Supplementary Information for: Super-luminescent jet light
generated by femtosecond laser pulses
Zhijun Xu, Xiaonong Zhu*, Yang Yu, Nan Zhang & Jiefeng Zhao
Institute of Modern Optics, Nankai University, Key Laboratory of Optical Information Science and
Technology, Education Ministry of China, Tianjin 300071, P. R. China
Correspondence: Xiaonong Zhu; Email: xnzhu1@nankai.edu.cn
This PDF file includes:
Supplementary Figures S1-S6,
Supplementary Table S1.
Supplementary Figures
Supplementary Figure S1
a
b
Light propagation direction
Supplementary Figure S1. Photographs of the single (a) and double (b)
super-luminescent jet beams (SJBs) emanating from the micro air plasma (the
bright spots in the middle of the pictures) for the input laser pulses of 50 fs duration,
1.1 mJ pulse energy. Two call-out insets show respective zoom-in views of the micro air
plasma. The vertical ellipses on the right part of (a) and (b) show the edge of the 1-inch
diameter lens tube illuminated by the scattered light.
Supplementary Figure S2
Transverse shift: ~2 mm
Single SJB
Lens tilt: 0°
Conical Emission
A
a
b
Horizontal lens tilt: ~7°
Double SJBs
c
50 mm
A
d
e
Supplementary Figure S2. Nonlinear beam profiles and collimated
super-luminescent jet beams. (a-c) Cross sections of the existing beam of focused 50 fs
excitation pulses for the same 100 mm focal lens but three different focal conditions.
Closed dot lines in (a-c) indicate the distinctive features in the exiting laser beam profiles.
These rather special beam structures may be attributed to the extremely strong nonlinear
interactions between the propagating laser pulses and the laser-induced micro air plasma.
Note that because the 800 nm pump beam is essentially invisible, the colored pictures in
(a-c) do not tell us the real power distribution (See Methods). (d) Cross section A-A
(corresponding to the dashed vertical line in (a)) shows the conical emission at normal
incidence. (e) Collimated double super-luminescent jet beams with yellowish color
propagating toward the left. The SJBs are collimated by a single lens of 75 mm focal
length and intercepted by a piece of black carton paper on the left.
Supplementary Figure S3
a
b
c
Supplementary Figure S3. Polarization dependence of the spectrally integrated
signal strength of sideways emission from one of the double SJBs (a) and the air
plasma at the focus (b). The polarization direction of the excitation laser beam (50 fs, 2
mJ) is varied by rotating a half-wave plate from 22.5° to 112.5° inserted in the input
excitation beam path. Part of the data trace in (b) is expanded in the inserted plot (c) so
that a better view of the fluctuation detail can be shown. (Note that the reading of 22.5° in
this figure corresponds to the vertical polarization of the incident laser beam). From Fig.
S3a we can see that the integrated scattering signal from the jet beam (in the horizontal
plane) varies periodically with the rotation of the half-wave plate, and the
maximum/minimum signal strength appears when the pump beam is vertically/horizontally
polarized. In particular, the signal strength for SJB sideways emission has a modulation
depth as high as 80%, in sharp contrast to the recorded plasma emission (see Fig. S3b)
whose modulation is no more than 10%. Such a phenomenon may be well explained by a
simple dipole emission model, where air molecules driven by the relatively narrow-band
coherent optical field of SJBs act like dipole oscillators. In contrast, the much less
modulated and fluctuating signal from the plasma at focused area is a good indication that
the orientation of the molecule dipole emitters is largely randomized inside the hot plasma.
Supplementary Figure S4
a
b
A
B
C
FE D
G
H I J
K
Supplementary Figure S4. The spectral traces (a) measured at the corresponding
locations across the nonlinearly diffracted laser beams (b) after generating a micro
plasma ball in air under four different focal conditions. In addition to the distinctive
Stokes and anti-Stokes waves of four-wave mixing, these spatially resolved spectral data
also reveal dominant spectral components within the shorter wavelength range. Such a
phenomenon is most likely caused by strong self-steepening effect. The largely
blue-shifted spectral extension implies that the influence of the limited response time of
Kerr effect is inferior to that associated with the plasma generation related phase
modulation on the propagating pulses.
Supplementary Figure S5
a
b
Supplementary Figure S5. Angle-wavelength (θ-λ) plots. Contour plots (in logarithmic
scale) of the diffraction angle-dependent spectra measured along the central line of the
cross section of the transmitted laser beams that encompass single (a) and double (b)
super-luminescent jet beams are displayed. Four-wave mixing is evidenced by the
presence of distinctive Stokes and anti-Stokes waves at specific cone angles. In obtaining
these angle-resolved spectra with the setup similar to that shown in Fig. 2a of the Article,
the sampling head of the fiber-pigtailed spectrometer (Model SD2000, Ocean Optics)
placed approximately 1.2 m away from the focal lens is moved step by step along a rail in
the direction perpendicular to the beam propagation direction. Only single-shot spectrum
is recorded for each spectral trace. The corresponding input pulse energy is ~2.3 mJ.
Supplementary Figure S6
Nonlinear/anomalous diffraction
50 fs pulses
19.8°
f = 100 mm
Linear/ordinary diffraction
∆E = 2 mJ
F = 1 kHz
6 ns pulses
8.0°
Supplementary Figure S6. The side view conical emission (top) in comparison with
linearly diffracted beam (bottom) associated with 6 ns laser pulses. (The latter is
obtained by blocking the seed pulses from entering the femtosecond laser amplifier.
Under the same focal conditions, the 6 ns laser pulses cannot ionize the air due to much
lower peak intensity). From these two pictures, we can see that for 50 fs laser pulses (with
single pulse energy of 2 mJ) much stronger diffraction exists with noticeably larger
diffraction angle as a result of laser-plasma interaction. Note that since the recorded
nonlinearly diffracted beam consists of double SJBs in the horizontal plane, if the carton
paper is flipped by 90 degree to the vertical plane the two bright beams at the edge of the
beam cone will not be present.
Supplementary Figure S7
Supplementary Figure S7. Experimentally determined power dependence of the
nonlinear diffraction angle of conical emission together with the corresponding
simulation data. The starting point (near zero Watt) is taken for the 6 ns pulses (see the
text as well as the information in Fig. S6) and all the rest are for 50 fs laser pulses. The
data in this figure show how the diffraction angle increases with the average power of the
pulses and such an increase appears to be much less obvious for power above 0.8 W (or
pulse energy of 0.8 mJ). We believe that this may be taken as good evidence of saturation
in air ionization for relatively tight focusing.
Supplementary Tables
Supplementary Table 1. Comparisons of major characteristics of SJBs and OFs
Super-luminescent Jet Beams (SJBs)
Appearance
Optical Filaments (OFs)
Jet-like beam (without collimation)
Very thin channel, diverging
Relatively large far-filed diffraction angle
at the end with a divergence
(~0.3 radian; see Figure S5)
angle in the milliradian range
Location
Surface of distorted conical emission
Along the propagation axis of
the pump beam
Spectrum
Primary
Mechanism(s)
Visible and near IR color bands
Four-wave mixing
White light supercontinuum
Kerr effect & plasma-induced
refractive index change
Focal condition
Relatively tight focusing
Weak focusing
Nonlinear phase
Large n (relative refractive index
change), small interaction length (plasma
ball)
Small n, large interaction
length (weak plasma channel)
Electron density
of plasma
Close to or complete saturation
Three orders
below saturation
Far field pattern
Severely distorted large diffraction beam
with a great many of colored speckles
Well-shaped conical emission
with regular colored rings or
bands
magnitude
A detailed comparison of major characteristics of SJBs and OFs is presented in this table.
It is noted that branched filaments produced with a pair of orthogonal cylindrical lenses are
recently reported32, where the branched filaments are regarded as a type of controlled
multiple filamentation due to the interaction between two distinctly asymmetrical diffraction
foci pattern, and no spectral data are presented on four-wave mixing.
Supplementary references
32. Fu, Y. et al. Control of filament branching in air by astigmatically focused femtosecond laser
pulses. Appl. Phys. B 103, 435–439 (2011).