Abstract

High-energy coherent continuum radiation is generated by the interaction of rare gases with a high-power many-cycle laser field, utilizing the interferometric polarization gating technique. A narrow temporal gate is formed in the laser pulse within which the extreme ultraviolet (XUV) emission is restricted. An analytical expression for the gate function is derived. A super-XUV continuum down to 15 nm, broad enough to support synthesis of single pulses of 260 as duration and a few tens of nanojoule energy, has been measured. These results directly challenge the perspectives of single-attosecond pulse XUV-pump–XUV-probe applications.

© 2009 Optical Society of America

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2009

Y. Nomura, R. Horlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, Nat. Phys. 5, 124 (2009).
[CrossRef]

2008

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, Phys. Rev. Lett. 100, 103906 (2008).
[CrossRef] [PubMed]

V. V. Strelkov, E. Mevel, and E. Constant, New J. Phys. 10, 083040 (2008).
[CrossRef]

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. Peralta Conde, and G. D. Tsakiris, New J. Phys. 10, 025018 (2008).
[CrossRef]

2007

P. Tzallas, E. Skantzakis, C. Kalpouzos, E. P. Benis, G. D. Tsakiris, and D. Charalambidis, Nat. Phys. 3, 846 (2007).
[CrossRef]

P. B. Corkum and F. Krausz, Nat. Phys. 3, 381 (2007).
[CrossRef]

2006

D. Oron, Y. Silberberg, N. Dudovich, and D. M. Villeneuve, Phys. Rev. A 72, 063816 (2006).
[CrossRef]

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, Nat. Phys. 2, 319 (2006).
[CrossRef]

Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, Phys. Rev. Lett. 96, 083901 (2006).
[CrossRef] [PubMed]

2004

2003

P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte, and G. D. Tsakiris, Nature 426, 267 (2003).
[CrossRef] [PubMed]

1998

V. T. Platonenko and V. V. Strelkov, Quantum Electron. 28, 749 (1998).
[CrossRef]

1994

1993

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L'Huillier, Phys. Rev. A 48, 4709, (1993).
[CrossRef] [PubMed]

1976

G. V. Marr and J. B. West, At. Data Nucl. Data Tables 18, 497 (1976).
[CrossRef]

1972

F. Lukes, Surf. Sci. 30, 91 (1972).
[CrossRef]

Balcou, Ph.

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L'Huillier, Phys. Rev. A 48, 4709, (1993).
[CrossRef] [PubMed]

Benedetti, E.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, Nat. Phys. 2, 319 (2006).
[CrossRef]

Benis, E. P.

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. Peralta Conde, and G. D. Tsakiris, New J. Phys. 10, 025018 (2008).
[CrossRef]

P. Tzallas, E. Skantzakis, C. Kalpouzos, E. P. Benis, G. D. Tsakiris, and D. Charalambidis, Nat. Phys. 3, 846 (2007).
[CrossRef]

Burnett, N. H.

Caumes, J. -P.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, Nat. Phys. 2, 319 (2006).
[CrossRef]

Chang, Z.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, Phys. Rev. Lett. 100, 103906 (2008).
[CrossRef] [PubMed]

Charalambidis, D.

Y. Nomura, R. Horlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, Nat. Phys. 5, 124 (2009).
[CrossRef]

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. Peralta Conde, and G. D. Tsakiris, New J. Phys. 10, 025018 (2008).
[CrossRef]

P. Tzallas, E. Skantzakis, C. Kalpouzos, E. P. Benis, G. D. Tsakiris, and D. Charalambidis, Nat. Phys. 3, 846 (2007).
[CrossRef]

P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte, and G. D. Tsakiris, Nature 426, 267 (2003).
[CrossRef] [PubMed]

Constant, E.

V. V. Strelkov, E. Mevel, and E. Constant, New J. Phys. 10, 083040 (2008).
[CrossRef]

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, Nat. Phys. 2, 319 (2006).
[CrossRef]

Corkum, P. B.

Dromey, B.

Y. Nomura, R. Horlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, Nat. Phys. 5, 124 (2009).
[CrossRef]

Dudovich, N.

D. Oron, Y. Silberberg, N. Dudovich, and D. M. Villeneuve, Phys. Rev. A 72, 063816 (2006).
[CrossRef]

Elouga, L.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, Nat. Phys. 2, 319 (2006).
[CrossRef]

Furusawa, K.

Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, Phys. Rev. Lett. 96, 083901 (2006).
[CrossRef] [PubMed]

Gilbertson, S.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, Phys. Rev. Lett. 100, 103906 (2008).
[CrossRef] [PubMed]

Hasegawa, H.

Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, Phys. Rev. Lett. 96, 083901 (2006).
[CrossRef] [PubMed]

E. J. Takahashi, H. Hasegawa, Y. Nabekawa, and K. Midorikawa, Opt. Lett. 29, 507 (2004).
[CrossRef] [PubMed]

Horlein, R.

Y. Nomura, R. Horlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, Nat. Phys. 5, 124 (2009).
[CrossRef]

Ivanov, M. Y.

Kalpouzos, C.

P. Tzallas, E. Skantzakis, C. Kalpouzos, E. P. Benis, G. D. Tsakiris, and D. Charalambidis, Nat. Phys. 3, 846 (2007).
[CrossRef]

Karsch, S.

Y. Nomura, R. Horlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, Nat. Phys. 5, 124 (2009).
[CrossRef]

Khan, S. D.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, Phys. Rev. Lett. 100, 103906 (2008).
[CrossRef] [PubMed]

Krausz, F.

Y. Nomura, R. Horlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, Nat. Phys. 5, 124 (2009).
[CrossRef]

P. B. Corkum and F. Krausz, Nat. Phys. 3, 381 (2007).
[CrossRef]

Larsson, J.

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L'Huillier, Phys. Rev. A 48, 4709, (1993).
[CrossRef] [PubMed]

L'Huillier, A.

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L'Huillier, Phys. Rev. A 48, 4709, (1993).
[CrossRef] [PubMed]

Li, C.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, Phys. Rev. Lett. 100, 103906 (2008).
[CrossRef] [PubMed]

Lukes, F.

F. Lukes, Surf. Sci. 30, 91 (1972).
[CrossRef]

Major, Zs.

Y. Nomura, R. Horlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, Nat. Phys. 5, 124 (2009).
[CrossRef]

Maravelias, G.

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. Peralta Conde, and G. D. Tsakiris, New J. Phys. 10, 025018 (2008).
[CrossRef]

Marr, G. V.

G. V. Marr and J. B. West, At. Data Nucl. Data Tables 18, 497 (1976).
[CrossRef]

Mashiko, H.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, Phys. Rev. Lett. 100, 103906 (2008).
[CrossRef] [PubMed]

Mevel, E.

V. V. Strelkov, E. Mevel, and E. Constant, New J. Phys. 10, 083040 (2008).
[CrossRef]

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, Nat. Phys. 2, 319 (2006).
[CrossRef]

Midorikawa, K.

Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, Phys. Rev. Lett. 96, 083901 (2006).
[CrossRef] [PubMed]

E. J. Takahashi, H. Hasegawa, Y. Nabekawa, and K. Midorikawa, Opt. Lett. 29, 507 (2004).
[CrossRef] [PubMed]

Moon, E.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, Phys. Rev. Lett. 100, 103906 (2008).
[CrossRef] [PubMed]

Nabekawa, Y.

Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, Phys. Rev. Lett. 96, 083901 (2006).
[CrossRef] [PubMed]

E. J. Takahashi, H. Hasegawa, Y. Nabekawa, and K. Midorikawa, Opt. Lett. 29, 507 (2004).
[CrossRef] [PubMed]

Nikolopoulos, L. A. A.

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. Peralta Conde, and G. D. Tsakiris, New J. Phys. 10, 025018 (2008).
[CrossRef]

Nisoli, M.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, Nat. Phys. 2, 319 (2006).
[CrossRef]

Nomura, Y.

Y. Nomura, R. Horlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, Nat. Phys. 5, 124 (2009).
[CrossRef]

Okino, T.

Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, Phys. Rev. Lett. 96, 083901 (2006).
[CrossRef] [PubMed]

Oron, D.

D. Oron, Y. Silberberg, N. Dudovich, and D. M. Villeneuve, Phys. Rev. A 72, 063816 (2006).
[CrossRef]

Osterhoff, J.

Y. Nomura, R. Horlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, Nat. Phys. 5, 124 (2009).
[CrossRef]

Papadogiannis, N. A.

P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte, and G. D. Tsakiris, Nature 426, 267 (2003).
[CrossRef] [PubMed]

Peralta Conde, A.

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. Peralta Conde, and G. D. Tsakiris, New J. Phys. 10, 025018 (2008).
[CrossRef]

Persson, A.

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L'Huillier, Phys. Rev. A 48, 4709, (1993).
[CrossRef] [PubMed]

Platonenko, V. T.

V. T. Platonenko and V. V. Strelkov, Quantum Electron. 28, 749 (1998).
[CrossRef]

Poletto, L.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, Nat. Phys. 2, 319 (2006).
[CrossRef]

Rykovanov, S.

Y. Nomura, R. Horlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, Nat. Phys. 5, 124 (2009).
[CrossRef]

Salieres, P.

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L'Huillier, Phys. Rev. A 48, 4709, (1993).
[CrossRef] [PubMed]

Sansone, G.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, Nat. Phys. 2, 319 (2006).
[CrossRef]

Shakya, M. M.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, Phys. Rev. Lett. 100, 103906 (2008).
[CrossRef] [PubMed]

Shimizu, T.

Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, Phys. Rev. Lett. 96, 083901 (2006).
[CrossRef] [PubMed]

Silberberg, Y.

D. Oron, Y. Silberberg, N. Dudovich, and D. M. Villeneuve, Phys. Rev. A 72, 063816 (2006).
[CrossRef]

Skantzakis, E.

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. Peralta Conde, and G. D. Tsakiris, New J. Phys. 10, 025018 (2008).
[CrossRef]

P. Tzallas, E. Skantzakis, C. Kalpouzos, E. P. Benis, G. D. Tsakiris, and D. Charalambidis, Nat. Phys. 3, 846 (2007).
[CrossRef]

Sola, I. J.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, Nat. Phys. 2, 319 (2006).
[CrossRef]

Stagira, S.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, Nat. Phys. 2, 319 (2006).
[CrossRef]

Starczewski, T.

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L'Huillier, Phys. Rev. A 48, 4709, (1993).
[CrossRef] [PubMed]

Strelkov, V.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, Nat. Phys. 2, 319 (2006).
[CrossRef]

Strelkov, V. V.

V. V. Strelkov, E. Mevel, and E. Constant, New J. Phys. 10, 083040 (2008).
[CrossRef]

V. T. Platonenko and V. V. Strelkov, Quantum Electron. 28, 749 (1998).
[CrossRef]

Svanberg, S.

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L'Huillier, Phys. Rev. A 48, 4709, (1993).
[CrossRef] [PubMed]

Takahashi, E. J.

Tsakiris, G. D.

Y. Nomura, R. Horlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, Nat. Phys. 5, 124 (2009).
[CrossRef]

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. Peralta Conde, and G. D. Tsakiris, New J. Phys. 10, 025018 (2008).
[CrossRef]

P. Tzallas, E. Skantzakis, C. Kalpouzos, E. P. Benis, G. D. Tsakiris, and D. Charalambidis, Nat. Phys. 3, 846 (2007).
[CrossRef]

P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte, and G. D. Tsakiris, Nature 426, 267 (2003).
[CrossRef] [PubMed]

Tzallas, P.

Y. Nomura, R. Horlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, Nat. Phys. 5, 124 (2009).
[CrossRef]

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. Peralta Conde, and G. D. Tsakiris, New J. Phys. 10, 025018 (2008).
[CrossRef]

P. Tzallas, E. Skantzakis, C. Kalpouzos, E. P. Benis, G. D. Tsakiris, and D. Charalambidis, Nat. Phys. 3, 846 (2007).
[CrossRef]

P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte, and G. D. Tsakiris, Nature 426, 267 (2003).
[CrossRef] [PubMed]

Veisz, L.

Y. Nomura, R. Horlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, Nat. Phys. 5, 124 (2009).
[CrossRef]

Villeneuve, D. M.

D. Oron, Y. Silberberg, N. Dudovich, and D. M. Villeneuve, Phys. Rev. A 72, 063816 (2006).
[CrossRef]

Villoresi, P.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, Nat. Phys. 2, 319 (2006).
[CrossRef]

Vozzi, C.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. P1, P2; W1; and BS1, BS2, BS3 represent the delay plates, λ / 2 wave plates, and beam splitters, respectively. B1, B2 are 50/50 beam splitters, while B3 has 20% reflectivity and 80% transmission.

Fig. 2
Fig. 2

(a) τ g as a function of the delay δ and the intensity ratio I c 0 / I d 0 = 1 / λ 2 for a 55 fs pulse and ε th = 0.15 . (b) Intensity ratio I g / I in as a function of δ and I c 0 / I d 0 . In both graphs the black solid curve depicts the locus where τ g 5   fs , and the shaded area indicates the parameter range of I c / I d = 0.25 and δ = 68   fs used in the present experiment.

Fig. 3
Fig. 3

(a) Black solid curve, single-photon ionization cross section of Ar. Gray dotted–dashed, gray dotted, and gray dashed curves, reflectivity of the oxidized Si, Si, and SiO 2 plate, respectively. (b) Black and gray solid curves, harmonic spectrum generated in Xe and Kr, respectively, by a 115 fs IR pulse. (c) Black solid curve and gray filled area, quasi-continuum spectrum generated in Xe and Kr gases when a temporal gate of τ g 4.5   fs duration is on.

Equations (4)

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E c ( t ) = y ̂ E c 0 ( exp [ ( t δ / 2 τ L / 2   ln   2 ) 2 ] cos ( ω L t ) + exp [ ( t + δ / 2 τ L / 2   ln   2 ) 2 ] cos ( ω L t ) ) ,
E d ( t ) = x ̂ E d 0 ( exp [ ( t δ / 2 τ L / 2   ln   2 ) 2 ] cos ( ω L t π / 2 ) + exp [ ( t + δ / 2 τ L / 2   ln   2 ) 2 ] cos ( ω L t + π / 2 ) ) ,
ε ( t ) = tan ( 1 2 sin 1 ( 2 | E c ( t ) | | E d ( t ) | | E c ( t ) | 2 + | E d ( t ) | 2 ) ) = tan ( 1 2 sin 1 ( 2 ( 2 8 δ t / τ L 2 1 ) λ λ 2 ( 1 2 4 δ t / τ L 2 ) 2 + ( 1 + 2 4 δ t / τ L 2 ) 2 ) ) ,
I g = τ L τ g τ g / 2 τ g / 2 | E c ( t ) | 2 d t | E in ( t ) | 2 d t I in = τ L τ g 1 E c 0 2 τ g / 2 τ g / 2 | E c ( t ) | 2 d t 1 R c | E c ( t ) | 2 d t + λ 2 1 R c | E d ( t ) | 2 d t I in ,

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