- Email: [email protected]
Spectral broadening of femtosecond laser pulse through ionizing-gas-filled capillary
Optik 124 (2013) 501–504
Contents lists available at SciVerse ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Spectral broadening of femtosecond laser pulse through ionizing-gas-filled capillary Xiaowei Song, Jingquan Lin ∗ Department of Physics, Changchun University of Science and Technology, Weixing Road 7089, Changchun 130022, China
a r t i c l e
i n f o
Article history: Received 11 August 2011 Accepted 14 December 2011
Keywords: Gas-filled capillary Spectral broadening Plasma nonlinear source Few-optical-cycle pulse generation
a b s t r a c t This paper presents experimental results of spectral broadening of femtosecond laser pulses induced by self phase modulation from plasma nonlinearity while propagating through ionizing-gas-filled capillary. Spectral broadening of the output laser pulses from capillary is in excess of 50 nm under experimental conditions of 10 mm long capillary and with a back pressure of 50 Torr nitrogen. The input and output laser pulse energy is 27 and 5.4 mJ, respectively. Both the maximal input and output energy of laser pulses under this scheme are much higher than those employing Kerr-effect exclusively with laser intensity lower than multi-photon or self-focusing threshold of the gas. Phase of the spectrally broadened laser pulses is measured to be quadratic at exit of the capillary. This novel plasma nonlinear source has the potential application in the direct generation of few-optical-cycle pulses with energies of at least several mJ. © 2012 Elsevier GmbH. All rights reserved.
1. Introduction The spectral broadening of optical pulses employing Kerr-effect in gas-filled capillary and their subsequently compression in a dispersion delay line has been reported in several papers [1–3], and this technique has the ability to generate 5 fs pulses with moderate level pulses energy. The maximum of input energy for ultrashort pulses compression in gas-filled hollow capillary is limited by the multiphoton ionization or self-focusing threshold, this gives the usable pulses energies in sub-mJ level according to recent experiment [3]. As a solution, a novel nonlinear source used for pulses compression, which shows that pulses energy constraint can be relaxed by use of plasma nonlinearity of an ionizing gas in a hollow capillary, has been proposed [4]. A capillary tube with dielectric walls is a leaky guide. Besides the losses that are due to coupling laser pulses at the entrance of the capillary tube, losses associated with refraction of the beam at the wall occur during propagation. Wave propagation along the hollow capillary can be thought as occurring through grazing incidence reflections at the dielectric surface. Since the losses caused by these multiple reflections greatly discriminate against higher order modes, only the fundamental mode can propagate in a sufficiently long capillary. Therefore, it is important to select a suitable capillary to minimize the energy loss caused by propagation. The modes of hollow capillary with diameters much larger than laser
∗ Corresponding author. Tel.: +86 431 85582496. E-mail address: [email protected] (J. Lin). 0030-4026/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2011.12.050
wavelength were considered by Marcatili and Schmeltzer [5]. For the fused silica hollow capillary the lowest loss mode is the EH11 mode. The intensity profile as a function of the radial coordinate r is given by I(r) = I0 J02 (2.405r/a), where I0 is the peak intensity, J02 is the zero-order Bessel function, and a is the bore radius. For this mode, the damping length is given by
Ld−1
= Im
2.4052 2a3
2 1 + ε2 2
(1)
1 − ε2
where is the laser wavelength in free space, and ε the index of refraction of dielectric capillary tube. Theoretically, it is most favorable for EH11 mode excitation when ω0 /a = 0.645, where ω0 is the focal spot radius at 1/e2 intensity. Laser pulses with high intensity will experience spectral broadening due to the arising nonlinearity effect when propagating through the gas-filled hollow capillary. If laser intensity is lower than multiphoton or self-focusing threshold of a gas, the broadened spectrum exhibits a feature of shifting towards both red and blue sides. However, spectral broadening with intensity higher than multiphoton or self-focusing threshold shows a different picture. As an intensive femtosecond laser pulse propagates through a gasfilled capillary, around pulse peak ionization can cause a rapid increase in the electron density. The plasma refractive index can be written as n = (1 − Ne /Ncr )1/2 , where Ne is free electron density, and Ncr is critical electron density of plasma. Hence a decrease in the refractive index will be resulted from increase of the electron density. This self-phase-modulation leads to the complementary effects of spatial defocusing and spectral broadening. The effects
502
X. Song, J. Lin / Optik 124 (2013) 501–504
are remarkably different to those which result from self-phasemodulation at lower intensity [6], because the polarizibility is relatively large and the rate of ionization is a highly nonlinear function of the intensity. In addition, the ionization process is essentially irreversible in a femtosecond time scale, and as a result the spectral broadening is mainly towards one side, containing predominantly blue-shift component. More importantly, around pulse peak the refractive-index change due to the free electron is far larger than that due to Kerr nonlinearity of neutral gas, and so it is with the extent of spectral broadening. This kind of plasma-induced spectral broadening has been analyzed in the reference [7]. The spectral broadening can be expressed as e2 Ni 30 L dZ = − 8ε0 me c 3 dt
a
Output spectra 16 2 1x10 W/cm
15 2 5x10 W/cm 15 2 3x10 W/cm 15 2 1x10 W/cm
Input spectrum 660
720
740
760
780
800
a=63 m, p=50 torr, L=10mm, N2
b
Output spectra
3 mm 10 mm 16 mm Input spectrum 680
700
720
740
760
780
800
Wavelength(nm) 15
2
N2, P=50 torr, a= 63 m, I=3x10 W/cm
c
Output spectra
100torr 50torr
2. Experiment The laser system we used is a commercially available (Coherent), 10 Hz Ti:sapphire chirped pulse amplification system with a pulse duration of 100 fs and a maximum energy output of 30 mJ. Fig. 1 shows the target configuration for the gas-filled capillary experiment. The linearly polarized laser pulse passed though a 5 mm MgF2 window into an evacuated chamber, and was focused by an f = 400 mm MgF2 lens onto a capillary target. The Rayleigh range of the focusing optics was ZR = 0.8 mm. The capillary was put in small chamber as shown in Fig. 1. In order to couple the high intensity laser pulse into the capillary, we fixed the capillary holder on a 5-dimensional translation stage. For each experiment, we first pump down the chamber to 10−3 Torr, and then filled the chamber with nitrogen gas. We measured the input and output laser energies with a calorimeter (FieldMaxII-Top, Coherent, USA), and the output broadening spectra is measured by fiber spectrometer with an operating spectral range between 300 and 1700 nm
Capillary
700
Wavelength(nm)
(2)
where Ni is the ion density, Z is the degree of ionization, is the incident wavelength, L is the effective plasma length. Therefore, it is possible to efficiently broaden the spectrum of high energy pulses by optimizing experimental parameters such as gas pressure, laser intensity, and capillary length according to above equation. Naturally, the usable input laser energies employing plasma nonlinearity in spectral broadening is higher than that based on neutral electronic nonlinearity. In this paper, we report the experimental results of efficient spectral broadening by self phase modulation from plasma nonlinearity in gas-filled hollow capillary. The aim of this work is to study the nonlinear source which is potential for the direct generation of ultrashort and high energies pulses. The experimental results show that we have succeeded in obtaining spectral-broadened pulse with energy of 5.4 mJ while the input pulse energy is 27 mJ. These values are higher by an order of magnitude than the pulses energies that have been realized to date in hollow-capillary pulse-compression systems that used Kerr nonlinearity exclusively [3]. The measured phase over the temporal FWHM is quadratic and can be potentially compensated by a chirped mirror.
Laser
680
Mirror/Wedge
20torr 5torr Input spectrum 680
700
720
740
760
780
800
Wavelength(nm) 16
2
a=63 m, I=1 X 10 W/cm , L=10mm, N2 Fig. 2. Spectral broadening of the output pulses from plasma-filled capillar, where (a) shows the spectral broadening vs laser intensity, (b) vs capillary length, and (c) vs nitrogen pressure.
(AvaSpec-2048-NIR256-USB2). Phase of the output pulse is measured by frequency resolved optical grating (FROG) technology [8]. Different bore radius fused silica was tested, and the highest laser energy transmission for our case of ω0 = 30m was obtained by use of the capillary with bore radius of 63 m. 3. Results and discussion
Gas cell Fiber spectrometer (or calorimeter /FROG)
Fig. 1. Experimental setup for the nonlinear plasma source and its characterization.
Fig. 2 shows results of spectral broadening measured at the exit of the gas-filled capillary versus gas pressure, laser intensity and capillary length. As shown in the figure, spectral broadening generally increases with the increasing of those parameters. The spectral broadening (FWHM) is about 50 nm after a capillary with length of only 10 mm at input laser intensity of 1 × 1016 W/cm2 as shown
X. Song, J. Lin / Optik 124 (2013) 501–504
503
Laser transmission
1.00
0.75
0.50
0.25
0.00
0
20
40
60
80
100
Nitrogen pressure (torr) Fig. 3. Dependence of laser transmission through gas-filled capillary on nitrogen pressure, where a = 63 m, L = 10 mm, I = 1 × 1016 W/cm2 (27 mJ).
1.0
a=63mm L=10mm
0.8
Intensity (Arb.Unit)
in Fig. 2(a). Fig. 2(b) shows that the spectral broadening increases with capillary length. The dependence of spectral broadening on back pressure of nitrogen up to 100 Torr is displayed in Fig. 2(c). In the experiment, we further increased gas pressure to higher than 100 Torr and tried to get a more broadened spectrum, however, we found that we could not get a gain in spectral broadening by increasing of gas pressure. The main reason of no extra spectral broadening occurred as pressure increase should be attributed to defocusing happened both at entrance and inside the gas-filled capillary. Notably, the spectral broadening shown in Fig. 2 is only towards blue-side, and remarkably different from the result of laser propagation with intensity lower than multi-photon ionization or self-focusing threshold in nitrogen-filled capillary [2], where the broadening spectrum showed a large portion of red-shift components, since the neutral electronic nonlinearity mainly contributes in their experiment. The laser intensity we used is higher than 1 × 1015 W/cm2 , for which a significant of valence electron of nitrogen is ionized around the pulse peak. The measured pure blue-shift spectrum in our experiment indicates that the change of the spectrum is caused by self phase modulation from plasma nonlinearity, where the free electron is responsible for the blue-shift [7]. We cannot see any evidences of emerging of red-shift component from Fig. 2, which suggests that the effect of nonlinearity from Kerr-effect of neutral gas is comparatively negligible under present experimental parameters. Fig. 3 shows the measured laser energy transmission versus gas pressure of the capillary. When pressure of nitrogen in the chamber is set to lower than 5 Torr, it is found that energy loss due to transmission through the 10 mm long gas-filled capillary is less than 20%. Notably, Fig. 3 shows that the measured absolute laser transmission is about 25% at nitrogen pressure of 50 Torr, this corresponds to output pulse energy of 5.4 mJ arising from input pulse energy of 27 mJ (1 × 1016 W/cm2 ) in the experiment. As it can be seen from this figure, laser transmission decreases with the increasing of nitrogen pressure. This should be due to the following reason: it is known that several factors contribute to the energy losses for high intensity femtosecond laser pulses transmit through the gas-filled capillary. Laser coupling efficiency drops due to the defocusing at the entrance of the capillary, causing straying ray and be blocked by capillary entrance wall. Moreover, gas ionization inside capillary leads to laser mode from fundamental into high order, and results in a lower laser transmission. The mode change when passing through the ionizing gas is due to that in the transverse direction of the ionized electrons acts as a negative lens, which leads to self-defocusing. The influence of those negative effects becomes stronger when gas pressure increase in the case of gas-filled capillary experiment. Considering that plasmainduced spectral broadening increases with interaction length, a
Fig. 4. Intensity profile and phase of the laser pulses after passing through a 50 Torr, 10 mm long nitrogen-filled capillary. The temporal FWHM of the output pulse is about 120 fs. Phase over the temporal FWHM shows quadratic.
I =10 16 W/cm 2 P=50 torr
0.6 0.4 0.2 0.0 -80
-60
-40
-20
0
20
40
60
80
Time(fs) Fig. 5. The calculated fringe autocorrelation of the broadening spectra after the pulse is compressed under assumption of an optimum chirp compensation (i.e. transform limit).
better strategy of increasing spectral broadening as well as laser energy transmission is to use low gas pressure and prolong the capillary. Fig. 4 shows a typical measured result of temporal duration and phase profile of the output pulses by use of frequency-resolved optical gating technique (FROG). The results show that the pulse duration of the output spectrum is about 120 fs, and the phase of the laser pulses is quadratic when passing through the gas-filled capillary. Knowing from the measured phase curve shape, the laser pulses are negatively chirped by the plasma. Fig. 5 shows the calculated fringe autocorrelation trace as obtained by taking the inverse Fourier transform of the spectrum under experimental conditions of 50 Torr and 10 mm long capillary (from Fig. 2(a) with laser intensity of 1 × 1016 W/cm2 ), and this autocorrelation is obtained under assumption of an optimum chirp compensation (i.e. transform limit). Fig. 5 show that pulse duration of around 29 fs is obtained from the autocorrelation curve assuming a sech2 pulse shape. 4. Conclusions We obtained spectral broadening to a bandwidth in excess of 50 nm with available pulses energies of 5.4 mJ by plasma nonlinearity after passing through only 10 mm long, nitrogen-filled capillary. The use of plasma nonlinearity is released from the strict restrain in the case of employing Kerr-effect exclusively with laser
504
X. Song, J. Lin / Optik 124 (2013) 501–504
intensity lower than multi-photon or self-focusing threshold of the gas. The measured phase with FROG technology of the output pulse indicates phase across the pulse show a quadratic. This phase can be potentially compensated with a chirped mirror, and one can obtain a compressed pulse with energies of at least several mJ. The experiment of spectral broadening by plasma nonlinearity holds the promise for the direct generation of few-optical-cycle with at least several mJ level pulse energies if shorter duration laser pulses are used as input femtosecond laser pulse in future experiment. Acknowledgments This work is supported by National Natural Science Foundation of China (Grant no. 60978014), Jingquan Lin would like to thank the illuminating discussion with Dr .H. Nakano at NTT basic Research Labs, Japan, and Prof. Zhiyi Wei at Institute of Physics, Chinese Academy of Science, for calculation of the fringe autocorrelation.
References [1] M. Nisoli, S. De Silvestri, O. Svelto, Generation of high energy 10 fs pulses by a new pulse compression technique, Appl. Phys. Lett. 68 (1996) 2793–2795. [2] M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, F. Krausz, A novel-high energy pulse compression system: generation of multigigawatt sub-5 fs pulses, Appl. Phys. B 65 (1997) 189–196. [3] M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, C. Spielmann, S. Sartania, F. Krausz, Compression of high-energy laser pulses below 5 fs, Opt. Lett. 22 (1997) 522–524. [4] G. Tempea, T. Brabec, Nonlinear source for the generation of high-energy fewcycle optical pulses, Opt. Lett. 23 (1998) 1286–1288. [5] E.A.J. Marcatili, R.A. Schmetzer, Hollow metallic and dielectric waveguides for long distance optical transmission and lasers, Bell Syst. Tech. J. 43 (1964) 1783–1786. [6] G.P. Agrawal, Nonlinear Fiber Optics, 2nd ed., Academic Press, San Diego, 1995. [7] S.C. Rae, K. Burnett, Detailed simulations of plasma-induced spectral blueshifting, Phys. Rev. A 46 (1992) 1084–1090. [8] D.J. Kane, R. Trebino, Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating, Opt. Lett. 18 (1993) 823–825.
Contents lists available at SciVerse ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Spectral broadening of femtosecond laser pulse through ionizing-gas-filled capillary Xiaowei Song, Jingquan Lin ∗ Department of Physics, Changchun University of Science and Technology, Weixing Road 7089, Changchun 130022, China
a r t i c l e
i n f o
Article history: Received 11 August 2011 Accepted 14 December 2011
Keywords: Gas-filled capillary Spectral broadening Plasma nonlinear source Few-optical-cycle pulse generation
a b s t r a c t This paper presents experimental results of spectral broadening of femtosecond laser pulses induced by self phase modulation from plasma nonlinearity while propagating through ionizing-gas-filled capillary. Spectral broadening of the output laser pulses from capillary is in excess of 50 nm under experimental conditions of 10 mm long capillary and with a back pressure of 50 Torr nitrogen. The input and output laser pulse energy is 27 and 5.4 mJ, respectively. Both the maximal input and output energy of laser pulses under this scheme are much higher than those employing Kerr-effect exclusively with laser intensity lower than multi-photon or self-focusing threshold of the gas. Phase of the spectrally broadened laser pulses is measured to be quadratic at exit of the capillary. This novel plasma nonlinear source has the potential application in the direct generation of few-optical-cycle pulses with energies of at least several mJ. © 2012 Elsevier GmbH. All rights reserved.
1. Introduction The spectral broadening of optical pulses employing Kerr-effect in gas-filled capillary and their subsequently compression in a dispersion delay line has been reported in several papers [1–3], and this technique has the ability to generate 5 fs pulses with moderate level pulses energy. The maximum of input energy for ultrashort pulses compression in gas-filled hollow capillary is limited by the multiphoton ionization or self-focusing threshold, this gives the usable pulses energies in sub-mJ level according to recent experiment [3]. As a solution, a novel nonlinear source used for pulses compression, which shows that pulses energy constraint can be relaxed by use of plasma nonlinearity of an ionizing gas in a hollow capillary, has been proposed [4]. A capillary tube with dielectric walls is a leaky guide. Besides the losses that are due to coupling laser pulses at the entrance of the capillary tube, losses associated with refraction of the beam at the wall occur during propagation. Wave propagation along the hollow capillary can be thought as occurring through grazing incidence reflections at the dielectric surface. Since the losses caused by these multiple reflections greatly discriminate against higher order modes, only the fundamental mode can propagate in a sufficiently long capillary. Therefore, it is important to select a suitable capillary to minimize the energy loss caused by propagation. The modes of hollow capillary with diameters much larger than laser
∗ Corresponding author. Tel.: +86 431 85582496. E-mail address: [email protected] (J. Lin). 0030-4026/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2011.12.050
wavelength were considered by Marcatili and Schmeltzer [5]. For the fused silica hollow capillary the lowest loss mode is the EH11 mode. The intensity profile as a function of the radial coordinate r is given by I(r) = I0 J02 (2.405r/a), where I0 is the peak intensity, J02 is the zero-order Bessel function, and a is the bore radius. For this mode, the damping length is given by
Ld−1
= Im
2.4052 2a3
2 1 + ε2 2
(1)
1 − ε2
where is the laser wavelength in free space, and ε the index of refraction of dielectric capillary tube. Theoretically, it is most favorable for EH11 mode excitation when ω0 /a = 0.645, where ω0 is the focal spot radius at 1/e2 intensity. Laser pulses with high intensity will experience spectral broadening due to the arising nonlinearity effect when propagating through the gas-filled hollow capillary. If laser intensity is lower than multiphoton or self-focusing threshold of a gas, the broadened spectrum exhibits a feature of shifting towards both red and blue sides. However, spectral broadening with intensity higher than multiphoton or self-focusing threshold shows a different picture. As an intensive femtosecond laser pulse propagates through a gasfilled capillary, around pulse peak ionization can cause a rapid increase in the electron density. The plasma refractive index can be written as n = (1 − Ne /Ncr )1/2 , where Ne is free electron density, and Ncr is critical electron density of plasma. Hence a decrease in the refractive index will be resulted from increase of the electron density. This self-phase-modulation leads to the complementary effects of spatial defocusing and spectral broadening. The effects
502
X. Song, J. Lin / Optik 124 (2013) 501–504
are remarkably different to those which result from self-phasemodulation at lower intensity [6], because the polarizibility is relatively large and the rate of ionization is a highly nonlinear function of the intensity. In addition, the ionization process is essentially irreversible in a femtosecond time scale, and as a result the spectral broadening is mainly towards one side, containing predominantly blue-shift component. More importantly, around pulse peak the refractive-index change due to the free electron is far larger than that due to Kerr nonlinearity of neutral gas, and so it is with the extent of spectral broadening. This kind of plasma-induced spectral broadening has been analyzed in the reference [7]. The spectral broadening can be expressed as e2 Ni 30 L dZ = − 8ε0 me c 3 dt
a
Output spectra 16 2 1x10 W/cm
15 2 5x10 W/cm 15 2 3x10 W/cm 15 2 1x10 W/cm
Input spectrum 660
720
740
760
780
800
a=63 m, p=50 torr, L=10mm, N2
b
Output spectra
3 mm 10 mm 16 mm Input spectrum 680
700
720
740
760
780
800
Wavelength(nm) 15
2
N2, P=50 torr, a= 63 m, I=3x10 W/cm
c
Output spectra
100torr 50torr
2. Experiment The laser system we used is a commercially available (Coherent), 10 Hz Ti:sapphire chirped pulse amplification system with a pulse duration of 100 fs and a maximum energy output of 30 mJ. Fig. 1 shows the target configuration for the gas-filled capillary experiment. The linearly polarized laser pulse passed though a 5 mm MgF2 window into an evacuated chamber, and was focused by an f = 400 mm MgF2 lens onto a capillary target. The Rayleigh range of the focusing optics was ZR = 0.8 mm. The capillary was put in small chamber as shown in Fig. 1. In order to couple the high intensity laser pulse into the capillary, we fixed the capillary holder on a 5-dimensional translation stage. For each experiment, we first pump down the chamber to 10−3 Torr, and then filled the chamber with nitrogen gas. We measured the input and output laser energies with a calorimeter (FieldMaxII-Top, Coherent, USA), and the output broadening spectra is measured by fiber spectrometer with an operating spectral range between 300 and 1700 nm
Capillary
700
Wavelength(nm)
(2)
where Ni is the ion density, Z is the degree of ionization, is the incident wavelength, L is the effective plasma length. Therefore, it is possible to efficiently broaden the spectrum of high energy pulses by optimizing experimental parameters such as gas pressure, laser intensity, and capillary length according to above equation. Naturally, the usable input laser energies employing plasma nonlinearity in spectral broadening is higher than that based on neutral electronic nonlinearity. In this paper, we report the experimental results of efficient spectral broadening by self phase modulation from plasma nonlinearity in gas-filled hollow capillary. The aim of this work is to study the nonlinear source which is potential for the direct generation of ultrashort and high energies pulses. The experimental results show that we have succeeded in obtaining spectral-broadened pulse with energy of 5.4 mJ while the input pulse energy is 27 mJ. These values are higher by an order of magnitude than the pulses energies that have been realized to date in hollow-capillary pulse-compression systems that used Kerr nonlinearity exclusively [3]. The measured phase over the temporal FWHM is quadratic and can be potentially compensated by a chirped mirror.
Laser
680
Mirror/Wedge
20torr 5torr Input spectrum 680
700
720
740
760
780
800
Wavelength(nm) 16
2
a=63 m, I=1 X 10 W/cm , L=10mm, N2 Fig. 2. Spectral broadening of the output pulses from plasma-filled capillar, where (a) shows the spectral broadening vs laser intensity, (b) vs capillary length, and (c) vs nitrogen pressure.
(AvaSpec-2048-NIR256-USB2). Phase of the output pulse is measured by frequency resolved optical grating (FROG) technology [8]. Different bore radius fused silica was tested, and the highest laser energy transmission for our case of ω0 = 30m was obtained by use of the capillary with bore radius of 63 m. 3. Results and discussion
Gas cell Fiber spectrometer (or calorimeter /FROG)
Fig. 1. Experimental setup for the nonlinear plasma source and its characterization.
Fig. 2 shows results of spectral broadening measured at the exit of the gas-filled capillary versus gas pressure, laser intensity and capillary length. As shown in the figure, spectral broadening generally increases with the increasing of those parameters. The spectral broadening (FWHM) is about 50 nm after a capillary with length of only 10 mm at input laser intensity of 1 × 1016 W/cm2 as shown
X. Song, J. Lin / Optik 124 (2013) 501–504
503
Laser transmission
1.00
0.75
0.50
0.25
0.00
0
20
40
60
80
100
Nitrogen pressure (torr) Fig. 3. Dependence of laser transmission through gas-filled capillary on nitrogen pressure, where a = 63 m, L = 10 mm, I = 1 × 1016 W/cm2 (27 mJ).
1.0
a=63mm L=10mm
0.8
Intensity (Arb.Unit)
in Fig. 2(a). Fig. 2(b) shows that the spectral broadening increases with capillary length. The dependence of spectral broadening on back pressure of nitrogen up to 100 Torr is displayed in Fig. 2(c). In the experiment, we further increased gas pressure to higher than 100 Torr and tried to get a more broadened spectrum, however, we found that we could not get a gain in spectral broadening by increasing of gas pressure. The main reason of no extra spectral broadening occurred as pressure increase should be attributed to defocusing happened both at entrance and inside the gas-filled capillary. Notably, the spectral broadening shown in Fig. 2 is only towards blue-side, and remarkably different from the result of laser propagation with intensity lower than multi-photon ionization or self-focusing threshold in nitrogen-filled capillary [2], where the broadening spectrum showed a large portion of red-shift components, since the neutral electronic nonlinearity mainly contributes in their experiment. The laser intensity we used is higher than 1 × 1015 W/cm2 , for which a significant of valence electron of nitrogen is ionized around the pulse peak. The measured pure blue-shift spectrum in our experiment indicates that the change of the spectrum is caused by self phase modulation from plasma nonlinearity, where the free electron is responsible for the blue-shift [7]. We cannot see any evidences of emerging of red-shift component from Fig. 2, which suggests that the effect of nonlinearity from Kerr-effect of neutral gas is comparatively negligible under present experimental parameters. Fig. 3 shows the measured laser energy transmission versus gas pressure of the capillary. When pressure of nitrogen in the chamber is set to lower than 5 Torr, it is found that energy loss due to transmission through the 10 mm long gas-filled capillary is less than 20%. Notably, Fig. 3 shows that the measured absolute laser transmission is about 25% at nitrogen pressure of 50 Torr, this corresponds to output pulse energy of 5.4 mJ arising from input pulse energy of 27 mJ (1 × 1016 W/cm2 ) in the experiment. As it can be seen from this figure, laser transmission decreases with the increasing of nitrogen pressure. This should be due to the following reason: it is known that several factors contribute to the energy losses for high intensity femtosecond laser pulses transmit through the gas-filled capillary. Laser coupling efficiency drops due to the defocusing at the entrance of the capillary, causing straying ray and be blocked by capillary entrance wall. Moreover, gas ionization inside capillary leads to laser mode from fundamental into high order, and results in a lower laser transmission. The mode change when passing through the ionizing gas is due to that in the transverse direction of the ionized electrons acts as a negative lens, which leads to self-defocusing. The influence of those negative effects becomes stronger when gas pressure increase in the case of gas-filled capillary experiment. Considering that plasmainduced spectral broadening increases with interaction length, a
Fig. 4. Intensity profile and phase of the laser pulses after passing through a 50 Torr, 10 mm long nitrogen-filled capillary. The temporal FWHM of the output pulse is about 120 fs. Phase over the temporal FWHM shows quadratic.
I =10 16 W/cm 2 P=50 torr
0.6 0.4 0.2 0.0 -80
-60
-40
-20
0
20
40
60
80
Time(fs) Fig. 5. The calculated fringe autocorrelation of the broadening spectra after the pulse is compressed under assumption of an optimum chirp compensation (i.e. transform limit).
better strategy of increasing spectral broadening as well as laser energy transmission is to use low gas pressure and prolong the capillary. Fig. 4 shows a typical measured result of temporal duration and phase profile of the output pulses by use of frequency-resolved optical gating technique (FROG). The results show that the pulse duration of the output spectrum is about 120 fs, and the phase of the laser pulses is quadratic when passing through the gas-filled capillary. Knowing from the measured phase curve shape, the laser pulses are negatively chirped by the plasma. Fig. 5 shows the calculated fringe autocorrelation trace as obtained by taking the inverse Fourier transform of the spectrum under experimental conditions of 50 Torr and 10 mm long capillary (from Fig. 2(a) with laser intensity of 1 × 1016 W/cm2 ), and this autocorrelation is obtained under assumption of an optimum chirp compensation (i.e. transform limit). Fig. 5 show that pulse duration of around 29 fs is obtained from the autocorrelation curve assuming a sech2 pulse shape. 4. Conclusions We obtained spectral broadening to a bandwidth in excess of 50 nm with available pulses energies of 5.4 mJ by plasma nonlinearity after passing through only 10 mm long, nitrogen-filled capillary. The use of plasma nonlinearity is released from the strict restrain in the case of employing Kerr-effect exclusively with laser
504
X. Song, J. Lin / Optik 124 (2013) 501–504
intensity lower than multi-photon or self-focusing threshold of the gas. The measured phase with FROG technology of the output pulse indicates phase across the pulse show a quadratic. This phase can be potentially compensated with a chirped mirror, and one can obtain a compressed pulse with energies of at least several mJ. The experiment of spectral broadening by plasma nonlinearity holds the promise for the direct generation of few-optical-cycle with at least several mJ level pulse energies if shorter duration laser pulses are used as input femtosecond laser pulse in future experiment. Acknowledgments This work is supported by National Natural Science Foundation of China (Grant no. 60978014), Jingquan Lin would like to thank the illuminating discussion with Dr .H. Nakano at NTT basic Research Labs, Japan, and Prof. Zhiyi Wei at Institute of Physics, Chinese Academy of Science, for calculation of the fringe autocorrelation.
References [1] M. Nisoli, S. De Silvestri, O. Svelto, Generation of high energy 10 fs pulses by a new pulse compression technique, Appl. Phys. Lett. 68 (1996) 2793–2795. [2] M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, F. Krausz, A novel-high energy pulse compression system: generation of multigigawatt sub-5 fs pulses, Appl. Phys. B 65 (1997) 189–196. [3] M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, C. Spielmann, S. Sartania, F. Krausz, Compression of high-energy laser pulses below 5 fs, Opt. Lett. 22 (1997) 522–524. [4] G. Tempea, T. Brabec, Nonlinear source for the generation of high-energy fewcycle optical pulses, Opt. Lett. 23 (1998) 1286–1288. [5] E.A.J. Marcatili, R.A. Schmetzer, Hollow metallic and dielectric waveguides for long distance optical transmission and lasers, Bell Syst. Tech. J. 43 (1964) 1783–1786. [6] G.P. Agrawal, Nonlinear Fiber Optics, 2nd ed., Academic Press, San Diego, 1995. [7] S.C. Rae, K. Burnett, Detailed simulations of plasma-induced spectral blueshifting, Phys. Rev. A 46 (1992) 1084–1090. [8] D.J. Kane, R. Trebino, Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating, Opt. Lett. 18 (1993) 823–825.