Abstract

We study the effect of pump-seed timing fluctuations on the carrier-envelope phase (CEP) of signal and idler pulses emerging from an OP(CP)A. A simple analytical model is derived in order to provide an intuitive explanation of the origin of CEP fluctuations, while split-step simulations are performed to cover a broad range of different seeding schemes. Finally, we compare the simulation results with real observations of the CEP of idler pulses generated by an OPA. The quantitative model presented provides a key tool for designing the next generation of low-noise CEP-stable OP(CP)A-based sources.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
  4. V. Gruson, G. Ernotte, P. Lassonde, A. Laramée, M. R. Bionta, M. Chaker, L. D. Mauro, P. B. Corkum, H. Ibrahim, B. E. Schmidt, and F. Legaré, Opt. Express 25, 27706 (2017).
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    [Crossref]
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    [Crossref]
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    [Crossref]

2017 (1)

2016 (2)

2015 (1)

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S. H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
[Crossref]

2014 (3)

2012 (1)

2011 (1)

G. Cerullo, A. Baltuška, O. Mücke, and C. Vozzi, Laser Photon. Rev. 5, 323 (2011).
[Crossref]

2008 (2)

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, New J. Phys. 10, 025024 (2008).
[Crossref]

D. Brida, G. Cirmi, C. Manzoni, S. Bonora, P. Villoresi, S. D. Silvestri, and G. Cerullo, Opt. Lett. 33, 741 (2008).
[Crossref]

2002 (1)

A. Baltuška, T. Fuji, and T. Kobayashi, Phys. Rev. Lett. 88, 133901 (2002).
[Crossref]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Baltuška, A.

G. Cerullo, A. Baltuška, O. Mücke, and C. Vozzi, Laser Photon. Rev. 5, 323 (2011).
[Crossref]

A. Baltuška, T. Fuji, and T. Kobayashi, Phys. Rev. Lett. 88, 133901 (2002).
[Crossref]

Biegert, J.

Bionta, M. R.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Bonora, S.

Brida, D.

Buades, B.

Calendron, A.-L.

Çankaya, H.

Cerullo, G.

C. Manzoni and G. Cerullo, J. Opt. 18, 103501 (2016).
[Crossref]

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S. H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
[Crossref]

J. Vogelsang, J. Robin, B. Piglosiewicz, C. Manzoni, P. Farinello, S. Melzer, P. Feru, G. Cerullo, C. Lienau, and P. Groß, Opt. Express 22, 25295 (2014).
[Crossref]

B. Piglosiewicz, S. Schmidt, D. J. Park, J. Vogelsang, P. Grosz, C. Manzoni, P. Farinello, G. Cerullo, and C. Lienau, Nat. Photonics 8, 37 (2014).
[Crossref]

G. Cerullo, A. Baltuška, O. Mücke, and C. Vozzi, Laser Photon. Rev. 5, 323 (2011).
[Crossref]

D. Brida, G. Cirmi, C. Manzoni, S. Bonora, P. Villoresi, S. D. Silvestri, and G. Cerullo, Opt. Lett. 33, 741 (2008).
[Crossref]

Chaker, M.

Chia, S. H.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S. H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
[Crossref]

Chia, S.-H.

Cirmi, G.

H. Çankaya, A.-L. Calendron, C. Zhou, S.-H. Chia, O. D. Mücke, G. Cirmi, and F. X. Kärtner, Opt. Express 24, 25169 (2016).
[Crossref]

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S. H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
[Crossref]

D. Brida, G. Cirmi, C. Manzoni, S. Bonora, P. Villoresi, S. D. Silvestri, and G. Cerullo, Opt. Lett. 33, 741 (2008).
[Crossref]

Corkum, P. B.

Cousin, S. L.

Demmler, S.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Ernotte, G.

Fang, S.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S. H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
[Crossref]

Farinello, P.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S. H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
[Crossref]

B. Piglosiewicz, S. Schmidt, D. J. Park, J. Vogelsang, P. Grosz, C. Manzoni, P. Farinello, G. Cerullo, and C. Lienau, Nat. Photonics 8, 37 (2014).
[Crossref]

J. Vogelsang, J. Robin, B. Piglosiewicz, C. Manzoni, P. Farinello, S. Melzer, P. Feru, G. Cerullo, C. Lienau, and P. Groß, Opt. Express 22, 25295 (2014).
[Crossref]

Feru, P.

Fuji, T.

A. Baltuška, T. Fuji, and T. Kobayashi, Phys. Rev. Lett. 88, 133901 (2002).
[Crossref]

Groß, P.

Grosz, P.

B. Piglosiewicz, S. Schmidt, D. J. Park, J. Vogelsang, P. Grosz, C. Manzoni, P. Farinello, G. Cerullo, and C. Lienau, Nat. Photonics 8, 37 (2014).
[Crossref]

Gruson, V.

Hädrich, S.

Hasovic, E.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, New J. Phys. 10, 025024 (2008).
[Crossref]

Hemmer, M.

Ibrahim, H.

Kärtner, F. X.

H. Çankaya, A.-L. Calendron, C. Zhou, S.-H. Chia, O. D. Mücke, G. Cirmi, and F. X. Kärtner, Opt. Express 24, 25169 (2016).
[Crossref]

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S. H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
[Crossref]

Kling, M. F.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, New J. Phys. 10, 025024 (2008).
[Crossref]

Kobayashi, T.

A. Baltuška, T. Fuji, and T. Kobayashi, Phys. Rev. Lett. 88, 133901 (2002).
[Crossref]

Krebs, M.

Laramée, A.

Lassonde, P.

Legaré, F.

Lienau, C.

B. Piglosiewicz, S. Schmidt, D. J. Park, J. Vogelsang, P. Grosz, C. Manzoni, P. Farinello, G. Cerullo, and C. Lienau, Nat. Photonics 8, 37 (2014).
[Crossref]

J. Vogelsang, J. Robin, B. Piglosiewicz, C. Manzoni, P. Farinello, S. Melzer, P. Feru, G. Cerullo, C. Lienau, and P. Groß, Opt. Express 22, 25295 (2014).
[Crossref]

Limpert, J.

Mainz, R.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S. H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
[Crossref]

Manzoni, C.

C. Manzoni and G. Cerullo, J. Opt. 18, 103501 (2016).
[Crossref]

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S. H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
[Crossref]

J. Vogelsang, J. Robin, B. Piglosiewicz, C. Manzoni, P. Farinello, S. Melzer, P. Feru, G. Cerullo, C. Lienau, and P. Groß, Opt. Express 22, 25295 (2014).
[Crossref]

B. Piglosiewicz, S. Schmidt, D. J. Park, J. Vogelsang, P. Grosz, C. Manzoni, P. Farinello, G. Cerullo, and C. Lienau, Nat. Photonics 8, 37 (2014).
[Crossref]

D. Brida, G. Cirmi, C. Manzoni, S. Bonora, P. Villoresi, S. D. Silvestri, and G. Cerullo, Opt. Lett. 33, 741 (2008).
[Crossref]

Mauro, L. D.

Melzer, S.

Miloševic, D. B.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, New J. Phys. 10, 025024 (2008).
[Crossref]

Mücke, O.

G. Cerullo, A. Baltuška, O. Mücke, and C. Vozzi, Laser Photon. Rev. 5, 323 (2011).
[Crossref]

Mücke, O. D.

H. Çankaya, A.-L. Calendron, C. Zhou, S.-H. Chia, O. D. Mücke, G. Cirmi, and F. X. Kärtner, Opt. Express 24, 25169 (2016).
[Crossref]

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S. H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
[Crossref]

Muller, H. G.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, New J. Phys. 10, 025024 (2008).
[Crossref]

Park, D. J.

B. Piglosiewicz, S. Schmidt, D. J. Park, J. Vogelsang, P. Grosz, C. Manzoni, P. Farinello, G. Cerullo, and C. Lienau, Nat. Photonics 8, 37 (2014).
[Crossref]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Piglosiewicz, B.

J. Vogelsang, J. Robin, B. Piglosiewicz, C. Manzoni, P. Farinello, S. Melzer, P. Feru, G. Cerullo, C. Lienau, and P. Groß, Opt. Express 22, 25295 (2014).
[Crossref]

B. Piglosiewicz, S. Schmidt, D. J. Park, J. Vogelsang, P. Grosz, C. Manzoni, P. Farinello, G. Cerullo, and C. Lienau, Nat. Photonics 8, 37 (2014).
[Crossref]

Rauschenberger, J.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, New J. Phys. 10, 025024 (2008).
[Crossref]

Robin, J.

Rossi, G. M.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S. H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
[Crossref]

Rothhardt, J.

Schmidt, B. E.

Schmidt, S.

B. Piglosiewicz, S. Schmidt, D. J. Park, J. Vogelsang, P. Grosz, C. Manzoni, P. Farinello, G. Cerullo, and C. Lienau, Nat. Photonics 8, 37 (2014).
[Crossref]

Silva, F.

Silvestri, S. D.

Teichmann, S.

Tünnermann, A.

Uphues, T.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, New J. Phys. 10, 025024 (2008).
[Crossref]

Verhoef, A. J.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, New J. Phys. 10, 025024 (2008).
[Crossref]

Villoresi, P.

Vogelsang, J.

J. Vogelsang, J. Robin, B. Piglosiewicz, C. Manzoni, P. Farinello, S. Melzer, P. Feru, G. Cerullo, C. Lienau, and P. Groß, Opt. Express 22, 25295 (2014).
[Crossref]

B. Piglosiewicz, S. Schmidt, D. J. Park, J. Vogelsang, P. Grosz, C. Manzoni, P. Farinello, G. Cerullo, and C. Lienau, Nat. Photonics 8, 37 (2014).
[Crossref]

Vozzi, C.

G. Cerullo, A. Baltuška, O. Mücke, and C. Vozzi, Laser Photon. Rev. 5, 323 (2011).
[Crossref]

Vrakking, M. J. J.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, New J. Phys. 10, 025024 (2008).
[Crossref]

Yang, Y.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S. H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
[Crossref]

Ye, H.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S. H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
[Crossref]

Zhou, C.

IEEE J. Sel. Top. Quantum Electron. (1)

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S. H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
[Crossref]

J. Opt. (1)

C. Manzoni and G. Cerullo, J. Opt. 18, 103501 (2016).
[Crossref]

Laser Photon. Rev. (1)

G. Cerullo, A. Baltuška, O. Mücke, and C. Vozzi, Laser Photon. Rev. 5, 323 (2011).
[Crossref]

Nat. Photonics (1)

B. Piglosiewicz, S. Schmidt, D. J. Park, J. Vogelsang, P. Grosz, C. Manzoni, P. Farinello, G. Cerullo, and C. Lienau, Nat. Photonics 8, 37 (2014).
[Crossref]

New J. Phys. (1)

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, New J. Phys. 10, 025024 (2008).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Phys. Rev. Lett. (1)

A. Baltuška, T. Fuji, and T. Kobayashi, Phys. Rev. Lett. 88, 133901 (2002).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1. Left column: representation of the electric field of pump and seed pulses before the OPA process begins. Central and left columns: E ( t ) of signal and idler pulses after the OPA process. In the upper case, the envelope of the pump (solid red line) is shorter than the seed’s one, and it is imprinted on signal and idler envelopes. In the lower case, the envelope of the seed (solid green line) is shorter than the pump one, and it is imprinted on envelopes of signal and idler pulses. The corresponding CEP variations, induced by the pump-seed ATD fluctuation Δ T , are reported. The contributions due to pump CEP variations are shown in red.
Fig. 2.
Fig. 2. CEP variations of signal (green lines) and idler (orange lines) induced by a pump-seed timing fluctuation of 0.5 fs (solid lines) and 1 fs (dashed lines), as a function of the seed pulse duration, while τ p is fixed to 150 fs. The corresponding τ seed τ p and τ seed τ p analytic limits are shown by the blue-colored gradients for the signal and by the red-colored gradients for the idler.
Fig. 3.
Fig. 3. Comparison between the CEP fluctuations of signal and idler introduced by a Δ T of 1 fs in a broadband OPA in the case of a TL seed (dashed lines) and broadband chirped seed (solid lines) as a function of their pulse durations, while τ p is fixed to 150 fs.
Fig. 4.
Fig. 4. Comparison of the CEP variation ( Δ T = 1    fs ) for the signal pulse produced by a broadband stretched seed pulse in the case of no compression (dotted lines), half compression (dashed lines), and full compression (solid line). In (a) the TL pulse duration is 10 fs, while in (b) it is 50 fs. The CEP fluctuations of the compressed signal goes quickly to zero for the broadband seed pulse, while they reach zero only for large amounts of chirping/compressing for the narrower seed.
Fig. 5.
Fig. 5. Single-shot and every-shot CEP measurement of the SH of the idler obtained via two independent f-2f setups: in-loop (a) and out-of-loop (b). (c) Extracted phase: during the first second, the CEP is freely drifting; afterward, a sinusoidal ATD, with a peak-to-valley amplitude of ( 14.2 ± 1.4 )    fs , is introduced by a delay line in the pump path; in the last second, the CEP is locked to a fixed value. The measured peak-to-valley CEP variation, after calibration of the two f-2f setups, is ( 22.0 ± 2.4 )    rad , leading to ( 1.55 ± 0.17 )    rad / fs or ( 88.8 ± 9.8 ) ° / fs , whereas the analytic model predicts 83.0°/fs.

Equations (4)

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

E p ( t ) = A p ( t ) e i ( ω p t + ϕ p ) , E seed ( t T ) = e i ( ω seed ( t T ) + ϕ p ) ,
E s ( t ) = α s A p ( t ) e i ( ω seed ( t T ) + ϕ p ) and E i ( t ) = α i A p ( t ) e i ( ω p t + ϕ p ω seed ( t T ) ϕ p π / 2 ) = α i A p ( t ) e i ( ω i t + ω seed T π / 2 ) ,
E p ( t T ) = A p e i ( ω p ( t T ) + ϕ p ) and E seed ( t ) = A seed ( t ) e i ( ω seed t + ϕ p ) ,
E s ( t ) = α s A p A seed ( t ) e i ( ω seed t + ϕ p ) and E i ( t ) = α i A p A seed ( t ) e i ( ω p ( t T ) + ϕ p ω seed t ϕ p π / 2 ) = α i A p A seed ( t ) e i ( ω i t ω p T π / 2 ) .

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