Abstract

We report on the formation mechanism of element distribution in glass under high-repetition-rate femtosecond laser irradiation. We simultaneously focused two beams of femtosecond laser pulses inside a glass and confirmed the formation of characteristically shaped element distributions. The results of the numerical simulation in which we considered concentration- and temperature-gradient-driven diffusions were in excellent qualitative agreement with the experimental results, indicating that the main driving force is the sharp temperature gradient. Since the composition of a glass affects its refractive index, absorption, and luminescence property, the results in this study provide a framework to fabricate a functional optical device such as optical circuits with a high-repetition- rate femtosecond laser.

© 2011 Optical Society of America

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  1. H. Takebe, T. Murata, and K. Morinaga, J. Am. Ceram. Soc. 79, 681 (1996).
    [Crossref]
  2. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
    [Crossref] [PubMed]
  3. S. M. Eaton, H. B. Zhang, and P. R. Herman, Opt. Express 13, 4708 (2005).
    [Crossref] [PubMed]
  4. R. R. Gattass and E. Mazur, Nat. Photon. 2, 219 (2008).
    [Crossref]
  5. S. Kanehira, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 023112 (2008).
    [Crossref]
  6. Y. Liu, B. Zhu, L. Wang, J. R. Qiu, Y. Dai, and H. L. Ma, Appl. Phys. Lett. 92, 121113 (2008).
    [Crossref]
  7. F. F. Luo, B. Qian, G. Lin, J. Xu, Y. Liao, J. Song, H. Y. Sun, B. Zhu, J. R. Qiu, Q. Z. Zhao, and Z. Z. Xu, Opt. Express 18, 6262 (2010).
    [Crossref] [PubMed]
  8. M. Shimizu, K. Miura, N. Yasuda, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, and K. Hirao, Mater. Res. Soc. Symp. Proc. 1230, 1230-MM07-04 (2009).
    [Crossref]
  9. Y. Liu, M. Shimizu, B. Zhu, Y. Dai, B. Qian, J. R. Qiu, Y. Shimotsuma, K. Miura, and K. Hirao, Opt. Lett. 34, 136(2009).
    [Crossref] [PubMed]
  10. S. Zhou, N. Jiang, K. Miura, S. Tanabe, M. Shimizu, M. Sakakura, Y. Shimotsuma, M. Nishi, J. Qiu, and K. Hirao, J. Am. Chem. Soc. 132, 17945 (2010).
    [Crossref] [PubMed]
  11. M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 231112 (2008).
    [Crossref]
  12. M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, J. Appl. Phys. 108, 073533 (2010).
    [Crossref]
  13. A. A. Appen, ed., The Chemistry of Glass (Chimia, 1970).
  14. Y. Oishi, M. Nanba, and J. A. Pask, J. Am. Ceram. Soc. 65, 247 (1982).
    [Crossref]
  15. S. Prager and H. Eyring, J. Chem. Phys. 21, 1347 (1953).
    [Crossref]
  16. R. Terai and R. Hayami, J. Non-Cryst. Solids 18, 217 (1975).
    [Crossref]
  17. C. E. Lesher and D. Walker, Geochim. Cosmochim. Acta 50, 1397 (1986).
    [Crossref]
  18. F. Huang, P. Chakraborty, C. C. Lundstrom, C. Holmden, J. J. G. Glessner, S. W. Kieffer, and C. E. Lesher, Nature 464, 396 (2010).
    [Crossref] [PubMed]

2010 (4)

F. F. Luo, B. Qian, G. Lin, J. Xu, Y. Liao, J. Song, H. Y. Sun, B. Zhu, J. R. Qiu, Q. Z. Zhao, and Z. Z. Xu, Opt. Express 18, 6262 (2010).
[Crossref] [PubMed]

S. Zhou, N. Jiang, K. Miura, S. Tanabe, M. Shimizu, M. Sakakura, Y. Shimotsuma, M. Nishi, J. Qiu, and K. Hirao, J. Am. Chem. Soc. 132, 17945 (2010).
[Crossref] [PubMed]

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, J. Appl. Phys. 108, 073533 (2010).
[Crossref]

F. Huang, P. Chakraborty, C. C. Lundstrom, C. Holmden, J. J. G. Glessner, S. W. Kieffer, and C. E. Lesher, Nature 464, 396 (2010).
[Crossref] [PubMed]

2009 (2)

M. Shimizu, K. Miura, N. Yasuda, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, and K. Hirao, Mater. Res. Soc. Symp. Proc. 1230, 1230-MM07-04 (2009).
[Crossref]

Y. Liu, M. Shimizu, B. Zhu, Y. Dai, B. Qian, J. R. Qiu, Y. Shimotsuma, K. Miura, and K. Hirao, Opt. Lett. 34, 136(2009).
[Crossref] [PubMed]

2008 (4)

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 231112 (2008).
[Crossref]

R. R. Gattass and E. Mazur, Nat. Photon. 2, 219 (2008).
[Crossref]

S. Kanehira, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 023112 (2008).
[Crossref]

Y. Liu, B. Zhu, L. Wang, J. R. Qiu, Y. Dai, and H. L. Ma, Appl. Phys. Lett. 92, 121113 (2008).
[Crossref]

2005 (1)

1996 (2)

H. Takebe, T. Murata, and K. Morinaga, J. Am. Ceram. Soc. 79, 681 (1996).
[Crossref]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
[Crossref] [PubMed]

1986 (1)

C. E. Lesher and D. Walker, Geochim. Cosmochim. Acta 50, 1397 (1986).
[Crossref]

1982 (1)

Y. Oishi, M. Nanba, and J. A. Pask, J. Am. Ceram. Soc. 65, 247 (1982).
[Crossref]

1975 (1)

R. Terai and R. Hayami, J. Non-Cryst. Solids 18, 217 (1975).
[Crossref]

1953 (1)

S. Prager and H. Eyring, J. Chem. Phys. 21, 1347 (1953).
[Crossref]

Appen, A. A.

A. A. Appen, ed., The Chemistry of Glass (Chimia, 1970).

Chakraborty, P.

F. Huang, P. Chakraborty, C. C. Lundstrom, C. Holmden, J. J. G. Glessner, S. W. Kieffer, and C. E. Lesher, Nature 464, 396 (2010).
[Crossref] [PubMed]

Dai, Y.

Davis, K. M.

Eaton, S. M.

Eyring, H.

S. Prager and H. Eyring, J. Chem. Phys. 21, 1347 (1953).
[Crossref]

Gattass, R. R.

R. R. Gattass and E. Mazur, Nat. Photon. 2, 219 (2008).
[Crossref]

Glessner, J. J. G.

F. Huang, P. Chakraborty, C. C. Lundstrom, C. Holmden, J. J. G. Glessner, S. W. Kieffer, and C. E. Lesher, Nature 464, 396 (2010).
[Crossref] [PubMed]

Hayami, R.

R. Terai and R. Hayami, J. Non-Cryst. Solids 18, 217 (1975).
[Crossref]

Herman, P. R.

Hirao, K.

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, J. Appl. Phys. 108, 073533 (2010).
[Crossref]

S. Zhou, N. Jiang, K. Miura, S. Tanabe, M. Shimizu, M. Sakakura, Y. Shimotsuma, M. Nishi, J. Qiu, and K. Hirao, J. Am. Chem. Soc. 132, 17945 (2010).
[Crossref] [PubMed]

M. Shimizu, K. Miura, N. Yasuda, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, and K. Hirao, Mater. Res. Soc. Symp. Proc. 1230, 1230-MM07-04 (2009).
[Crossref]

Y. Liu, M. Shimizu, B. Zhu, Y. Dai, B. Qian, J. R. Qiu, Y. Shimotsuma, K. Miura, and K. Hirao, Opt. Lett. 34, 136(2009).
[Crossref] [PubMed]

S. Kanehira, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 023112 (2008).
[Crossref]

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 231112 (2008).
[Crossref]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
[Crossref] [PubMed]

Holmden, C.

F. Huang, P. Chakraborty, C. C. Lundstrom, C. Holmden, J. J. G. Glessner, S. W. Kieffer, and C. E. Lesher, Nature 464, 396 (2010).
[Crossref] [PubMed]

Huang, F.

F. Huang, P. Chakraborty, C. C. Lundstrom, C. Holmden, J. J. G. Glessner, S. W. Kieffer, and C. E. Lesher, Nature 464, 396 (2010).
[Crossref] [PubMed]

Jiang, N.

S. Zhou, N. Jiang, K. Miura, S. Tanabe, M. Shimizu, M. Sakakura, Y. Shimotsuma, M. Nishi, J. Qiu, and K. Hirao, J. Am. Chem. Soc. 132, 17945 (2010).
[Crossref] [PubMed]

Kanehira, S.

M. Shimizu, K. Miura, N. Yasuda, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, and K. Hirao, Mater. Res. Soc. Symp. Proc. 1230, 1230-MM07-04 (2009).
[Crossref]

S. Kanehira, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 023112 (2008).
[Crossref]

Kieffer, S. W.

F. Huang, P. Chakraborty, C. C. Lundstrom, C. Holmden, J. J. G. Glessner, S. W. Kieffer, and C. E. Lesher, Nature 464, 396 (2010).
[Crossref] [PubMed]

Lesher, C. E.

F. Huang, P. Chakraborty, C. C. Lundstrom, C. Holmden, J. J. G. Glessner, S. W. Kieffer, and C. E. Lesher, Nature 464, 396 (2010).
[Crossref] [PubMed]

C. E. Lesher and D. Walker, Geochim. Cosmochim. Acta 50, 1397 (1986).
[Crossref]

Liao, Y.

Lin, G.

Liu, Y.

Lundstrom, C. C.

F. Huang, P. Chakraborty, C. C. Lundstrom, C. Holmden, J. J. G. Glessner, S. W. Kieffer, and C. E. Lesher, Nature 464, 396 (2010).
[Crossref] [PubMed]

Luo, F. F.

Ma, H. L.

Y. Liu, B. Zhu, L. Wang, J. R. Qiu, Y. Dai, and H. L. Ma, Appl. Phys. Lett. 92, 121113 (2008).
[Crossref]

Mazur, E.

R. R. Gattass and E. Mazur, Nat. Photon. 2, 219 (2008).
[Crossref]

Miura, K.

S. Zhou, N. Jiang, K. Miura, S. Tanabe, M. Shimizu, M. Sakakura, Y. Shimotsuma, M. Nishi, J. Qiu, and K. Hirao, J. Am. Chem. Soc. 132, 17945 (2010).
[Crossref] [PubMed]

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, J. Appl. Phys. 108, 073533 (2010).
[Crossref]

M. Shimizu, K. Miura, N. Yasuda, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, and K. Hirao, Mater. Res. Soc. Symp. Proc. 1230, 1230-MM07-04 (2009).
[Crossref]

Y. Liu, M. Shimizu, B. Zhu, Y. Dai, B. Qian, J. R. Qiu, Y. Shimotsuma, K. Miura, and K. Hirao, Opt. Lett. 34, 136(2009).
[Crossref] [PubMed]

S. Kanehira, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 023112 (2008).
[Crossref]

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 231112 (2008).
[Crossref]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
[Crossref] [PubMed]

Morinaga, K.

H. Takebe, T. Murata, and K. Morinaga, J. Am. Ceram. Soc. 79, 681 (1996).
[Crossref]

Murata, T.

H. Takebe, T. Murata, and K. Morinaga, J. Am. Ceram. Soc. 79, 681 (1996).
[Crossref]

Nakaya, T.

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, J. Appl. Phys. 108, 073533 (2010).
[Crossref]

Nanba, M.

Y. Oishi, M. Nanba, and J. A. Pask, J. Am. Ceram. Soc. 65, 247 (1982).
[Crossref]

Nishi, M.

S. Zhou, N. Jiang, K. Miura, S. Tanabe, M. Shimizu, M. Sakakura, Y. Shimotsuma, M. Nishi, J. Qiu, and K. Hirao, J. Am. Chem. Soc. 132, 17945 (2010).
[Crossref] [PubMed]

M. Shimizu, K. Miura, N. Yasuda, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, and K. Hirao, Mater. Res. Soc. Symp. Proc. 1230, 1230-MM07-04 (2009).
[Crossref]

Ohnishi, M.

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, J. Appl. Phys. 108, 073533 (2010).
[Crossref]

Oishi, Y.

Y. Oishi, M. Nanba, and J. A. Pask, J. Am. Ceram. Soc. 65, 247 (1982).
[Crossref]

Pask, J. A.

Y. Oishi, M. Nanba, and J. A. Pask, J. Am. Ceram. Soc. 65, 247 (1982).
[Crossref]

Prager, S.

S. Prager and H. Eyring, J. Chem. Phys. 21, 1347 (1953).
[Crossref]

Qian, B.

Qiu, J.

S. Zhou, N. Jiang, K. Miura, S. Tanabe, M. Shimizu, M. Sakakura, Y. Shimotsuma, M. Nishi, J. Qiu, and K. Hirao, J. Am. Chem. Soc. 132, 17945 (2010).
[Crossref] [PubMed]

Qiu, J. R.

Sakakura, M.

S. Zhou, N. Jiang, K. Miura, S. Tanabe, M. Shimizu, M. Sakakura, Y. Shimotsuma, M. Nishi, J. Qiu, and K. Hirao, J. Am. Chem. Soc. 132, 17945 (2010).
[Crossref] [PubMed]

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, J. Appl. Phys. 108, 073533 (2010).
[Crossref]

M. Shimizu, K. Miura, N. Yasuda, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, and K. Hirao, Mater. Res. Soc. Symp. Proc. 1230, 1230-MM07-04 (2009).
[Crossref]

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 231112 (2008).
[Crossref]

Shimizu, M.

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, J. Appl. Phys. 108, 073533 (2010).
[Crossref]

S. Zhou, N. Jiang, K. Miura, S. Tanabe, M. Shimizu, M. Sakakura, Y. Shimotsuma, M. Nishi, J. Qiu, and K. Hirao, J. Am. Chem. Soc. 132, 17945 (2010).
[Crossref] [PubMed]

M. Shimizu, K. Miura, N. Yasuda, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, and K. Hirao, Mater. Res. Soc. Symp. Proc. 1230, 1230-MM07-04 (2009).
[Crossref]

Y. Liu, M. Shimizu, B. Zhu, Y. Dai, B. Qian, J. R. Qiu, Y. Shimotsuma, K. Miura, and K. Hirao, Opt. Lett. 34, 136(2009).
[Crossref] [PubMed]

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 231112 (2008).
[Crossref]

Shimotsuma, Y.

S. Zhou, N. Jiang, K. Miura, S. Tanabe, M. Shimizu, M. Sakakura, Y. Shimotsuma, M. Nishi, J. Qiu, and K. Hirao, J. Am. Chem. Soc. 132, 17945 (2010).
[Crossref] [PubMed]

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, J. Appl. Phys. 108, 073533 (2010).
[Crossref]

M. Shimizu, K. Miura, N. Yasuda, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, and K. Hirao, Mater. Res. Soc. Symp. Proc. 1230, 1230-MM07-04 (2009).
[Crossref]

Y. Liu, M. Shimizu, B. Zhu, Y. Dai, B. Qian, J. R. Qiu, Y. Shimotsuma, K. Miura, and K. Hirao, Opt. Lett. 34, 136(2009).
[Crossref] [PubMed]

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 231112 (2008).
[Crossref]

Song, J.

Sugimoto, N.

Sun, H. Y.

Takebe, H.

H. Takebe, T. Murata, and K. Morinaga, J. Am. Ceram. Soc. 79, 681 (1996).
[Crossref]

Tanabe, S.

S. Zhou, N. Jiang, K. Miura, S. Tanabe, M. Shimizu, M. Sakakura, Y. Shimotsuma, M. Nishi, J. Qiu, and K. Hirao, J. Am. Chem. Soc. 132, 17945 (2010).
[Crossref] [PubMed]

Terai, R.

R. Terai and R. Hayami, J. Non-Cryst. Solids 18, 217 (1975).
[Crossref]

Walker, D.

C. E. Lesher and D. Walker, Geochim. Cosmochim. Acta 50, 1397 (1986).
[Crossref]

Wang, L.

Y. Liu, B. Zhu, L. Wang, J. R. Qiu, Y. Dai, and H. L. Ma, Appl. Phys. Lett. 92, 121113 (2008).
[Crossref]

Xu, J.

Xu, Z. Z.

Yasuda, N.

M. Shimizu, K. Miura, N. Yasuda, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, and K. Hirao, Mater. Res. Soc. Symp. Proc. 1230, 1230-MM07-04 (2009).
[Crossref]

Zhang, H. B.

Zhao, Q. Z.

Zhou, S.

S. Zhou, N. Jiang, K. Miura, S. Tanabe, M. Shimizu, M. Sakakura, Y. Shimotsuma, M. Nishi, J. Qiu, and K. Hirao, J. Am. Chem. Soc. 132, 17945 (2010).
[Crossref] [PubMed]

Zhu, B.

Appl. Phys. Lett. (3)

S. Kanehira, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 023112 (2008).
[Crossref]

Y. Liu, B. Zhu, L. Wang, J. R. Qiu, Y. Dai, and H. L. Ma, Appl. Phys. Lett. 92, 121113 (2008).
[Crossref]

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 231112 (2008).
[Crossref]

Geochim. Cosmochim. Acta (1)

C. E. Lesher and D. Walker, Geochim. Cosmochim. Acta 50, 1397 (1986).
[Crossref]

J. Am. Ceram. Soc. (2)

Y. Oishi, M. Nanba, and J. A. Pask, J. Am. Ceram. Soc. 65, 247 (1982).
[Crossref]

H. Takebe, T. Murata, and K. Morinaga, J. Am. Ceram. Soc. 79, 681 (1996).
[Crossref]

J. Am. Chem. Soc. (1)

S. Zhou, N. Jiang, K. Miura, S. Tanabe, M. Shimizu, M. Sakakura, Y. Shimotsuma, M. Nishi, J. Qiu, and K. Hirao, J. Am. Chem. Soc. 132, 17945 (2010).
[Crossref] [PubMed]

J. Appl. Phys. (1)

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, J. Appl. Phys. 108, 073533 (2010).
[Crossref]

J. Chem. Phys. (1)

S. Prager and H. Eyring, J. Chem. Phys. 21, 1347 (1953).
[Crossref]

J. Non-Cryst. Solids (1)

R. Terai and R. Hayami, J. Non-Cryst. Solids 18, 217 (1975).
[Crossref]

Mater. Res. Soc. Symp. Proc. (1)

M. Shimizu, K. Miura, N. Yasuda, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, and K. Hirao, Mater. Res. Soc. Symp. Proc. 1230, 1230-MM07-04 (2009).
[Crossref]

Nat. Photon. (1)

R. R. Gattass and E. Mazur, Nat. Photon. 2, 219 (2008).
[Crossref]

Nature (1)

F. Huang, P. Chakraborty, C. C. Lundstrom, C. Holmden, J. J. G. Glessner, S. W. Kieffer, and C. E. Lesher, Nature 464, 396 (2010).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (2)

Other (1)

A. A. Appen, ed., The Chemistry of Glass (Chimia, 1970).

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Figures (3)

Fig. 1
Fig. 1

OM images and element distributions after laser irradiation. (a) One-spot irradiation. (b) Two-spot irradiation with a distance of 42.7 μm between the two focal spots. (c) Two-spot irradiation with a distance of 31.9 μm between the two focal spots.

Fig. 2
Fig. 2

(a)–(c) Temperature distributions for simulation and calculated concentration distributions of (d)–(f) CaO and (g)–(i)  SiO 2 after 10 ms . (a), (d), (g) One-spot irradiation. (b), (e), (h) Two-spot irradiation with a distance of 1.40 μm between the two focal spots. (c), (f), (i) Two-spot irradiation with a distance of 1.12 μm between the two focal spots.

Fig. 3
Fig. 3

Simulation results under additional temperature conditions. We used the temperature distribution shown in Fig. 2a as the default temperature distribution, which is shown in (d). (a)–(c) Schematic diagrams of the temperature profiles added to the default temperature. (d)–(f) Two-dimensional image of temperature distribution. (g) Concentration profile of CaO along the position on the white dotted line in (d)–(f).

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

J 1 = D 1 C 1 D 1 Q 1 C 1 R T 2 T ( x , y ) + C 1 v ,
J 2 = D 2 C 2 D 2 Q 2 C 2 R T 2 T ( x , y ) + C 2 v ,
C 1 t = [ { ( 1 Ω 1 C 1 ) D 1 + Ω 1 C 1 D 2 } C 1 ] [ C 1 ( 1 Ω 1 C 1 ) D 2 Q 2 D 1 Q 1 R T 2 T ( x , y ) ] .

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