Abstract

Increases in the extraordinary refractive index sufficient to produce single and multimode optical waveguides have been produced by the outdiffusion of lithium oxide from the surfaces of lithium niobate and lithium tantalate crystals. The outdiffusion kinetics have been studied in detail by optical interferometry. The data fit a diffusion model for which the vaporizing surface flux is constant with time. For lithium niobate, the activation energy for diffusion is 68 ± 1.2 kcal/mol and does not vary with orientation. However the gradient of refractive index change at the surface is larger for diffusion normal to the c-axis than parallel to the c-axis. Activation energies for vaporization of 71 kcal/mol and 59 kcal/mol were calculated from the model for diffusion perpendicular and parallel to the c-axis, respectively. The evaporation coefficient, α, was estimated to be less than 10−4 with α/α ≈ 3 so vaporization is surface reaction limited. For lithium tantalate, the activation energy for diffusion is 51 ± 6 kcal/mol and also does not vary with orientation. The activation energy for vaporization, Qυ, is approximately 63 kcal/mol and, within experimental error, is quite similar to that for lithium niobate. These values of Qυ indicate that the major vaporization species are probably lithium ions and oxygen ions. The characteristics of graded index waveguides are discussed and compared with those of slab guides. It is shown that in many respects the behavior of the two types is equivalent. We have produced a single-mode guide in lithium niobate with an effective thickness of 12 μm. Effective thicknesses as small as 6 μm are possible in lithium tantalate.

© 1974 Optical Society of America

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  1. I. P. Kaminow, J. R. Carruthers, Appl. Phys. Lett. 22, 326 (1973).
    [Crossref]
  2. J. R. Carruthers, G. E. Peterson, M. Grasso, P. M. Bridenbaugh, J. Appl. Phys. 42, 1846 (1971).
    [Crossref]
  3. R. L. Barns, J. R. Carruthers, J. Appl. Cryst., 3, 395 (1970).
    [Crossref]
  4. I. P. Kaminow, J. R. Carruthers, E. H. Turner, L. W. Stulz, Appl. Phys. Lett. 22, 326 (1973).
    [Crossref]
  5. R. V. Schmidt, I. P. Kaminow, J. R. Carruthers, Appl. Phys. Lett. 23, 417 (1973).
    [Crossref]
  6. H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford Univ. Press, 1971), p. 75.
  7. J. Crank, Mathematics of Diffusion (Oxford Univ. Press, 1970), p. 31.
  8. J. Berkowitz, W. A. Chupka, G. D. Blue, J. L. Margrave, J. Phys. Chem. 63, 644 (1959).
    [Crossref]
  9. J. R. Carruthers, J. Crys. Growth 16, 45 (1972).
    [Crossref]
  10. A. N. Nesmeyanov, L. P. Belykh, Russ. J. Phys. Chem. 34, 399 (1960).
  11. P. J. Jorgensen, R. W. Bartlett, J. Phys. Chem. Solids 30, 2639 (1969).
    [Crossref]
  12. H. Engan, IEEE Trans. Electron Devices ED-16, 1014 (1969).
    [Crossref]
  13. J. M. Hammer, D. J. Channin, M. T. Duffy, Appl. Phys. Lett. 23, 176 (1973).
    [Crossref]
  14. D. F. Nelson, J. McKenna, J. Appl. Phys. 38, 4057 (1967).
    [Crossref]
  15. D. Marcuse, IEEE J. Quantum Electron. QE-9, 1000 (1973).
    [Crossref]
  16. D. H. Smithgall, F. W. Dabby, R. B. Runk, IEEE J. Quantum Electron. QE-9, 1023 (1973).
    [Crossref]
  17. E. M. Conwell, Appl. Phys. Lett. 23, 328 (1973).
    [Crossref]
  18. D. Marcuse, BTL; private communication.
  19. E. Jahnke, F. Ende, F. Lösch, Tables of Higher Functions (McGraw-Hill, New York1960).
  20. W. Mammel, BTL; to be published.
  21. I. P. Kaminow, V. Ramaswamy, R. V. Schmidt, E. H. Turner, Appl. Phys. Lett., 24, 622 (1974).
    [Crossref]

1974 (1)

I. P. Kaminow, V. Ramaswamy, R. V. Schmidt, E. H. Turner, Appl. Phys. Lett., 24, 622 (1974).
[Crossref]

1973 (7)

J. M. Hammer, D. J. Channin, M. T. Duffy, Appl. Phys. Lett. 23, 176 (1973).
[Crossref]

D. Marcuse, IEEE J. Quantum Electron. QE-9, 1000 (1973).
[Crossref]

D. H. Smithgall, F. W. Dabby, R. B. Runk, IEEE J. Quantum Electron. QE-9, 1023 (1973).
[Crossref]

E. M. Conwell, Appl. Phys. Lett. 23, 328 (1973).
[Crossref]

I. P. Kaminow, J. R. Carruthers, Appl. Phys. Lett. 22, 326 (1973).
[Crossref]

I. P. Kaminow, J. R. Carruthers, E. H. Turner, L. W. Stulz, Appl. Phys. Lett. 22, 326 (1973).
[Crossref]

R. V. Schmidt, I. P. Kaminow, J. R. Carruthers, Appl. Phys. Lett. 23, 417 (1973).
[Crossref]

1972 (1)

J. R. Carruthers, J. Crys. Growth 16, 45 (1972).
[Crossref]

1971 (1)

J. R. Carruthers, G. E. Peterson, M. Grasso, P. M. Bridenbaugh, J. Appl. Phys. 42, 1846 (1971).
[Crossref]

1970 (1)

R. L. Barns, J. R. Carruthers, J. Appl. Cryst., 3, 395 (1970).
[Crossref]

1969 (2)

P. J. Jorgensen, R. W. Bartlett, J. Phys. Chem. Solids 30, 2639 (1969).
[Crossref]

H. Engan, IEEE Trans. Electron Devices ED-16, 1014 (1969).
[Crossref]

1967 (1)

D. F. Nelson, J. McKenna, J. Appl. Phys. 38, 4057 (1967).
[Crossref]

1960 (1)

A. N. Nesmeyanov, L. P. Belykh, Russ. J. Phys. Chem. 34, 399 (1960).

1959 (1)

J. Berkowitz, W. A. Chupka, G. D. Blue, J. L. Margrave, J. Phys. Chem. 63, 644 (1959).
[Crossref]

Barns, R. L.

R. L. Barns, J. R. Carruthers, J. Appl. Cryst., 3, 395 (1970).
[Crossref]

Bartlett, R. W.

P. J. Jorgensen, R. W. Bartlett, J. Phys. Chem. Solids 30, 2639 (1969).
[Crossref]

Belykh, L. P.

A. N. Nesmeyanov, L. P. Belykh, Russ. J. Phys. Chem. 34, 399 (1960).

Berkowitz, J.

J. Berkowitz, W. A. Chupka, G. D. Blue, J. L. Margrave, J. Phys. Chem. 63, 644 (1959).
[Crossref]

Blue, G. D.

J. Berkowitz, W. A. Chupka, G. D. Blue, J. L. Margrave, J. Phys. Chem. 63, 644 (1959).
[Crossref]

Bridenbaugh, P. M.

J. R. Carruthers, G. E. Peterson, M. Grasso, P. M. Bridenbaugh, J. Appl. Phys. 42, 1846 (1971).
[Crossref]

Carruthers, J. R.

R. V. Schmidt, I. P. Kaminow, J. R. Carruthers, Appl. Phys. Lett. 23, 417 (1973).
[Crossref]

I. P. Kaminow, J. R. Carruthers, E. H. Turner, L. W. Stulz, Appl. Phys. Lett. 22, 326 (1973).
[Crossref]

I. P. Kaminow, J. R. Carruthers, Appl. Phys. Lett. 22, 326 (1973).
[Crossref]

J. R. Carruthers, J. Crys. Growth 16, 45 (1972).
[Crossref]

J. R. Carruthers, G. E. Peterson, M. Grasso, P. M. Bridenbaugh, J. Appl. Phys. 42, 1846 (1971).
[Crossref]

R. L. Barns, J. R. Carruthers, J. Appl. Cryst., 3, 395 (1970).
[Crossref]

Carslaw, H. S.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford Univ. Press, 1971), p. 75.

Channin, D. J.

J. M. Hammer, D. J. Channin, M. T. Duffy, Appl. Phys. Lett. 23, 176 (1973).
[Crossref]

Chupka, W. A.

J. Berkowitz, W. A. Chupka, G. D. Blue, J. L. Margrave, J. Phys. Chem. 63, 644 (1959).
[Crossref]

Conwell, E. M.

E. M. Conwell, Appl. Phys. Lett. 23, 328 (1973).
[Crossref]

Crank, J.

J. Crank, Mathematics of Diffusion (Oxford Univ. Press, 1970), p. 31.

Dabby, F. W.

D. H. Smithgall, F. W. Dabby, R. B. Runk, IEEE J. Quantum Electron. QE-9, 1023 (1973).
[Crossref]

Duffy, M. T.

J. M. Hammer, D. J. Channin, M. T. Duffy, Appl. Phys. Lett. 23, 176 (1973).
[Crossref]

Ende, F.

E. Jahnke, F. Ende, F. Lösch, Tables of Higher Functions (McGraw-Hill, New York1960).

Engan, H.

H. Engan, IEEE Trans. Electron Devices ED-16, 1014 (1969).
[Crossref]

Grasso, M.

J. R. Carruthers, G. E. Peterson, M. Grasso, P. M. Bridenbaugh, J. Appl. Phys. 42, 1846 (1971).
[Crossref]

Hammer, J. M.

J. M. Hammer, D. J. Channin, M. T. Duffy, Appl. Phys. Lett. 23, 176 (1973).
[Crossref]

Jaeger, J. C.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford Univ. Press, 1971), p. 75.

Jahnke, E.

E. Jahnke, F. Ende, F. Lösch, Tables of Higher Functions (McGraw-Hill, New York1960).

Jorgensen, P. J.

P. J. Jorgensen, R. W. Bartlett, J. Phys. Chem. Solids 30, 2639 (1969).
[Crossref]

Kaminow, I. P.

I. P. Kaminow, V. Ramaswamy, R. V. Schmidt, E. H. Turner, Appl. Phys. Lett., 24, 622 (1974).
[Crossref]

R. V. Schmidt, I. P. Kaminow, J. R. Carruthers, Appl. Phys. Lett. 23, 417 (1973).
[Crossref]

I. P. Kaminow, J. R. Carruthers, Appl. Phys. Lett. 22, 326 (1973).
[Crossref]

I. P. Kaminow, J. R. Carruthers, E. H. Turner, L. W. Stulz, Appl. Phys. Lett. 22, 326 (1973).
[Crossref]

Lösch, F.

E. Jahnke, F. Ende, F. Lösch, Tables of Higher Functions (McGraw-Hill, New York1960).

Mammel, W.

W. Mammel, BTL; to be published.

Marcuse, D.

D. Marcuse, IEEE J. Quantum Electron. QE-9, 1000 (1973).
[Crossref]

D. Marcuse, BTL; private communication.

Margrave, J. L.

J. Berkowitz, W. A. Chupka, G. D. Blue, J. L. Margrave, J. Phys. Chem. 63, 644 (1959).
[Crossref]

McKenna, J.

D. F. Nelson, J. McKenna, J. Appl. Phys. 38, 4057 (1967).
[Crossref]

Nelson, D. F.

D. F. Nelson, J. McKenna, J. Appl. Phys. 38, 4057 (1967).
[Crossref]

Nesmeyanov, A. N.

A. N. Nesmeyanov, L. P. Belykh, Russ. J. Phys. Chem. 34, 399 (1960).

Peterson, G. E.

J. R. Carruthers, G. E. Peterson, M. Grasso, P. M. Bridenbaugh, J. Appl. Phys. 42, 1846 (1971).
[Crossref]

Ramaswamy, V.

I. P. Kaminow, V. Ramaswamy, R. V. Schmidt, E. H. Turner, Appl. Phys. Lett., 24, 622 (1974).
[Crossref]

Runk, R. B.

D. H. Smithgall, F. W. Dabby, R. B. Runk, IEEE J. Quantum Electron. QE-9, 1023 (1973).
[Crossref]

Schmidt, R. V.

I. P. Kaminow, V. Ramaswamy, R. V. Schmidt, E. H. Turner, Appl. Phys. Lett., 24, 622 (1974).
[Crossref]

R. V. Schmidt, I. P. Kaminow, J. R. Carruthers, Appl. Phys. Lett. 23, 417 (1973).
[Crossref]

Smithgall, D. H.

D. H. Smithgall, F. W. Dabby, R. B. Runk, IEEE J. Quantum Electron. QE-9, 1023 (1973).
[Crossref]

Stulz, L. W.

I. P. Kaminow, J. R. Carruthers, E. H. Turner, L. W. Stulz, Appl. Phys. Lett. 22, 326 (1973).
[Crossref]

Turner, E. H.

I. P. Kaminow, V. Ramaswamy, R. V. Schmidt, E. H. Turner, Appl. Phys. Lett., 24, 622 (1974).
[Crossref]

I. P. Kaminow, J. R. Carruthers, E. H. Turner, L. W. Stulz, Appl. Phys. Lett. 22, 326 (1973).
[Crossref]

Appl. Phys. Lett. (6)

I. P. Kaminow, J. R. Carruthers, E. H. Turner, L. W. Stulz, Appl. Phys. Lett. 22, 326 (1973).
[Crossref]

R. V. Schmidt, I. P. Kaminow, J. R. Carruthers, Appl. Phys. Lett. 23, 417 (1973).
[Crossref]

I. P. Kaminow, J. R. Carruthers, Appl. Phys. Lett. 22, 326 (1973).
[Crossref]

J. M. Hammer, D. J. Channin, M. T. Duffy, Appl. Phys. Lett. 23, 176 (1973).
[Crossref]

E. M. Conwell, Appl. Phys. Lett. 23, 328 (1973).
[Crossref]

I. P. Kaminow, V. Ramaswamy, R. V. Schmidt, E. H. Turner, Appl. Phys. Lett., 24, 622 (1974).
[Crossref]

IEEE J. Quantum Electron. (2)

D. Marcuse, IEEE J. Quantum Electron. QE-9, 1000 (1973).
[Crossref]

D. H. Smithgall, F. W. Dabby, R. B. Runk, IEEE J. Quantum Electron. QE-9, 1023 (1973).
[Crossref]

IEEE Trans. Electron Devices (1)

H. Engan, IEEE Trans. Electron Devices ED-16, 1014 (1969).
[Crossref]

J. Appl. Cryst. (1)

R. L. Barns, J. R. Carruthers, J. Appl. Cryst., 3, 395 (1970).
[Crossref]

J. Appl. Phys. (2)

J. R. Carruthers, G. E. Peterson, M. Grasso, P. M. Bridenbaugh, J. Appl. Phys. 42, 1846 (1971).
[Crossref]

D. F. Nelson, J. McKenna, J. Appl. Phys. 38, 4057 (1967).
[Crossref]

J. Crys. Growth (1)

J. R. Carruthers, J. Crys. Growth 16, 45 (1972).
[Crossref]

J. Phys. Chem. (1)

J. Berkowitz, W. A. Chupka, G. D. Blue, J. L. Margrave, J. Phys. Chem. 63, 644 (1959).
[Crossref]

J. Phys. Chem. Solids (1)

P. J. Jorgensen, R. W. Bartlett, J. Phys. Chem. Solids 30, 2639 (1969).
[Crossref]

Russ. J. Phys. Chem. (1)

A. N. Nesmeyanov, L. P. Belykh, Russ. J. Phys. Chem. 34, 399 (1960).

Other (5)

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford Univ. Press, 1971), p. 75.

J. Crank, Mathematics of Diffusion (Oxford Univ. Press, 1970), p. 31.

D. Marcuse, BTL; private communication.

E. Jahnke, F. Ende, F. Lösch, Tables of Higher Functions (McGraw-Hill, New York1960).

W. Mammel, BTL; to be published.

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Figures (11)

Fig. 1
Fig. 1

Diffusion profiles—analytical curves for π1/2ierfc(x/b), erfc(x/b) and exp(x/b). A typical set of experimental data is fitted as shown with a = a = a″ and b = 1.36 b′ = 1.97 b″.

Fig. 2
Fig. 2

Variation of diffusion depths, b, with time as t1/2 for various temperatures in lithium niobate for diffusion normal to the c-axis.

Fig. 3
Fig. 3

Variation of diffusion depths, b, with time as t1/2 for various temperatures in lithium niobate for diffusion parallel to the c-axis.

Fig. 4
Fig. 4

Variation of diffusion coefficients with temperature as 1/T in lithium niobate for diffusion normal and parallel to the c-axis. Straight lines have been fitted by least-squares regression analyses—see Table I.

Fig. 5
Fig. 5

Variation of the gradient of the refractive index change at the surfaces of lithium niobate given as π1/2a/b with temperature as 1/T—see Table II.

Fig. 6
Fig. 6

Variation of diffusion coefficients with temperature as 1/T in lithium tantalate for diffusion normal and parallel to the c-axis. Straight lines have been fitted by least-squares regression analyses—see Table I.

Fig. 7
Fig. 7

Variation of the gradient of the refractive index change at the surfaces of lithium tantalate given as π1/2a/b with temperature as 1/T—see Table II.

Fig. 8
Fig. 8

Weight changes occurring during the outdiffusion of a lithium niobate specimen of total area 2.30 cm2 at 1100°C as compared with a blank run in a Mettler Thermoanalyzer I.

Fig. 9
Fig. 9

Calculated sample weight loss from Figure 8.

Fig. 10
Fig. 10

Refractive index profiles for (a) an asymmetric planar slab waveguide and (b) a planar graded index waveguide. TE0 and TE1 wavefunctions are indicated schematically along with turning points x ¯ i.

Fig. 11
Fig. 11

Normalized guide index (β/kn)/a″ vs normalized frequency ξ = 2kb″ (2na)1/2.

Tables (3)

Tables Icon

Table I Diffusion Equation Parameters

Tables Icon

Table II Refractive Index Gradient Equation Parameters from Regression Analysis

Tables Icon

Table III Calculated Evaporation Fluxes and Kinetic Vapor Pressures for LiNbO3

Equations (41)

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d n e / d ν = 1.6 ,
d n e / d ν = 0.8 ,
( C ) / ( t ) = D [ ( 2 C ) / ( x 2 ) ] 0 < x <
C = Δ ν ( M L i 2 O / M LiNb O 3 ) ρ LiNb O 3 ,
C = 0 at t = 0 for 0 < x < .
D = D 0 exp ( Q D / R T ) ,
J υ = D [ C / x ] x = 0 .
C = 2 J υ [ t / D ] 1 / 2 i e r f c [ x / 2 D t ] ,
C ( 0 , t ) = ( 2 J υ / D ) ( D t / π ) 1 / 2 .
Δ n e = 1.75 C .
Δ n e = a π 1 / 2 i erfc ( x / b ) ,
a = Δ n e ( 0 , t ) = ( 3.51 J υ ) ( t / π D ) 1 / 2 ;
b = 2 ( D t ) 1 / 2
J υ = α p eq ( 2 π R T / M L i 2 O ) 1 / 2 ;
J υ ( gm c m 2 sec 1 ) = 44.4 p L ( atm ) / [ T / M L i 2 O ] 1 / 2
p L = α p eq ,
p eq = p 0 exp ( Q υ / R T ) ,
a = a = a , b = 1.36 , b = 1.97 b .
{ [ d ( Δ n e ) ] / ( d x ) } x = 0 = J υ / ( 0.57 D ) .
{ [ d ( Δ n e ) ] / ( d x ) } x = 0 = π 1 / 2 a / b .
{ [ d ( Δ n e ) ] / ( d x ) } x = 0 = G 0 exp [ ( Q υ Q D ) / R T ] ,
l n [ d ( Δ n e ) / d x ] x = 0 ( 1 / T ) = ( Q υ Q D ) R .
L i 2 O ( solid ) 2 L i ( gas ) + O ( gas ) , Δ H T ° ,
n = n + A for 0 < x < B n = n for B < x < ;
n ( x ) = n + π 1 / 2 a i e r e f c ( x / b ) .
w i s = B .
N s = 1 2 + ( 2 B / λ ) ( 2 n A ) 1 / 2 ,
N g = 1 4 + ( 1.38 b / λ ) ( 2 n a ) 1 / 2 .
w i g = x ¯ i ,
x ¯ 0 = [ ( 81 λ 2 b ) / ( 512 n π 1 / 2 a ) ] 1 / 3 ,
x ¯ 0 = 0.69 b ( N 0.25 ) 2 / 3
n ( x ) = n + a exp ( x / b )
ξ = 2 k b ( 2 n a ) 1 / 2 ,
μ = 2 [ ( β b ) 2 ( n k b ) 2 ] 1 / 2 ;
( β i / k n ) / a = ( μ i / ξ i ) 2 ,
J μ i ( ξ i ) = 0 ; i = 0,1,2 .
μ i = ( 2 / π ) ξ i 2 i ( 3 / 2 ) .
N e = 1 / 4 + ( 4 b / λ ) ( 2 n a ) 1 / 2 ,
w i e = x ¯ i = 2 b ln [ ( 2 / π ) ( 4 i + 3 ) / ( 2 ξ ) ] .
μ 0 = ξ 0 1.856 ξ 0 1 / 3 .
w i e = x ¯ 0 = 0.659 [ ( λ 2 b ) / ( n π 1 / 2 a ) ] 1 / 3 ,

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