Enhanced harmonic emission from a polar molecule ... - OSA Publishing

Enhanced harmonic emission from a polar molecule medium driven by few-cycle laser pulses Chaojin Zhang,1,2,* Jinping Yao,2 Jielei Ni,2 and Fadhil A. Umran2,3 1

2

School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, P.O. Box 800-211, Shanghai 201800, China 3 Institute of Laser for Post Graduate Studies, Baghdad University, Baghdad, Iraq * [email protected]

Abstract: We investigate theoretically the enhancement of the low-order harmonic emission from a polar molecular medium. The results show that, by using a control laser field, the intensity of the spectral signals near fourth-order harmonics will increase over 25 times as a result of the fourwave mixing process. Moreover, the enhancement effects depend strongly on the carrier-envelope phase of the initial laser fields, which cannot be found in a symmetric system. ©2012 Optical Society of America OCIS codes: (190.7110) Ultrafast nonlinear optics; (320.7150) Ultrafast spectroscopy; (320.2250) Femtosecond phenomena; (190.5530) Pulse propagation and temporal solitons.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

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Received 13 Sep 2012; revised 24 Oct 2012; accepted 28 Oct 2012; published 12 Nov 2012 19 November 2012 / Vol. 20, No. 24 / OPTICS EXPRESS 26521

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The rapidly development of ultrafast laser technology, caused the pulse duration to be decreased to a few cycles, and this can be shown from the series of novel phenomena [1–8], such as the carrier-wave Rabi flopping [6, 7], the enhancement of four-wave mixing [8], and so on. In this regime, the investigations on few-cycle laser pulses interaction with asymmetric systems have been attracted and interested in the recent years [8–15]. The information of the carrier-envelope phase (CEP) can be obtained by utilizing the pulse duration and intensity [11], or by using a static electric field [12]. The main reason of the phenomena results from the permanent dipole moment (PDM) of asymmetric system. It directly affects the Lorentz local field correction and transmitted spectra [14, 15]. It has been well known in resonant extreme nonlinear optics regime, the harmonic spectra can be effectively controlled by waveform-shaped techniques which are realized by manipulating CEP of driving laser field [9–12] or the synthesis of multi-color fields [16–25]. In the presence of additional control laser field, the transmitted spectra have been significantly modified [16–18]. In this paper, we study theoretically the results of the interaction of few-cycle laser pulses with a polar molecular medium. These result can be shown in this kind of medium, even-order harmonics are generated due to PDM effects and third-order harmonic emission is enhanced about 2 times even under the condition of singlecolor laser field, and after using a weak control laser field, the intensity of third-order harmonics is further improved. And the intensity near the fourth-order harmonic (resulted

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from the four-wave mixing) increases over 25 times in two-color field regime. Moreover, the spectral signal depends strongly on the initial CEP of the fundamental laser fields. We consider that the interaction is between the few-cycle laser pulses and a polar molecular medium (para-nitroaniline (PNA)) [15, 26]. When the laser field propagates along z direction, the Maxwell-Bloch equations can be written in the following forms [8, 16, 17]: ∂H y ∂t ∂ρ12 ∂t

=−

1 ∂E x

μ0 ∂z

∂E x

,

 

∂t

= −i ω12 ρ12 + ∂n ∂t

=i

2u 

Ex 

=−

1 ∂H y

ε 0 ∂z

−

( un − Δd ρ )  − 12

E x ( ρ12 − ρ12 ) − *

1

τ2

1 ∂Px

ε 0 ∂t 1

 τ

,

ρ12 ,

(1) (2)

1

n,

(3)

where Hy, μ0 and ε0 are magnetic field, permeability and permittivity of the free space, respectively. u is the dipole moment and Δd is the difference between the PDMs. ρ12 is the offdiagonal element of the density matrix, n = ρ22-ρ11 is the population difference between the excited and ground states, ħω12 (~3.85 eV) is the transition energy of the asymmetric system [15]. Px = 2NμRe[ρ12] is the macroscopic nonlinear polarization which connects with the offdiagonal element of the density matrix in the medium. Usually, the dephasing time τ1 and the excited-state lifetime τ2 are set to be τ1 = τ2 = 1 ps [8, 15]. The number density of medium is taken to be N = 8.0 × 1025 m−3. The full-wave Maxwell-Bloch equations are solved by employing Yee's finite-difference time-domain (FDTD) discretization scheme [27–34]. Then the initial laser field propagating along z direction is [16, 17] E x (t = 0, z ) = E0 sec h [1.76( z / c − z0 / c ) / τ 0 ] cos [ω0 (t − t0 ) + φ ]

+ Ec sec h [1.76( z / c − z0 / c ) / τ c ] cos [ 2.2ω0 (t − t0 ) ]

(4)

where E0, Ec (Ec = 0.3E0) are the electric field amplitudes of the fundamental pulse and the weak control pulse, respectively. The weak control field is used for slight modifying the shape of the fundamental field and further adjusting the spectral signals. It has been extensively studied in strong regime [35, 36]. ω0 denotes the angular frequency at λ = 750 nm. φ is the initial CEP of the fundamental laser field. τ0, τc (τc = 3τ0) are the full width at half maximum (FWHM) of the fundamental pulse intensity envelope and the control pulse intensity envelope, respectively. As shown in previous work [31], that a laser pulse propagates along the z axis normally to an input interface of the medium at z = 0. Initially the pulse moved and is focused in the free space; then it partially penetrated into the PNA gas jet. The selection of z0 ensures that there is no pulse penetrating into the medium at t = 0. Therefore we use the following laser parameters: z0 = 15 μm, τ0 = 5 fs, Δd = 1.718 × 10−29 C·m, μ = 1.621 × 10−29 C·m [15, 26], and incident pulses intensity E0 = 9.16 × 107 V/cm.

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Fig. 1. Transmitted spectra of fundamental few-cycle laser pulse with (dashed line) and without the PDM effects (solid line).

In this work we first studied the influence of the PDM effects on the spectra of the single fundamental laser pulse in the polar molecular medium, in order to show the importance of PDM effects, we also assume that there exists a symmetric medium with the same parameters as asymmetric system except for d = 0 [14]. Only odd-order harmonics were generated in this case without considering the PDM effects (see black solid line in Fig. 1). In contrast, both odd- and even-order harmonics can be obtained in the presence of the PDM (red dashed line in Fig. 1), which is consistent with the previous works [14, 15]. Furthermore, in this case, the intensity of third-order harmonics enhances about 2 times and there are no changes in the spectra with adjusting the CEPs of the fundamental few-cycle pulse.

Fig. 2. (a) Transmitted spectra of the laser fields in the presence of the PDM effects. (b) Transmitted spectra of the two-color laser fields without considering the PDM effects.

Interestingly, harmonic intensity significantly increases by using a synthesized laser field, which consists of the two laser fields at different wavelengths Eq (4). It can be shown in Fig. 2(a), the intensity of third-order harmonics only slightly increases comparing with that in the case of single-color laser field. Suddenly the third-order harmonic emission shows an extremely significant enhancement and the spectral intensity harmonics at the frequency 4.2ω0 is improved by ~25 times. However, as shown in Fig. 2(b), the enhancement of harmonic emission at 4.2ω0 in the absence of PDM effects is almost negligible as compared to the case in the presence of the PDM effects. Thus, our work demonstrates an obvious relation between the second- and the third-order nonlinear susceptibilities, χ(2) and χ(3) respectively. When we used a media with permanent dipole moment, or alternatively a media which can be excited to excited states with an electronic density is not symmetrical, the

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values of χ(2) and χ(3) will be increased [37], and the results of harmonic waves will be enhanced too. In order to give a clear view on the enhancement of the harmonic emission at the frequencies 3ω0 and 4.2ω0, we perform the corresponding shape of the synthesized field. As it is shown in Fig. 3(a), the intensities of driving pulses paralleling to the PDM increases as a consequence of the excited process enlarged of the three-photons [8]. This further determines the spectral intensity of harmonics as described in our previous work [13], so that enhanced harmonic emissions at third-order and at the frequency 4.2ω0 are observed. In contrast, the phenomenon of the enhancement will disappear when the PDM effect is absent (red dashed line in Fig. 2(b). Furthermore, in the presence of the control field at the frequency of 2.2ω0, the four-wave mixing effect (i.e., ω0 + ω0 + 2.2ω0 = 4.2ω0) can be obtained in an extremely enhancement of the harmonic emission at 4.2ω0. If when the frequency of the control laser field we used is 2ω0, there will be peak at frequency 4ω0. It may result from the two-photon resonant process (2ω0 + 2ω0 = 4ω0) or four-wave mixing process (ω0 + ω0 + 2ω0 = 4ω0). In order to differentiate the origin of the above phenomenon, we use the control field slight detuning (2.2ω0) in our calculation. Because of the weakness of intensity of the control field, the peak at the frequency 5.4ω0 ( = ω0 + 2.2ω0 + 2.2ω0) cannot be found as a result from the four-wave mixing process, which is different from that of previous work [8]. In order to examine the feasibility of the experimental demonstration of our method, we investigate the influences of the laser angular frequency, the laser intensity (Ec) and the duration (τc) on the enhanced harmonic emissions. As shown in Fig. 4, the enhancement effects of harmonic emissions can exist in a broad parameter range.

Fig. 3. (a) Shape of the electric fields at three different cases. (b) Shape of the reemitted spectra of the laser fields.

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Fig. 4. Transmitted spectra of the laser fields at (a) λ = 740 nm, (b) λ = 760 nm, (c) Ec = 0.4E0 and (d) τc = 4τ0.

The above analysis can be further proved by the signal of the reemitted field. The socalled reemitted field depends sensitively on the macroscopic coherent polarization Px(t), i.e., Eem(ω)∝FFT(∂Px/∂t) [11, 33]. As indicated in Fig. 3(b), there is also a significant enhancement for the reemitted laser spectra at 3ω0 and 4.2ω0, which is consistent with the spectra of synthesized laser field (see red dashed line of Fig. 2(a)). Finally, the enhancement of harmonic emission depends strongly on the CEP of the fundamental laser pulses Fig. 5(a), then the intensity of third order harmonics will be changed with adjusting the CEP of the laser pulses, and cannot be obtained in symmetric system (Fig. 5(b)). Moreover, more obvious changing can be observed for the spectral signal at frequency 4.2ω0. In this work, due to the employment of a non-resonant two-color field with a weak control field, there will be the same harmonic emissions at the CEPs of φ = 0 and φ = π (see Fig. 5(a)). This means that the period of the CEP-dependent spectral signal is π, which is different from the Ref [8]. Hence, in our work the intensities of the harmonic emission can be more effectively controlled not only by using a weak control field but also by adjusting CEPs of fundamental laser field, which may provide more ways for experimental demonstration of this scheme.

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Fig. 5. (a) Transmitted spectra versus the CEPs of the initial fundamental laser pulses. (b) Same as in Fig. 5(a) but for the PDM d = 0.

In conclusion, we investigated a new method to enhance harmonic emission from the polar molecular system, by using a control laser field with consideration of PDM effects, therefore the intensity of harmonic emission at 4.2ω0 was improved by ~25 times due to the four-wave mixing process. Moreover, the harmonic enhancement depends strongly on the CEP of the fundamental laser field, and could provide a useful method to obtain the CEP information in the polar molecular system. Acknowledgments C. Zhang and J. Yao attribute equally to this work. The work is supported by National Basic Research Program of China (Grant No. 2011CB808102), National Natural Science Foundation of China (Grants No. 11134010, No. 60825406, No. 60921004, No. 61008061, No. 11204332, and No. 11104236) and Education Committee Foundation of Jiangsu Province (Grant No. 10KJB140012). C. Zhang gratefully acknowledges the support of K.C.Wong Education Foundation, China and Shanghai Postdoctoral Science Foundation funded project (2012M511145 and 12R21416700), and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

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