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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 5 — Feb. 27, 2012
  • pp: 5196–5203
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Generation of two attosecond pulses with tunable delay using orthogonally-polarized chirped laser pulses

Jing Miao, Zhinan Zeng, Peng Liu, Yinghui Zheng, Ruxin Li, Zhizhan Xu, V. T. Platonenko, and V. V. Strelkov  »View Author Affiliations


Optics Express, Vol. 20, Issue 5, pp. 5196-5203 (2012)
http://dx.doi.org/10.1364/OE.20.005196


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Abstract

We investigate theoretically the high-order harmonic generation (HHG) by two orthogonally-polarized linearly chirped laser pulses. We show that such generating field has a specific temporal variation of the ellipticity which provides generation of two XUV attosecond pulses with tunable delay between them. This delay is controlled by the delay between the two generating pulses. Perspectives of application of this technique for the attosecond pump – attosecond probe experiments are discussed.

© 2012 OSA

1. Introduction

When an atom is exposed to the strong laser field, many nonlinear phenomena appear, e.g. above threshold ionization and high order harmonic generation (HHG). Since the first observation of HHG in a gas [1

1. A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4(4), 595–601 (1987). [CrossRef]

], the generation of tunable coherent radiation in the XUV spectra range has opened a new era of ultrafast x-ray science. For instance, HHG has been successfully used to study electron dynamics in pump-probe experiments [2

2. M. Bauer, C. Lei, K. Read, R. Tobey, J. Gland, M. M. Murnane, and H. C. Kapteyn, “Direct observation of surface chemistry using ultrafast soft-X-ray pulses,” Phys. Rev. Lett. 87(2), 025501 (2001). [CrossRef]

4

4. L. Nugent-Glandorf, M. Scheer, D. A. Samuels, V. M. Bierbaum, and S. R. Leone, “Ultrafast photodissociation of Br2: Laser-generated high-harmonic soft x-ray probing of the transient photoelectron spectra and ionization cross section,” J. Chem. Phys. 117(13), 6108 (2002). [CrossRef]

].

One of the most important applications of the HHG is to produce the subfemtosecond or attosecond XUV pulses. Generation and application of the attosecond pulses is actively investigated during about ten years. The duration of the experimentally achievable isolated attosecond pulse has been shortened down to 80 as [5

5. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008). [CrossRef] [PubMed]

]. The main methods applied experimentally for isolated attosecond pulse generation involve using few-cycle generating pulse [6

6. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001). [CrossRef] [PubMed]

, 7

7. A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003). [CrossRef] [PubMed]

] (amplitude gating), time-varying ellipticity of the generating field (polarization gating) [8

8. P. B. Corkum, N. H. Burnett, and M. Y. Ivanov, “Subfemtosecond pulses,” Opt. Lett. 19(22), 1870–1872 (1994). [CrossRef] [PubMed]

11

11. G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314(5798), 443–446 (2006). [CrossRef] [PubMed]

], and rapid ionization of the medium (ionization gating [12

12. V. V. Strelkov, A. F. Sterjantov, N. Yu. Shubin, and V. T. Platonenko, “XUV generation with several-cycle laser pulse in barrier-suppression regime,” J. Phys. B 39(3), 577–589 (2006). [CrossRef]

16

16. G. Sansone, L. Poletto, and M. Nisoli, “High-energy attosecond light sources,” Nat. Photonics 5(11), 655–663 (2011). [CrossRef]

]). Besides, several techniques are based on combination of one of these methods with using second harmonic in conjunction to the fundamental field [17

17. Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98(20), 203901 (2007). [CrossRef] [PubMed]

20

20. Z. Chang, “Controlling attosecond pulse generation with a double optical gating,” Phys. Rev. A 76(5), 051403 (2007). [CrossRef]

]. In the presence of the second harmonic the period of the recollision evens is the full optical cycle [21

21. T. Pfeifer, L. Gallmann, M. J. Abel, D. M. Neumark, and S. R. Leone, “Single attosecond pulse generation in the multicycle-driver regime by adding a weak second-harmonic field,” Opt. Lett. 31(7), 975–977 (2006). [CrossRef] [PubMed]

, 22

22. J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97(1), 013001 (2006). [CrossRef] [PubMed]

] (but not the half-cycle as in the case of one-color field), thus using of the second harmonic provides additional time for “closing” of the gate.

The first polarization gating method was proposed by Corkum et al [8

8. P. B. Corkum, N. H. Burnett, and M. Y. Ivanov, “Subfemtosecond pulses,” Opt. Lett. 19(22), 1870–1872 (1994). [CrossRef] [PubMed]

]. By combining two short perpendicularly polarized pulses with frequencies ω1 andω2, where (ω12)/ω1<<1, a pulse with polarization that sweeps from circular through linear back to circular can be created, which can generate a single (also called an isolated) attosecond pulse. But generation of such laser field was quite difficult that time. More practical way to obtain generating field with time-varying ellipticity was suggested in [9

9. V. T. Platonenko and V. V. Strelkov, “Single attosecond soft-x-ray pulse generated with a limited laser beam,” J. Opt. Soc. Am. B 16(3), 435–440 (1999). [CrossRef]

]. This approach assumes using only one initial laser pulse. After some modification this approach was successfully used to generate an isolated attosecond pulse [10

10. I. J. Sola, E. Mével, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, M. Nisoli, C. Vozzi4, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2(5), 319–322 (2006). [CrossRef]

, 11

11. G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314(5798), 443–446 (2006). [CrossRef] [PubMed]

], where 5fs laser pulse is used. With the two-color scheme, driving laser pulse can be further extended to be multi-cycle; such technique is known as double optical gating (DOG) [20

20. Z. Chang, “Controlling attosecond pulse generation with a double optical gating,” Phys. Rev. A 76(5), 051403 (2007). [CrossRef]

].

While first applications of the attosecond pulses involved using the isolated attosecond pulse in conjunction with strong IR field (for instance, IR pump – XUV probe), generation of intense isolated attosecond pulses makes possible attosecond XUV pump – attosecond XUV probe experiments. This raises a problem of a pair of attosecond pulses generation with a controllable delay between them. When the polarization gating confines the XUV generation within the temporal window which duration is longer than optical half-cycle and shorter than the cycle, the pair of attosecond pulses can be generated [23

23. G. Sansone, E. Benedetti, J. P. Caumes, S. Stagira, C. Vozzi, M. Nisoli, V. Strelkov, I. Sola, L. B. Elouga, A. Zaïr, E. Mével, and E. Constant, “Shaping of attosecond pulses by phase-stabilized polarization gating,” Phys. Rev. A 80(6), 063837 (2009). [CrossRef]

]. However, the delay between the pulses is almost fixed (one half-cycle).

In this paper, we suggest and investigate theoretically a new polarization gating technique allowing generation of a pair of attopulses with controllable delay. This technique is based on using two orthogonally polarized linearly chirped laser pulses. We calculate the XUV emission in such field using the Lewenstein model [24

24. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994). [CrossRef] [PubMed]

, 25

25. Ph. Antoine, A. L’Huillier, M. Lewenstein, P. Salières, and B. Carré, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53(3), 1725–1745 (1996). [CrossRef] [PubMed]

] and find that a pair of attosecond pulses can be generated under proper choice of the field parameters. The time delay between these two XUV pulses is controlled by simply changing the delay between the two generating fields. We find analytical equations describing the ellipticity of such generating field. This allows analyzing the perspectives of the suggested polarization gating technique.

2. Result and discussion

The laser pulses used in our simulation are linearly chirped. Note that experimentally the linear chirp can be easily controlled by changing the distance between the gratings [26

26. D. G. Lee, J.-H. Kim, K.-H. Hong, and C. H. Nam, “Coherent control of high-order harmonics with chirped femtosecond laser pulses,” Phys. Rev. Lett. 87(24), 243902 (2001). [CrossRef] [PubMed]

]. To simplify the simulation, the pulses have the same chirp, but one is negative and the other positive, respectively. Two crossed linearly polarized fields, Ex and Ey, can be written as below, which have the same spectral amplitude with the initial pulse,
Ex=E0exp[(t+Td/2)2×a]sin[ω(t+Td/2)+b(t+Td/2)2]Ey=E0exp[(tTd/2)2×a]sin[ω(tTd/2)b(tTd/2)2]
(1)
where Td is the relative delay between the two pulses, ω is the angular frequency, a = 1/(τpN)2, b = a(N2-1)1/2 and N is a parameter describing the chirp, τp is the duration of the initial pulse. In our simulations we use the initial laser pulse with the peak intensity of 8 × 1013W/cm2. The initial pulse duration is 25fs and N = 3, which means that the durations of both chirped laser pulses are Nτp = 75fs.

We are using the Lewenstein model [24

24. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994). [CrossRef] [PubMed]

, 25

25. Ph. Antoine, A. L’Huillier, M. Lewenstein, P. Salières, and B. Carré, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53(3), 1725–1745 (1996). [CrossRef] [PubMed]

] in our simulations. In this model, the dipole of an atom can be calculated by the following formula:
ndnl(t)=2Re(i0+dτ(πε+iτ/2)3/2E(tτ)d[pst(tτ,t)A(tτ)]×nd*[pst(tτ,t)A(t)]exp[iSst(tτ,t)])×exp[tw(t')dt']
(2)
where E(t) is the field of the laser pulse, A(t) is its vector potential, ε is a positive regularization constant, pst=1τtτtA(t')dt' is the stationary value of the momentum and Sst=12tτt(pstA(t'))2dt' is the stationary quasi-classical action. ndnl(t) is the project of dipole in the direction of a unit vector n. The last term in Eq. (2) describes the ground-state depletion. We calculate the ionization rate w(t) using the ADK model [27

27. M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in a varing electromagnetic-field,” Zh. Eksp. Teor. Fiz. 91, 2008 (1986).

]. Then, we calculate x- and y-projections of the dnl(t) using n along x- and y-axis, and find the amplitude of the HHG spectrum as the Fourier transform of the dipole acceleration, p(ω)=nd¨nl(t)ejωtdt. The ionization potential of the Kr atom is used in our simulation. In the calculation of the dipole d[pstA], the wavefunction of s-state is used.

Using 800 nm generating field, we calculate the HHG spectra as a function of the delay Td between the laser pulses. Selecting a single harmonic, we apply inversed Fourier transform to study its temporal behavior. Figure 1(a)
Fig. 1 (a) Temporal profiles of H25 intensity vs delay between two orthogonally polarized linearly chirped pulses. (b) The time interval between two XUV pulses vs delay between the two laser pulses. The driving wavelength is 800 nm, the peak laser intensity is 8 × 1013W/cm2, the initial pulse duration is 25fs and N = 3, thus the durations of both chirped pulses are 75fs.
shows the temporal profiles of H25 changing with the delay between the two laser pulses. When the delay is about 0.225 cycles (0.6fs), the time interval between two XUV pulses is about 24 cycles. When the delay is adjusted between 0.15 cycles and 0.45 cycles, the time interval between two femtosecond XUV pulses varies from about 12 cycles to 26 cycles (Fig. 1(b)). Note that this behavior is typical for other harmonics as well.

With this kind of gating, we can also produce the double attopulses with controllable delay. Figure 2(a)
Fig. 2 (a) Attopulses generated by the 800nm driving field; the other field parameters are the same as for Fig. 1. The harmonics above 19th order are chosen to produce the attopulse. (b) The same for the 2 μm, 75 fs chirped laser pulse under N = 3, the other parameters are the same as for the panel (a). Note that when the delay Td is changed from 1fs (0.15 cycles) to 3fs (0.45 cycles), the intensity of the linear field in the gate changes almost linearly from 5x1013W/cm2 to 9x1013W/cm2.
shows the attopulses with the harmonics above 19th order generated by the same laser pulse as used in Fig. 1. In each gate several bursts appear. This is because each gate is too long, namely longer than the laser half-cycle. The gate duration can be decreased using the shorter original pulse, or providing generation conditions when the threshold ellipticity is lower (see the analytical studies in the final part of the paper). The second option can be realized using the mid-infrared laser pulse and higher order harmonics, because the threshold ellipticity decreases when the harmonic order increases [10

10. I. J. Sola, E. Mével, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, M. Nisoli, C. Vozzi4, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2(5), 319–322 (2006). [CrossRef]

] and the driving wavelength increases [28

28. S. D. Khan, Y. Cheng, M. Möller, K. Zhao, B. Zhao, M. Chini, G. G. Paulus, and Z. Chang, “Ellipticity dependence of 400 nm-driven high harmonic generation,” Appl. Phys. Lett. 99(16), 161106 (2011). [CrossRef]

]. Figure 2(b) shows the generation of the double attopulses with the harmonics above 141st order. In this simulation, the wavelength of the laser pulse is 2 μm. From the figure we can see, that the time interval between the two pulses can be controlled.

Note, that the exact emission time of every attosecond pulse is defined by the instantaneous generating filed. Here we deal with the attosecond pulses from the cut-off region, so they are emitted close to time when the field is zero. Changing the position of the gate, we do not change these time instants. That is why the emission time for every attosecond pulse in Fig. 2 does not change with the delay, but the efficiency of the emission depends (continuously) on the gate position. Under certain delays the emission times miss the gate, and two weak attopulses are generated for every window. For the “usual” polarization gating similar behavior was studied in Refs [10

10. I. J. Sola, E. Mével, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, M. Nisoli, C. Vozzi4, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2(5), 319–322 (2006). [CrossRef]

, 23

23. G. Sansone, E. Benedetti, J. P. Caumes, S. Stagira, C. Vozzi, M. Nisoli, V. Strelkov, I. Sola, L. B. Elouga, A. Zaïr, E. Mével, and E. Constant, “Shaping of attosecond pulses by phase-stabilized polarization gating,” Phys. Rev. A 80(6), 063837 (2009). [CrossRef]

]. (however, in this papers the gate position was fixed, and the emission times were varied changing the carrier-envelope phase of the laser pulse). Thus, in conditions of Fig. 2(b) two isolated attosecond pulses are generated, separated with the integer number of half-cycles. This number is controlled with the delay Td, besides, under certain delays a pair of weak attopulses is generated inside every gate.

In order to understand the physical mechanisms in the generation of these two XUV pulses, we calculate the ellipticity of the electric field. Let us consider the generating field,
Ex(t)=E0x(t)sin(ϕx(t))Ey(t)=E0y(t)sin(ϕy(t))
(3)
where E0x(t) and E0y(t) are slowly varying envelopes of the x- and y-projections of the field, E0x(t) = E0exp[-a(t-Td/2)2], E0y(t) = E0exp[-a(t + Td/2)2], and ϕx(t) and ϕy(t) are the phases of the field projections, ϕx(t) = ω(t-Td/2) + b(t-Td/2)2, ϕy(t) = ω(t + Td/2)- b(t + Td/2)2. Then the ellipticity of the field and the rotation angle of the polarization ellipse are [29

29. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964).

],

ε=tan[12arcsin[2E0xE0ysin(ϕyϕx)E0x2+E0y2]]
(4)
φ=12arctan[2E0xE0ycos(ϕyϕx)E0x2E0y2]
(5)

The ellipticity of the field is presented in Fig. 3
Fig. 3 The ellipticity modulus of the field vs the delay between two laser pulse. The parameters of the laser pulse are the same as for Fig. 1. The region where the ellipticity is lower than the threshold ellipticity for H25 (0.125) is shown in the figure.
. One can clearly see that the region of low ellipticities in this figure corresponds to the region where the attopulses are generated (see Fig. 2). In Fig. 3 we see that when the delay is increased, the two gates get closer to each other, and finally for Td equal to a half-cycle they overlap. In this case the resulting gate is longer and several attopulses are generated within it, see Fig. 2. Thus, one can conclude that the suggested gating scheme is not suitable for generating a pair of attopulses with very short delay between them.

The used delays Td are much less than the pulse duration. So the generating pulse given by Eq. (1) has almost the same duration Nτp, as the initial chirped pulse. If the time interval between the two gates exceeds this duration, the gates take place at the edges of the pulse, so intensity within the gate is low. Thus, this duration gives the upper limit of the time separating the attosecond pulses achieved with the suggested technique.

From Eq. (4) we find that zero ellipticity is achieved at ϕy-ϕx = ± kπ. We can get a general expression for the position of zero ellipticity t˜=±kπωTd2b (under bTd2<<1), where k = [ωTd/π] + 1, [x] means nearest integer less than x. If 0<ωTd<π, we have k = 1 and the time instant for zero ellipticity is approximately,

t˜=±πωTd2b,ωTdπ(6).

The gate duration Δ can also be found from Eq. (4) as the time interval during which the ellipticity modulus is less than the threshold ellipticity εth (i.e. the fundamental ellipticity for which XUV generation efficiency is decreased by half),

Δ=12b(πωTd)arcsin(E0x2(t˜)+E0y2(t˜)2E0x(t˜)E0y(t˜)sin(2arctanεth))
(7)

Taking into account that E0x2(t˜)+E0y2(t˜)E0x(t˜)E0y(t˜)2 and εth is small, we find the following approximate equation:

Δ=2b(πωTd)εth
(8)

One can see from Eq. (6), Eq. (8) that the gate duration decreases with ͂t and thus formally can be infinitively short. However, practically ͂t should not exceed the pulses duration because otherwise the gate would occur under too weak fundamental intensity. Let us consider the case ͂t = τFWHM/2, where τFWHM = (2ln2)1/2p is the full width of the chirped pulse at the level of the half of the maximal intensity. This equation is satisfied under
TdT=12(1ln2N21π)
(9)
where T is the laser cycle.

Then

Δ=2εthτpln2NN21
(10)

For high N this equation can be further simplified:

Δ=2εthτpln2
(11)

Note that this gate duration is very close to the one provided by the usual ellipticity gating technique [30

30. Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A 70(4), 043802 (2004). [CrossRef]

, 31

31. V. V. Strelkov, A. Zaïr, O. Tcherbakoff, R. López-Martens, E. Cormier, E. Mével, and E. Constant, “Single attosecond pulse production with an ellipticity-modulated driving IR pulse,” J. Phys. B 38(10), L161–L167 (2005). [CrossRef]

]: Δ = εthτp/(ln2). Thus, the main difference is that in the suggested technique we have a pair of gates taking place in the time instants given by Eq. (6).

The gate duration given by Eq. (11) agrees well with the numerical results shown in Fig. 2. Calculating the 25th harmonic generation efficiency as a function of the laser ellipticity for the 800nm wavelength we find that the threshold ellipticity is about 0.125, in agreement with experiment [10

10. I. J. Sola, E. Mével, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, M. Nisoli, C. Vozzi4, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2(5), 319–322 (2006). [CrossRef]

] reporting εth = 0.12 for this harmonic. Equation (10) gives Δ = 5.1fs fs for the conditions of Fig. 2(a). Thus the gate duration is about 4 half-cycles, which agrees with approximately 4 attosecond pulses emitted within every gate in Fig. 2(a) for Td/T<0.3. For conditions of Fig. 2(b), Eq. (11) gives Δ = 2.0fs. This is less than the driving field half-cycle for the 2 μm wavelength, so it agrees with generation of an isolated attosecond pulse within every gate in Fig. 2(b).

The rotation angle of the driving field (given by Eq. (5)) is almost constant inside both gates; it is equal to π/4. The found rotation angle for the XUV field is very close to π/4. This is natural because the driving field inside the gate is almost linearly polarized, and thus the XUV rotation angle is almost identical to the one of the driving field (see Refs [23

23. G. Sansone, E. Benedetti, J. P. Caumes, S. Stagira, C. Vozzi, M. Nisoli, V. Strelkov, I. Sola, L. B. Elouga, A. Zaïr, E. Mével, and E. Constant, “Shaping of attosecond pulses by phase-stabilized polarization gating,” Phys. Rev. A 80(6), 063837 (2009). [CrossRef]

, 32

32. V. V. Strelkov, A. A. Gonoskov, I. A. Gonoskov, and M. Yu. Ryabikin, “Origin for ellipticity of high-order harmonics generated in atomic gases and the sublaser-cycle evolution of harmonic polarization,” Phys. Rev. Lett. 107(4), 043902 (2011). [CrossRef] [PubMed]

]).

Finally, we would like to discuss the limitations of the experimental applicability of the suggested scheme caused by the medium ionization. The ionization decreases the XUV generation efficiency due to the ground state depletion, and also affects phase-matching of the generation. This limitation is important for all polarization gating schemes: laser intensity outside the gate is enough to provide some ionization, although the rate is less than inside the gate because of the elliptical (or circular) polarization. In the suggested scheme this limitation is especially important if the generation of the pair of attopulses with similar intensities is required. The effect of the ionization on the phase-matching depends on the medium density and propagation distance. In general, the role of phase-matching can be minimized using a dilute and thin generating target (certainly, this would limit the total XUV generation efficiency). In this case the difference of the attosecond pulse intensities is only due to the ground state depletion. In our simulations we have found 35% ground state depletion using the ADK ionization rate for 800nm, 1014 W/cm2 laser pulse under Td equal to quarter-cycle. Corresponding attopulse intensity decrease can be seen in Fig. 1(a), Fig. 2(a).

3. Conclusion

In summary, we show that double gating for XUV generation with controllable delay can be realized by using orthogonally-polarized linearly chirped laser pulses. Note that the suggested polarization gating technique is quite easy for the experimental realization: the chirp can be introduced by changing the distance between the gratings or passing through the dispersion media, thus no nonlinear process is required. This will make possible using this technique, in particular, for high energy driving laser pulse, e.g. the laser pulse from the PW laser system. Generation of the pair of intense attosecond pulses with easily controllable delay can be very useful for forthcoming application of attopulses in XUV pump – XUV probe experiments.

Acknowledgments

This research was supported by Chinese National Science Foundation (Grant Nos. 11011120246, 10734080, 60921004, 10904157, 60978012, 61078022), 973Project (Grant No. 2011CB808103), and Shanghai Commission of Science and Technology (Grant Nos. 10QA1407600). Russian Foundation for Basic Research (10-02-91165-GFEN_a, 11-02-01217-а) and Presidential Council on Grants of RF (MD-6596.2012.2).

References and links

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2.

M. Bauer, C. Lei, K. Read, R. Tobey, J. Gland, M. M. Murnane, and H. C. Kapteyn, “Direct observation of surface chemistry using ultrafast soft-X-ray pulses,” Phys. Rev. Lett. 87(2), 025501 (2001). [CrossRef]

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4.

L. Nugent-Glandorf, M. Scheer, D. A. Samuels, V. M. Bierbaum, and S. R. Leone, “Ultrafast photodissociation of Br2: Laser-generated high-harmonic soft x-ray probing of the transient photoelectron spectra and ionization cross section,” J. Chem. Phys. 117(13), 6108 (2002). [CrossRef]

5.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008). [CrossRef] [PubMed]

6.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001). [CrossRef] [PubMed]

7.

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003). [CrossRef] [PubMed]

8.

P. B. Corkum, N. H. Burnett, and M. Y. Ivanov, “Subfemtosecond pulses,” Opt. Lett. 19(22), 1870–1872 (1994). [CrossRef] [PubMed]

9.

V. T. Platonenko and V. V. Strelkov, “Single attosecond soft-x-ray pulse generated with a limited laser beam,” J. Opt. Soc. Am. B 16(3), 435–440 (1999). [CrossRef]

10.

I. J. Sola, E. Mével, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, M. Nisoli, C. Vozzi4, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2(5), 319–322 (2006). [CrossRef]

11.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314(5798), 443–446 (2006). [CrossRef] [PubMed]

12.

V. V. Strelkov, A. F. Sterjantov, N. Yu. Shubin, and V. T. Platonenko, “XUV generation with several-cycle laser pulse in barrier-suppression regime,” J. Phys. B 39(3), 577–589 (2006). [CrossRef]

13.

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76(5), 051801 (2007). [CrossRef]

14.

T. Pfeifer, A. Jullien, M. J. Abel, P. M. Nagel, L. Gallmann, D. M. Neumark, and S. R. Leone, “Generating coherent broadband continuum soft-x-ray radiation by attosecond ionization gating,” Opt. Express 15(25), 17120–17128 (2007). [CrossRef] [PubMed]

15.

V. V. Strelkov, E. Mével, and E. Constant, “Generation of isolated attosecond pulses by spatial shaping of a femtosecond laser beam,” New J. Phys. 10(8), 083040 (2008). [CrossRef]

16.

G. Sansone, L. Poletto, and M. Nisoli, “High-energy attosecond light sources,” Nat. Photonics 5(11), 655–663 (2011). [CrossRef]

17.

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98(20), 203901 (2007). [CrossRef] [PubMed]

18.

X. Feng, S. Gilbertson, H. Mashiko, H. Wang, S. D. Khan, M. Chini, Y. Wu, K. Zhao, and Z. Chang, “Generation of isolated attosecond pulses with 20 to 28 femtosecond lasers,” Phys. Rev. Lett. 103(18), 183901 (2009). [CrossRef] [PubMed]

19.

Y. Xiang, Y. Niu, and S. Gong, “Control of the high-order harmonics cutoff through the combination of a chirped laser and static electric field,” Phys. Rev. A 79(5), 053419 (2009). [CrossRef]

20.

Z. Chang, “Controlling attosecond pulse generation with a double optical gating,” Phys. Rev. A 76(5), 051403 (2007). [CrossRef]

21.

T. Pfeifer, L. Gallmann, M. J. Abel, D. M. Neumark, and S. R. Leone, “Single attosecond pulse generation in the multicycle-driver regime by adding a weak second-harmonic field,” Opt. Lett. 31(7), 975–977 (2006). [CrossRef] [PubMed]

22.

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97(1), 013001 (2006). [CrossRef] [PubMed]

23.

G. Sansone, E. Benedetti, J. P. Caumes, S. Stagira, C. Vozzi, M. Nisoli, V. Strelkov, I. Sola, L. B. Elouga, A. Zaïr, E. Mével, and E. Constant, “Shaping of attosecond pulses by phase-stabilized polarization gating,” Phys. Rev. A 80(6), 063837 (2009). [CrossRef]

24.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994). [CrossRef] [PubMed]

25.

Ph. Antoine, A. L’Huillier, M. Lewenstein, P. Salières, and B. Carré, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53(3), 1725–1745 (1996). [CrossRef] [PubMed]

26.

D. G. Lee, J.-H. Kim, K.-H. Hong, and C. H. Nam, “Coherent control of high-order harmonics with chirped femtosecond laser pulses,” Phys. Rev. Lett. 87(24), 243902 (2001). [CrossRef] [PubMed]

27.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in a varing electromagnetic-field,” Zh. Eksp. Teor. Fiz. 91, 2008 (1986).

28.

S. D. Khan, Y. Cheng, M. Möller, K. Zhao, B. Zhao, M. Chini, G. G. Paulus, and Z. Chang, “Ellipticity dependence of 400 nm-driven high harmonic generation,” Appl. Phys. Lett. 99(16), 161106 (2011). [CrossRef]

29.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964).

30.

Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A 70(4), 043802 (2004). [CrossRef]

31.

V. V. Strelkov, A. Zaïr, O. Tcherbakoff, R. López-Martens, E. Cormier, E. Mével, and E. Constant, “Single attosecond pulse production with an ellipticity-modulated driving IR pulse,” J. Phys. B 38(10), L161–L167 (2005). [CrossRef]

32.

V. V. Strelkov, A. A. Gonoskov, I. A. Gonoskov, and M. Yu. Ryabikin, “Origin for ellipticity of high-order harmonics generated in atomic gases and the sublaser-cycle evolution of harmonic polarization,” Phys. Rev. Lett. 107(4), 043902 (2011). [CrossRef] [PubMed]

OCIS Codes
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(320.0320) Ultrafast optics : Ultrafast optics
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

ToC Category:
Ultrafast Optics

History
Original Manuscript: December 2, 2011
Revised Manuscript: January 20, 2012
Manuscript Accepted: January 21, 2012
Published: February 16, 2012

Citation
Jing Miao, Zhinan Zeng, Peng Liu, Yinghui Zheng, Ruxin Li, Zhizhan Xu, V. T. Platonenko, and V. V. Strelkov, "Generation of two attosecond pulses with tunable delay using orthogonally-polarized chirped laser pulses," Opt. Express 20, 5196-5203 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5196


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References

  1. A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4(4), 595–601 (1987). [CrossRef]
  2. M. Bauer, C. Lei, K. Read, R. Tobey, J. Gland, M. M. Murnane, and H. C. Kapteyn, “Direct observation of surface chemistry using ultrafast soft-X-ray pulses,” Phys. Rev. Lett. 87(2), 025501 (2001). [CrossRef]
  3. R. I. Tobey, E. H. Gershgoren, M. E. Siemens, M. M. Murnane, H. C. Kapteyn, T. Feurer, and K. A. Nelson, “Nanoscale photo thermal and photo acoustic transients probed with extreme ultraviolet radiation,” Appl. Phys. Lett. 85(4), 564–566 (2004). [CrossRef]
  4. L. Nugent-Glandorf, M. Scheer, D. A. Samuels, V. M. Bierbaum, and S. R. Leone, “Ultrafast photodissociation of Br2: Laser-generated high-harmonic soft x-ray probing of the transient photoelectron spectra and ionization cross section,” J. Chem. Phys. 117(13), 6108 (2002). [CrossRef]
  5. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008). [CrossRef] [PubMed]
  6. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001). [CrossRef] [PubMed]
  7. A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003). [CrossRef] [PubMed]
  8. P. B. Corkum, N. H. Burnett, and M. Y. Ivanov, “Subfemtosecond pulses,” Opt. Lett. 19(22), 1870–1872 (1994). [CrossRef] [PubMed]
  9. V. T. Platonenko and V. V. Strelkov, “Single attosecond soft-x-ray pulse generated with a limited laser beam,” J. Opt. Soc. Am. B 16(3), 435–440 (1999). [CrossRef]
  10. I. J. Sola, E. Mével, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, M. Nisoli, C. Vozzi4, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2(5), 319–322 (2006). [CrossRef]
  11. G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314(5798), 443–446 (2006). [CrossRef] [PubMed]
  12. V. V. Strelkov, A. F. Sterjantov, N. Yu. Shubin, and V. T. Platonenko, “XUV generation with several-cycle laser pulse in barrier-suppression regime,” J. Phys. B 39(3), 577–589 (2006). [CrossRef]
  13. P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76(5), 051801 (2007). [CrossRef]
  14. T. Pfeifer, A. Jullien, M. J. Abel, P. M. Nagel, L. Gallmann, D. M. Neumark, and S. R. Leone, “Generating coherent broadband continuum soft-x-ray radiation by attosecond ionization gating,” Opt. Express 15(25), 17120–17128 (2007). [CrossRef] [PubMed]
  15. V. V. Strelkov, E. Mével, and E. Constant, “Generation of isolated attosecond pulses by spatial shaping of a femtosecond laser beam,” New J. Phys. 10(8), 083040 (2008). [CrossRef]
  16. G. Sansone, L. Poletto, and M. Nisoli, “High-energy attosecond light sources,” Nat. Photonics 5(11), 655–663 (2011). [CrossRef]
  17. Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98(20), 203901 (2007). [CrossRef] [PubMed]
  18. X. Feng, S. Gilbertson, H. Mashiko, H. Wang, S. D. Khan, M. Chini, Y. Wu, K. Zhao, and Z. Chang, “Generation of isolated attosecond pulses with 20 to 28 femtosecond lasers,” Phys. Rev. Lett. 103(18), 183901 (2009). [CrossRef] [PubMed]
  19. Y. Xiang, Y. Niu, and S. Gong, “Control of the high-order harmonics cutoff through the combination of a chirped laser and static electric field,” Phys. Rev. A 79(5), 053419 (2009). [CrossRef]
  20. Z. Chang, “Controlling attosecond pulse generation with a double optical gating,” Phys. Rev. A 76(5), 051403 (2007). [CrossRef]
  21. T. Pfeifer, L. Gallmann, M. J. Abel, D. M. Neumark, and S. R. Leone, “Single attosecond pulse generation in the multicycle-driver regime by adding a weak second-harmonic field,” Opt. Lett. 31(7), 975–977 (2006). [CrossRef] [PubMed]
  22. J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97(1), 013001 (2006). [CrossRef] [PubMed]
  23. G. Sansone, E. Benedetti, J. P. Caumes, S. Stagira, C. Vozzi, M. Nisoli, V. Strelkov, I. Sola, L. B. Elouga, A. Zaïr, E. Mével, and E. Constant, “Shaping of attosecond pulses by phase-stabilized polarization gating,” Phys. Rev. A 80(6), 063837 (2009). [CrossRef]
  24. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994). [CrossRef] [PubMed]
  25. Ph. Antoine, A. L’Huillier, M. Lewenstein, P. Salières, and B. Carré, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53(3), 1725–1745 (1996). [CrossRef] [PubMed]
  26. D. G. Lee, J.-H. Kim, K.-H. Hong, and C. H. Nam, “Coherent control of high-order harmonics with chirped femtosecond laser pulses,” Phys. Rev. Lett. 87(24), 243902 (2001). [CrossRef] [PubMed]
  27. M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in a varing electromagnetic-field,” Zh. Eksp. Teor. Fiz. 91, 2008 (1986).
  28. S. D. Khan, Y. Cheng, M. Möller, K. Zhao, B. Zhao, M. Chini, G. G. Paulus, and Z. Chang, “Ellipticity dependence of 400 nm-driven high harmonic generation,” Appl. Phys. Lett. 99(16), 161106 (2011). [CrossRef]
  29. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964).
  30. Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A 70(4), 043802 (2004). [CrossRef]
  31. V. V. Strelkov, A. Zaïr, O. Tcherbakoff, R. López-Martens, E. Cormier, E. Mével, and E. Constant, “Single attosecond pulse production with an ellipticity-modulated driving IR pulse,” J. Phys. B 38(10), L161–L167 (2005). [CrossRef]
  32. V. V. Strelkov, A. A. Gonoskov, I. A. Gonoskov, and M. Yu. Ryabikin, “Origin for ellipticity of high-order harmonics generated in atomic gases and the sublaser-cycle evolution of harmonic polarization,” Phys. Rev. Lett. 107(4), 043902 (2011). [CrossRef] [PubMed]

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