Abstract

The observation of the picosecond thermal expansion of an absorbing surface after a short heating pulse is reported for the first time to my knowledge. The measurement was performed on Si by adapting the method of photothermal deflection to a pump–probe technique using 1-psec laser pulses. This was achieved by separating out a novel deflection effect due to the gradient in the near-surface optical constants. The results are compared to a thermo-elastic model, and good agreement is found.

© 1988 Optical Society of America

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References

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  1. G. L. Eesley, Phys. Rev. B 33, 2144 (1986); R. W. Schoenlein, W. Z. Lin, J. G. Fujimoto, G. L. Eesley, Phys. Rev. Lett. 58, 1680 (1987). See also G. R. Fleming, A. E. Siegman, eds., Ultrafast Phenomena V (Springer, New York, 1986).
    [Crossref] [PubMed]
  2. M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
    [Crossref]
  3. C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, J. J. Hauser, Phys. Rev. Lett. 53, 989 (1984).
    [Crossref]
  4. C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 4129 (1986).
    [Crossref]
  5. G. L. Eesley, B. M. Clemens, C. A. Paddock, Appl. Phys. Lett. 50, 717 (1987).
    [Crossref]
  6. C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Opt. Commun. 60, 55 (1986).
    [Crossref]
  7. C. Karner, A. Mandel, F. Trager, Appl. Phys. A 38, 19 (1985).
    [Crossref]
  8. J. Opsal, M. W. Taylor, W. L. Smith, A. Rosencwaig, J. Appl. Phys. 61, 240 (1987).
    [Crossref]
  9. H. J. McSkimin, P. Andreatch, Jr. J. Appl. Phys. 35, 2161 (1964).
    [Crossref]
  10. D. E. Aspnes, A. A. Studna, Phys. Rev. B 27, 985 (1983).
    [Crossref]
  11. G. W. Gobeli, E. O. Kane, Phys. Rev. Lett. 15, 142 (1965).
    [Crossref]

1987 (2)

G. L. Eesley, B. M. Clemens, C. A. Paddock, Appl. Phys. Lett. 50, 717 (1987).
[Crossref]

J. Opsal, M. W. Taylor, W. L. Smith, A. Rosencwaig, J. Appl. Phys. 61, 240 (1987).
[Crossref]

1986 (3)

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Opt. Commun. 60, 55 (1986).
[Crossref]

G. L. Eesley, Phys. Rev. B 33, 2144 (1986); R. W. Schoenlein, W. Z. Lin, J. G. Fujimoto, G. L. Eesley, Phys. Rev. Lett. 58, 1680 (1987). See also G. R. Fleming, A. E. Siegman, eds., Ultrafast Phenomena V (Springer, New York, 1986).
[Crossref] [PubMed]

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 4129 (1986).
[Crossref]

1985 (1)

C. Karner, A. Mandel, F. Trager, Appl. Phys. A 38, 19 (1985).
[Crossref]

1984 (1)

C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, J. J. Hauser, Phys. Rev. Lett. 53, 989 (1984).
[Crossref]

1983 (2)

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[Crossref]

D. E. Aspnes, A. A. Studna, Phys. Rev. B 27, 985 (1983).
[Crossref]

1965 (1)

G. W. Gobeli, E. O. Kane, Phys. Rev. Lett. 15, 142 (1965).
[Crossref]

1964 (1)

H. J. McSkimin, P. Andreatch, Jr. J. Appl. Phys. 35, 2161 (1964).
[Crossref]

Amer, N. M.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[Crossref]

Andreatch, P.

H. J. McSkimin, P. Andreatch, Jr. J. Appl. Phys. 35, 2161 (1964).
[Crossref]

Aspnes, D. E.

D. E. Aspnes, A. A. Studna, Phys. Rev. B 27, 985 (1983).
[Crossref]

Boccara, A. C.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[Crossref]

Clemens, B. M.

G. L. Eesley, B. M. Clemens, C. A. Paddock, Appl. Phys. Lett. 50, 717 (1987).
[Crossref]

Eesley, G. L.

G. L. Eesley, B. M. Clemens, C. A. Paddock, Appl. Phys. Lett. 50, 717 (1987).
[Crossref]

G. L. Eesley, Phys. Rev. B 33, 2144 (1986); R. W. Schoenlein, W. Z. Lin, J. G. Fujimoto, G. L. Eesley, Phys. Rev. Lett. 58, 1680 (1987). See also G. R. Fleming, A. E. Siegman, eds., Ultrafast Phenomena V (Springer, New York, 1986).
[Crossref] [PubMed]

Fournier, D.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[Crossref]

Gobeli, G. W.

G. W. Gobeli, E. O. Kane, Phys. Rev. Lett. 15, 142 (1965).
[Crossref]

Grahn, H. T.

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Opt. Commun. 60, 55 (1986).
[Crossref]

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 4129 (1986).
[Crossref]

Hauser, J. J.

C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, J. J. Hauser, Phys. Rev. Lett. 53, 989 (1984).
[Crossref]

Kane, E. O.

G. W. Gobeli, E. O. Kane, Phys. Rev. Lett. 15, 142 (1965).
[Crossref]

Karner, C.

C. Karner, A. Mandel, F. Trager, Appl. Phys. A 38, 19 (1985).
[Crossref]

Kohn, S.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[Crossref]

Mandel, A.

C. Karner, A. Mandel, F. Trager, Appl. Phys. A 38, 19 (1985).
[Crossref]

Maris, H. J.

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Opt. Commun. 60, 55 (1986).
[Crossref]

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 4129 (1986).
[Crossref]

C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, J. J. Hauser, Phys. Rev. Lett. 53, 989 (1984).
[Crossref]

McSkimin, H. J.

H. J. McSkimin, P. Andreatch, Jr. J. Appl. Phys. 35, 2161 (1964).
[Crossref]

Olmstead, M. A.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[Crossref]

Opsal, J.

J. Opsal, M. W. Taylor, W. L. Smith, A. Rosencwaig, J. Appl. Phys. 61, 240 (1987).
[Crossref]

Paddock, C. A.

G. L. Eesley, B. M. Clemens, C. A. Paddock, Appl. Phys. Lett. 50, 717 (1987).
[Crossref]

Rosencwaig, A.

J. Opsal, M. W. Taylor, W. L. Smith, A. Rosencwaig, J. Appl. Phys. 61, 240 (1987).
[Crossref]

Smith, W. L.

J. Opsal, M. W. Taylor, W. L. Smith, A. Rosencwaig, J. Appl. Phys. 61, 240 (1987).
[Crossref]

Strait, J.

C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, J. J. Hauser, Phys. Rev. Lett. 53, 989 (1984).
[Crossref]

Studna, A. A.

D. E. Aspnes, A. A. Studna, Phys. Rev. B 27, 985 (1983).
[Crossref]

Tauc, J.

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Opt. Commun. 60, 55 (1986).
[Crossref]

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 4129 (1986).
[Crossref]

C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, J. J. Hauser, Phys. Rev. Lett. 53, 989 (1984).
[Crossref]

Taylor, M. W.

J. Opsal, M. W. Taylor, W. L. Smith, A. Rosencwaig, J. Appl. Phys. 61, 240 (1987).
[Crossref]

Thomsen, C.

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Opt. Commun. 60, 55 (1986).
[Crossref]

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 4129 (1986).
[Crossref]

C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, J. J. Hauser, Phys. Rev. Lett. 53, 989 (1984).
[Crossref]

Trager, F.

C. Karner, A. Mandel, F. Trager, Appl. Phys. A 38, 19 (1985).
[Crossref]

Vardeny, Z.

C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, J. J. Hauser, Phys. Rev. Lett. 53, 989 (1984).
[Crossref]

Appl. Phys. A (2)

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[Crossref]

C. Karner, A. Mandel, F. Trager, Appl. Phys. A 38, 19 (1985).
[Crossref]

Appl. Phys. Lett. (1)

G. L. Eesley, B. M. Clemens, C. A. Paddock, Appl. Phys. Lett. 50, 717 (1987).
[Crossref]

J. Appl. Phys. (1)

J. Opsal, M. W. Taylor, W. L. Smith, A. Rosencwaig, J. Appl. Phys. 61, 240 (1987).
[Crossref]

Jr. J. Appl. Phys. (1)

H. J. McSkimin, P. Andreatch, Jr. J. Appl. Phys. 35, 2161 (1964).
[Crossref]

Opt. Commun. (1)

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Opt. Commun. 60, 55 (1986).
[Crossref]

Phys. Rev. B (3)

D. E. Aspnes, A. A. Studna, Phys. Rev. B 27, 985 (1983).
[Crossref]

G. L. Eesley, Phys. Rev. B 33, 2144 (1986); R. W. Schoenlein, W. Z. Lin, J. G. Fujimoto, G. L. Eesley, Phys. Rev. Lett. 58, 1680 (1987). See also G. R. Fleming, A. E. Siegman, eds., Ultrafast Phenomena V (Springer, New York, 1986).
[Crossref] [PubMed]

C. Thomsen, H. T. Grahn, H. J. Maris, J. Tauc, Phys. Rev. B 34, 4129 (1986).
[Crossref]

Phys. Rev. Lett. (2)

C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, J. J. Hauser, Phys. Rev. Lett. 53, 989 (1984).
[Crossref]

G. W. Gobeli, E. O. Kane, Phys. Rev. Lett. 15, 142 (1965).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

Diagram of the experimental arrangement.

Fig. 2
Fig. 2

(a) Photodeflection (upper curve) and transient reflectivity (lower curve) from Si 〈100〉 surface. Peak ΔR/R = 5 × 10−4, and peak deflection is 20 μrad. (b) Difference of two curves of (a) (solid curve) with the theoretical fit of Eq. (2) (dashed line); time constant is 200 psec.

Fig. 3
Fig. 3

(a) Deflection of the reflected probe beam owing to standard photothermal deflection from the sloped shoulder of a bump. (b) Deflection from a completely flat surface with a transverse gradient in the optical constants. Shown below is the profile of the phase of the Fresnel reflection coefficient. The gradient in phase is optically equivalent to a deformed surface.

Equations (6)

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S ( z , t ) exp ( - z / t ) [ 1 - ½ exp ( - ν t / d ) ] - ½ sgn ( z - νt ) exp ( -∣ z - ν t ∣/ d ) ,
u ( 0 , t ) = 0 S ( z , t ) d z 1 - exp ( - ν t / d ) .
r = n + i κ - 1 n + i κ + 1 r 0 exp ( i ϕ 0 ) ,
r = r 0 exp ( i ϕ 0 ) + Δ n r n + Δ κ r κ r 0 exp ( i ϕ 0 ) + Δ r 1 ( t ) exp [ i ϕ 1 ( t ) ] ,
Δ ϕ ( t ) = arg ( r 0 + Δ r 1 ( t ) exp { i [ ϕ 1 ( t ) - ϕ 0 ] } ) Δ r 1 ( t ) r 0 sin [ ϕ 1 ( t ) - ϕ 0 ] .
Δ R = r 0 exp ( i ϕ 0 ) + Δ r 1 ( t ) exp [ i ϕ 1 ( t ) ] 2 - r 0 2 2 r 0 Δ r 1 ( t ) cos [ ϕ 1 ( t ) - ϕ 0 ] .

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