Abstract

We theoretically investigate the nonresonant two-photon absorption (TPA) process in a two-level atom induced by a weak chirped pulse in the frequency domain. According to the extremum condition of the two-photon transition probability (TPTP) at the transition center frequency, we propose a Fresnel-inspired pulse tailoring scheme for TPA that is significantly different from that of Broers et al. [Phys. Rev. A 46, 2749 (1992)]. Using this scheme, the TPTP can be focused or eliminated completely by constructively or destructively modulating various pathways of the quantum interference. Our results are a significant improvement on those obtained by Broers et al. and will have potential applications in selective two-photon microscopy and spectroscopy.

© 2014 Optical Society of America

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  1. A. P. Heberle, J. J. Baumberg, and K. Köhler, Phys. Rev. Lett. 75, 2598 (1995).
    [CrossRef]
  2. M. Bellini, A. Bartoli, and T. W. Hänsch, Opt. Lett. 22, 540 (1997).
    [CrossRef]
  3. V. Blanchet, C. Nicole, M. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
    [CrossRef]
  4. A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).
    [CrossRef]
  5. D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
    [CrossRef]
  6. D. Meshulach and Y. Silberberg, Phys. Rev. A 60, 1287 (1999).
    [CrossRef]
  7. Y. Silberberg, Annu. Rev. Phys. Chem. 60, 277 (2009).
    [CrossRef]
  8. A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
    [CrossRef]
  9. M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, Nature 446, 301 (2007).
    [CrossRef]
  10. V. V. Lozovoy and M. Dantus, Chem. Phys. Chem. 6, 1970 (2005).
    [CrossRef]
  11. M. Comstock, V. V. Lozovoy, I. Pastirk, and M. Dantus, Opt. Express 12, 1061 (2004).
    [CrossRef]
  12. V. V. Lozovoy, J. C. Shane, B. W. Xu, and M. Dantus, Opt. Express 13, 10882 (2005).
    [CrossRef]
  13. V. V. Lozovoy, B. W. Xu, J. C. Shane, and M. Dantus, Phys. Rev. A 74, 041805(R) (2006).
    [CrossRef]
  14. B. Broers, L. D. Noordam, and H. B. L. van den Heuvell, Phys. Rev. A 46, 2749 (1992).
    [CrossRef]
  15. Z. Zheng and A. M. Weiner, Opt. Lett. 25, 984 (2000).
    [CrossRef]
  16. Z. Zheng and A. M. Weiner, Chem. Phys. 267, 161 (2001).
    [CrossRef]

2009 (1)

Y. Silberberg, Annu. Rev. Phys. Chem. 60, 277 (2009).
[CrossRef]

2007 (1)

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, Nature 446, 301 (2007).
[CrossRef]

2006 (1)

V. V. Lozovoy, B. W. Xu, J. C. Shane, and M. Dantus, Phys. Rev. A 74, 041805(R) (2006).
[CrossRef]

2005 (2)

2004 (1)

2001 (1)

Z. Zheng and A. M. Weiner, Chem. Phys. 267, 161 (2001).
[CrossRef]

2000 (2)

Z. Zheng and A. M. Weiner, Opt. Lett. 25, 984 (2000).
[CrossRef]

A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).
[CrossRef]

1999 (1)

D. Meshulach and Y. Silberberg, Phys. Rev. A 60, 1287 (1999).
[CrossRef]

1998 (1)

D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
[CrossRef]

1997 (3)

V. Blanchet, C. Nicole, M. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
[CrossRef]

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

M. Bellini, A. Bartoli, and T. W. Hänsch, Opt. Lett. 22, 540 (1997).
[CrossRef]

1995 (1)

A. P. Heberle, J. J. Baumberg, and K. Köhler, Phys. Rev. Lett. 75, 2598 (1995).
[CrossRef]

1992 (1)

B. Broers, L. D. Noordam, and H. B. L. van den Heuvell, Phys. Rev. A 46, 2749 (1992).
[CrossRef]

Aeschlimann, M.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, Nature 446, 301 (2007).
[CrossRef]

Atanasov, R.

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

Bartoli, A.

Bauer, M.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, Nature 446, 301 (2007).
[CrossRef]

Baumberg, J. J.

A. P. Heberle, J. J. Baumberg, and K. Köhler, Phys. Rev. Lett. 75, 2598 (1995).
[CrossRef]

Bayer, D.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, Nature 446, 301 (2007).
[CrossRef]

Bellini, M.

Blanchet, V.

V. Blanchet, C. Nicole, M. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
[CrossRef]

Bouchene, M.

V. Blanchet, C. Nicole, M. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
[CrossRef]

Brixner, T.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, Nature 446, 301 (2007).
[CrossRef]

Broers, B.

B. Broers, L. D. Noordam, and H. B. L. van den Heuvell, Phys. Rev. A 46, 2749 (1992).
[CrossRef]

Comstock, M.

Dantus, M.

V. V. Lozovoy, B. W. Xu, J. C. Shane, and M. Dantus, Phys. Rev. A 74, 041805(R) (2006).
[CrossRef]

V. V. Lozovoy and M. Dantus, Chem. Phys. Chem. 6, 1970 (2005).
[CrossRef]

V. V. Lozovoy, J. C. Shane, B. W. Xu, and M. Dantus, Opt. Express 13, 10882 (2005).
[CrossRef]

M. Comstock, V. V. Lozovoy, I. Pastirk, and M. Dantus, Opt. Express 12, 1061 (2004).
[CrossRef]

García de Abajo, F. J.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, Nature 446, 301 (2007).
[CrossRef]

Girard, B.

V. Blanchet, C. Nicole, M. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
[CrossRef]

Haché, A.

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

Hänsch, T. W.

Heberle, A. P.

A. P. Heberle, J. J. Baumberg, and K. Köhler, Phys. Rev. Lett. 75, 2598 (1995).
[CrossRef]

Hughes, J. L. P.

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

Köhler, K.

A. P. Heberle, J. J. Baumberg, and K. Köhler, Phys. Rev. Lett. 75, 2598 (1995).
[CrossRef]

Kostoulas, Y.

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

Lozovoy, V. V.

V. V. Lozovoy, B. W. Xu, J. C. Shane, and M. Dantus, Phys. Rev. A 74, 041805(R) (2006).
[CrossRef]

V. V. Lozovoy and M. Dantus, Chem. Phys. Chem. 6, 1970 (2005).
[CrossRef]

V. V. Lozovoy, J. C. Shane, B. W. Xu, and M. Dantus, Opt. Express 13, 10882 (2005).
[CrossRef]

M. Comstock, V. V. Lozovoy, I. Pastirk, and M. Dantus, Opt. Express 12, 1061 (2004).
[CrossRef]

Meshulach, D.

D. Meshulach and Y. Silberberg, Phys. Rev. A 60, 1287 (1999).
[CrossRef]

D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
[CrossRef]

Nicole, C.

V. Blanchet, C. Nicole, M. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
[CrossRef]

Noordam, L. D.

B. Broers, L. D. Noordam, and H. B. L. van den Heuvell, Phys. Rev. A 46, 2749 (1992).
[CrossRef]

Pastirk, I.

Pfeiffer, W.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, Nature 446, 301 (2007).
[CrossRef]

Rohmer, M.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, Nature 446, 301 (2007).
[CrossRef]

Shane, J. C.

V. V. Lozovoy, B. W. Xu, J. C. Shane, and M. Dantus, Phys. Rev. A 74, 041805(R) (2006).
[CrossRef]

V. V. Lozovoy, J. C. Shane, B. W. Xu, and M. Dantus, Opt. Express 13, 10882 (2005).
[CrossRef]

Silberberg, Y.

Y. Silberberg, Annu. Rev. Phys. Chem. 60, 277 (2009).
[CrossRef]

D. Meshulach and Y. Silberberg, Phys. Rev. A 60, 1287 (1999).
[CrossRef]

D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
[CrossRef]

Sipe, J. E.

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

Spindler, C.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, Nature 446, 301 (2007).
[CrossRef]

Steeb, F.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, Nature 446, 301 (2007).
[CrossRef]

van den Heuvell, H. B. L.

B. Broers, L. D. Noordam, and H. B. L. van den Heuvell, Phys. Rev. A 46, 2749 (1992).
[CrossRef]

van Driel, H. M.

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

Weiner, A. M.

Z. Zheng and A. M. Weiner, Chem. Phys. 267, 161 (2001).
[CrossRef]

Z. Zheng and A. M. Weiner, Opt. Lett. 25, 984 (2000).
[CrossRef]

A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).
[CrossRef]

Xu, B. W.

V. V. Lozovoy, B. W. Xu, J. C. Shane, and M. Dantus, Phys. Rev. A 74, 041805(R) (2006).
[CrossRef]

V. V. Lozovoy, J. C. Shane, B. W. Xu, and M. Dantus, Opt. Express 13, 10882 (2005).
[CrossRef]

Zheng, Z.

Z. Zheng and A. M. Weiner, Chem. Phys. 267, 161 (2001).
[CrossRef]

Z. Zheng and A. M. Weiner, Opt. Lett. 25, 984 (2000).
[CrossRef]

Annu. Rev. Phys. Chem. (1)

Y. Silberberg, Annu. Rev. Phys. Chem. 60, 277 (2009).
[CrossRef]

Chem. Phys. (1)

Z. Zheng and A. M. Weiner, Chem. Phys. 267, 161 (2001).
[CrossRef]

Chem. Phys. Chem. (1)

V. V. Lozovoy and M. Dantus, Chem. Phys. Chem. 6, 1970 (2005).
[CrossRef]

Nature (2)

D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
[CrossRef]

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, Nature 446, 301 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (3)

V. V. Lozovoy, B. W. Xu, J. C. Shane, and M. Dantus, Phys. Rev. A 74, 041805(R) (2006).
[CrossRef]

B. Broers, L. D. Noordam, and H. B. L. van den Heuvell, Phys. Rev. A 46, 2749 (1992).
[CrossRef]

D. Meshulach and Y. Silberberg, Phys. Rev. A 60, 1287 (1999).
[CrossRef]

Phys. Rev. Lett. (3)

V. Blanchet, C. Nicole, M. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
[CrossRef]

A. P. Heberle, J. J. Baumberg, and K. Köhler, Phys. Rev. Lett. 75, 2598 (1995).
[CrossRef]

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

Rev. Sci. Instrum. (1)

A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Fresnel sine and cosine functions.

Fig. 2.
Fig. 2.

(a) Extremum condition of the TPTP as a function of the bandwidth Δω at Ω=0. The open and solid circles correspond to the maximum and minimum values of the transition probability, respectively. (b) Tailoring scheme of the excitation pulse based on the TPTP extremum condition.

Fig. 3.
Fig. 3.

Calculated TPTPs after tailoring and modulation of the excitation pulse (a) and (b) with the method reported in Ref. [14] and (c)–(f) with our proposed scheme. The contrast ratio C is defined as the ratio between integrated signal S and integrated background B.

Equations (17)

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ρE2(t)exp(i2ω0t)dt.
P=|ρ|2|E(ω0+Ω)E(ω0Ω)dΩ|2=|A(ω0+Ω)A(ω0Ω)exp{i[ϕ(ω0+Ω)+ϕ(ω0Ω)]dΩ|2,
ϕ(ω)=α(ωω0)2,
ρ(Δω,Ω)Δω/2+ΩΔω/2+Ωei2αω2dω,
ρ(Δω,Ω){c(Δω,Ω)+is(Δω,Ω)},
{c(Δω,Ω)=π/4α{FresnelC[(Δω2Ω)α/π]+FresnelC[(Δω+2Ω)α/π]}s(Δω,Ω)=π/4α{FresnelS[(Δω2Ω)α/π]+FresnelS[(Δω+2Ω)α/π]},
P(Δω,Ω)=|ρ|2|c|2+|s|2.
dPdΔω|Ω=0=2π/α{cos[α(Δω)2/2]FresnelC(Δωα/π)+sin[α(Δω)2/2]FresnelS(Δωα/π)}.
Δωn=±(3/2+2n)π/α(n=0,1,2,3),
ρ0Ω0+ΩΩ0+Ωei2αω2dω,
ρ1Ω0+ΩΩ1+Ωei2αω2dω,ρ1Ω1+ΩΩ0+Ωei2αω2dω,
P(Ω)|kρk(Ω)|2,
P(Ω)|kρ±2k|2,k=0,1,2,
P(Ω)|kρ±2kkρ±(2k+1)|2,k=0,1,2.
P(Ω)|kρ±2kkρ±(2k+1)|2,k=0,1,2,3,
P(Ω)|k=6k=1ρkk=1k=6ρk|2.
P(Ω)|k=6k=5ρkk=5k=6ρk|2,

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