Abstract

A resonant waveguide grating based on a high reflectivity mirror causes a 2π phaseshift of adjustable slope in the spectrum of an ultrashort light pulse, giving rise to a controllable, lossless temporal pulse splitting. This monolithic phase shifter can simply be placed on the path of the beam as a mirror. A functional element was designed and fabricated. Temporal splitting of a femtosecond laser pulse is experimentally demonstrated. The possibility of obtaining variable delay between subpulses is theoretically discussed.

© 2008 Optical Society of America

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References

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  1. A.M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
    [CrossRef]
  2. C. Daniel, J. Full, L. Gonzalez, C. Lupulescu, J. Manz, A. Merli, S. Vajda, and L. Woste, "Deciphering the reaction dynamics underlying optimal control laser fields," Science 299, 536-539 (2003).
    [CrossRef] [PubMed]
  3. A. Semerok and C. Dutouquet, "Ultrashort double pulse laser ablation of metals," Thin Solid Films, 456-454, 501-505 (2004).
    [CrossRef]
  4. M. Renard, R. Chaux, B. Lavorel, and O. Faucher, "Pulse trains produce by phase modulation of ultrashort optical pulses: tailoring and characterization," Opt. Express 12, 473-482 (2004).
    [CrossRef] [PubMed]
  5. G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
    [CrossRef]
  6. B. A. Usievich, V. A. Sychugov, J. K. Nurligareev, and O. Parriaux, "Multilayer resonances sharpened by grating waveguide resonance," Opt. Quantum Electron. 36, 109-117 (2004).
    [CrossRef]
  7. H. Ichikawa and K. Fukuoka, "Femtosecond pulse shaping by a reflection grating in the resonance domain," Opt. Commun. 223, 247-254 (2003).
    [CrossRef]
  8. D. Pietroy, A. Tishchenko, M. Flury, and O. Parriaux, "Bridging pole and coupled wave formalisms for grating waveguide resonance analysis and design synthesis," Opt. Express 15, 9831-9842 (2007).
    [CrossRef] [PubMed]
  9. N. Lyndin, "MC grating : diffraction grating analysis," http://www.mcgrating.com.
  10. Botten, M. Craig, R. McPhedran, J. Adams, and R. Andrewartha, "The dielectric lamellar diffraction grating," Optica Acta 28, 413-428 (1981).
    [CrossRef]
  11. M. Wollenhaupt, A. Assion, and T. Baumert, "Femtosecond Laser Pulses: Linear Properties, Manipulation, Generation and Measurement," in Handbook of Lasers and Optics, F. Träger, ed. Springer, New York, Chap. 12 (2007).
    [CrossRef]
  12. R. Stoian, A. Mermillod-Blondin, S. Winkler, A. Rosenfeld, I. Hertel, M. Spyridaki, P. Tzanetakis, C. Fotakis, I. Burakov, and N. Bulgakova, "Temporal pulse manipulation and consequences for ultrafast laser processing of materials," Opt. Eng. 44, 051106 (2005).
    [CrossRef]

2007 (1)

2005 (1)

R. Stoian, A. Mermillod-Blondin, S. Winkler, A. Rosenfeld, I. Hertel, M. Spyridaki, P. Tzanetakis, C. Fotakis, I. Burakov, and N. Bulgakova, "Temporal pulse manipulation and consequences for ultrafast laser processing of materials," Opt. Eng. 44, 051106 (2005).
[CrossRef]

2004 (2)

B. A. Usievich, V. A. Sychugov, J. K. Nurligareev, and O. Parriaux, "Multilayer resonances sharpened by grating waveguide resonance," Opt. Quantum Electron. 36, 109-117 (2004).
[CrossRef]

M. Renard, R. Chaux, B. Lavorel, and O. Faucher, "Pulse trains produce by phase modulation of ultrashort optical pulses: tailoring and characterization," Opt. Express 12, 473-482 (2004).
[CrossRef] [PubMed]

2003 (2)

C. Daniel, J. Full, L. Gonzalez, C. Lupulescu, J. Manz, A. Merli, S. Vajda, and L. Woste, "Deciphering the reaction dynamics underlying optimal control laser fields," Science 299, 536-539 (2003).
[CrossRef] [PubMed]

H. Ichikawa and K. Fukuoka, "Femtosecond pulse shaping by a reflection grating in the resonance domain," Opt. Commun. 223, 247-254 (2003).
[CrossRef]

2000 (1)

A.M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

1985 (1)

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
[CrossRef]

1981 (1)

Botten, M. Craig, R. McPhedran, J. Adams, and R. Andrewartha, "The dielectric lamellar diffraction grating," Optica Acta 28, 413-428 (1981).
[CrossRef]

Botten,

Botten, M. Craig, R. McPhedran, J. Adams, and R. Andrewartha, "The dielectric lamellar diffraction grating," Optica Acta 28, 413-428 (1981).
[CrossRef]

Bulgakova, N.

R. Stoian, A. Mermillod-Blondin, S. Winkler, A. Rosenfeld, I. Hertel, M. Spyridaki, P. Tzanetakis, C. Fotakis, I. Burakov, and N. Bulgakova, "Temporal pulse manipulation and consequences for ultrafast laser processing of materials," Opt. Eng. 44, 051106 (2005).
[CrossRef]

Burakov, I.

R. Stoian, A. Mermillod-Blondin, S. Winkler, A. Rosenfeld, I. Hertel, M. Spyridaki, P. Tzanetakis, C. Fotakis, I. Burakov, and N. Bulgakova, "Temporal pulse manipulation and consequences for ultrafast laser processing of materials," Opt. Eng. 44, 051106 (2005).
[CrossRef]

Chaux, R.

Daniel, C.

C. Daniel, J. Full, L. Gonzalez, C. Lupulescu, J. Manz, A. Merli, S. Vajda, and L. Woste, "Deciphering the reaction dynamics underlying optimal control laser fields," Science 299, 536-539 (2003).
[CrossRef] [PubMed]

Dutouquet, C.

A. Semerok and C. Dutouquet, "Ultrashort double pulse laser ablation of metals," Thin Solid Films, 456-454, 501-505 (2004).
[CrossRef]

Faucher, O.

Flury, M.

Fotakis, C.

R. Stoian, A. Mermillod-Blondin, S. Winkler, A. Rosenfeld, I. Hertel, M. Spyridaki, P. Tzanetakis, C. Fotakis, I. Burakov, and N. Bulgakova, "Temporal pulse manipulation and consequences for ultrafast laser processing of materials," Opt. Eng. 44, 051106 (2005).
[CrossRef]

Fukuoka, K.

H. Ichikawa and K. Fukuoka, "Femtosecond pulse shaping by a reflection grating in the resonance domain," Opt. Commun. 223, 247-254 (2003).
[CrossRef]

Full, J.

C. Daniel, J. Full, L. Gonzalez, C. Lupulescu, J. Manz, A. Merli, S. Vajda, and L. Woste, "Deciphering the reaction dynamics underlying optimal control laser fields," Science 299, 536-539 (2003).
[CrossRef] [PubMed]

Golubenko, G. A.

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
[CrossRef]

Gonzalez, L.

C. Daniel, J. Full, L. Gonzalez, C. Lupulescu, J. Manz, A. Merli, S. Vajda, and L. Woste, "Deciphering the reaction dynamics underlying optimal control laser fields," Science 299, 536-539 (2003).
[CrossRef] [PubMed]

Hertel, I.

R. Stoian, A. Mermillod-Blondin, S. Winkler, A. Rosenfeld, I. Hertel, M. Spyridaki, P. Tzanetakis, C. Fotakis, I. Burakov, and N. Bulgakova, "Temporal pulse manipulation and consequences for ultrafast laser processing of materials," Opt. Eng. 44, 051106 (2005).
[CrossRef]

Ichikawa, H.

H. Ichikawa and K. Fukuoka, "Femtosecond pulse shaping by a reflection grating in the resonance domain," Opt. Commun. 223, 247-254 (2003).
[CrossRef]

Lavorel, B.

Lupulescu, C.

C. Daniel, J. Full, L. Gonzalez, C. Lupulescu, J. Manz, A. Merli, S. Vajda, and L. Woste, "Deciphering the reaction dynamics underlying optimal control laser fields," Science 299, 536-539 (2003).
[CrossRef] [PubMed]

Manz, J.

C. Daniel, J. Full, L. Gonzalez, C. Lupulescu, J. Manz, A. Merli, S. Vajda, and L. Woste, "Deciphering the reaction dynamics underlying optimal control laser fields," Science 299, 536-539 (2003).
[CrossRef] [PubMed]

Merli, A.

C. Daniel, J. Full, L. Gonzalez, C. Lupulescu, J. Manz, A. Merli, S. Vajda, and L. Woste, "Deciphering the reaction dynamics underlying optimal control laser fields," Science 299, 536-539 (2003).
[CrossRef] [PubMed]

Mermillod-Blondin, A.

R. Stoian, A. Mermillod-Blondin, S. Winkler, A. Rosenfeld, I. Hertel, M. Spyridaki, P. Tzanetakis, C. Fotakis, I. Burakov, and N. Bulgakova, "Temporal pulse manipulation and consequences for ultrafast laser processing of materials," Opt. Eng. 44, 051106 (2005).
[CrossRef]

Nurligareev, J. K.

B. A. Usievich, V. A. Sychugov, J. K. Nurligareev, and O. Parriaux, "Multilayer resonances sharpened by grating waveguide resonance," Opt. Quantum Electron. 36, 109-117 (2004).
[CrossRef]

Parriaux, O.

D. Pietroy, A. Tishchenko, M. Flury, and O. Parriaux, "Bridging pole and coupled wave formalisms for grating waveguide resonance analysis and design synthesis," Opt. Express 15, 9831-9842 (2007).
[CrossRef] [PubMed]

B. A. Usievich, V. A. Sychugov, J. K. Nurligareev, and O. Parriaux, "Multilayer resonances sharpened by grating waveguide resonance," Opt. Quantum Electron. 36, 109-117 (2004).
[CrossRef]

Pietroy, D.

Renard, M.

Rosenfeld, A.

R. Stoian, A. Mermillod-Blondin, S. Winkler, A. Rosenfeld, I. Hertel, M. Spyridaki, P. Tzanetakis, C. Fotakis, I. Burakov, and N. Bulgakova, "Temporal pulse manipulation and consequences for ultrafast laser processing of materials," Opt. Eng. 44, 051106 (2005).
[CrossRef]

Semerok, A.

A. Semerok and C. Dutouquet, "Ultrashort double pulse laser ablation of metals," Thin Solid Films, 456-454, 501-505 (2004).
[CrossRef]

Spyridaki, M.

R. Stoian, A. Mermillod-Blondin, S. Winkler, A. Rosenfeld, I. Hertel, M. Spyridaki, P. Tzanetakis, C. Fotakis, I. Burakov, and N. Bulgakova, "Temporal pulse manipulation and consequences for ultrafast laser processing of materials," Opt. Eng. 44, 051106 (2005).
[CrossRef]

Stoian, R.

R. Stoian, A. Mermillod-Blondin, S. Winkler, A. Rosenfeld, I. Hertel, M. Spyridaki, P. Tzanetakis, C. Fotakis, I. Burakov, and N. Bulgakova, "Temporal pulse manipulation and consequences for ultrafast laser processing of materials," Opt. Eng. 44, 051106 (2005).
[CrossRef]

Svakhin, A. S.

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
[CrossRef]

Sychugov, V. A.

B. A. Usievich, V. A. Sychugov, J. K. Nurligareev, and O. Parriaux, "Multilayer resonances sharpened by grating waveguide resonance," Opt. Quantum Electron. 36, 109-117 (2004).
[CrossRef]

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
[CrossRef]

Tishchenko, A.

Tishchenko, A. V.

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
[CrossRef]

Tzanetakis, P.

R. Stoian, A. Mermillod-Blondin, S. Winkler, A. Rosenfeld, I. Hertel, M. Spyridaki, P. Tzanetakis, C. Fotakis, I. Burakov, and N. Bulgakova, "Temporal pulse manipulation and consequences for ultrafast laser processing of materials," Opt. Eng. 44, 051106 (2005).
[CrossRef]

Usievich, B. A.

B. A. Usievich, V. A. Sychugov, J. K. Nurligareev, and O. Parriaux, "Multilayer resonances sharpened by grating waveguide resonance," Opt. Quantum Electron. 36, 109-117 (2004).
[CrossRef]

Vajda, S.

C. Daniel, J. Full, L. Gonzalez, C. Lupulescu, J. Manz, A. Merli, S. Vajda, and L. Woste, "Deciphering the reaction dynamics underlying optimal control laser fields," Science 299, 536-539 (2003).
[CrossRef] [PubMed]

Weiner, A.M.

A.M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

Winkler, S.

R. Stoian, A. Mermillod-Blondin, S. Winkler, A. Rosenfeld, I. Hertel, M. Spyridaki, P. Tzanetakis, C. Fotakis, I. Burakov, and N. Bulgakova, "Temporal pulse manipulation and consequences for ultrafast laser processing of materials," Opt. Eng. 44, 051106 (2005).
[CrossRef]

Woste, L.

C. Daniel, J. Full, L. Gonzalez, C. Lupulescu, J. Manz, A. Merli, S. Vajda, and L. Woste, "Deciphering the reaction dynamics underlying optimal control laser fields," Science 299, 536-539 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

H. Ichikawa and K. Fukuoka, "Femtosecond pulse shaping by a reflection grating in the resonance domain," Opt. Commun. 223, 247-254 (2003).
[CrossRef]

Opt. Eng. (1)

R. Stoian, A. Mermillod-Blondin, S. Winkler, A. Rosenfeld, I. Hertel, M. Spyridaki, P. Tzanetakis, C. Fotakis, I. Burakov, and N. Bulgakova, "Temporal pulse manipulation and consequences for ultrafast laser processing of materials," Opt. Eng. 44, 051106 (2005).
[CrossRef]

Opt. Express (2)

Opt. Quantum Electron. (1)

B. A. Usievich, V. A. Sychugov, J. K. Nurligareev, and O. Parriaux, "Multilayer resonances sharpened by grating waveguide resonance," Opt. Quantum Electron. 36, 109-117 (2004).
[CrossRef]

Optica Acta (1)

Botten, M. Craig, R. McPhedran, J. Adams, and R. Andrewartha, "The dielectric lamellar diffraction grating," Optica Acta 28, 413-428 (1981).
[CrossRef]

Rev. Sci. Instrum. (1)

A.M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

Science (1)

C. Daniel, J. Full, L. Gonzalez, C. Lupulescu, J. Manz, A. Merli, S. Vajda, and L. Woste, "Deciphering the reaction dynamics underlying optimal control laser fields," Science 299, 536-539 (2003).
[CrossRef] [PubMed]

Sov. J. Quantum Electron. (1)

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
[CrossRef]

Other (3)

A. Semerok and C. Dutouquet, "Ultrashort double pulse laser ablation of metals," Thin Solid Films, 456-454, 501-505 (2004).
[CrossRef]

M. Wollenhaupt, A. Assion, and T. Baumert, "Femtosecond Laser Pulses: Linear Properties, Manipulation, Generation and Measurement," in Handbook of Lasers and Optics, F. Träger, ed. Springer, New York, Chap. 12 (2007).
[CrossRef]

N. Lyndin, "MC grating : diffraction grating analysis," http://www.mcgrating.com.

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Figures (8)

Fig. 1.
Fig. 1.

Sketch of the resonant mirror principle. The mode is excited using the −1st order diffracted into the dielectric layer.

Fig. 2.
Fig. 2.

Intensity of a 130 fs Gaussian input pulse after reflection onto a mirror-based resonant grating for different spectral widths.

Fig. 3.
Fig. 3.

Fabricated resonant mirror. (a) Sketch of the layered structure with corrugation in the last HfO2 layer. (b) Corresponding spectral phase of the TM reflection under 46° incidence.

Fig. 4.
Fig. 4.

(a) Cross-correlation of the temporal profile obtained after reflection of a 85 fs incident Gaussian pulse onto the resonant mirror (crosses : experimental results, grey dotted line: theoretic results and black line: numerical calculation of the cross-correlation signal considering 15% energy losses). (b) Theoretical spectral intensity of the Gaussian incident pulse before (dashed line) and after reflection (solid line). Losses are considered.

Fig. 5.
Fig. 5.

Basic set-up for adjustable temporal pulse shaping using cascaded phaseshifts.

Fig. 6.
Fig. 6.

Examples of intensity, phase and instantaneous frequency for double pulses with larger delay obtained after 8 reflections of a 130 fs-Gaussian pulse: (a) tilt angle γ=0.2 (b) tilt angle γ=0.5.

Fig. 7.
Fig. 7.

Example of cascaded phase modulation (solid line) induced in the spectrum of a 130 fs- Gaussian pulse (dashed line). This modulation results in the shaped pulse of Fig. 6(a).

Fig. 8.
Fig. 8.

(a) Theoretical evolution of the temporal shape of a 130 fs-Gaussian pulse upon a slight variation of the incidence angle. (b) Theoretical evolution of the delay between the two subpulses as a function of the tilt angle considering 8 reflections on the structure depicted in Fig. 3(a).

Equations (20)

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r ( ω ) = r 0 + a ω ( ω ω 0 ) j Δ ω
C = r 0 + j a ω 2 Δ ω
a ω = 2 j Δ ω · r 0
r ( ω ) = r 0 ( 1 + 2 j Δ ω ( ω ω 0 ) j Δ ω ) = r 0 ( ( ω ω 0 ) + j Δ ω ( ω ω 0 ) j Δ ω )
r ( ω ) = r 0 [ Δ ω j ( ω ω 0 ) ] 2 Δ ω 2 + ( ω ω 0 ) 2 = [ e j φ 0 ( Δ ω j ω ) 2 Δ ω 2 + ω 2 ] * δ ( ω ω 0 )
φ ( ω ) = φ 0 2 arctan ( ω ω 0 Δ ω )
H ( ω ) = ( Δ ω j ω ) 2 Δ ω 2 + ω 2
h ( t ) = exp ( Δ ω t ) * ( Δ ω 2 δ ( t ) δ ( t ) + 1 2 Δ ω δ ( t ) )
f t = Δ ω sign ( t ) exp ( Δ ω | t | ) 2 f t 2 = 2 Δ ω δ ( t ) + Δ ω 2 exp ( Δ ω | t | )
h ( t ) = ( Δ ω 2 + Δ ω · sin ( t ) + Δ ω 2 ) . exp ( Δ ω t ) δ ( t )
= 2 Δ ω U ( t ) · exp ( Δ ω t ) δ ( t )
e o ( t ) = h ( t ) * e i ( t )
= ( 2 Δ ω · U ( t ) · exp ( Δ ω t ) δ ( t ) ) * exp ( t 2 p 2 )
e o ( t ) = 2 Δ ω · exp ( p 2 · Δ ω 2 4 ) · exp ( Δ ω t ) · t exp [ ( τ p + p · Δ ω 2 ) 2 ] exp ( t 2 p 2 )
e o ( t ) = 2 p Δ ω · exp ( p 2 Δ ω 2 4 ) · exp ( Δ ω t ) · t p + p Δ ω 2 exp ( X 2 ) dX exp ( t 2 p 2 )
= 2 p Δ ω · exp ( p 2 Δ ω 2 4 ) · exp ( Δ ω t ) · ( π 2 + π 2 erf ( t p p Δ ω 2 ) ) exp ( t 2 p 2 )
e o ( t ) = π Δ ω Δ t 2 ln 2 exp [ ( Δ ω Δ t 2 2 ln 2 ) 2 ] · exp ( Δ ω t ) · [ 1 + erf ( 2 ln 2 Δ t t Δ ω Δ t 2 2 ln 2 ) ]
exp ( 2 ln 2 Δ t 2 t 2 )
r ( ω ) = ω 2 + ( 1 R min ) Δ ω 2 ω 2 + Δ ω 2 exp { j [ φ 0 2 arctan ( ω ω 0 Δ ω ) ] }
φ ( ω ) = 2 n = 1 N arctan ( ω ω n Δ ω n )

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