Abstract

Generation of an ultrabroadband optical pulse with a fluent frequency dependency of the phase is important for creating a monocyclelike optical pulse and for shaping multiwavelength optical pulses. A previously proposed method that uses induced phase modulation between a femtosecond fundamental wave ω1 and its second-harmonic wave ω2=2ω1 in a fused-silica fiber is applied to a capillary fiber filled with noble gas. Analytic results of chirps without dispersion but with loss in the fiber are shown, and the optimum conditions relating to a delay time between two pulses and to input peak powers are found for fully covering the spectrum between ω1 and ω2. Furthermore, numerical calculations, including dispersion effects of the fundamental and the second-harmonic waves from a Ti:sapphire laser-amplifier system with experimentally realizable parameters, are presented. These calculations show that it is possible to generate an ultrabroadband optical pulse whose spectrum ranges from 300 to 900 THz (330 to 1000 nm) with quasi-linear chirp by this method.

© 1999 Optical Society of America

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  1. M. Yamashita, H. Sone, and R. Morita, Jpn. J. Appl. Phys., Part 2 35, L1194 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. A. Baltuška, Z. Wei, M. S. Pshenichnikov, and D. A. Wiersma, Opt. Lett. 22, 102 (1997).
    [CrossRef]
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    [CrossRef]
  6. M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996).
    [CrossRef]
  7. M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B: Lasers Opt. 65, 189 (1997).
    [CrossRef]
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    [CrossRef]
  9. G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  16. A. Dalgarno and A. E. Kingston, Proc. R. Soc. London, Ser. A 259, 424 (1960).
    [CrossRef]
  17. A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, IEEE J. Quantum Electron. 28, 908 (1992).
    [CrossRef]
  18. The authors thank a reviewer for pointing out this issue.
  19. D. Yelin, D. Meshulach, and Y. Silberberg, Opt. Lett. 22, 1793 (1997).
    [CrossRef]
  20. G. Tempea and T. Brabec, Opt. Lett. 23, 762 (1998).
    [CrossRef]

1998 (2)

M. Yamashita, H. Sone, R. Morita, and H. Shigekawa, IEEE J. Quantum Electron. 34, 2145 (1998).
[CrossRef]

G. Tempea and T. Brabec, Opt. Lett. 23, 762 (1998).
[CrossRef]

1997 (4)

D. Yelin, D. Meshulach, and Y. Silberberg, Opt. Lett. 22, 1793 (1997).
[CrossRef]

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, Appl. Phys. B: Lasers Opt. 65, 175 (1997).
[CrossRef]

A. Baltuška, Z. Wei, M. S. Pshenichnikov, and D. A. Wiersma, Opt. Lett. 22, 102 (1997).
[CrossRef]

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B: Lasers Opt. 65, 189 (1997).
[CrossRef]

1996 (2)

M. Yamashita, H. Sone, and R. Morita, Jpn. J. Appl. Phys., Part 2 35, L1194 (1996).
[CrossRef]

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996).
[CrossRef]

1995 (2)

1992 (1)

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, IEEE J. Quantum Electron. 28, 908 (1992).
[CrossRef]

1989 (1)

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 40, 5063 (1989).
[CrossRef] [PubMed]

1985 (1)

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, Opt. Commun. 56, 67 (1985).
[CrossRef]

1968 (1)

G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

1962 (1)

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

1960 (1)

A. Dalgarno and A. E. Kingston, Proc. R. Soc. London, Ser. A 259, 424 (1960).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 40, 5063 (1989).
[CrossRef] [PubMed]

Alfano, R. R.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 40, 5063 (1989).
[CrossRef] [PubMed]

Armstrong, J. A.

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

Baldeck, P. L.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 40, 5063 (1989).
[CrossRef] [PubMed]

Baltuška, A.

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, Appl. Phys. B: Lasers Opt. 65, 175 (1997).
[CrossRef]

A. Baltuška, Z. Wei, M. S. Pshenichnikov, and D. A. Wiersma, Opt. Lett. 22, 102 (1997).
[CrossRef]

Bloembergen, N.

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

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

Brabec, T.

Cheng, Z.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B: Lasers Opt. 65, 189 (1997).
[CrossRef]

Coste, O.

Dalgarno, A.

A. Dalgarno and A. E. Kingston, Proc. R. Soc. London, Ser. A 259, 424 (1960).
[CrossRef]

De Silvestri, S.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B: Lasers Opt. 65, 189 (1997).
[CrossRef]

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996).
[CrossRef]

Ducuing, J.

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

Kingston, A. E.

A. Dalgarno and A. E. Kingston, Proc. R. Soc. London, Ser. A 259, 424 (1960).
[CrossRef]

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

Krausz, F.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B: Lasers Opt. 65, 189 (1997).
[CrossRef]

Leaird, D. E.

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, IEEE J. Quantum Electron. 28, 908 (1992).
[CrossRef]

Lehmeier, H. J.

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, Opt. Commun. 56, 67 (1985).
[CrossRef]

Lenzner, M.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B: Lasers Opt. 65, 189 (1997).
[CrossRef]

Leupacher, W.

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, Opt. Commun. 56, 67 (1985).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Meschede, D.

Meshulach, D.

Morita, R.

M. Yamashita, H. Sone, R. Morita, and H. Shigekawa, IEEE J. Quantum Electron. 34, 2145 (1998).
[CrossRef]

M. Yamashita, H. Sone, and R. Morita, Jpn. J. Appl. Phys., Part 2 35, L1194 (1996).
[CrossRef]

Nishioka, H.

Nisoli, M.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B: Lasers Opt. 65, 189 (1997).
[CrossRef]

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996).
[CrossRef]

Odajima, W.

Patel, J. S.

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, IEEE J. Quantum Electron. 28, 908 (1992).
[CrossRef]

Penzkofer, A.

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, Opt. Commun. 56, 67 (1985).
[CrossRef]

Pershan, P. S.

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

Pshenichnikov, M. S.

A. Baltuška, Z. Wei, M. S. Pshenichnikov, and D. A. Wiersma, Opt. Lett. 22, 102 (1997).
[CrossRef]

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, Appl. Phys. B: Lasers Opt. 65, 175 (1997).
[CrossRef]

Rembe, C.

Sartania, S.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B: Lasers Opt. 65, 189 (1997).
[CrossRef]

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Shigekawa, H.

M. Yamashita, H. Sone, R. Morita, and H. Shigekawa, IEEE J. Quantum Electron. 34, 2145 (1998).
[CrossRef]

Silberberg, Y.

Sone, H.

M. Yamashita, H. Sone, R. Morita, and H. Shigekawa, IEEE J. Quantum Electron. 34, 2145 (1998).
[CrossRef]

M. Yamashita, H. Sone, and R. Morita, Jpn. J. Appl. Phys., Part 2 35, L1194 (1996).
[CrossRef]

Spielmann, Ch.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B: Lasers Opt. 65, 189 (1997).
[CrossRef]

Stagira, S.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B: Lasers Opt. 65, 189 (1997).
[CrossRef]

Svelto, O.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B: Lasers Opt. 65, 189 (1997).
[CrossRef]

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996).
[CrossRef]

Szipöcs, R.

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, Appl. Phys. B: Lasers Opt. 65, 175 (1997).
[CrossRef]

Takuma, H.

Tempea, G.

Ueda, K.

Wei, Z.

A. Baltuška, Z. Wei, M. S. Pshenichnikov, and D. A. Wiersma, Opt. Lett. 22, 102 (1997).
[CrossRef]

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, Appl. Phys. B: Lasers Opt. 65, 175 (1997).
[CrossRef]

Weiner, A. M.

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, IEEE J. Quantum Electron. 28, 908 (1992).
[CrossRef]

Wiersma, D. A.

A. Baltuška, Z. Wei, M. S. Pshenichnikov, and D. A. Wiersma, Opt. Lett. 22, 102 (1997).
[CrossRef]

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, Appl. Phys. B: Lasers Opt. 65, 175 (1997).
[CrossRef]

Wullert II, J. R.

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, IEEE J. Quantum Electron. 28, 908 (1992).
[CrossRef]

Wynands, R.

Yamashita, M.

M. Yamashita, H. Sone, R. Morita, and H. Shigekawa, IEEE J. Quantum Electron. 34, 2145 (1998).
[CrossRef]

M. Yamashita, H. Sone, and R. Morita, Jpn. J. Appl. Phys., Part 2 35, L1194 (1996).
[CrossRef]

Yelin, D.

Appl. Phys. B: Lasers Opt. (2)

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, Appl. Phys. B: Lasers Opt. 65, 175 (1997).
[CrossRef]

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B: Lasers Opt. 65, 189 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996).
[CrossRef]

Bell Syst. Tech. J. (1)

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, IEEE J. Quantum Electron. 28, 908 (1992).
[CrossRef]

M. Yamashita, H. Sone, R. Morita, and H. Shigekawa, IEEE J. Quantum Electron. 34, 2145 (1998).
[CrossRef]

J. Appl. Phys. (1)

G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

Jpn. J. Appl. Phys., Part 2 (1)

M. Yamashita, H. Sone, and R. Morita, Jpn. J. Appl. Phys., Part 2 35, L1194 (1996).
[CrossRef]

Opt. Commun. (1)

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, Opt. Commun. 56, 67 (1985).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. (1)

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

Phys. Rev. A (1)

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 40, 5063 (1989).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A (1)

A. Dalgarno and A. E. Kingston, Proc. R. Soc. London, Ser. A 259, 424 (1960).
[CrossRef]

Other (3)

The authors thank a reviewer for pointing out this issue.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

A. Yariv, Optical Electronics (Saunders, Philadelphia, Pa., 1991).

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Figures (4)

Fig. 1
Fig. 1

Calculated chirps versus normalized time for (a) δω1 and (b) δω2 when dispersion terms are neglected. Solid curves show chirps from SPM, long- and short-dashed curves show chirps from IPM, and dotted curves show the total chirps. Pulse centers are at 0 for (a) and at -2.32 for (b). In calculations ω1 is the fundamental wave and ω2 is the second-harmonic wave of a Ti:sapphire laser system (λ1=790 nm). These are propagated in an argon-filled (300 K, 3.3 atm) capillary fiber with a radius of 50 µm and a length of 29.2 cm. Also, P1=P2=1.29 GW, T01=T02=30/(2ln 2) fs (τ1=τ2, τ1=τ2), n2=3.234×10-23 m2/W, and Td2=-41.8 fs (Td2-zld) are used.

Fig. 2
Fig. 2

Calculated intensity, phase, and group delay versus frequency of the fundamental and second-harmonic waves after propagation through an argon-filled capillary fiber under the condition P1=P2=1.29 GW, Td2=-41.8 fs.

Fig. 3
Fig. 3

Calculated intensity, phase, and group delay versus frequency of the fundamental and second-harmonic waves after propagation through an argon-filled capillary fiber under the condition P1=P2=1.29 GW, Td2=0 fs.

Fig. 4
Fig. 4

Calculated intensity versus time of the compressed pulse after its phase is compensated for by the spatial phase modulator. Other parameters are the same as those of Fig. 2.

Equations (38)

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Ei(ri, t)=½ xˆ{Fi(x, y)Ai(z, t)×exp[i(β0iz-ωit+ϕ0i)]+c.c.},
A1z=-α12A1+in2ω1c[f11|A1|2+2 f12|A2|2]A1,
A2z=-α22A2+in2ω2c[f22|A2|2+2 f12|A1|2]A2,
Ai=Pi exp-αiz2Ui(z, Ti),
Ui(z, Ti)=exp[iϕi(z, Ti)]Ui(0, Ti).
ϕ1(zl, T1)=n2ω1cf11P1|U1|2z1 eff+2 f12P2×0zl exp(-α2x)|U2(0, T1-xd)|2dx,
ϕ2(zl, T2)=n2ω2cf22P2|U2|2z2 eff+2 f12P1×0zl exp(-α1x)|U1(0, T2+xd)|2dx,
d=β12-β11.
zi eff=[1-exp(-αizl)]/αi.
δωi=-ϕiTi,
A1(0, T1)=P1 exp[-T12/(2T012)],
A2(0, T2)=P2 exp[-(T2-Td2)2/(2T022)];
δω1(zl, T1)=2n2ω1czlT01z1 effzlf11τ1 exp(-τ12)P1+f12δ1×exp[-2η2(τ2-τd2)+η22]P2πη2×{erf(τ2-τd2-η2)-erf(τ2-τd2-η2-δ2)}+f12δ1exp[-2η2(τ2-τd2)+η22]P2×{exp[-(τ2-τd2-η2-δ2)2]-exp[-(τ2-τd2-η2)2]},
δω2(zl, T2)=2n2ω2czlT02z2 effzlf22(τ2-τd2)exp[-(τ2-τd2)2]P2-f12δ2exp(2η1τ1+η12)P1πη1×{erf(τ1+η1+δ1)-erf(τ1+η1)}-f12δ2exp(2η1τ1+η12)P1{exp[-(τ1+η1+δ1)2]-exp[-(τ1+η1)2]}.
τi=T1/T0i,τi=T2/T0i,τd2=Td2/T02,
δi=zld/T0i,ηi=αiT0i/2d.
Td2=T01/2-T02η2-zld.
Td2=T02/2-T01η1-zld.
Td2=T02/2-zld
(δω1)max=2n2ω1cπa23d0.4289z1 effzlP1+13exp[-η2(η2+6)]P2,
(-δω2)max=4n2ω1cπa23d0.4289z2 effzlP2+13exp[-η1(η1+6)]P1.
0.4289z1 effzl+23exp[-η1(η1+6)]P1+0.8578z2 effzl+13exp[-η2(η2+6)]P2=cπa22n2d3.
β=2πλ1-122.405λ2πa2,
α2=2.4052π2λ22a3ν2+1(ν2-1)1/2.
n=2n02-1n02+2pT0p0T+11/21-n02-1n02+2pT0p0T-1/2,
n02-1=5.547×10-41+5.15×105λ02+4.19×1011λ04+4.09×1017λ06+4.32×1023λ08,
n2=3.234×10-23m2/W,
λ1=790nm,λ2=395nm,
α1/2=1.0807m-1,α2/2=0.2702m-1,
η1=0.1051,η2=0.0263,
d=β12-β11=3.338737×10-09s/m-3.338552×10-09s/m
=1.85×10-13s/m.
Td2/T01=1/2-δi-η2=-2.3192,
Td2=-41.8fs.
0.298P1+0.480P2=1,
β21=9.18fs2/m,β22=132fs2/m,
β31=91.9fs3/m,β32=44.1fs3/m.
Pc=λ2/2πn2=3.1GW(λ=790nm)0.77GW(λ=395nm),

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