Abstract

We present a new approach for designing dispersion-engineered optics based on a simple unitless spectral quantity we call the phase distortion ratio (PDR). In contrast to minimizing the group delay dispersion (GDD) deviation from the ideal, minimizing the PDR is optimal in the sense that it minimizes the fraction of pulse energy lost to phase distortions. As an example, a mirror system optimized via PDR is empirically found to result in significantly better compression of single-cycle pulses than a system designed in terms of GDD. In the context of coupling pulse trains to cavities, minimizing the PDR of the cavity is shown to maximize throughput.

© 2010 Optical Society of America

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2008 (2)

C.-H. Li, A. Benedick, P. Fendel, A. Glenday, F. X. Kärtner, D. Phillips, D. Sasselov, A. Szentgyorgyil, and R. Walsworth, Nature 452, 610 (2008).
[CrossRef] [PubMed]

M. Trubetskov, A. Tikhonravov, and V. Pervak, Opt. Express 16, 20637 (2008).
[CrossRef] [PubMed]

2007 (1)

2005 (1)

2001 (1)

1998 (1)

1997 (1)

1994 (1)

1987 (1)

Angelow, G.

Benedick, A.

C.-H. Li, A. Benedick, P. Fendel, A. Glenday, F. X. Kärtner, D. Phillips, D. Sasselov, A. Szentgyorgyil, and R. Walsworth, Nature 452, 610 (2008).
[CrossRef] [PubMed]

Birge, J. R.

J. R. Birge and F. X. Kärtner, Appl. Opt. 46, 2656(2007).
[CrossRef] [PubMed]

J. R. Birge, “Methods for engineering few-cycle mode-locked lasers,” Ph.D. thesis (MIT, 2009).

J. R. Birge, in Optical Interference Coatings, OSA Technical Digest (CD) (Optical Society of America, 2007), p. WA7.

Dombi, P.

Ell, R.

Fendel, P.

C.-H. Li, A. Benedick, P. Fendel, A. Glenday, F. X. Kärtner, D. Phillips, D. Sasselov, A. Szentgyorgyil, and R. Walsworth, Nature 452, 610 (2008).
[CrossRef] [PubMed]

Ferencz, K.

Fuji, T.

Fujimoto, J. G.

Glenday, A.

C.-H. Li, A. Benedick, P. Fendel, A. Glenday, F. X. Kärtner, D. Phillips, D. Sasselov, A. Szentgyorgyil, and R. Walsworth, Nature 452, 610 (2008).
[CrossRef] [PubMed]

Haus, H. A.

Heine, C.

Ippen, E. P.

Kärtner, F. X.

Keller, U.

Krausz, F.

Lezius, M.

Li, C.-H.

C.-H. Li, A. Benedick, P. Fendel, A. Glenday, F. X. Kärtner, D. Phillips, D. Sasselov, A. Szentgyorgyil, and R. Walsworth, Nature 452, 610 (2008).
[CrossRef] [PubMed]

Matuschek, N.

Morf, R.

Morgner, U.

O’Keeffe, K.

Ouellette, F.

Pervak, V.

Phillips, D.

C.-H. Li, A. Benedick, P. Fendel, A. Glenday, F. X. Kärtner, D. Phillips, D. Sasselov, A. Szentgyorgyil, and R. Walsworth, Nature 452, 610 (2008).
[CrossRef] [PubMed]

Risvik, K. M.

Sasselov, D.

C.-H. Li, A. Benedick, P. Fendel, A. Glenday, F. X. Kärtner, D. Phillips, D. Sasselov, A. Szentgyorgyil, and R. Walsworth, Nature 452, 610 (2008).
[CrossRef] [PubMed]

Scheuer, V.

Schibli, T.

Skaar, J.

Spielmann, C.

Szentgyorgyil, A.

C.-H. Li, A. Benedick, P. Fendel, A. Glenday, F. X. Kärtner, D. Phillips, D. Sasselov, A. Szentgyorgyil, and R. Walsworth, Nature 452, 610 (2008).
[CrossRef] [PubMed]

Szipöcs, R.

Tempea, G.

Tikhonravov, A.

Tilsch, M.

Trubetskov, M.

Tschudi, T.

Walsworth, R.

C.-H. Li, A. Benedick, P. Fendel, A. Glenday, F. X. Kärtner, D. Phillips, D. Sasselov, A. Szentgyorgyil, and R. Walsworth, Nature 452, 610 (2008).
[CrossRef] [PubMed]

Yakovlev, V. S.

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Figures (4)

Fig. 1
Fig. 1

Comparison of residual GDD for test rate enhancement cavity mirror design.

Fig. 2
Fig. 2

Rate enhancement cavity transmission comparison. The transmission curve represents the fraction of power transmitted relative to the maximum possible, assuming an ideally locked pulse train.

Fig. 3
Fig. 3

Mean reflectivity (top) and residual GDD (bottom) comparison for pulse compression mirror pairs.

Fig. 4
Fig. 4

Comparison of pulse intensity after compression, alongside a transform limited pulse for reference. The inset panel shows the intensity on a linear scale around the main pulse; the minimum PDR pulse is indistinguishable from the transform limited pulse.

Equations (5)

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Δ ϕ = ω 1 ω 2 d ω 2 D 2 ( ω ) D ^ 2 ( ω ) ,
min ϕ 0 , ϕ 1 d ω P ( ω ) [ r 2 ( ω ) + r ^ 2 ( ω ) ] - 2 r ( ω ) r ^ ( ω ) cos [ Δ ϕ ( ω ) + ϕ 0 + ϕ 1 ω ] ,
d ω P ( ω ) [ r ( ω ) - r ^ ( ω ) ] 2 + min ϕ 0 , ϕ 1 d ω P ( ω ) r ( ω ) r ^ ( ω ) [ Δ ϕ ( ω ) + ϕ 0 + ϕ 1 ω ] 2 PDR .
PDR ( ω ) [ Δ ϕ ( ω ) Δ ω 2 + ω 0 2 ω ω 0 Δ ω 2 Δ ϕ + ω ω 0 Δ ω 2 ω Δ ϕ ] 2 ,
T ( ω ) = 1 4 R ( ω ) [ 1 R ( ω ) ] 2 PDR ( ω ) + O [ PDR 2 ( ω ) ] ,

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