Abstract

We present two new x-ray optical effects observed on a whispering-gallery waveguide. The first is a gradual in-surface deflection of guided waves caused by the non-Euclidean intrinsic curvature of the waveguide surface. The second is the excitation of in-surface dynamical diffraction modes that reflects the strong influence of the surface photonic band structure of a crystalline waveguide. Both phenomena portend a rich array of basic and applied x-ray optical potentialities.

© 1999 Optical Society of America

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  1. Chien Liu and J. A. Golovchenko, Phys. Rev. Lett. 79, 788 (1997).
    [CrossRef]
  2. Rayleigh, The Theory of Sound, American ed. (Dover, New York, 1945).
  3. J. P. Braud and P. L. Hagelstein, IEEE J. Quantum Electron. 27, 1069 (1991)N. V. Smith and M. R. Howells, Nucl. Instrum. Methods Phys. Res. A 347, 115 (1994)I. N. Bukreva, I. V. Kozhevnikov, and A. V. Vinogradov, Proc. SPIE 2453, 80 (1995).
    [CrossRef]
  4. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).
  5. A. Ishizaka and Y. Shiraki, J. Electrochem. Soc. 133, 666 (1986).
    [CrossRef]
  6. R. E. Martinez, “Impurity atoms on a silicon surface:?structures, forces and dynamics,” Ph.D. dissertation (Harvard University, Cambridge, Mass., 1992)J. A. Golovchenko, R. A. Levesque, and P. L. Cowan, Rev. Sci. Instrum. 52, 509 (1981).
    [CrossRef]
  7. T. Jach, P. L. Cowan, Q. Shen, and M. J. Bedzyk, Phys. Rev. B 39, 5739 (1989).
    [CrossRef]
  8. B. W. Batterman and H. Cole, Rev. Mod. Phys. 36, 681 (1964).
    [CrossRef]
  9. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1969).
  10. R. F. S. Hearmon, An Introduction to Applied Anisotropic Elasticity (Oxford University, London, 1961)S. Muramatsu and M. Kitamura, J. Appl. Phys. 73, 4270 (1993).
    [CrossRef]
  11. F. A. McClintock and A. S. Argon, eds., Mechanical Behavior of Materials (Addison-Wesley, Reading, 1966), p. 349.
  12. C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, Nature (London) 390, 490 (1997).
    [CrossRef]
  13. M. M. Murnane, H. C. Kapteyn, M. D. Rosen, and R. W. Falcone, Science 251, 531 (1991).
    [CrossRef] [PubMed]

1997 (2)

Chien Liu and J. A. Golovchenko, Phys. Rev. Lett. 79, 788 (1997).
[CrossRef]

C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, Nature (London) 390, 490 (1997).
[CrossRef]

1991 (2)

M. M. Murnane, H. C. Kapteyn, M. D. Rosen, and R. W. Falcone, Science 251, 531 (1991).
[CrossRef] [PubMed]

J. P. Braud and P. L. Hagelstein, IEEE J. Quantum Electron. 27, 1069 (1991)N. V. Smith and M. R. Howells, Nucl. Instrum. Methods Phys. Res. A 347, 115 (1994)I. N. Bukreva, I. V. Kozhevnikov, and A. V. Vinogradov, Proc. SPIE 2453, 80 (1995).
[CrossRef]

1989 (1)

T. Jach, P. L. Cowan, Q. Shen, and M. J. Bedzyk, Phys. Rev. B 39, 5739 (1989).
[CrossRef]

1986 (1)

A. Ishizaka and Y. Shiraki, J. Electrochem. Soc. 133, 666 (1986).
[CrossRef]

1964 (1)

B. W. Batterman and H. Cole, Rev. Mod. Phys. 36, 681 (1964).
[CrossRef]

Albouy, P.-A.

C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, Nature (London) 390, 490 (1997).
[CrossRef]

Antonetti, A.

C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, Nature (London) 390, 490 (1997).
[CrossRef]

Audebert, P.

C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, Nature (London) 390, 490 (1997).
[CrossRef]

Batterman, B. W.

B. W. Batterman and H. Cole, Rev. Mod. Phys. 36, 681 (1964).
[CrossRef]

Bedzyk, M. J.

T. Jach, P. L. Cowan, Q. Shen, and M. J. Bedzyk, Phys. Rev. B 39, 5739 (1989).
[CrossRef]

Braud, J. P.

J. P. Braud and P. L. Hagelstein, IEEE J. Quantum Electron. 27, 1069 (1991)N. V. Smith and M. R. Howells, Nucl. Instrum. Methods Phys. Res. A 347, 115 (1994)I. N. Bukreva, I. V. Kozhevnikov, and A. V. Vinogradov, Proc. SPIE 2453, 80 (1995).
[CrossRef]

Cole, H.

B. W. Batterman and H. Cole, Rev. Mod. Phys. 36, 681 (1964).
[CrossRef]

Cowan, P. L.

T. Jach, P. L. Cowan, Q. Shen, and M. J. Bedzyk, Phys. Rev. B 39, 5739 (1989).
[CrossRef]

Falcone, R. W.

M. M. Murnane, H. C. Kapteyn, M. D. Rosen, and R. W. Falcone, Science 251, 531 (1991).
[CrossRef] [PubMed]

Forster, E.

C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, Nature (London) 390, 490 (1997).
[CrossRef]

Gauthier, J.-C.

C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, Nature (London) 390, 490 (1997).
[CrossRef]

Geindre, J.-P.

C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, Nature (London) 390, 490 (1997).
[CrossRef]

Golovchenko, J. A.

Chien Liu and J. A. Golovchenko, Phys. Rev. Lett. 79, 788 (1997).
[CrossRef]

Goodier, J. N.

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1969).

Hagelstein, P. L.

J. P. Braud and P. L. Hagelstein, IEEE J. Quantum Electron. 27, 1069 (1991)N. V. Smith and M. R. Howells, Nucl. Instrum. Methods Phys. Res. A 347, 115 (1994)I. N. Bukreva, I. V. Kozhevnikov, and A. V. Vinogradov, Proc. SPIE 2453, 80 (1995).
[CrossRef]

Hearmon, R. F. S.

R. F. S. Hearmon, An Introduction to Applied Anisotropic Elasticity (Oxford University, London, 1961)S. Muramatsu and M. Kitamura, J. Appl. Phys. 73, 4270 (1993).
[CrossRef]

Ishizaka, A.

A. Ishizaka and Y. Shiraki, J. Electrochem. Soc. 133, 666 (1986).
[CrossRef]

Jach, T.

T. Jach, P. L. Cowan, Q. Shen, and M. J. Bedzyk, Phys. Rev. B 39, 5739 (1989).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Kapteyn, H. C.

M. M. Murnane, H. C. Kapteyn, M. D. Rosen, and R. W. Falcone, Science 251, 531 (1991).
[CrossRef] [PubMed]

Liu, Chien

Chien Liu and J. A. Golovchenko, Phys. Rev. Lett. 79, 788 (1997).
[CrossRef]

Martin, J.-L.

C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, Nature (London) 390, 490 (1997).
[CrossRef]

Martinez, R. E.

R. E. Martinez, “Impurity atoms on a silicon surface:?structures, forces and dynamics,” Ph.D. dissertation (Harvard University, Cambridge, Mass., 1992)J. A. Golovchenko, R. A. Levesque, and P. L. Cowan, Rev. Sci. Instrum. 52, 509 (1981).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Murnane, M. M.

M. M. Murnane, H. C. Kapteyn, M. D. Rosen, and R. W. Falcone, Science 251, 531 (1991).
[CrossRef] [PubMed]

Rayleigh,

Rayleigh, The Theory of Sound, American ed. (Dover, New York, 1945).

Rischel, C.

C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, Nature (London) 390, 490 (1997).
[CrossRef]

Rosen, M. D.

M. M. Murnane, H. C. Kapteyn, M. D. Rosen, and R. W. Falcone, Science 251, 531 (1991).
[CrossRef] [PubMed]

Rousse, A.

C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, Nature (London) 390, 490 (1997).
[CrossRef]

Shen, Q.

T. Jach, P. L. Cowan, Q. Shen, and M. J. Bedzyk, Phys. Rev. B 39, 5739 (1989).
[CrossRef]

Shiraki, Y.

A. Ishizaka and Y. Shiraki, J. Electrochem. Soc. 133, 666 (1986).
[CrossRef]

Timoshenko, S. P.

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1969).

Uschmann, I.

C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, Nature (London) 390, 490 (1997).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

IEEE J. Quantum Electron. (1)

J. P. Braud and P. L. Hagelstein, IEEE J. Quantum Electron. 27, 1069 (1991)N. V. Smith and M. R. Howells, Nucl. Instrum. Methods Phys. Res. A 347, 115 (1994)I. N. Bukreva, I. V. Kozhevnikov, and A. V. Vinogradov, Proc. SPIE 2453, 80 (1995).
[CrossRef]

J. Electrochem. Soc. (1)

A. Ishizaka and Y. Shiraki, J. Electrochem. Soc. 133, 666 (1986).
[CrossRef]

Nature (London) (1)

C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.-C. Gauthier, E. Forster, J.-L. Martin, and A. Antonetti, Nature (London) 390, 490 (1997).
[CrossRef]

Phys. Rev. B (1)

T. Jach, P. L. Cowan, Q. Shen, and M. J. Bedzyk, Phys. Rev. B 39, 5739 (1989).
[CrossRef]

Phys. Rev. Lett. (1)

Chien Liu and J. A. Golovchenko, Phys. Rev. Lett. 79, 788 (1997).
[CrossRef]

Rev. Mod. Phys. (1)

B. W. Batterman and H. Cole, Rev. Mod. Phys. 36, 681 (1964).
[CrossRef]

Science (1)

M. M. Murnane, H. C. Kapteyn, M. D. Rosen, and R. W. Falcone, Science 251, 531 (1991).
[CrossRef] [PubMed]

Other (6)

R. E. Martinez, “Impurity atoms on a silicon surface:?structures, forces and dynamics,” Ph.D. dissertation (Harvard University, Cambridge, Mass., 1992)J. A. Golovchenko, R. A. Levesque, and P. L. Cowan, Rev. Sci. Instrum. 52, 509 (1981).
[CrossRef]

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1969).

R. F. S. Hearmon, An Introduction to Applied Anisotropic Elasticity (Oxford University, London, 1961)S. Muramatsu and M. Kitamura, J. Appl. Phys. 73, 4270 (1993).
[CrossRef]

F. A. McClintock and A. S. Argon, eds., Mechanical Behavior of Materials (Addison-Wesley, Reading, 1966), p. 349.

Rayleigh, The Theory of Sound, American ed. (Dover, New York, 1945).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

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Figures (3)

Fig. 1
Fig. 1

Relative orientations of an incident x-ray beam and a bent Si(111) waveguide. Parallel curves indicate 2¯20 lattice planes. The synchrotron radiation E field is horizontal, normal to the waveguide surface, and parallel to the 2¯20 lattice planes.

Fig. 2
Fig. 2

Schematic beam-path and film exposures taken at (a) θ-θB=1.745 mrad, (b) θ-θB=-0.122 mrad, and (c) θ-θB=0 mrad for 17.5-keV x rays on a R=15 cm Si(111) waveguide with grazing angle φ=0.5 mrad. (d) θ=θB, R=10 cm, φ=0.75 mrad.

Fig. 3
Fig. 3

(a) and (b) X-ray path on a bent Si plate with a saddlelike surface and a relaxed lattice. (c) Inset, θ scan showing the dynamic diffraction peak at θ=θB and the edge diffraction peak at θ-θB=-0.231 mrad for 17.5-keV WG x-rays on a R=10 cm Si(111) waveguide. The graph shows the angular separation of the two peaks, Δθθ-θB, as a function of R.

Equations (1)

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Eν,kz0ρ,ϕ,z,tE0ρexpikz0z+EHρexpikzHzexpiνϕ-iωt,

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