Picosecond optical vortex converted from multigigahertz self-mode-locked high-order Hermite-Gaussian Nd:GdVO(4) lasers.
ABSTRACT We report on a gigahertz self-mode-locked high-order Hermite-Gaussian (HG) Nd:GdVO(4) laser. With a pump power of 2.2 W, the average output power for the TEM(0,m) modes from m=9 to m=0 are among 350-780 mW at a repetition rate of 3.5 GHz. The mode-locked pulse width is in the range of 20-25 ps for various HG TEM(0,m) modes. With a simple cylindrical-lens converter, the mode-locked HG beams are converted to generate picosecond optical vortex pulses.
Picosecond optical vortex converted from
multigigahertz self-mode-locked high-order
H. C. Liang,1Y. J. Huang,1Y. C. Lin,1T. H. Lu,2Y. F. Chen,1,* and K. F. Huang1
1Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan
2Department of Physics, National Taiwan Normal University, Taipei, Taiwan
* Corresponding author: email@example.com
Received August 19, 2009; revised November 4, 2009; accepted November 11, 2009;
posted November 17, 2009 (Doc. ID 115983); published December 9, 2009
We report on a gigahertz self-mode-locked high-order Hermite–Gaussian (HG) Nd:GdVO4laser. With a
pump power of 2.2 W, the average output power for the TEM0,mmodes from m=9 to m=0 are among
350–780 mW at a repetition rate of 3.5 GHz. The mode-locked pulse width is in the range of 20–25 ps for
various HG TEM0,mmodes. With a simple cylindrical-lens converter, the mode-locked HG beams are con-
verted to generate picosecond optical vortex pulses. © 2009 Optical Society of America
OCIS codes: 140.4050, 140.3480, 080.4865.
Optical vortex beams [1,2] that possess orbital angu-
lar momentum because of a phase singularity have
been extensively used in the study of optical tweezers
[3–7], trapping and guiding of cold atoms [8–10], ro-
tational frequency shift [11,12], and entanglement
states of photons . Several devices, including spi-
ral phase plates , computer-generated holo-
graphic converters , and astigmatic mode con-
demonstrated to transform high-order Hermite–
Gaussian (HG) modes into optical vortex beams.
Optical vortex pulses have recently been attracting
great interest because they can open up various
fields, including high-quality material processing
, controllable specificity of chiral matter , and
nonlinear frequency conversion . Furthermore,
optical vortex pulses in picosecond or femtosecond la-
ser fields can be potentially utilized to investigate
high-field laser physics [20–23]. However, AMC can-
not be used directly, since conventional mode-locked
lasers are usually designed to emit the fundamental
TEM00mode. Therefore, it is highly desirable to de-
velop high-order HG mode-locked lasers for generat-
ing ultrafast vortex pulses.
Recently, the large third-order nonlinearities of
Nd-doped vanadate crystals have been successfully
exploited to achieve the self-starting self-mode-
locking operation without the need of any additional
components . In this Letter we report for the first
time (to our knowledge) on a multigigahertz self-
mode-locked high-order HG Nd-doped GdVO4laser
with an off-axis pumping scheme. With a pump
power of 2.2 W, the average output powers for
3.5 GHz mode-locked HG modes vary in the range of
350–780 mW for the TEM0,mmodes from m=9 to m
=0. The mode-locked pulse width is found to be ap-
proximately 20–25 ps for various HG TEM0,mmodes,
with m=0–9. We also use simple AMC to convert the
mode-locked HG TEM0,m beams into Laguerre–
Gaussian (LG) modes for generating picosecond opti-
cal vortex pulses.
Figure 1 depicts the experimental setup for the
self-mode-locked high-order HG TEM0,mlaser with
an off-axis pumping scheme [25,26]. The cavity con-
figuration is a simple concave-plano resonator. The
active medium is an a-cut 0.25 at. % Nd:GdVO4crys-
tal with a length of 10 mm. Both end surfaces of the
Nd:GdVO4 crystal were antireflection coated at
1064 nm and wedged 2° to suppress the Fabry–Perot
etalon effect. The laser crystal was wrapped with in-
dium foil and mounted in a water-cooled copper
holder. The water temperature was maintained
around 20°C to ensure stable laser output. The laser
crystal was placed very near ?2–3 mm? the input
mirror, which was a 50 cm radius-of-curvature con-
cave mirror with antireflection coating at 808 nm on
the entrance face and with high-reflectance coating
at 1064 nm ??99.8%? and high transmittance coat-
ing at 808 nm on the second surface. A flat wedged
output coupler with 15% transmission at 1064 nm
was used throughout the experiment. The pump
source was a 2.5 W, 808 nm fiber-coupled laser diode
with a core diameter of 100 ?m and an NA of 0.16. A
focusing lens with 5 mm focal length and 85% cou-
pling efficiency was used to reimage the pump beam
into the laser crystal. The average pump size was ap-
proximately 70 ?m. The optical cavity length was set
high-order HG TEM0,mlaser with an off-axis pumping
(Color online) Schematic of a self-mode-locked
OPTICS LETTERS / Vol. 34, No. 24 / December 15, 2009
0146-9592/09/243842-3/$15.00© 2009 Optical Society of America
to be approximately 4.3 cm with the corresponding
free spectral range (FSR) of 3.5 GHz.
First of all, the pumping beam was focused right on
the optical axis of the laser cavity to obtain the maxi-
mum output power for the TEM0,0mode. After finely
adjusting the cavity alignment, the laser output can
be found to display a stable self-mode-locking opera-
tion. Subsequently the high-order HG TEM0,mmode-
locked lasers can be generated with off-axis pumping
[25,26]. The larger the off-axis displacement ?x is,
the higher the HG TEM0,morder is. With varying ?x
from 0 to 0.5 mm, the average output power was
found to decrease gradually from 780 to 350 mW at a
pump power of 2.2 W, as shown in Fig. 2. Ten HG
TEM0,mmodes were generated during the variation
of off-axis displacement. The inset of Fig. 2 shows the
experimental patterns that were measured using a
CCD camera. All observed HG TEM0,mmodes are
found to be in the pure longitudinal mode-locking re-
gime. Note that once the pump power reaches the las-
ing threshold, the laser system instantaneously steps
into a stable mode-locked operation without any me-
chanical perturbation. The locking mechanism is pre-
sumed to be the Kerr effect. However, the laser sys-
tem has high stability over day-long operation and is
insensitive to mechanical vibrations and air current.
As a result, some auxiliary mechanism seems to exist
in the locking process. Bai et al.  proposed a novel
self-mode-locking mechanism in narrowband lasers
based on the analysis of the gain-line splitting in-
duced by an intracavity laser field. Although the
present experimental results are fairly consistent
with this mechanism, further identification is still
The mode-locked pulses were detected by a high-
speed InGaAs photodetector (Electro-optics Technol-
ogy, Inc. ET-3500 with rise time 35 ps), whose output
signal was connected to a digital oscilloscope (Agilent
DSO 80000) with 10 GHz electrical bandwidth and a
sampling interval of 25 ps. Figures 3(a) and 3(b)
show the pulse trains for the TEM0,5mode on two dif-
ferent time scales, one with time span of 5 ns, dem-
onstrating mode-locked pulses, and the other with
time span of 5 ?s, demonstrating the amplitude sta-
bility. It can be seen that the pulse trains display full
modulation, and the complete mode locking is
achieved. The corresponding power spectrum is mea-
sured by an rf spectrum analyzer (Advantest,
R3265A) with bandwidth of 8.0 GHz. Experiment re-
sults reveal that the relative frequency deviation of
power spectrum, ??/v, is smaller than 10−4over day-
long operation, where v is the center frequency of the
power spectrum and ?? is the frequency deviation of
FWHM. The laser was cw mode locked at 3.5 GHz
with only weak noise at the relaxation oscillation fre-
quency around 2 MHz, and the difference between
the peak of mode-locked frequency and that of relax-
ation oscillation frequency was experimentally found
to be larger than 55 dBm. The overall characteristics
are almost the same as the results observed for the
self-mode-locked fundamental TEM0,0mode . The
pulse width at the cw mode-locked operation was
measured with an autocorrelator (APE pulse check,
Angewandte physik & Elektronik GmbH). Assuming
the sech2-shaped temporal profile, the FWHM was
measured to be in the range of 20–25 ps for HG
TEM0,m modes with m=0–9. The result for the
TEM0,5mode is shown in Fig. 3(c). The spectral infor-
mation of the laser was monitored by a Fourier opti-
cal spectrum analyzer (Advantest, Q8347) that is
constructed with a Michelson interferometer with
resolution of 0.003 nm. Figure 3(d) shows the optical
spectrum for the TEM0,5mode. It can be seen that
the longitudinal mode with 3.5 GHz is clearly re-
solved and the FWHM of the spectrum is approxi-
mately 0.1 nm. Consequently, the time–bandwidth
product of the mode-locked pulse is approximately
0.4, indicating the pulses to be frequency chirped. On
the whole, there are no significant difference for the
mode-locked performances of the HG TEM0,mmodes
The mode-locked HG TEM0,mbeam was converted
into the mode-locked LG TEM0,m beam with a
power on the variation off-axis displacement. Inset, trans-
verse patterns observed in the mode-locked operation.
(Color online) Dependence of the average output
scales: (a) time span of 5 ?s, demonstrating mode-locked
pulses; (b) time span of 5 ns, demonstrating the amplitude
oscillation. (c) Autocorrelation trace of the output pulses.
(d) Corresponding optical spectrum. All results are for HG
(Color online) Pulse trains on two different time
December 15, 2009 / Vol. 34, No. 24 / OPTICS LETTERS
cylindrical-lens mode converter outside the laser
resonator, as shown in Fig. 4(a). The focal length of
the cylindrical lenses was f=25 mm, and the distance
was precisely adjusted to be?2f for the operation of
the ?/2 converter. Figure 4(b) depicts the results of
the transformation of HG modes, shown in Fig. 2, to
the corresponding LG modes. It can be seen that the
mode-locked LG TEM0,mmodes are successfully gen-
erated for azimuthal index from 0 to 9.
3.5 GHz self-mode-locked Nd:GdVO4laser for HG
TEM0,mmodes with m=0–9. The average output
powers for the TEM0,mmodes from m=9 to m=0
were among 350–780 mW at a pump power of 2.2 W.
The mode-locked pulse width was found to be in the
range of 20–25 ps for various HG TEM0,mmodes.
With a simple cylindrical-lens converter, the picosec-
ond optical vortex pulses have been generated by con-
verting the mode-locked HG beams into LG modes.
We believe that the generated picosecond optical vor-
tices can be potentially beneficial to a number of ap-
The authors thank the National Science Council
(NSC)for their financial support of this research un-
der contract NSC-97-2112-M-009-016-MY3.
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the HG modes shown in Fig. 2.
(Color online) (a) Schematic of a cylindrical-lens
OPTICS LETTERS / Vol. 34, No. 24 / December 15, 2009