DOI 10.1007/s00340-011-4483-6
High-power Q-switched laser with high-order Laguerre–Gaussian
modes: application for extra-cavity harmonic generations
Y.J. Huang· P.Y. Chiang · H.C. Liang · K.W. Su · Y.F. Chen
Received: 14 January 2011 / Revised version: 14 February 2011 / Published online: 15 April 2011 © Springer-Verlag 2011
Abstract We present a compact efficient scheme for gener-ation of high-order Laguerre–Gaussian TEMp,0modes in a
diode-pumped actively Q-switched Nd:YVO4laser. The
res-onator is composed of two plane mirrors with an intracavity concave lens to expand the cavity mode size for generating a high-power Laguerre–Gaussian TEM5,0mode. We further
confirm that the TEM5,0mode is noticeably superior to the
TEM0,0mode in the processes of second and third harmonic
generations.
1 Introduction
In recent years, ultraviolet (UV) light sources have rapidly attracted a lot of interest because they are useful in numer-ous applications such as rapid prototyping, laser printing, laser processing, spectroscopy, optical data storage, med-ical treatment and so on. Compared with other UV lasers, diode-pumped all-solid-state lasers with extra-cavity non-linear frequency conversion intrinsically possess advantages of smaller focused size, higher efficiency, longer life time, higher stability, easier implementation and smaller system size, etc. [1,2]. Currently, the fundamental Gaussian modes are usually used in the processes of second and third har-monic generations (SHG and THG) because of the good spa-tial property [3,4].
In cylindrical coordinates, the transverse modes can be expressed in terms of Laguerre–Gaussian modes with the
la-Y.J. Huang· P.Y. Chiang · H.C. Liang · K.W. Su · Y.F. Chen (
) Department of Electrophysics, National Chiao Tung University, 1001 TA Hsueh Road, Hsinchu 30050, Taiwane-mail:[email protected] Fax: +886-35-725230
bel of TEMp,l, where p and l represent the number of radial nodes and azimuthal nodes, respectively. In the past years, several investigations have been carried out to generate low-and higher-order TEMp,l modes in solid-state lasers [5–11]. Among these studies, TEMp,l modes with p= 0 and l = 0 have been demonstrated [5,12] to be similar to the Bessel-like beam that possesses a central peak with a divergence considerably lower than that of the Gaussian beam with the same waist [13–17]. Bessel-like modes have already been utilized as light sources in lithographic patterning, laser ma-chining, and nonlinear optics [18–22]. However, so far high-order Laguerre–Gaussian TEMp,0modes have not been
em-ployed in processes of SHG and THG.
In this work, we originally design a compact three-element resonator to excite high-order Laguerre–Gaussian TEMp,0 modes in a diode-pumped actively Q-switched
Nd:YVO4laser. We use flat-flat cavity with an intra-cavity
concave lens to expand the cavity mode size for efficiently generating the Laguerre–Gaussian TEM5,0 mode with the
output power up to 8.52 W at a pulse repetition rate of 40 kHz. We experimentally confirm that the conversion ef-ficiencies in the processes of SHG and THG obtained with the TEM5,0mode are noticeably higher than the results
ob-tained with the TEM0,0 mode. The optical-to-optical
con-version efficiencies from 1064 nm to 355 nm are found to be 35.6% and 28.1% for the TEM5,0mode and TEM0,0mode,
respectively.
2 Cavity configuration and analysis
The radial intensity of the Laguerre–Gaussian TEMp,l modes is given by
Fig. 1 Schematic of the cavity setup for a diode-pumped AO Q-switched Nd:YVO4laser
Ip,l(ρ, z)= 2p! π(p+ |l|)! 1 w2(z) 2ρ2 w(z)2 l Llp 2ρ2 w(z)2 × exp − 2ρ2 w(z)2 , (1)
where w(z)= w01+ (z/zR)2, w0is the beam radius at the
waist, and zR = πw20/λ is the Rayleigh range, and Llp(·) are the associated Laguerre polynomials. Flood et al. [5] demonstrated that high-order Laguerre–Gaussian TEMp,0
modes could be generated in an end-pumped solid-state laser when the pump spot size ωpwas considerably smaller than the fundamental TEM0,0-mode spot size ωo of the cavity, i.e., ωo/ωp 1. Although the pump beams can be tightly focused to reach the criterion of ωo/ωp 1, the tight focusing of pump beam inevitably causes strong thermal ef-fects such as thermal lensing, thermal fracture, etc., leading to the obstruction for the power scale-up. Therefore, a prac-tical way is to expand the cavity mode size without tight focusing of the pump beam. Here, we design a compact effi-cient three-element resonator, consisting of a flat front mir-ror, a concave lens and a flat output coupler, to obtain large fundamental mode sizes.
Figure 1 shows the configuration of the three-element cavity for an end-pumped acousto-optic (AO) solid-state laser, where L1is the distance between the front mirror and
the concave lens, L2 is the distance between the concave
lens and the flat output coupler, and f is the focal length of the concave lens. The flat front mirror was antireflec-tion (AR) coated at 808 nm on the entrance face and was coated at 808 nm for high transmission as well as 1064 nm for high reflection (HR) on the second surface. The gain medium was a 0.1 at.% Nd:YVO4 crystal with dimensions
of 3× 3 × 12 mm3and was located to be adjacent the front mirror for convenience of end-pumping scheme. Both facets of the laser crystal were AR coated at 808 nm and 1064 nm. The laser crystal was wrapped with indium foil and mounted in a water-cooled copper heat sink at 20°C. Although us-ing the laser crystal with the HR-AR coatus-ing is preferable for more compact configuration, we use a separate front
mirror and the AR-AR coated laser crystal in the present setup because of the availability of experimental compo-nents. A concave lens with AR coating at 1064 nm on both faces was placed just behind the laser crystal. A 20-mm-long AO Q-switch (NEOS technologies) with AR coating at 1064 nm on both faces was placed in the center of the cav-ity and was driven at a central frequency of 41 MHz with RF power of 25 W. The pump source was a 30-W 808-nm fiber-coupled laser diode with a core diameter of 600 µm and a numerical aperture of 0.16. The pump beam was reim-aged into the laser crystal with a lens set that has the focal length of 25 mm with a magnification of unity and the cou-pling efficiency of 90%. As mentioned earlier, the use of the relatively large pump radius is beneficial for power scal-ing with the avoidance of serious thermal problems. The flat output coupler with 50% transmission was employed dur-ing the experiment. For constructdur-ing a compact Q-switched laser, we set the optical cavity length to be L1= 20 mm and
L2= 120 mm.
The effective focal length of the thermal lens in a Nd:YVO4crystal could be expressed as [23]:
1 fth = ξ π Kc l 0 αe−αz 1− e−αl 1 ω2 p(z) × 1 2 dn dT + (n − 1)αTωp(z)/ l dz, (2)
where ξ is the fraction of pump power that results in heat, Kc is the thermal conductivity of the laser material, α is the ab-sorption coefficient, n is the refractive index, l is the length of the gain medium, dn/dT is the thermal-optic coefficient, αT is the thermal expansion coefficient, and ωp(z) is the variation of the pump radius. With the following parameters: Kc= 5.23 W/m K, α = 0.2 mm−1, n= 2.1652, l = 12 mm, dn/dT = 3 × 10−6 K−1, αT = 4.43 × 10−6 K−1, the ef-fective focal length of thermal lens was estimated to be ap-proximately fth= 220 mm at a pump power of 25 W. We
then use the ABCD-matrix method to calculate the cavity mode size at the front mirror as a function of the effective
thermal focal length for a given focal length of the concave lens. Figure2depicts the calculated results for the four cases of f = −200 mm, −300 mm, −400 mm, and −∞. Note that the case of f = −∞ means the cavity without the con-cave lens. As seen in Fig.2, the cavity mode size without a concave lens is approximately equal to the pump spot size. Although a concave lens can effectively enlarge the cavity mode size in some regime, the cavity needs an appropriate thermal focal length to step into the stable region. With the ABCD-matrix theory, we can find that the stable region is given by (L1− f ) 1− f 2 f2+ L1L 2− (L1+ L2)f ≤ fth≤ (L1− f ). (3)
The thermal focal length in the present setup approximately changes from 320 mm to 220 mm for the pump power
in-Fig. 2 Calculated results for the ratio of cavity mode size at the front mirror to pump size as a function of the effective thermal focal length for the cases of f= −200 mm, −300 mm, −400 mm, and −∞
creasing from 10 W to 25 W. As a result, we chose a concave lens with f = −300 mm to meet the range of the thermal fo-cal length.
3 High-order Laguerre–Gaussian TEMp,0modes First of all, the laser experiment for the standard flat-flat cav-ity without a concave lens was performed to measure the transverse pattern as a baseline for comparison. To record the transverse profiles of the different structure, the laser output was directly projected on a screen at a distance of approximately 1220 mm behind the output coupler and the scattered light was captured by a digital camera. As seen in Fig.3(a), the transverse mode in the resonator without a con-cave lens is a pure fundamental TEM0,0mode. Figure3(b)
depicts the experimental transverse pattern observed in the laser cavity with a concave lens of f = −300 mm at a pump power of 25 W. It can be seen that the spatial dis-tribution displays the lasing mode to be dominated by a Laguerre–Gaussian TEM5,0 mode with negligible
funda-mental Gaussian mode. When the pump radius was changed from 300 µm to 100 µm, we found that the dominated trans-verse mode varied from TEM5,0 mode to TEM8,0mode, as
shown in Fig.3(c). In short, we have experimentally con-firmed the proportionality between the transverse order and the ratio ωo/ωp, but the detailed theoretical analysis of the dependence of the transverse order on the ratio ωo/ωp is beyond the scope of this work.
As found by Flood et al. [5], we confirmed that the ex-perimental Laguerre–Gaussian TEM5,0 mode has a central
peak with a divergence considerably lower than that of a TEM0,0 mode with the same waist. This observation
indi-cates that the experimental TEM5,0mode might be
benefi-cial for the achievement of the higher frequency conversion efficiency in processes of SHG and THG. Before investigat-ing the conversion efficiency in nonlinear optics, we make
Fig. 3 Experimental transverse mode patterns of (a) TEM00 mode
without a concave lens at a pump power of 25 W; (b) TEM5,0mode
with a concave lens (f = −300 mm) and a pump radius of 300 µm at a pump power of 25 W; (c) TEM8,0 mode with a concave lens
(f = −300 mm) and a pump radius of 100 µm at a pump power of 25 W. The patterns were measured at a distance of approximately 1220 mm behind the output coupler
a comparison of the laser performances of the cavities with and without the concave lens. Figure 4 shows the average output power as a function of the incident pump power for both configurations operating at a pulse repetition rate of 40 kHz. The cavity with the concave lens has a considerably lager pump threshold because the thermal focal power of the crystal should be greater than (L1− f )−1to result in the
cavity to be stable. At a pump power of 25 W, the maximum average output powers at a repetition rate of 40 kHz were 8.52 W and 8.76 W for the cavities with and without con-cave lens. In other words, the difference of the maximum av-erage output power between both cavity configurations was rather small. Figure5depicts the dependence of the average output powers, pulse energies and peak powers on the pulse repetition rate at a pump power of 25 W for both cavity con-figurations. On the whole, the average output power of the cavity with a concave lens was smaller than that of the cavity without a concave lens by approximately 5–10%, as shown in Fig.5(a). The pulse temporal behavior was recorded by a LeCroy digital oscilloscope (Wavepro 7100, 10 G samples/s,
Fig. 4 Average output power at a repetition rate of 40 kHz as a func-tion of the incident pump power for the cavities with and without the concave lens
1 GHz bandwidth) with a fast Si photodiode. The pulse du-rations for both configudu-rations were experimentally found nearly the same. With increasing the pulse repetition rate from 20 kHz to 80 kHz, the pulse duration was found to vary from 7 to 16 ns. As a result, the pulse energy and the peak power obtained with a concave lens were generally smaller than the results obtained without a concave lens, as shown in Fig.5(b) and5(c). In the following section, we make a comparison of the high-order TEM5,0mode and the
funda-mental TEM0,0mode in the processes of extra-cavity SHG
and THG.
4 Conversion efficiencies of extra-cavity SHG and THG Here lithium triborate (LBO) crystals are exploited as non-linear frequency converters for SHG and THG since they have the advantages of high damage threshold, relatively large acceptance angle, and small walk-off angle. One LBO crystal with dimensions of 3× 3 × 15 mm3 was cut at
θ= 90◦, ϕ= 10.4◦for type-I phase-matched SHG at tem-perature of 46.6°C. Both facets of the SHG crystal were AR coated at 1064 nm and 532 nm. Another LBO crystal with dimensions of 3× 3 × 10 mm3 was cut at θ = 44◦, ϕ= 90◦ for type-II phase-matched THG at temperature of 48°C. Both facets of the THG crystal were AR coated at 1064 nm, 532 nm, and 355 nm. The temperatures of the SHG and THG nonlinear crystals were monitored by ther-moelectric controllers with the precision of 0.1°C. Two con-vex lenses were used to focus the laser beams into the SHG and THG nonlinear crystals for achieving efficient nonlinear conversion. The former one with focal length of 38 mm was AR coated at 1064 nm on both sides, the latter one with focal length of 19 mm was AR coated at 1064 nm and 532 nm on both sides. The optimized geometrical distances of L3, L4,
L5, and L6 indicated in Fig.6 were experimentally found
to be approximately 70 mm, 30 mm, 25 mm, and 30 mm, respectively.
Fig. 5 Dependence of the (a) average output power, (b) pulse energy, and (c) peak power on the pulse repetition rate at a pump power of 25 W for the cavities with and without the concave lens
Fig. 6 Schematic of the experimental setup for extra-cavity SHG and THG
Fig. 7 Harmonic generation performances: (a) average output power, (b) pulse energy, (c) peak power at 532 nm; and (d) average output power, (e) pulse energy, (f) peak power at 355 nm versus the pulse
repetition rate at a pump power of 25 W for the high-order TEM5,0
mode and the fundamental TEM0,0mode
At a pump power of 25 W, the maximum output powers, pulse energies, and peak powers at 532 nm and 355 nm ver-sus the pulse repetition rate for the high-order TEM5,0mode
and the fundamental TEM0,0mode are shown in Fig.7,
re-spectively. Note that, as shown in Fig.5, the average power at 1064 nm of the TEM5,0 mode is 5–10% lower than that
of the fundamental TEM0,0 mode. However, it is
intrigu-ing that the conversion efficiencies in the processes of SHG and THG obtained with the TEM5,0 mode are noticeably
higher than the results obtained with the TEM0,0mode, as
illustrated in Fig.7(a) and (d). At a pulse repetition rate of 40 kHz, the maximum output power at 355 nm obtained with the TEM5,0mode was 3.1 W; the optical-to-optical
conver-sion efficiencies were 35.6% (from 1064 nm to 355 nm) and 12.4% (from 808 nm to 355 nm), respectively. On the other hand, the maximum output power at 355 nm obtained with the TEM0,0 mode was 2.45 W; the optical-to-optical
con-version efficiencies were 28.1% (from 1064 nm to 355 nm) and 9.8% (from 808 nm to 355 nm), respectively. Based on
the calculated results for the case of f = −∞ in Fig. 2, the mode radius of the TEM0,0 mode is about 300 µm.
A Rayleigh range of such a TEM0,0 beam is estimated to
be 26.6 cm, so the divergence of the beam would be rather low. However, we experimentally found that the superiority of the TEM5,0mode over the fundamental TEM0,0mode in
the processes of extra-cavity SHG and THG. This experi-mental observation is regard as a result of the considerable narrowness of the central peak of the high-order Laguerre– Gaussian TEMp,0mode than that of the Gaussian beam.
It is worthwhile to mention that although the genera-tion of high-order Laguerre–Gaussian TEMp,0 modes in a
Q-switched laser has been reported with the other method [9], our experimental setup intrinsically owns the advan-tages of compactness, simplicity and is potentially bene-ficial for power scaling. In comparison with [5], expand-ing the cavity mode size instead of tight focusexpand-ing of the pump beam can remarkably relieve the thermal problems under high-power operation. Furthermore, the application
of high-order Laguerre–Gaussian modes in the process of extra-cavity SHG and THG was investigated for the first time and we experimentally found the TEMp,0mode is
no-ticeably superior to the TEM0,0mode in the harmonic
gen-eration process.
5 Conclusion
In summary, we have successfully designed a compact res-onator to generate high-power Laguerre–Gaussian TEM5,0
mode. The resonator is composed of two plane mirrors with an intra-cavity concave lens to expand the cavity mode size. At a pump power of 25 W, the average output power for the Laguerre–Gaussian TEM5,0 mode was found to be up
to 8.52 W at a pulse repetition rate of 40 kHz. Furthermore, we experimentally verify that the TEM5,0mode is
conspicu-ously superior to the TEM0,0mode in the processes of SHG
and THG. At an incident pump power of 25 W at 808 nm and a repetition rate of 40 kHz, the maximum output powers at 355 nm obtained with the TEM5,0mode and TEM0,0mode
were 3.1 W and 2.45 W, respectively. The optical-to-optical conversion efficiencies from 1064 nm to 355 nm were found to be 35.6% and 28.1% for the TEM5,0 mode and TEM0,0
mode, respectively.
Acknowledgements The authors thank the National Science Coun-cil for their financial support of this research under Contract No. NSC-97-2112-M-009-016-MY3.
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