Dynamics of the Laguerre Gaussian TEM
0,l
* mode in a solid-state laser
Y. F. Chen*
Department of Electrophysics, National Chiao Tung University, 1001 TA Hsueh Road, Hsinchu, Taiwan 30050, Republic of China
Y. P. Lan
Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30050, Republic of China
Received 21 November 2000; published 10 May 2001
The dynamics of a solid-state laser sustaining the oscillation of the Laguerre–Gaussian TEM
0,l
* mode is
theoretically and experimentally studied. The results of investigations of the existence conditions of self-
modulation, chaotic, frequency locking, and self-pulsing regimes are given. The experimental results, obtained
using a diode-pumped solid-state laser, are well confirmed by the theoretical model. From the observations of
the locking phenomena of the first-order family, we also confirm the theoretical predictions that the locking
occurs as a subcritical bifurcation in a solid-state laser.
DOI: 10.1103/PhysRevA.63.063807 PACS numbers: 42.60.Mi, 42.65.Sf
I. INTRODUCTION
The recent rapid progress of diode-pumped microchip la-
sers has driven a renaissance of solid-state laser physics re-
search and led to phenomena 1. Fiber delivery of the pump
power enables us to keep the laser resonator apart from the
pump source, so that the laser resonator can be isolated from
disturbances of the pump sources. In previous works, the
high-order Hermite-Gaussian modes have been systemati-
cally generated by a fiber-coupled diode end-pumped
Nd:yttrium-aluminum-garnet YAG laser 2,3. The high-
order Laguerre–Gaussian LG TEM
p , l
mode exhibits inter-
esting physics and has the potential for technological appli-
cations, where p and l are the radial and azimuthal indices of
the LG mode 4. Recently, we developed a technique for the
generation of the cylindrical symmetry LG modes with
p =0 and specified values of l in a fiber-coupled diode end-
pumped solid-state laser. The key novelty is to produce a
doughnut-shaped pump profile by defocusing a standard
fiber-coupled diode. The experimental results demonstrate
that the stable transverse-mode pattern near the pump thresh-
old is usually a LG TEM
0,l
mode with the distribution
cos
2
l or sin
2
l) in azimuthal angle, having 2 l nodes in
azimuth. Even though the geometry is cylindrical symmetry,
there is still certain astigmatism in the cavity due to the
thermal lensing effect and anisotropic properties of the gain
medium. This is the reason why sine or cosine LG modes,
instead of doughnut modes, were generated near the pump
threshold. A similar high-order LG TEM
0,l
mode has been
reported in electrically pumped 5 and optically pumped 6
vertical-cavity surface-emitting semiconductor lasers
VCSEL’s. However, the main difficulty of the emission of
high-order LG modes in VCSEL’s is that the processed wa-
fer is in need of extraordinary homogeneity.
Slightly above the pump threshold in our laser setup, a
LG TEM
0,l
* or TEM
0,-l
* mode, having a circle of constant
intensity in the radial direction, can be generated by the su-
perposition of two like TEM
0,l
modes, one rotated /2 about
the optical axis relative to the other. In recent years, the
TEM
0,l
* modes have attracted a great deal of interest in the
mechanical and optical effects because they possess well-
defined angular momentum along the optical axis when l is
not zero 7. These modes are also important in laser cooling
and trapping experiment 8. Therefore, it is of great interest
to study the generation of the LG TEM
0,l
* modes.
Astigmatism-induced splitting of the two like mode fre-
quencies has a significant influence on laser dynamics. Tem-
poral instabilities and chaotic emission caused by the nonlin-
ear interaction of transverse modes in a class-A laser have
been reported by Tamm 9 who experimentally confirmed
the existence of ‘‘cooperative frequency locking’’ state 10
for the nearly degenerate TEM
0,1
and TEM
1,0
modes of a
helium-neon laser. However, the dynamic characteristics of a
solid-state laser are those of an oscillator with an inertial
noninstantaneous nonlinearity. In the case of such oscilla-
tors the perturbations exhibit oscillatory relaxation. Because
of relaxation oscillations, the two-mode locking in class-B
laser occurs as a subcritical bifurcation 11–13, differently
from class-A laser where the locking is a supercritical bifur-
cation. Not much has been done so far to observe this differ-
ence.
In this paper, we perform theoretical and experimental
investigations of the relaxation oscillations in a LG TEM
0,l
*
mode solid-state laser for the standing-wave states and the
traveling-wave states. Theoretical analysis shows that the re-
laxation oscillations play an important role not only in lock-
ing processes, but also under conditions of stationary states.
On the other hand, a rich set of dynamical behaviors, such as
periodic and quasiperiodic self-modulation, chaotic pulsing,
and frequency locking, was experimentally observed in the
generated TEM
0,l
* hybrid mode. It was found that the experi-
mental data exhibit a general satisfactory agreement with
theoretical predictions.
*Author to whom correspondence should be addressed. FAX:
886-35 729134. E-mail address: yfchen@cc.nctu.edu.tw
PHYSICAL REVIEW A, VOLUME 63, 063807
1050-2947/2001/636/0638079/$20.00 ©2001 The American Physical Society 63 063807-1