Generation of highly efficient, nanosecond Ince-Gaussian
beams in Cr,Nd:YAG microchip lasers 11112DONG Jun, Ma Jian, REN Yingying, Xu Guozhang, Kaminskii A. Alexander
5 (1. Department of Electronics Engineering, School of Information Science and Technology,
Xiamen University, FuJian XiaMen 361005;
2. Institute of Crystallography, Russian Academy of Sciences, Leninsky Prospekt 59, Moscow
Abstract: Direct generation of higher-order Ince-Gaussian (IG) beams from laser-diode end-pumped
10 Cr,Nd:YAG self-Q-switched microchip laser was achieved with high efficiency and high repetition rate. Average output power over 2 W was obtained with absorbed pump power of 8.2 W, corresponding optical-to-optical efficiency of 25% was achieved. Various IG modes with nanosecond pulse width and peak power of over 2 kW level were obtained in laser-diode pumped Cr,Nd:YAG microchip lasers under different pump power levels by applying titled, large area pump beam. The effect of the
15 inversion population distribution induced by the titled pump beam and nonlinear absorption of Cr4+-ions on the oscillation of higher-order IG modes in Cr,Nd:YAG microchip lasers were addressed. The effect of higher-order IG mode oscillation on the laser performance of Cr,Nd:YAG microchip lasers was also discussed.
Keywords: Laser technology; Ince-Gaussian modes; Cr,Nd:YAG; microchip lasers; solid-state lasers
Besides Laguerre-Gaussian (LG) and Hermite-Gaussian (HG) beams generated in stable laser resonators are used for different transversal laser filed distribution, Ince-Gaussian (IG) beams proposed recently have gained lots of attention for their various transversal distribution and
25 flexibilities. IG beams generated in stable laser resonators are not only a third complete family of the paraxial wave equation in elliptic cylindrical coordinates, but also they constitute the continuous transition modes between HG and LG modes when their ellipticity is chosen
[1, 2]appropriately. Ince-Gaussian beams have been demonstrated for manipulation of
microparticles , formation of various optical vortices for optical trapping and optical tweezers.
30 IG beams have been generated in laser-diode pumped solid-state Nd:YVOlasers by breaking the 4
symmetry of the resonator through shifting the output coupler sideways several tens of
micrometers or introducing additional cross hair. Forced IG mode operations were achieved in
LiNdPO(LNP) and Nd:GdVOminiature laser by tilting the central axis of the resonator with 412 4 respect to the axis of the laser diode pump beam. However, output power from these lasers is
35 low and the lasers are less efficient. Cr,Nd:YAG crystal is one of excellent self-Q-switched laser materials and formed by co-doping Cr ions and Nd ions into YAG crystal by adding extra
2+Ca-ions as charge compensators. Laser-diode pumped self-Q-switched Cr,Nd:YAG monolithic
[7, 8] miniature lasers have been demonstrated with nanosecond and picosecond pulse width.
Complicated transverse patterns have been generated in Cr,Nd:YAG microchip lasers by adjusting
3+ 40 the pump beam diameter inside the Cr,Nd:YAG crystal . The high gain of Ndions together
4+ with the nonlinear absorption of Crions in Cr,Nd:YAG crystal make generation of nanosecond
pulse width, high peak power higher order IG modes possible by applying tilted large pump beam from laser-diode. Compact, highly efficient, nanosecond pulse width and high peak power
Cr,Nd:YAG microchip lasers may have potential applications in manipulation of microparticles
Foundations: Program for New Century Excellent Talents in University (NCET) under Grant (No.
NCET-09-0669); the Ph.D. Programs Foundation of Ministry of Education of China (No. 20100121120019); the Fundamental Research Funds for the Central Universities (No. 2010121058)
Brief author introduction:DONG Jun, (1970-), Male, Professor, PhD, Research interests: solid-state lasers and applications, Optical materials. E-mail: firstname.lastname@example.org
45 and formation of optical soliton and optical vertices.
In this paper, we report, for the first time to our best knowledge, direct generation of the
highly efficient nanosecond pulse-width Ince-Gaussian beams from laser-diode end-pumped
Cr,Nd:YAG self-Q-switched microchip lasers by adjusting the azimuthal symmetry of pump beam
incident on the Cr,Nd:YAG crystal. Optical-to-optical efficiency of 25% has been obtained. 50 Various high-order IG beams were generated under different pump power levels. The obtained
higher-order IG mode from Cr,Nd:YAG microchip lasers was determined from the corresponding
patterns calculated analytically using IG mode expressions by adjusting the ellipticity. The
saturated inversion population distribution induced by the tilted pump beam and nonlinear
4+absorption of Cr-ions in Cr,Nd:YAG crystal play important roles on generation of higher-order 55 IG beams in Cr,Nd:YAG microchip lasers. The effect of higher-order IG mode oscillation on the
average output power of Cr,Nd:YAG microchip lasers was also addressed.
Figure 1 shows the schematic diagram of experiment setup for generation of IG beams from
laser-diode end-pumped Cr,Nd:YAG self-Q-switched microchip laser. A plane-parallel 60 1.8-mm-thick Cr,Nd:YAG crystal doped with 1 at.% Nd and 0.01 at.% Cr was used as gain
medium for generating self-Q-switched laser pulses. One surface of Cr,Nd:YAG crystal was
coated for antireflection at 808 nm and high reflection at 1064 nm to act as the rear mirror of the
laser cavity, the other surface was coated for antireflection at 1064 nm to reduce the intracavity
loss and high reflection at 808 nm to increase the absorption efficiency of pump power. 65 Plane-parallel BK7 output coupler with reflection (R) of 90% at 1064 nm was mechanically oc
attached to Cr,Nd:YAG crystal tightly. The total cavity length is 1.9 mm by considering the
coating thickness on both sides of Cr,Nd:YAG crystal. A high power fiber coupled 808-nm laser
diode with a core diameter of 400 μm and numerical aperture of 2.2 was used as the pump source. Optical coupling system with two lens with focal lengths of f= 8 mm and f= 15 mm were used1 2
70 to collimate and focus pump beam on the rear surface of the Cr,Nd:YAG crystal. Pump beam
diameter of 200 μm was incident on Cr,Nd:YAG self-Q-switched crystal after optical collimate and focus system. Cr,Nd:YAG crystal was tilted several degrees away from the incident pump
beam for generation of IG higher-order modes as shown in Fig. 1. Output laser characteristics
were recorded with an InGaAs photodiode and 400 MHz oscilloscope. Laser emitting spectra was 75 monitored with an Ando optical spectral analyzer and beam profile was monitored and recorded
with a Thorlabs BC106-VIS CCD beam profiler.
Fig. 1 Schematic diagram of laser-diode pumped Cr,Nd:YAG self-Q-switched microchip laser for generation of IG beams
80 2 Results and discussion
Fig. 2 Various IG beam transversal intensity distribution observed in laser-diode pumped Cr,Nd:YAG self-Q-switched lasers under different pump power levels. (a) P= 1.3 W, (b) P= 1.7 W, (c) P= 2.2 W, (d) abs abs abs 85 P= 3.5 W, (e) P= 3.9 W, (f) P= 4.3 W, (g) P= 4.8 W, (h) P= 5.6 W, (h) P= 6.5 W, (h) P= abs abs abs abs abs abs abs 7.3 W, (h) P= 7.8 W, (h) P= 8.2 W. abs abs 3+ Because Nd-ions in YAG is four-level laser system and has large emission cross section, therefore, the laser threshold is easier to reach for higher-order transverse modes. In the 90
laser-diode pumped Cr,Nd:YAG self-Q-switched microchip lasers, plane-parallel Fabry-Perot cavity is used in the experiments, the laser emitting area is still in good matchup with laser pump
beam even with pump beam tilted away from the laser propagation direction of Cr,Nd:YAG microchip lasers. Under large beam diameter pumping, inversion population distribution in Cr,Nd:YAG crystal under tilted laser beam pumping and nonlinearly absorption distribution of 95
Cr4+-ions along laser propagation direction and radial direction in Cr,Nd:YAG crystal induced by the longitudinal Gaussian beam pumping force plane-parallel microchip lasers oscillate in IG
modes. And higher-order IG modes were excited at high pump power level when the pump beam diameter was kept constant in the laser experiments. The IG mode oscillation in laser-diode pumped Cr,Nd:YAG microchip lasers can be chosen by adjusting the tilting angle of incident 100
pump beam on Cr,Nd:YAG crystal. Fig. 2 shows some typical IG mode transverse field
distribution observed experimentally under different pump power levels when the incident pump
beam was 5 degrees away from laser propagation direction of Cr,Nd:YAG microchip lasers.
e IG 2, 2 Stablemode was observed at absorbed pump power of 1.3 W, as shown in Fig. 2(a). The
mode number increases with the absorbed pump power. Various stable higher-order IG modes
oeoee IGIGIG IG IG 6,2 4, 4 5,3 10, 4 10,8 105such as, , , , modes were obtained at different pump power
levels when the absorbed pump power was kept lower than 5.5 W, as shown in Fig. 2(b–g). More
complicated transverse laser field distribution was observed when the absorbed pump power was
igher than 5.5 W owing to two or three sets of IG modes oscillated simultaneously as shown inh
ee IG IG 4, 2 8,8 + Fig. 2(h–l). Fig. 2(h) shows the superposition of two IG modesoscillating
110 simultaneously. The laser beam exhibits symmetric transverse distribution even with higher-order IG mode oscillation or complicated mixed modes oscillation. The mode numbers and ellipticity of the different IG modes generated in Cr,Nd:YAG microchip lasers were determined from correspondence to patterns calculated analytically using the IG mode expressions. The transversal field distribution of IG modes in any plane z can be m m 115expressed in the terms of even ( C ) and odd ( S ) Ince polynomials of order p and degree m,p p
[1, 2] and ellipticity parameterε , 2 2 ? ? ??Aw?r kr e m m0 () ()()( )()(1)IGr,ε = C iξ ,ε C η , ε exp× expkz + ? p + 1ψ z p , m p p z ? 2 ? ?? wz w z 2Rz ()()()? ? ?? Bw2 2 o m m0 ?? ? ?kr ?r
IGr,ε = S i ,ε S ,ε exp× expkz + ? p + 1ψ z (2) ()(ξ)(η)()()p , m p p z ?? ? ? 2
? ? ? ? 120 at z = 0, the superscript e and with normalized constant A, B, beam width w(z), beam waist w0 w(z ) w (z ) 2R(z ) o refer to even and odd modes, respectively. The elliptic coordinates were defined as x =
f(z)cosh(ξ)cos(η), y = f(z)sinh(ξ)sin(η), and z = z, where f(z) = fw(z)/w, fis the semifocal 000 separation at the waist plane z = 0, and ξ, η are the radial and angular elliptic variables, 2 respectively. r is the radial distance from the central axis of the cavity, R(z) = z + z/z is the radius R 2of curvature of the phase front, and ψ(z) = arctan(z/z) is the Gouy shift, z= kw/2 is thezRR 0 125 Rayleigh length, k is the wave number. Fig. 3 Analytical reconstruction of various IG modes observed in laser-diode pumped Cr,Nd:YAG self-Q-switched microchip lasers.
130 The theoretical prediction of IG modes oscillation in laser-diode pumped Cr,Nd:YAG
self-Q-switched lasers was done by applying Eq. (1) and Eq. (2). The mode number [p, m] and the
ellipticity parameter ε of different IG transverse modes observed in laser-diode pumped Cr,Nd:YAG self-Q-switched microchip lasers are determined by corresponding numerical
calculations of laser transversal distribution, as shown in Fig. 3. The theoretical calculated 豆丁网地址，/msn369
transverse patterns (as shown in Fig. 3) are in good agreement with the transverse patterns 135
observed in experiments (as shown in Fig. 2(a-h)) and further confirmed that the laser oscillated at different even and odd IG modes.
The formation of high-order IG modes in laser-diode end-pumped Cr,Nd:YAG microchip laser is attributed to the tilted large pump beam incident on Cr,Nd:YAG crystal and nonlinear 4+ 140 ion saturable absorber. For the Cr,Nd:YAG self-Q-switched laser crystal used absorption of Cr 3+ 20 -34+ in experiments, the concentration of Ndions is about 1.38 × 10cm, the concentration of Cr 16 -33+ 4+ ions is about 4.65 × 10cm, therefore, the ratio of Ndions to Crions is about 3000. It is 3+ 4+ reasonable to assume that Ndions and Crions are homogeneously distributed in Cr,Nd:YAG 4+ crystal, nonlinear absorption of Crions enhances the intracavity laser intensity, which has great
effects on the saturated inversion population distribution inside the Cr,Nd:YAG crystal and forms 145
ation, therefore, the higher-order IG modes were forced gain guiding for higher-order mode oscill
to oscillate in Cr,Nd:YAG microchip lasers.
= 7.3 W P abs
= 5.6 W Pabs
= 3.9 W Pabs
= 2.2 W Pabs
1063 1064 1065 1066 1067
Fig. 4 Laser spectra of Cr,Nd:YAG self-Q-switched lasers under different pump power levels. 150 3+ Although the emission bandwidth of Ndions in Cr,Nd:YAG is very narrow (about 1 nm ), the Cr,Nd:YAG microchip lasers oscillated in multi-longitudinal modes owing to 1.8-mm-thick Cr,Nd:YAG was used in the experiments. The laser emitting spectra of laser-diode pumped Cr,Nd:YAG microchip lasers at different pump power levels are shown in Fig. 4. Laser
oscillated in two longitudinal modes when the absorbed pump power is lower than 2.3 W. Then 155
the laser oscillated in three longitudinal modes with further increase of the pump power until absorbed pump power is lower than 7.2 W. The laser oscillated in four longitudinal modes with further increase of pump power. The separation of longitudinal modes of laser-diode pumped Cr,Nd:YAG microchip laser is estimated to be 0.16 nm, which is in good agreement with the free
spectral range between the resonant modes (0.163 nm) in the laser cavity filled with gain medium 160
 2predicted byΔλ= λ/2L, where Lis the optical length of the resonator and λ is the laser ccc
wavelength. The laser emitting wavelength shifts to longer wavelength with absorbed pump power
[12, 13] owing to the emission spectra change with temperature due to the heat generated in
Cr,Nd:YAG crystal under high pump power levels. 豆丁网地址，/msn369
II III 0.5 5 Average output power (W)
0.0 0 0 1 2 3 4 5 6 7 8 9
Absorbed pump power (W)
165 Fig. 5 Average output power and optical-to-optical efficiency of Cr,Nd:YAG self-Q-switched microchip laser as a function of absorbed pump power.
Multi-longitudinal modes oscillation in Cr,Nd:YAG microchip lasers have some influence on
170 the average output power, however the evolution of higher-order IG modes oscillation with pump
power in Cr,Nd:YAG microchip lasers has great effects on the laser performance. Average output power and optical-to-optical efficiency of laser-diode pumped Cr,Nd:YAG self-Q-switched
microchip laser as a function of absorbed pump power is shown in Fig. 5. The absorbed pump power threshold for lasing is about 0.68 W. The average output power of Cr,Nd:YAG microchip
laser does not increase linearly with absorbed pump power in the whole available pump power 175
region. There are three regions for variation of average output power with absorbed pump power. Average output power increases linearly with absorbed pump power when the absorbed pump
power is higher than the absorbed pump power threshold, however, the average output power tends to saturated when the absorbed pump power is higher than 2 W. This is caused by the
variation of IG modes under different absorbed pump power. The mode number of the IG mode 180 Optical efficiency (%) increases with absorbed pump power, and IG modes compete each other for the inversion population provided by the pump power; therefore, higher-order IG modes oscillation competing
for the inversion population makes the average output power increase slowly with absorbed pump power. When the higher-order IG mode fully oscillating simultaneously, the average output power
increases linearly again at region II in Fig. 5 when the absorbed pump power is higher than 3.1 W 185
and the slope efficiency is about 65% with respect to the absorbed pump power. The average output power increases slowly with absorbed pump power when the absorbed pump power is higher than 4.5W and tends to be saturated until the absorbed pump power of 6.9 W. This is caused by the second IG mode oscillating and competiting for the inversion population provided
by the pump power. Therefore, two or three IG modes competiting each other for the inversion 190
population around the threshold of second or third IG mode oscillation is the cause of slowly increase average output power with absorbed pump power. When the absorbed pump power is higher than 6.9 W, the second or third IG modes fully oscillate and fully extract the energy stored in Cr,Nd:YAG crystal together with the main IG modes, therefore, the average output power
increases linearly with the absorbed pump power (as shown in region III in Fig. 5) and slope 195
efficiency is over 55%. Maximum average output power of over 2 W was obtained when the
respect to the absorbed pump power. The corresponding optical-to-optical efficiency as a function of the absorbed pump power is also given in Fig. 5. The nonlinearly variation of the average
output power with absorbed pump power of Cr,Nd:YAG self-Q-switched microchip lasers is 200
attributed to the higher-order IG modes oscillation.
5.6 ns 1.0 Peak power (kW) 0.5
0.0 -10 -5 0 5 10 15 20 Time (ns)
Fig. 6 Nanosecond pulse-width, peak power of over 2.2 kW laser pulse of Cr,Nd:YAG self-Q-switched lasers obtained, the repetition rate is 73.3 kHz. 205
Fig. 6 shows a typical oscilloscope pulse profile of Cr,Nd:YAG self-Q-switched microchip laser when the absorbed pump power is 4.3 W. Laser pulse with pulse energy of 12.4 μJ and pulse width (FWHM) of 5.6 ns was obtained under absorbed pump power of 4.3 W. The corresponding peak power of Cr,Nd:YAG self-Q-switched microchip laser is over 2.2 kW. The
laser works at 73.3 kHz. The repetition rate of laser-diode pumped Cr,Nd:YAG microchip lasers 210
increases nearly linearly with absorbed pump power, as shown in Fig. 7. The repetition rate
increases from several kHz just above the absorbed pump power threshold up to 190 kHz when
the absorbed pump power of 8.2 W was applied.
50 Repetition rate (kHz)
00 1 2 3 4 5 6 7 8 9
Absorbed pump power (W)
Fig. 7 Repetition rate of Cr,Nd:YAG self-Q-switched lasers as a function of absorbed pump power. 215
Highly efficient, nanosecond pulse width Ince-Gaussian mode oscillation was achieved in
laser-diode pumped Cr,Nd:YAG self-Q-switched microchip laser by tilting the pump beam
220 incident on Cr,Nd:YAG crystal for the first time to our best knowledge. Various IG beams with
nanosecond pulse width and over kW peak power were obtained by adjusting the pump power levels. Single IG beam was obtained when the absorbed pump power is lower than 5.5 W and
complicated IG beams combining two or three IG modes have been observed when the absorbed pump power is higher than 5.5 W. Average output power over 2 W was obtained with absorbed
pump power of 8.2 W, corresponding optical-to-optical efficiency of 25% was achieved. The laser 225
oscillated at high repetition rate depending on the pump power level, 190 kHz repetition rate has been achieved in laser-diode pumped Cr,Nd:YAG microchip laser.
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1111Ince-Gaussian 光束 董俊，马剑，任滢滢，许国章， 2 Kaminskii A. Alexander ？1. 厦门大学信息科学与技术学院电子工程系，福建 厦门 361005(
2. Institute of Crystallography, Russian Academy of Sciences, Leninsky Prospekt 59, Moscow
260 119333, Russia？ 摘要，本文报道了激光二极管端面泵浦的 Cr,Nd:YAG 微片激光器直接产生了高效、高重复 频率和纳秒脉宽的高阶 Ince-Guassian？IG？光束。在吸收泵浦光功率为 8.2 W 时获得了平均 输出功率为 2 W 的激光输出，相应的光！光转化效率为 25%。通过调整入射到 Cr,Nd:YAG
晶体上大泵浦光斑面积光束的入射倾斜角度，在激光二极管泵浦的 Cr,Nd:YAG 微片激光器
265 中获得了脉冲宽度为几个纳秒、峰值功率高达 2 kW 的各种 IG 模式。倾斜的泵浦入射光及 Cr4+离子的非线性可饱和吸收特性所导致反转粒子数的分布是造成 Cr,Nd:YAG 微片激光器 高阶 IG 模式振荡的主要原因。同时分析了不同泵浦功率下高阶 IG 模式振荡对激光平均输 出功率特性的影响。
关键词，激光技术(Ince-Gaussian 模式(Cr,Nd:YAG 自调 Q 激光晶体(微片激光器; 固体 270 激光器