Abstract

Diffraction puts a fundamental limit on the distance over which a light beam can remain focused. For about 30 years, several techniques to overcome this limit have been demonstrated. Here, we propose a reflective optics, namely, the axiparabola, that allows to extend the production of “diffraction-free” beams to high-peak-power and broadband laser pulses. We first describe the properties of this aspheric optics. We then analyze and compare its performances in numerical simulations and in experiments. Finally, we use it to produce a plasma waveguide that can guide an intense laser pulse over 10 millimeters.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

2018 (1)

R. J. Shalloo, C. Arran, L. Corner, J. Holloway, J. Jonnerby, R. Walczak, H. M. Milchberg, and S. M. Hooker, Phys. Rev. E 97, 053203 (2018).
[Crossref]

2017 (1)

2011 (2)

2009 (1)

E. Esarey, C. B. Schroeder, and W. P. Leemans, Rev. Mod. Phys. 81, 1229 (2009).
[Crossref]

2008 (1)

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

2007 (2)

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[Crossref]

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

2002 (2)

1997 (1)

1996 (1)

1993 (2)

1992 (2)

1991 (1)

1987 (1)

1976 (1)

1954 (1)

Ackermann, R.

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

Ahlawat, S.

André, Y.-B.

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

Arran, C.

R. J. Shalloo, C. Arran, L. Corner, J. Holloway, J. Jonnerby, R. Walczak, H. M. Milchberg, and S. M. Hooker, Phys. Rev. E 97, 053203 (2018).
[Crossref]

Bará, S.

Botton, M.

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

Chanteloup, J.-C.

Chen, Z.

Corner, L.

R. J. Shalloo, C. Arran, L. Corner, J. Holloway, J. Jonnerby, R. Walczak, H. M. Milchberg, and S. M. Hooker, Phys. Rev. E 97, 053203 (2018).
[Crossref]

Couairon, A.

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[Crossref]

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Courvoisier, F.

D’Amico, C.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Dasgupta, R.

Davidson, N.

Dey, I.

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

Ding, Z.

Dong, B.-Z.

Dudley, J. M.

Durfee, C. G.

C. G. Durfee and H. M. Milchberg, Phys. Rev. Lett. 71, 2409 (1993).
[Crossref]

Durnin, J.

Ersoy, O. K.

Esarey, E.

E. Esarey, C. B. Schroeder, and W. P. Leemans, Rev. Mod. Phys. 81, 1229 (2009).
[Crossref]

Ferencz, K.

Fleck, A.

V. Lakshminarayanan and A. Fleck, J. Mod. Opt. 58, 545 (2011).
[Crossref]

Franco, M.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Friesem, A. A.

Furfaro, L.

Giust, R.

Gu, B.-Y.

Gupta, P. K.

Hasman, E.

Henis, Z.

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

Holloway, J.

R. J. Shalloo, C. Arran, L. Corner, J. Holloway, J. Jonnerby, R. Walczak, H. M. Milchberg, and S. M. Hooker, Phys. Rev. E 97, 053203 (2018).
[Crossref]

Hooker, S. M.

R. J. Shalloo, C. Arran, L. Corner, J. Holloway, J. Jonnerby, R. Walczak, H. M. Milchberg, and S. M. Hooker, Phys. Rev. E 97, 053203 (2018).
[Crossref]

Houard, A.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Jacquot, M.

Jana, K.

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

Jaroszewicz, Z.

Jonnerby, J.

R. J. Shalloo, C. Arran, L. Corner, J. Holloway, J. Jonnerby, R. Walczak, H. M. Milchberg, and S. M. Hooker, Phys. Rev. E 97, 053203 (2018).
[Crossref]

Kasparian, J.

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

Kolodziejczyk, A.

Krausz, F.

Kumar, G. R.

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

Lacourt, P.-A.

Lad, A. D.

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

Lakshminarayanan, V.

V. Lakshminarayanan and A. Fleck, J. Mod. Opt. 58, 545 (2011).
[Crossref]

Leemans, W. P.

E. Esarey, C. B. Schroeder, and W. P. Leemans, Rev. Mod. Phys. 81, 1229 (2009).
[Crossref]

McLeod, J. H.

Méchain, G.

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

Méjean, G.

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

Meyer, R.

Migus, A.

Milchberg, H. M.

R. J. Shalloo, C. Arran, L. Corner, J. Holloway, J. Jonnerby, R. Walczak, H. M. Milchberg, and S. M. Hooker, Phys. Rev. E 97, 053203 (2018).
[Crossref]

C. G. Durfee and H. M. Milchberg, Phys. Rev. Lett. 71, 2409 (1993).
[Crossref]

Mysyrowicz, A.

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[Crossref]

Nelson, J. S.

Nisoli, M.

Noll, R. J.

Papeer, J.

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

Prade, B.

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Rapp, L.

Ren, H.

Rohwetter, P.

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

Roy, S. L.

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

Safioui, J.

Salmon, E.

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

Sarkar, D.

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

Sartania, S.

Sauerbrey, R.

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

Sauteret, C.

Schroeder, C. B.

E. Esarey, C. B. Schroeder, and W. P. Leemans, Rev. Mod. Phys. 81, 1229 (2009).
[Crossref]

Shaikh, M.

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

Shalloo, R. J.

R. J. Shalloo, C. Arran, L. Corner, J. Holloway, J. Jonnerby, R. Walczak, H. M. Milchberg, and S. M. Hooker, Phys. Rev. E 97, 053203 (2018).
[Crossref]

Silvestri, S. D.

Sochacki, J.

Spielmann, C.

Staronski, L. R.

Stelmaszczyk, K.

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

Svelto, O.

Szipöcs, R.

Tata, S.

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

Tikhonchuk, V. T.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Ved, Y. M.

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

Verma, R. S.

Walczak, R.

R. J. Shalloo, C. Arran, L. Corner, J. Holloway, J. Jonnerby, R. Walczak, H. M. Milchberg, and S. M. Hooker, Phys. Rev. E 97, 053203 (2018).
[Crossref]

Wattellier, B.

Woeste, L.

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

Wolf, J.-P.

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

Yang, G.-Z.

Yu, J.

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

Zhao, Y.

Zigler, A.

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

Appl. Opt. (2)

J. Eur. Opt. Soc. (1)

J. Kasparian, R. Ackermann, Y.-B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J.-P. Wolf, J. Eur. Opt. Soc. 3, 08035 (2008).
[Crossref]

J. Mod. Opt. (1)

V. Lakshminarayanan and A. Fleck, J. Mod. Opt. 58, 545 (2011).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Lett. (7)

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[Crossref]

Phys. Rev. E (1)

R. J. Shalloo, C. Arran, L. Corner, J. Holloway, J. Jonnerby, R. Walczak, H. M. Milchberg, and S. M. Hooker, Phys. Rev. E 97, 053203 (2018).
[Crossref]

Phys. Rev. Lett. (2)

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

C. G. Durfee and H. M. Milchberg, Phys. Rev. Lett. 71, 2409 (1993).
[Crossref]

Rev. Mod. Phys. (1)

E. Esarey, C. B. Schroeder, and W. P. Leemans, Rev. Mod. Phys. 81, 1229 (2009).
[Crossref]

Sci. Rep. (1)

J. Papeer, I. Dey, M. Botton, Z. Henis, A. D. Lad, M. Shaikh, D. Sarkar, K. Jana, S. Tata, S. L. Roy, Y. M. Ved, G. R. Kumar, and A. Zigler, Sci. Rep. 9, 407 (2019).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1. Geometrical parameters and schematic presentation of rays focused by an axiparabola with positive δ z g . (a) On-axis case: incident rays that are far from the optical axis z are focused after the nominal focus f 0 on the same axis; (b) off-axis case: incident rays that are far from the optical axis z are focused after the nominal focus f 0 on the axis z . The off-axis angle is defined between axes z and z .
Fig. 2.
Fig. 2. (a) Axiparabola peak intensity as a function of the focal distance: red circles are the experimental data and the blue line comes from a polychromatic PSF simulation for a 0.85 J, 30 fs pulse. (b) Simulated time integrated axiparabola beam profile cross section as function of the focal distance. Inset: Illumination profile used in simulation.
Fig. 3.
Fig. 3. Normalized beam profiles (for each plot) for different focal plane distances. The first row corresponds to simulated axiparabola focal spots. The second row depicts the experimental focal spots measured along the focal line of the axiparabola. The four columns correspond to the different focal plane distances: 190 mm, 195 mm, 200 mm, and 205 mm, respectively. The colormap is the same as used in Fig. 2(b), while maximal value of each plot is 1.
Fig. 4.
Fig. 4. (a) Experimental setup of the plasma waveguide experiment. A “generation pulse” is focused by an axiparabola on a hydrogen cloud above a 10 mm long gas jet. A “guided pulse” is then focused at the entrance of the pre-formed plasma channel. The output of the guided pulse is attenuated with two wedges and a set of neutral density (ND) filters. Different planes along the gas jet are imaged on a CCD camera. (b) Guided pulse spot at the entrance of the gas jet (no gas). (c) Guided pulse spot at the exit of the 10 mm gas nozzle without the plasma channel (no gas). (d) Guided pulse spot at the exit of the nozzle with the plasma. (e) Guided pulse spot at the exit of the nozzle with the preformed plasma channel.

Tables (1)

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Table 1. Zernike Coefficients of the Axiparabola Sag for the On-Axis and Off-Axis Cases and Specific Parameters Presented in the Text

Equations (5)

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s ( r ) + r 2 ( 1 D ( r ) D ( r ) ) = f ( r ) ,
s ( r ) f ( r ) r + 1 r ( f ( r ) s ( r ) ) 2 + r 2 = D ( r ) .
f ( r ) = f 0 + δ z g ( r / R ) 2 ,
s ( r ) = 1 4 f 0 r 2 δ z g 8 f 0 2 R 2 r 4 + δ z g ( R 2 + 8 f 0 δ z g ) 96 f 0 4 R 4 r 6 + O ( r 8 ) .
s ( r ) = m , n a n m Z n m ( ρ , ϕ ) , s ( x , y ) = m , n a n m Z n m ( ρ , ϕ ) ,

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