Abstract

The isolated attosecond pulse (IAP) generated from high-order harmonic (HH) radiation has been established as an important technique for the ultrafast optics over past decade. The applications of IAP in ultrafast processes can be greatly extended by further developing the high-intensity IAP. Here, we theoretically propose to shape a two-color field by performing peak amplitude-wavelength analysis. It is found that a 240-as IAP can be generated even without carrier envelop phase (CEP) stabilization using a 25 fs/800 nm fundamental field and a relative weak 25 fs/1330 nm control field, which enables us to markedly relax the requirements of the driving laser fields both in pulse duration and CEP control. On the other hand, if the CEPs of driving laser fields are stabilized, a 65-eV broadband continual harmonic, supporting a 81-as IAP, can be directly produced with the optimized intensity ratio of 0.866 and control wavelength of 1400 nm. Moreover, the propagation effect of two-color field on the macroscopic build-up of HH for generating a high-energy IAP is discussed. We found that the method of phase match still works for the efficient continuous harmonic generation as long as the ionization level and the pressure of gas medium are kept low enough. Since the phase-matched short IAP can be generated with our shaped two-color scheme in combination with a relaxed requirement of driving laser fields, the commercial available high-energy laser source with a loosely focused geometry is promising for scaling up the energy of IAP, showing the potential for the realization of IAP with high focused intensity toward 100 attoseconds.

© 2014 Optical Society of America

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2013

R. E. F. Silva, F. Catoire, P. Rivière, H. Bachau, F. Martín, “Correlated electron and nuclear dynamics in strong field photoionization of H2+,” Phys. Rev. Lett. 110, 113001 (2013).
[CrossRef]

E. Turgut, C. La-o-vorakiat, J. M. Shaw., P. Grychtol, H. T. Nembach, D. Rudolf, R. Adam, M. Aeschlimann, C. M. Schneider, T. J. Silva, M. M. Murnane, H. C. Kapteyn, S. Mathias, “Controlling the competition between optically induced ultrafast spin-flip scattering and spin transport in magnetic multilayers,” Phys. Rev. Lett. 110, 197201 (2013).
[CrossRef] [PubMed]

E. Allaria, F. Bencivenga, R. Borghes, F. Capotondi, D. Castronovo, P. Charalambous, P. Cinquegrana, M. B. Danailov, G. De Ninno, A. Demidovich, S. Di Mitri, B. Diviacco, D. Fausti, W. M. Fawley, E. Ferrari, L. Froehlich, D. Gauthier, A. Gessini, L. Giannessi, R. Ivanov, M. Kiskinova, G. Kurdi, B. Mahieu, N. Mahne, I. Nikolov, C. Masciovecchio, E. Pedersoli, G. Penco, L. Raimondi, C. Serpico, P. Sigalotti, S. Spampinati, C. Spezzani, C. Svetina, M. Trovo, M. Zangrando, “Two-colour pump-probe experiments with a twin-pulse-seed extreme ultraviolet free-electron laser,” Nat. Commun. 4, 2476 (2013).
[CrossRef] [PubMed]

Y. Wu, E. Cunningham, H. Zang, J. Li, M. Chini, X. Wang, Y. Wang, K. Zhao, Z. Chang, “Generation of high-flux attosecond extreme ultraviolet continuum with a 10 TW laser,” Appl. Phys. Lett. 102, 201104 (2013).
[CrossRef]

P. Rudawski, C. M. Heyl, F. Brizuela, J. Schwenke, A. Persson, E. Mansten, R. Rakowski, L. Rading, F. Campi, B. Kim, P. Johnsson, A. L’Huillier, “A high-flux high-order harmonic source,” Rev. Sci. Instrum. 84, 073103 (2013).
[CrossRef] [PubMed]

E. J. Takahashi, P. Lan, Oliver D. Muöcke, Y. Nabekawa, K. Midorikawa, “Attosecond nonlinear optics using gigawatt-scale isolated attosecond pulses,” Nat. Commun. 4, 2691 (2013).
[CrossRef] [PubMed]

Z. Hong, Q. Zhang, P. Lu, “Compact dual-crystal optical parametric amplification for broadband IR pulse generation using a collinear geometry,” Opt. Express 21, 9491–9504 (2013).
[CrossRef] [PubMed]

2012

K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, Z. Chang, “Tailoring a 67 attosecond pulse through advantageous phase-mismatch,” Opt. Lett. 37, 3891–3893 (2012).
[CrossRef] [PubMed]

K. Liu, Q. Zhang, P. Lu, “Enhancing electron localization in molecular dissociation by two-color mid- and near-infrared laser fields,” Phys. Rev. A 86, 033410 (2012).
[CrossRef]

K. T. Kim, D. H. Ko, J. Park, N. N. Choi, C. M. Kim, K. L. Ishikawa, J. Lee, C. H. Nam, “Amplitude and phase reconstruction of electron wave packets for probing ultrafast photoionization dynamics,” Phys. Rev. Lett. 108, 093001 (2012).
[CrossRef] [PubMed]

Y. Zhou, C. Huang, Q. Liao, P. Lu, “Classical Simulations Including Electron Correlations for Sequential Double Ionization,” Phys. Rev. Lett. 109, 053004 (2012).
[CrossRef] [PubMed]

Y. Zhou, Q. Zhang, C. Huang, P. Lu, “Classical description of strong-field double ionization by elliptical laser pulses,” Phys. Rev. A 86, 043427 (2012).
[CrossRef]

2011

A. D. Shiner, B. E. Schmidt, C. Trallero-Herrero, H. J. Wörner, S. Patchkovskii, P. B. Corkum, J-C. Kieffer, F. Lègarè, D. M. Villeneuve, “Probing collective multi-electron dynamics in xenon with high-harmonic spectroscopy,” Nat. Phys. 7, 464–467 (2011).
[CrossRef]

T. Rohwer, S. Hellmann, M. Wiesenmayer, C. Sohrt, A. Stange, B. Slomski, A. Carr, Y. Liu, L. M. Avila, M. Kallane, S. Mathias, L. Kipp, K. Rossnagel, M. Bauer, “Collapse of long-range charge order tracked by time-resolved photoemission at high momenta,” Nature 471, 490–493 (2011).
[CrossRef] [PubMed]

Q. Zhang, E. J. Takahashi, O. D. Mücke, P. Lu, K. Midorikawa, “Dual-chirped optical parametric amplification for generating few hundred mJ infrared pulses,” Opt. Express 19, 7190–7212 (2011).
[CrossRef] [PubMed]

W. X. Chen, G. L. Chen, D. E. Kim, “Two-color field for the generation of an isolated attosecond pulse in water-window region,” Opt. Express 19, 20610–20615 (2011).
[CrossRef] [PubMed]

P. Tzallas, E. Skantzakis, L. A. A. Nikolopoulos, G. D. Tsakiris, D. Charalambidis, “Extreme-ultraviolet pumpCprobe studies of one-femtosecond-scale electron dynamics,” Nat. Physics 7, 781–784 (2011).
[CrossRef]

2010

P. Lan, E. J. Takahashi, K. Midorikawa, “Wavelength scaling of efficient high-order harmonic generation by two-color infrared laser fields,” Phys. Rev. A 81, 061802(R) (2010).
[CrossRef]

M. E. Siemens, Q. Li, R. Yang, K. A. Nelson, E. H. Anderson, M. M. Murnane, H. C. Kapteyn, “Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams,” Nature Mater. 9, 26–30 (2010).
[CrossRef]

2009

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H. C. Bandulet, D. Comtois, F. Legare, M. Giguere, J. C. Kieffer, P. B. Corkum, D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103, 073902 (2009).
[CrossRef] [PubMed]

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J.-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J.-F. Hergott, A.-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, H. Merdji, ”Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
[CrossRef] [PubMed]

Y. Nabekawa, T. Shimizu, Y. Furukawa, E. J. Takahashi, K. Midorikawa, “Interferometry of Attosecond Pulse Trains in the Extreme Ultraviolet Wavelength Region,” Phys. Rev. Lett. 102, 213904 (2009).
[CrossRef] [PubMed]

F. Krausz, M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
[CrossRef]

Y. Zheng, Z. Zeng, P. Zou, L. Zhang, X. Li, P. Liu, R. Li, Z. Xu, “Dynamic Chirp Control and Pulse Compression for Attosecond High-Order Harmonic Emission,” Phys. Rev. Lett 103, 043904 (2009).
[CrossRef] [PubMed]

X. Feng, S. Gilbertson, H. Mashiko, H. Wang, S. D. Khan, M. Chini, Y. Wu, K. Zhao, Z. Chang, “Generation of Isolated Attosecond Pulses with 20 to 28 Femtosecond Lasers,” Phys. Rev. Lett. 103, 183903 (2009).
[CrossRef]

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Nature

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, F. Krausz, “Atomic transient recorder,” Nature 427, 817 (2004).
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M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond real-time observation of electron tunnelling inatoms,” Nature 446, 627–632 (2007).
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Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, R. Dörner, “Correlated electron emission in multiphoton double ionization,” Nature 405, 658–661 (2000).
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T. Rohwer, S. Hellmann, M. Wiesenmayer, C. Sohrt, A. Stange, B. Slomski, A. Carr, Y. Liu, L. M. Avila, M. Kallane, S. Mathias, L. Kipp, K. Rossnagel, M. Bauer, “Collapse of long-range charge order tracked by time-resolved photoemission at high momenta,” Nature 471, 490–493 (2011).
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Nature Mater.

M. E. Siemens, Q. Li, R. Yang, K. A. Nelson, E. H. Anderson, M. M. Murnane, H. C. Kapteyn, “Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams,” Nature Mater. 9, 26–30 (2010).
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Opt Express

B. Kim, J. Ahn, Y. L. Yu, Y. Cheng, Z. Z. Xu, D. E. Kim, “Optimization of multi-cycle two-color laser fields for the generation of an isolated attosecond pulse,” Opt Express 16, 10331–10340 (2008).
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Opt. Express

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Phys. Rev. A

P. Lan, P. Lu, W. Cao, Y. Li, X. Wang, “Isolated sub-100-as pulse generation via controlling electron dynamics,” Phys. Rev. A 76, 011402(R) (2007).
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K. Liu, Q. Zhang, P. Lu, “Enhancing electron localization in molecular dissociation by two-color mid- and near-infrared laser fields,” Phys. Rev. A 86, 033410 (2012).
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Phys. Rev. Lett

Y. Zheng, Z. Zeng, P. Zou, L. Zhang, X. Li, P. Liu, R. Li, Z. Xu, “Dynamic Chirp Control and Pulse Compression for Attosecond High-Order Harmonic Emission,” Phys. Rev. Lett 103, 043904 (2009).
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Phys. Rev. Lett.

R. Lopez-Martens, K. Varju, P. Johnsson, J. Mauritsson, Y. Mairesse, P. Salieres, M. B. Gaarde, K. J. Schafer, A. Persson, S. Svanberg, C. G. Wahlstrom, A. L’Huillier, “Amplitude and phase control of attosecond light pulses,” Phys. Rev. Lett. 94, 033001 (2005).
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Y. Nabekawa, H. Hasegawa, E. J. Takahashi, K. Midorikawa, “Production of Doubly Charged Helium Ions by Two-Photon Absorption of an Intense Sub-10-fs Soft X-Ray Pulse at 42 eV Photon Energy,” Phys. Rev. Lett. 94, 043001 (2005).
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Y. Zhou, C. Huang, Q. Liao, P. Lu, “Classical Simulations Including Electron Correlations for Sequential Double Ionization,” Phys. Rev. Lett. 109, 053004 (2012).
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L. Miaja-Avila, G. Saathoff, S. Mathias, J. Yin, C. La-o-vorakiat, M. Bauer, M. Aeschlimann, M. M. Murnane, H. C. Kapteyn, “Direct measurement of core-level relaxation dynamics on a surface-adsorbate system,” Phys. Rev. Lett. 101, 046101 (2008).
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E. Turgut, C. La-o-vorakiat, J. M. Shaw., P. Grychtol, H. T. Nembach, D. Rudolf, R. Adam, M. Aeschlimann, C. M. Schneider, T. J. Silva, M. M. Murnane, H. C. Kapteyn, S. Mathias, “Controlling the competition between optically induced ultrafast spin-flip scattering and spin transport in magnetic multilayers,” Phys. Rev. Lett. 110, 197201 (2013).
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K. T. Kim, D. H. Ko, J. Park, N. N. Choi, C. M. Kim, K. L. Ishikawa, J. Lee, C. H. Nam, “Amplitude and phase reconstruction of electron wave packets for probing ultrafast photoionization dynamics,” Phys. Rev. Lett. 108, 093001 (2012).
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J. Breidbach, L. S. Cederbaum, “Universal attosecond response to the removal of an electron,” Physical review letters 94, 033901 (2005).
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Proc. Natl. Acad. Sci. USA

F. Remacle, R. D. Levine, “An electronic time scale in chemistry,” Proc. Natl. Acad. Sci. USA 103, 6793–6798 (2006).
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F. Krausz, M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
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P. Rudawski, C. M. Heyl, F. Brizuela, J. Schwenke, A. Persson, E. Mansten, R. Rakowski, L. Rading, F. Campi, B. Kim, P. Johnsson, A. L’Huillier, “A high-flux high-order harmonic source,” Rev. Sci. Instrum. 84, 073103 (2013).
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Science

E. Gagnon, P. Ranitovic, X. M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, A. S. Sandhu, “Soft X-ray-driven femtosecond molecular dynamics,” Science 317, 1374–1378 (2007).
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G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli, Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
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S. Fang, G. Cirmi, S.-H. Chia, O. D. Mücke, F. X. Kärtner, C. Manzoni, P. Farinello, G. Cerullo, “Multi-mJ parametric synthesizer generating two-octave-wide optical waveforms,” Conference on Lasers and Electro-Optics Pacific Rim, 1–2 (CLEO-PR, 2013).

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Figures (15)

Fig. 1
Fig. 1

The variation of the ratio R as a function of the control field wavelength using 25-fs two-color fields with different intensity ratios: (E1/E0)2=0.05 (blue solid line), (E1/E0)2=0.1 (green dashed line), and (E1/E0)2=0.15 (red chain line). Here, ϕ0 and ϕ1 are both set to π.

Fig. 2
Fig. 2

(a) The distribution of R values as a function of ϕ0 and ϕ1, (b) ϕ1-dependent R values with ϕ0=π and (c) ϕ0-dependent R values with ϕ1=π in the mixed field with a control field of 1330-nm. (d)–(f) Same to (a)–(c), but for a 1250-nm control field. Here, the intensity ratios (E1/E0)2 of the driving and control fields are chosen as 0.1.

Fig. 3
Fig. 3

(a) Calculated harmonic spectra for different CEP combinations with the 1330-nm control field. (b) Same to (a), but for the 1250-nm control field. Here, the intensity ratios E 1 2 / E 0 2 are fixed to 0.1.

Fig. 4
Fig. 4

(a) The CEP dependence of HHG with single-atom response in the optimized 25-fs two-color field. (b) Temporal profiles of attosecond pulses generated by selecting continuous harmonics in (a).

Fig. 5
Fig. 5

The dependence of the R value on both the CEPs of the fundamental and control laser fields. The wavelength of control field is chosen as (a) 1200 nm, (b) 1600 nm, (c) 2000 nm, and (d) 2400 nm, respectively

Fig. 6
Fig. 6

(a) The harmonic spectra calculated with different CEP combinations (ϕ0, ϕ1) of the fundamental and control fields: (π, π) (blue line), (π, 1.1π) (green line), and (π, 1.2π) (red line). The wavelength and intensity of the control field are 1600 nm and 1.1 × 1013 W/cm2, respectively. (b) Same to (a), but for 2400-nm control field.

Fig. 7
Fig. 7

(a) The variation of the R value as a function of the wavelength of control field. The R values at 1500 nm, 1776 nm and 2400 nm are indicated by green, blue and red lines, respectively. (b) the harmonic spectra calculated with different wavelengths of control field. Here, the CEP combination (ϕ0, ϕ1) is set to be (π, π) and the laser intensity of the control field is 1.1 × 1013 W/cm2.

Fig. 8
Fig. 8

The dependence of the ratio R on both the laser intensity ratio E 1 2 / E 0 2 and wavelength of the control field with the optimum CEP combination (π, π).

Fig. 9
Fig. 9

(a) The electric field of the optimum two-color field, (b) calculated harmonic spectra for single-atom response, (c) time-frequency diagram of the spectrum, and (d) the temporal profiles of the attosecond pulses by superposing the continuous harmonics. Inset: the TL pulse of the IAP shown in (d).

Fig. 10
Fig. 10

(a)–(e) The birth moment ti and recollision moment tr contributed to the 30th–120th harmonic with intensity ratios of 0, 0.2, 0.4, 0.6 and 0.8, respectively. The blue solid and red solid line denote the long and short trajectories, respectively. The marked blue squares and diamonds represent the ti and tr of 80th harmonic for long trajectory, the marked red circles and triangles correspond the ti and tr of 80th harmonic for short trajectory. (f)–(j) The calculated phases of 75th–85th harmonics for short trajectory, the intensity ratios are the same as (a)–(e). The marked stars represent the phases of 80th harmonic.

Fig. 11
Fig. 11

(a) The dependence of intensity ratio on different focal geometries across the focal region of the two-color field. (b) The phase Φq(z) of the generated 80th harmonic (contributed by short trajectory) for these three focal geometries along propagation direction. (c) The dispersion Φq(z)/∂z. In (a), (b) and (c) the intensity ratio is set to be 0.86 at the waist of the focused gaussian laser beam. (d). The comparison of calculated dispersion with f#= 300 for a constant intensity ratio along propagation direction (brown line) and varied intensity ratio same as that in (c) (green line).

Fig. 12
Fig. 12

(a) The CEP dependence of on-axis harmonic spectrum with collective response in the optimized 25 fs two-color field. (b)Temporal profiles of attosecond pulses generated by selecting continuous harmonics in (a). The focused beam waists are 35 μm and 45 μm for the fundamental and control fields, respectively. Other laser parameters are the same as Fig. 4.

Fig. 13
Fig. 13

(a) The produced IAPs with different CEPs. (b) The relationship between obtained pulse duration and CEP. The parameters are the same as Fig. 12.

Fig. 14
Fig. 14

The spatial distribution of harmonic radiation at the exit of gas medium. The thin white line denote the on-axis harmonic spectrum, and the single-atom response is plotted with cyan line for comparison. Inset: the obtained IAP by superposing the 105th to 135th harmonics in the continuous part. The focused beam waists are 35 μm and 45 μm for the fundamental and control fields, respectively. Other parameters are the same as Fig. 9.

Fig. 15
Fig. 15

Same as Fig. 14, but for loosely focused geometry. f0# = 600 and f1# = 464 correspond to the beam waists of 140 μm and 180 μm for the fundamental and control fields.

Equations (17)

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d n l ( t ) = i t d t [ π ε + i ( t t ) / 2 ] 3 / 2 × d rec [ p s t ( t , t ) A ( t ) ] d ion [ p s t ( t , t ) A ( t ) ] × exp [ i S s t ( t , t ) ] E ( t ) g ( t ) + c . c .
a q = | 1 T 0 T a ( t ) exp ( i q ω t ) | 2 ,
R = E 1 m / E 2 m ,
2 E l ( r , z , t ) 1 c 2 2 E l ( r , z , t ) t 2 = ω 2 c 2 ( 1 n eff 2 ) E l ( r , z , t ) ,
η eff = η 0 ( r , z , t ) + η 2 I ( r , z , t ) ω p 2 ( r , z , t ) 2 ω .
2 E h ( r , z , t ) 1 c 2 2 E h ( r , z , t ) t 2 = ω p 2 ( r , z , t ) c 2 E h ( r , z , t ) + μ 0 2 P n l ( r , z , t ) t 2 ,
E ( t ) = E 0 exp ( 2 ln 2 t 2 / τ 0 2 ) cos ( ω 0 t + ϕ 0 ) + E 1 exp ( 2 ln 2 t 2 / τ 1 2 ) cos ( ω 1 t + ϕ 1 ) ,
Δ k = Δ k n + Δ k p + Δ k g + Δ k p l .
Δ k i = q ϕ f , i ( z ) z ϕ q , i ( z ) z = q k f , i k q , i , ( i = n , p , g , p l ) ,
Δ k = Φ q ( z ) z Φ q , pro ( z ) z ,
Φ q , pro ( z ) = Φ q ( z 0 ) + [ 2 π λ + 2 π N a n ( λ q ) λ N e r e λ q ] ( z z 0 ) ,
ϕ ( S 0 , S 1 ) = E 0 2 { 1 2 ω 0 2 S 0 2 ( t r t i ) + E 1 2 E 0 2 1 2 ω 1 2 S 1 2 ( t r t i ) + E 1 E 0 1 ω 0 ω 1 S 0 S 1 + 1 8 ω 0 3 [ sin ( 2 ω 0 t r ) sin ( 2 ω 0 t i ) ] + E 1 2 E 0 2 1 8 ω 1 3 [ sin ( 2 ω 1 t r + 2 Δ ϕ ) sin ( 2 ω 1 t i + 2 Δ ϕ ) ] + E 1 E 0 1 ω 0 ω 1 { sin [ ( ω 0 + ω 1 ) t r + Δ ϕ ] ω 0 + ω 1 sin [ ( ω 0 ω 1 ) t r Δ ϕ ] ω 0 ω 1 } 1 4 ω 0 2 ( t r t i ) E 1 2 E 0 2 1 4 ω 1 2 ( t r t i ) } + q ω 0 t r ,
S 0 = cos ( ω 0 t r ) cos ( ω 0 t i ) ω 0 ( t i t r ) ,
S 1 = cos ( ω 1 t r + Δ ϕ ) cos ( ω 1 t i + Δ ϕ ) ω 1 ( t i t r ) ,
P s = 1 t i t r t r t i d t A ( t ) ,
[ P s + A ( t i ) ] 2 2 + I p ,
[ P s + A ( t r ) ] 2 2 + I p = q ω .

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