in the two sets of data are due to the slight differences in stoichiometry in the two kinds of materials. In the infrared, the lattice vibration bands have been studied in reflection by Barker and Loudon [-7], Axe and O'Kane [-8], and Poplavko et al. [9]. The refractive indices at 300 K have been provided by Barker and Loudon [7] in the transparent region by analysis of reflectivity directly as R = (x/~ - 1)2/(x/~ + 1)2. Barker and Loudon [7] fit oscillator models through the data of Boyd et al. !-5] and through their own data by using one bandgap oscillator and eight lattice oscillators for E II c and one band-gap oscillator and five lattice oscillators for E _L c. Since the given numbers did not reproduce the long-wavelength values for no(A-) and no(ll) given in a graph by Barker and Loudon [-7-], we chose to read the given graph of experimental data directly. The results are tabulated from 5 to 11 #m. In Barker and Loudon [7], Axe and O'Kane [-8], and Poplavko [9], the reflectivity was measured and KK analyzed. As an example of the differences, the vibration mode near 150 cm-1 has an imaginary peak eo2 = 230, 158, and 200, respectively. We tabulate the data of Axe and O'Kane I-8] at longer wavelength because it is more complete. The samples were probably stoichiometric material polished with 0.05-#m alumina and etched with H F - H N O 3 until certain reflection features present in mechanically polished surfaces cleared up or became sharper. Reflectivity was measured with an aluminized reference surface. Temperature was not stated but was no doubt near 300 K. Dispersionrelation analysis yielded graphs of el and e2 that we read and then converted to n and k. While two decimal places are given, the numbers are probably good to the first significant figure. In the far infrared, Bosomworth [10] and Sakai [-11] have measured no and ne by utilizing channel spectra, and the former has also measured the absorption coefficient, all at 300 K. We tabulate the refractive indices of Sakai [11] because they cover a somewhat wider spectral range and are virtually identical to the value of Bosomworth [-10] (both read off graphs). We read the values from a smooth line put through the data points that scatter by +0.05. The extinction coefficients of Bosomworth [10] are tabulated for a Czochralski-grown sample polished with diamond grit. In the 60-cm-1 region, ko and k~ from the KK analysis [8] are much larger than measured in transmission [10], suggesting that dispersion-relation analysis is poor when n >> k.

Poplavko et al. [-9] found that no = 7.19, ko = 0.8 and ne = 5.48, k~ = 0.2 at 300/~m. These n values are significantly larger than those of Barker and Loudon [7] and Axe and O'Kane [8]; the k values are one to two orders of magnitude larger, which is troublesome. Permittivity measurements at

Lithium Niobate (LiNbO3)

697

3000 #m using a waveguide-resonance reflection method yielded el and tan 6 = ez/el; then no = 7.21, ko = 0.04 and ne = 5.66, ke = 0.01, but the variation in eo ~ from sample to sample was typically 52-48 due to differences in stoichiometry and structure defects in the crystals. Measurements of e~ and ~2 down to ~ 50 Hz with standard bridge and resonance measurements methods showed a piezoelectric resonance n e a r 1 0 6 - 1 0 7 Hz. In the frequency range 126-132 G H z (2380-2270/~m), Vinogradov et al. [ 12] determined no = 7.2 _+ 0.2 and tan 6 = (2.5 _+ 0.5) x 10 -3. This gave eo~ = 51.8, eo2 = 0.13, so that no = 7.20 and ko = 9 x 10-3. Again we see the large variation in the data of Barker and Loudon [7], Axe and O'Kane [8], Poplavko et al. [9], Bosomworth [10], and Sakai [11], which is probably sample dependent. REFERENCES

E. Wiesendanger and G. Giintherodt, Solid State Commun. 14, 303 (1974). K. Barner, R. Braunstein, and H. A. Weakliem, Phys. Stat. Solidi B 68, 525 (1975). D. Redfield and W. J. Burke, J. Appl. Phys. 45, 4566 (1974). G. D. Boyd, W. L. Bond, and H. L. Carter, J. Appl. Phys. 38, 1941 (1967). G.D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, and A. Savage, Appl. Phys. Lett. 5, 934 (1964). D. F. Nelson and R. M. Mikulyak, J. Appl. Phys. 45, 3688 (1974). A. S. Barker and R. Loudon, Phys. Rev. 158, 433 (1967). J. D. Axe and D. F. O'Kane, Appl. Phys. Lett. 9, 58 (1966). Y. M. Poplavko, V. V. Meriakri, V. N. Aleshechkin, V. G. Tsykalov, E. F. Ushatkin, and A. S. Knyazev, Soy. Phys. Solid State 15, 991 (1973); Y. M. Poplavko, V. V. Meriakri, V. N. Aleshechkin, V. G. Tsykalov, E. F. Ushatkin, and A. S. Knyazev, Fiz. Tverd. Tela. 15, 1473 (1973). 10. D. R. Bosomworth, Appl. Phys. Lett. 9, 330 (1966). 11. K. Sakai, Appl. Opt. 11, 2894 (1972). 12. P. N. Vinogradov, N. A. Prisova, and G. V. Kozlov, Soy. Phys. Solid State 12, 605 (1970); P. N. Vinogradov, N. A. Prisova, and G. V. Kozlov, Fiz. Tverd. Tela. 12, 781 (1970). 1. 2. 3. 4. 5. 6. 7. 8. 9.

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Lithium Niobate (LiNbO3)

699

TABLE VII Values of n and k for Lithium Niobate Obtained from Various References" eV

cm-1

,urn

10.0 9.75 9.5 9.25 9.0 8.75 8.5 8.25 8.0 7.5 7.0 6.5 6.0 5.75 5.5 5.25 5.0 4.75 4.5 4.25

80,650 78,640 76,620 74,610 72,590 70,570 68,560 66,540 64,520 60,490 56,460 52,430 48,390 46,380 44,360 42,340 40,330 38,310 36,290 34,280

0.1240 0.1272 0.1305 0.1340 0.1378 0.1417 0.1459 0.1503 O.1550 0.1653 O.1771 0.1907 0.2066 0.2156 0.2254 0.2362 0.2480 0.2610 0.2755 0.2917

4.2 4.15 4.1 4.05 4.0 3.95 3.9 3.85 3.8 3.75 3.7

33,880 33,470 33,070 32,670 32,260 31,860 31,460 31,050 30,650 30,250 29,840

0.2952 0.2988 0.3024 0.3061 0.3100 0.3139 O.3179 0.3220 0.3263 0.3306 0.3351

eV 3.0642 2.952 2.8447 2.755 2.6503 2.5831 2.480 2.4379 2.2705 2.254 2.1489 2.1415 2.1102

cm - ' 24,714 23,810 22,944 22,220 21,376 20,834 20,000 19,663 18,313 18,180 17,332 17,272 17,019

pm 0.40463 0.42 0.43584 0.45 0.46782 0.47999 0.50 0.50858 0.54607 0.55 0.57696 0.57897 0.58756

no(l) 1.67 [-1] 1.88 2.04 2.19 2.32 2.12 1.82 1.58 1.43 1.38 1.54 1.82 2.16 2.36 2.68 3.22 3.62 3.52 3.19 2.91

ko(-[-) 1.22 [1] 1.28 1.17 1.09 0.75 0.45 0.36 0.46 0.59 0.98 1.30 1.48 1.60 1.67 1.75 1.60 1.27 0.43 0.11 0.00

2.76

no(l)

ne(l) 1.73 [-1] 1.97 2.14 2.32 2.42 2.17 1.89 1.63 1.48 1.48 1.75 2.07 2.30 2.46 2.76 2.98 3.10 2.99 2.79 2.59

2.49

he(l)

2.4317 [6]

2.3260 [6]

2.3928

2.2932

2.3634 2.3541

2.2683 2.2605

2.3356 2.3165

2.2448 2.2285

2.3040 2.3032 2.3002

2.2178 2.2171 2.2147

no(_L)

go(I) 1.1811] 1.22 1.12 1.03 0.72 0.34 0.29 0.40 0.57 0.94 1.24 1.26 1.22 1.22 1.16 1.00 0.64 0.25 0.06 0.00 1.02 x 10-2 [3] 5.87 • 10- 3 3.09 1.71 x 10 -3 9.01 • 10 -4 4.19 2.12 • 10 -4 7.84 • 10-5 3.33 1.69 • 10-5 8.16 x I0 -6 5.07

,,o~11

2.4089 [5]

2.3025 [5]

2.3780

2.2772

2.3410

2.2457

2.3132

2.2237

(continued)

700

Edward D. Palik TABLE VII

(Continued)

Lithium Niobate

eV

cm- 1

2.066 1.9257 1.8566 1.771 1.7549 1.550 1.5321 1.4224 1.378 1.3251 1.2915 1.240 1.2227 1.1352 1.0745 1.0707 1.033 0.96284 0.8856 0.86103 0.7749 0.75683 0.6888 0.64871 0.6199 0.56762 0.5636 0.51662 0.5166 0.4769 0.47412 0.45410 0.4428 0.42793 0.4133 0.40631 0.3875 0.3647 0.3444 0.3263 0.3100

16,670 15,532 14,974 14,290 14,154 12,500 12,357 11,472 11,110 10,688 10,417 10,000 9,961.9 9,156.34 8,666.11 8,636.03 8,333 7,765.78 7,143 6,944.59 6,250 6,104.22 5,556 5,232.18 5,000 4,578.17 4,545 4,166.75 4,167 3,846 3,824.03 3,662.53 3,571 3,451.45 3,333 3,277.10 3,125 2,941 2,778 2,632 2,500

eV

cm- 1

0.2480 0.2066 0.1771 0.1550 0.1378 0.1240

2,000 1,667 1,429 1,250 1,111 1,000

um 0.60 0.64385 0.66782 0.70 0.70652 0.80 0.80926 0.87168 0.90 0.93564 0.95998 1.00 1.0140 1.09214 1.15392 1.15794 1.20 1.28770 1.40 1.43997 1.60 1.63821 1.80 1.91125 2.00 2.18428 2.20 2.39995 2.40 2,60 2.61504 2.73035 2.80 2.89733 3.00 3.05148 3.20 3.40 3.60 3.80 4.00 jum 5.0 6.0 7.0 8.0 9.0 10

.o(•

.o(11)

2.2835 2.2778

2.2002 2.1953

2.2699

2.1886

2.2541 2.2471

2.1749 2.1688

2.2412 2.2393

2.1639 2.1622

2.2351 2.2304 2.2271 2.2269

2.1584 2.1545 2.1517 2.1515

2.2211

2.1464

2.2151

2.1413

2.2083

2.1356

2.1994

2.1280

2.1912

2.1211

2.1840

2.1151

2.1765 2.1724

2.1087 2.1053

2.1657

2.0999

2.1594

2.0946

no(Z) 2.05 [7] 1.97 1.84 1.71 1.52 1.20

ko(-L)

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.,,(11)

2.2967

2.2082

2.2716

2.1874

2.2571

2.1745

2.2448

2.1641

2.2370

2.1567

2.2269

2.1478

2.2184

2.1417

2.2113

2.1361

2.2049

2.1306

2.1974

2.1250

2.1909

2.1183

2.1850 2.1778

2.1129 2.1071

2.1703

2.1009

2.1625

2.0945

2.1543 2.1456 2.1363 2.1263 2.1155

2.0871 2.0804 2.0725 2.0642 2.0553

.o(11)

2.oo ['7-1 1.93 1.83 1.72 1.55 1.30

k~(ll)

Lithium Niobate (LiNb03)

701 T A B L E VII

(Continued)

Lithium Niobate eV

cm- 1

ltm

no(L)

O.1127 0.09919 0.09671 0.09423 0.09175 0.08927 0.08679 0.08431 0.08307 0.08183 0.07935 0.07811 0.07687 0.07563 0.07439 0.07315 0.07191 0.07067 0.06943 0.06819 0.06695 0.06447 0.06199 0.05951 0.05703 0.05455 0.05331 0.05207 0.04959 0.04711 0.04587 0.04463 0.04339 0.04215 0.04092 0.03968 0.03844 0.03720 0.03596 0.03472 0.03348 0.03286 0.03224 0.03100 0.02976 0.02852 0.02728

909.1 800 780 760 740 720 700 680 670 660 640 630 620 610 600 590 580 570 560 550 540 520 500 480 460 440 430 420 400 380 370 360 350 340 330 320 310 300 290 280 270 265 260 250 240 230 220

11 12.50 12.82 13.16 13.51 13.89 14.29 14.71 14.93 15.15 15.63 15.87 16.13 16.39 16.67 16.95 17.24 17.54 17.86 18.18 18.52 19.23 20.00 20.83 21.74 22.73 23.26 23.81 25.00 26.32 27.03 27.78 28.57 29.41 30.30 31.25 32.26 33.33 34.48 35.71 37.04 37.74 38.46 40.00 41.67 43.48 45.45

0.60 0.20 [8] 0.21 0.22 0.23 0.26 0.54 0.90 0.90 0.99 0.95

1.24 [8] 1.43 1.56 1.74 1.94 2.30 2.51 2.60 2.52 2.52

0.90

2.88

1.10

3.63

1.83 3.01 4.77 4.88 4.51 4.00 3.27 2.52 1.78 1.03 1.20 1.30 1.01 1.33 1.73 2.61 2.64 1.34 1.89 3.39 4.09 2.80

4.62 5.30 4.55 2.97 2.10 1.24 0.84 0.59 0.62 1.44 2.11 1.92 2.45 3.36 3.74 4.10 2.83 2.96 4.75 5.52 3.04 1.96

0.92 2.19 4.19 5.71 6.79 5.76 5.82 4.94

4.34 6.84 8.34 7.91 2.94 2.68 2.31 1.21

ko(•

ne(ll)

k~(l[)

0.81 0.46 [8] 0.44 0.45 0.46 0.53 0.56 0.75

1.1018] 1.48 1.78 2.17 2.34 2.67 3.01

1.05 1.44 1.85 2.52 3.42 4.02 4.24 4.47

3.33 3.83 4.05 4.16 4.09 3.48 2.83 2.12

4.17

1.20

3.67 3.20 2.67 2.28 2.06 1.82

0.68 0.47 0.37 0.44 0.48 0.55

1.27 0.83 0.48

0.79 1.09 1.65

0.32

2.47

0.37

3.34

0.70 1.16 1.20 0.75 0.80 0.94

4.30 4.51 4.35 4.64 5.62 6.91

3.04 6.58 7.48 8.55 8.32

9.86 10.4 7.34 4.91 3.36

(continued)

702

Edward D. Palik T A B L E VII (Continued)

Lithium Niobate eV

cm- 1

pm

0.02604 0.02480 0.02356 0.02232 0.02108 0.01984 0.01860 0.01736 0.01612 0.01488 0.01240 0.01054 0.009919

210 200 190 180 170 160 150 140 130 120 100 85 80

47.62 50.00 52.63 55.56 58.82 62.50 66.67 71.43 76.92 83.33 100 117.6 125

0.009299 0.008679 0.007439

75 70 60

133.3 142.9 166.7

0.006199 0.004959

50 40

200 250

0.003720 0.002480 0.001240

30 20 10

333.3 500 1000

no(Z )

ko(-L)

~(11)

2.54

1.57

0.98 2.04 5.43 7.96 10.1 10.6 9.83 8.57

5.09 7.36 10.1 9.92 5.68 3.06 1.67 0.70

7.66 6.78 7.08 7.86 8.03 6.93 6.33 6.17 6.01 5.84 5.66

7.87

0.13

5.52

7.34 7.06111] 6.90 6.85 [8-] 6.80111] 6.70 6.64 6.61

3.5 • 10 -2 [10] 3.0 7 [8] 1.9 x 10 -2 [10] 9.5 X 1 0 - 3

5.38 5.22111] 5.165

6.0 4.5 3.2 2.0

5.125 5.10 5.07 5.06

k~(ll) 2.60 2.35 2.85 2.4t 0.75 0.36 0.38 0.40 0.43 0.43 0.35 2.3 x 10 -2 [10] 0.18 [8] 1.8 • 10 -2 [10] 1.1 9 x 10 -2 [8] 8.0 x 10-3 [10] 4.8 3.6 2.9 2.0 1.6

a The reference is given in brackets at the beginning of the tabulation of n and k and is understood to refer to all n's or all k's below it until a new reference appears. When an exponent of 10 is given, all numbers below it have the same exponent until the power of 10 changes or the next number has 10 -1, which is usually written as a decimal. Boyd et al. [5] n values are for stoichiometric material and Nelson and Mikulyak [6] n values are for congruent material. We specify no(l) and ne(ll) for redundancy.