Direct measurements of the nonlinear index of refraction of water at 815
and 407 nm using single-shot supercontinuum spectral interferometry
Z. W. Wilkes,
1
S. Varma,
1
Y.-H. Chen,
1
H. M. Milchberg,
1
T. G. Jones,
2,a
and A. Ting
2
1
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park,
Maryland 20742, USA
2
Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375, USA
Received 17 October 2008; accepted 24 April 2009; published online 27 May 2009
Single-shot supercontinuum spectral interferometry was used to measure the nonlinear index of
refraction due to the optical Kerr effect in water at both 815 and 407 nm, with pump pulse lengths
of 90 and 250 fs, respectively. Knowledge of the nonlinear index at 407 nm allows pulse
tailoring to achieve remote underwater pulse compression and self-focusing. © 2009 American
Institute of Physics. DOI: 10.1063/1.3142384
The nonlinear index of refraction of water is a key physi-
cal parameter for any underwater use of high-powered lasers
for which peak power is greater than the critical power, P
crit
,
for self-focusing. Such lasers include typical Q-switched la-
sers with pulse energies above a few millijoules, and ul-
trashort pulse Ti:sapphire systems with pulse energies above
1 nJ. Applications of water propagation of intense laser
pulses include femtosecond laser surgery,
1
underwater fem-
tosecond laser ablation,
2
and underwater femtosecond laser
shock peening.
3
One potential application of particular inter-
est is remote underwater pulse compression. Underwater
transmission is optimal for blue-green wavelengths, where
low linear absorption, e.g., 0.005 m
-1
at 400 nm,
4
makes
these shorter wavelengths much more suitable for long range
nonlinear self-focusing. By combining nonlinear self-
focusing with temporal compression due to group velocity
dispersion of a prechirped broadband pulse, it is possible to
attain intensities high enough to cause breakdown in water.
Precise and accurate knowledge of the nonlinear index of
refraction of water, n
2
, which is in general a function of the
optical frequency, as well as the optical pulse duration,
5
is
necessary to model underwater pulse compression and to ex-
perimentally produce optical breakdown at predetermined re-
mote locations.
In this letter, we report the demonstration of a time-
resolved, profile-independent, and precise measurement of n
2
of water at 407 nm for a subpicosecond pulse duration. We
first perform the experiment at 815 nm 21 nm full width at
half maximum FWHM bandwidth as a benchmark and
proof of technique. Then a measurement at 407 nm pro-
duced by frequency doubling with a 240 m beta-barium
borate BBO crystal, yielding 4 nm FWHM bandwidth is
made by modification of the setup. Our technique, single-
shot supercontinuum spectral interferometry SSSI,
6,7
pro-
vides high temporal resolution 10 fs Ref. 7 and a wide
observation window 2 ps for measurement of the non-
linear response of an optical medium. Such measurements
can show whether or not the nonlinear response is nearly
instantaneous, that is primarily due to nearly instantaneous
and isotropic electronic response, or has delayed and possi-
bly nonisotropic contributions from molecular vibrations and
rotations.
8,9
Plasma contributions to the response can also be
distinguished in SSSI measurements,
7
an especially impor-
tant feature at the high intensities typical of ultrashort pulse
lasers, and for nonlinear optical interactions in general.
Many previously reported n
2
values were inferred from
measurement techniques dependent on self-focusing
dynamics.
10–13
Such techniques are highly dependent on the
spatial profile of the laser pulse, as well as its reproducibility,
and typically yield large errors, conflicting values for n
2
,
5,11
or both. Additional published techniques for measuring n
2
utilized elliptical polarization rotation,
14
spatial profile
analysis,
15
and spectral analysis of self-phase
modulation.
16,17
Some reported values of n
2
for water dif-
fered from the majority by an order of magnitude,
12
leaving
uncertainty about its true value. We believe these differences
have been resolved by the present measurements. Finally, the
excellent shot-to-shot stability of the kilohertz regenerative
amplifier system used here, in combination with the averag-
ing of hundreds of interferograms, allowed extraction of
small phase shifts 0.01 rad, resulting in a small n
2
mea-
surement error.
8
The pump-probe SSSI setup used was similar to the
setup in Ref. 7, with a flowing water interaction cell replac-
ing the gas cell. A 1 mJ, 1 kilohertz, Ti:sapphire laser with
FWHM pulse length of 90 fs and central wavelength of 815
nm was used to generate all pulses required for the SSSI
technique. The pulse width was reduced from the system’s
original 130 fs using acousto-optical pulse shaping in the
spectral domain.
18
SSSI allows extraction of a space and
time-domain phase shift, x , t from interferograms pro-
duced by the setup, where x and t correspond to the trans-
verse spatial location across the beam and time, respec-
tively. From x , t, the change in refractive index nx , t,
and thus n
2
, caused by cross-phase modulation XPM from
a pump beam can be obtained from,
7
x, t =
c
0
z
nx, z', tdz' =
c
nx, tL , 1
where L is the effective interaction length as discussed be-
low.
In the experiment, the laser output was split into two
beams. One beam was used to generate twin supercontinuum
SC pulses, reference followed by probe, each 2 ps long
with 100 nm bandwidth centered around 690 nm.
7
The
other beam acted as the pump, either 815 or 407 nm, and was
a
Electronic mail: ted.jones@nrl.navy.mil.
APPLIED PHYSICS LETTERS 94, 211102 2009
0003-6951/2009/9421/211102/3/$25.00 © 2009 American Institute of Physics 94, 211102-1
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