Power Scaling in a Diode-End-Pumped
Multisegmented Nd:YVO
4
Laser With
Double-Pass Power Amplification
Yu-Jen Huang, Wei-Zhe Zhuang, Kuan-Wei Su, and Yung-Fu Chen
Abstract—We demonstrate a high-power master oscillator
power amplifier with the double-pass configuration based on the specially designed multisegmented Nd:YVO4crystals. A powerful
mathematical technique on the basis of the Fourier eigenfunction expansion method is developed for precisely calculating the tem-perature distribution inside the gain medium. A seed Nd:YVO4
oscillator under dual-end pumping is subsequently constructed for efficiently emitting the output power of up to 50 W. Moreover, under a total incident pump power of 244 W at 808 nm, as high as 108 W of the output power at 1064 nm is further generated in our developed master oscillator power amplifier system. Theoret-ical and experimental results clearly reveal that the gain medium with multiple doping concentrations is practically valuable for con-structing a high-power end-pumped laser without bringing in sig-nificantly thermal effects.
Index Terms—Diode-pumped laser, high-power laser, master
oscillator power amplifier, multisegmented laser crystal.
I. INTRODUCTION
O
VER the past few decades, high-power solid-state lasers were rapidly developed because they are useful for many scientific studies and industrial applications [1]–[3]. For the ex-tension of the power scale-up in the end-pumped oscillator, the noticeable thermal gradient and accompanied mechanical stress inside the gain medium are the most critical issues to be solved. This is due to the fact that the homogeneous doping profile in the active element leads to the exponential decay of the pump light along the longitudinal direction. With an undoped mate-rial to effectively serve as a heat sink, the composite crystal has recently proven its feasibility in reducing the spatial gra-dient of the temperature and the thermally induced mechanical stress [4]–[7]. More recently, the Nd:YAG crystal with increas-ing dopincreas-ing concentrations was proposed to show that employincreas-ing the so-called multi-segmented crystal could not only avoid the risk of the thermal fracture inside the laser material, but also maintain the high optical conversion efficiency [8], [9].Manuscript received March 31, 2014; revised June 10, 2014; accepted June 25, 2014. This work was supported by the National Science Council under Grant NSC-100–2628-M-009-001-MY3.
Y.-J. Huang, W.-Z. Zhuang, and K.-W. Su are with the Department of Electrophysics, National Chiao Tung University, Hsinchu 30010, Taiwan (e-mail: [email protected]; [email protected]; sukuanwei @mail.nctu.edu.tw).
Y.-F. Chen is with the Department of Electrophysics, National Chiao Tung University, Hsinchu 30010, Taiwan, and also with the Department of Electronics Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan (e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JSTQE.2014.2336541
The concept of the master oscillator power amplifier (MOPA) offers another means for boosting the output power of a laser, and it has been widely realized in fiber- and bulk-based architec-tures [10]–[14]. The required high-power performance can be relatively easily achieved in the MOPA by partially decoupling the problems usually encountered in the high-power laser oscil-lator, including the possible instability caused by the multi-mode interactions, thermal-lensing effect, and so on. The Nd:YVO4
crystal, due to the large product of the stimulated emission cross section and the upper-state lifetime, can produce much higher optical gain as compared with other Nd-doped laser ma-terials. To date, most of the Nd:YVO4 amplifiers are based on
the single-pass configuration [12]–[14]. However, some recent works have shown that the double-pass architecture seems to be a more efficient design for scaling the output power of the pulsed oscillator [15], [16]. In this work, an efficient high-power MOPA based on the multi-segmented Nd:YVO4crystal is
suc-cessfully realized for emitting output power greater than one hundred watts in the continuous-wave operation. We first utilize the Fourier eigenfunction expansion method to develop a pow-erful mathematical technique for analytically solving the heat conduction equation of the anisotropic crystal with a rectangu-lar geometry. Theoretical analysis manifestly reveals that the smoother temperature distribution could be achieved inside the multi-segmented crystal than the conventional composite one. Based on the calculated results, we construct a dual-end-pumped multi-segmented Nd:YVO4 oscillator for efficiently producing
the output power of 50 W. We subsequently design two types of MOPA and make a systematical comparison between both configurations. It is experimentally found that the power gain obtained from the double-pass MOPA is generally larger than that obtained from the single-pass one. Consequently, the output power could be further scaled to reach 108 W at 1064 nm under a total incident pump power of 244 W at 808 nm, corresponding to the optical conversion efficiency of up to 44.3%.
II. THEORETICALANALYSIS ONTEMPERATUREDISTRIBUTION Fig. 1(a) schematically depicts the thermal model of the multi-segmented crystal with a rectangular geometry used for our theoretical analysis, which is end-pumped from two sides. The lengths for each side of the crystal are a, b, and c, re-spectively. The current multi-segmented crystal is made up of five sections with three doped materials between two undoped end-caps, where the doped parts are characterized by pump ab-sorptions α1, α2, and α3, and heat source densities q1(x, y, z), 1077-260X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
Fig. 1. (a) Configuration of the multi-segmented crystal with a rectangu-lar geometry for the theoretical model; Temperature fields inside the gain medium for: (b) YVO4/0.1 + 0.3 + 0.1% Nd:YVO4/YVO4, (c) YVO4/0.2%
Nd:YVO4/YVO4, and (d) YVO4/0.1% Nd:YVO4/YVO4crystals; (e) On-axis
temperature raise as a function of the axial position for the gain medium.
q2(x, y, z), and q3(x, y, z), respectively. The z coordinates for
every transverse plane are denoted as c0, c1, c2, c3, c4, and c5,
respectively. Note that c0 and c5 are virtually equal to 0 and c.
The temperature field inside a rectangular crystal obeys the heat conduction equation in the Cartesian coordinate, which is given by [17]: Kx ∂2T (x, y, z) ∂2x + Ky ∂2T (x, y, z) ∂2y +Kz ∂2T (x, y, z) ∂2z =−q(x, y, z) (1) where q(x, y, z) = q1(x, y, z) + q2(x, y, z) + q3(x, y, z) is the
total heat source density, Kx, Ky and Kz are the thermal con-ductivity coefficients along the x, y, and z axes, respectively. For the edge-cooled laser crystal, the temperatures at the lat-eral sides are assumed to be a constant value T0, while the
two end surfaces could be reasonably supposed to be adia-batic since the heat transfer coefficients between the crystal and air are very small. Therefore, the boundary conditions can be
expressed as [18]: T (0, y, z) = T0, T (a, y, z) = T0 T (x, 0, z) = T0, T (x, b, z) = T0 ∂T (x, y, z) ∂z z = 0 = 0, ∂T (x, y, z) ∂z z = c = 0. (2)
The solution to the temperature field subject to the above boundary conditions could be formally represented by a prod-uct of three orthogonal sets of eigenfunctions sin[(nπ/a)x],
sin[(mπ/b)y], and cos[(lπ/c)z] plus a constant value T0, that
is: T (x, y, z) = ∞ n = 1 ∞ m = 1 ∞ l= 0 An m lsin nπ a x × sinmπ b y cos lπ c z + T0 (3)
where An m l are the coefficients to be determined. Substituting (3) into (1), the heat conduction equation becomes:
∞ n = 1 ∞ m = 1 ∞ l= 0 Bn m lsin nπ a x sin mπ b y cos lπ c z =−q(x, y, z) (4) Bn m l =−An m l Kx nπ a 2 + Ky mπ b 2 + Kz lπ c 2 . (5) Using orthogonal properties of sine and cosine functions:
d 0 sin sπ d x sin sπ d x dx = d 2δs,s (6) d 0 cos sπ d x cos sπ d x dx = d 2δs,s (7)
where these are valid for integer numbers of s and s’, the coeffi-cients An m lcan thus be solved as a triple Fourier series for the function q(x, y, z): An m l = 8 abc 1 Kx nπ a 2 + Ky mπ b 2 + Kz lπ c 2 × c 0 b 0 a 0 q(x, y, z) sin nπ a x sin mπ b y cos lπ c z dxdydz. (8) For a fiber-coupled laser diode, the pump intensity distribu-tion could be approximately expressed as a top-hat funcdistribu-tion. When the pump beams are injected along the central axis of the
laser crystal, the heat source densities could be expressed as qi(x, y, z) = [qi,L(x, y, z) + qi,R(x, y, z)] ×H(z − ci)H(ci+ 1− z)H ω2p− x−a 2 2 − y−b 2 2 (9) qi,L(x, y, z) = η αiPin,Le−αi(z−ci) πω2 p i−1 s= 0 e−αs(cs + 1−cs) (10) qi,R(x, y, z) = η αiPin,Re−αi(ci + 1−z) πω2 p N −i s= 0 × e−αs (cN + 2−s −cN + 1−s ), i = 1, 2, 3 (11)
where H() is the Heaviside step function, ωpis the pump radius,
Pin,L and Pin,R are the incident pump power from the left
and right side of the crystal, N is the number of the doped sections, and η is the fractional thermal loading. For a four-level solid-state laser with low doping concentration under the laser condition, the fractional thermal loading can be simply given by the quantum defect 1− λp/λL, whereλpandλL are the pump and lasing wavelengths. Note that we intentionally introduce two null parameters α0 and α4 for the general expression of
qi(x, y, z). Substituting (9) into (8) and integrating z from 0 to
c, the coefficients An m l can be simplified as An m l = 8 abc (Al , L+ Al , R) Kx nπ a 2 + Ky mπ b 2 + Kz lπ c 2 × b 0 a 0 H ω2 p− x−a 2 2 − y−b 2 2 × sinnπ a x sin mπ b y dxdy (12) Ai , L = η αiPin , Leαici πω2 p(α2ic2 + l2π2) i−1 s = 0 eαs( cs + 1−cs) × lπc e−αici + 1 sin lπ cci + 1 − e−αicisin lπ cci −αic2 e−αici + 1 cos lπ cci + 1 − e−αicicos lπ cci (13) Ai , R = η αiPin , Re−αici + 1 πω2 p(α2ic2 + l2π2) N −i s= 0 e−α4−s ( cN + 2−s −cN + 1−s ) × lπc eαici + 1 sin lπ cci + 1 − eαicisin lπ c ci + αic2 eαici + 1cos lπ cci + 1 − eαicicos lπ cci (14) with the following parameters: N = 3, a = b = 3 mm, c0 = 0
mm, c1 = 2 mm, c2 = 10 mm, c3= 20 mm, c4 = 28 mm, c = c5 = 30 mm, Kx = 5.23 W/(m·K), Ky = 5.1 W/(m·K),
Kz = 5.1 W/(m·K), α1= 0.16 mm−1, α2 = 0.48 mm−1, α3 =
0.16 mm−1, ωp = 350 μm, T0= 291 K, λp = 808 nm, and
λL = 1064 nm, we calculate the distribution of the
tem-perature field inside the a-cut multi-segmented YVO4/0.1 +
0.3 + 0.1% Nd:YVO4/YVO4 crystal for the case of Pin,L=
Pin,R = 54 W, as shown in Fig. 1(b). For the purpose of
comparison, the temperature distributions for the conventional composite YVO4/0.2% Nd:YVO4/YVO4 and YVO4/0.1%
Nd:YVO4/YVO4 crystals with the same dimensions are also
calculated, as displayed in Fig. 1(c) and (d). The values of n and
m used for the calculation are both from 1 to 41 for symmetry,
while for l it is ranged from 0 to 80. Our calculation has shown that these chosen index values are sufficient for the tempera-ture variation within 10−2 while keeping the computation time to be not more than ten minutes. We also compare the Fourier eigenfunction expansion method with the finite-element analy-sis [17] and find that only a small difference between these two approaches is observed. However, the computation time for the Fourier eigenfunction expansion method is several times faster than that for the finite-element analysis. Fig. 1(e) illustrates the on-axis temperature raise with respect to the axial position for these three types of crystal. It can be clearly concluded that not only the maximum temperature raise could be effectually re-duced, but also the heat could be spread more uniformly inside the multi-segmented crystal. The theoretical analysis is consis-tent with the experimental results on the focal length of the thermal lens investigated in our previous study [19]. This indi-cates that the multi-segmented crystal is a promising approach for developing a high-power end-pumped laser, as will be fur-ther experimentally demonstrated as follows. It is worthwhile to mention that the similar analysis has been previously per-formed for the multi-segmented Nd:YAG rod with a cylindrical geometry, where the temperature field is expanded by a series of Bessel functions [20], and the potential for such crystal design in power scaling was experimentally realized. We also want to address that if the pump intensity distribution does not follow the top-hat function, the heat source densities (9)–(11) and thus the coefficients An m l expressed in (12)–(14) should be modi-fied, which would result in slightly different temperature values. For example, we have computationally found that the tempera-ture peak value for the Gaussian pump intensity distribution is 4–6% higher than the value obtained from the top-hat pumping, whereas the morphologies of temperature distribution are quite similar to each other.
III. PERFORMANCE OF THEDUAL-END-PUMPED MULTI-SEGMENTEDOSCILLATOR
The experimental arrangement of high-power dual-end-pumped continuous-wave oscillator with the five-segmented Nd:YVO4 crystal is schematically shown in Fig. 2(a). A plane
mirror with anti-reflection at 808 nm on the entrance side and high reflection at 1064 nm as well as high transmission at 808 nm on the other side was employed as the front mirror. The coating characteristic of the folding mirror was the same as that of the front mirror, except that the angle of incidence was designed to be 45°. The a-cut Y V O4/0.1 + 0.3 + 0.1% Nd:YVO4/YVO4
Fig. 2. Experimental setup for the: (a) diode-pumped YVO4/0.1 + 0.3 +
0.1% Nd:YVO4/YVO4 laser with dual-end pumping, (b) double-pass MOPA
configuration, and (c) single-pass MOPA configuration.
crystal consisted of two undoped end-caps with the lengths of 2 mm, and three active parts with the lengths of 8, 10, and 8 mm, corresponding to the doping concentrations of 0.1, 0.3, and 0.1%, respectively. Our multi-segmented crystal was de-signed for the dual-end pumping to make the generated heat more uniform inside the gain medium, and thus a superior laser performance could be achieved. The transverse cross section of the crystal is 3 mm× 3 mm. Both end faces of the gain medium were coated to be anti-reflective at pump and lasing wavelengths. The laser crystal was wrapped with indium foil and mounted in a water-cooled copper holder with the temperature at 18°C. A
flat mirror with the reflectivity of 85% at 1064 nm was utilized as the output coupler. The pump sources were two 808-nm fiber-coupled laser diodes with the nominal powers of 60 W for each. The numerical aperture and core diameter of the coupling fiber were 0.22 and 600 μm, respectively. The pump beams were reimaged into the laser crystal with the spot radii of 350 μm through two convex lenses with the focal lengths of 25.4 mm and the coupling efficiencies of 95%. The cavity length of the whole resonator was around 70 mm.
First of all, the laser oscillator was carefully optimized for the maximum output power under an incident pump power of 108 W. Then, the output power at 1064 nm as a function of the incident pump power at 808 nm was measured, as exhibited in Fig. 3. The pump threshold is around 5.2 W, and the maximum
Fig. 3. Dependence of the output power at 1064 nm on the incident pump power at 808 nm for the diode-pumped YVO4/0.1 + 0.3 + 0.1%
Nd:YVO4/YVO4 laser. Inset: corresponding optical spectrum for the laser
output.
output power as high as 50 W is efficiently generated under an incident pump power of 108 W. The corresponding slope and optical conversion efficiencies are evaluated to be 48.6 and 46.3%, respectively. The beam quality factor was measured to be better than 1.8 with a knife-edge method. The output radi-ation was linearly polarized along the c axis of the Nd:YVO4
crystal, and the extinction ratio was found to be larger than 200:1. More importantly, no thermal fracture inside the gain medium was observed during the experiment. Combined with our previous studies [19], it can be clearly deduced that utilizing the multi-segmented crystal is practically valuable in scaling the output power for diode-end-pumped laser system without intro-ducing considerable thermally accompanied detrimental effects. The spectral information for the developed Nd:YVO4 laser was
recorded with an optical spectrum analyzer (Advantest 8381A) with the resolution of 0.1 nm. The central wavelength of the laser output locates at 1064.8 nm with the full width at half maximum of approximately 0.3 nm, as displayed in the inset of Fig. 3. In the following section, we design two types of MOPA to further scale the output power at 1064 nm.
IV. COMPARATIVEINVESTIGATIONBETWEENDOUBLE -ANDSINGLE-PASSMOPA CONFIGURATIONS
Fig. 2(b) and (c) schematically depict the experimental lay-outs for the MOPAs with double- and single-pass configurations, respectively. All retro-reflecting mirrors were coated for high re-flection at 1064 nm. The same coupling system was also utilized in the amplification stage, except that the magnified ratio is dif-ferent. The amplified medium was a three-segmented Nd:YVO4
crystal with a 2-mm-long undoped YVO4 crystal bonded to a
0.1-% doping Nd:YVO4 crystal with the length of 8 mm, and
followed by a 0.3-% doping material with the length of 5 mm. The active medium was wrapped with indium foil and mounted in a water-cooled copper block at the temperature at 18°C. An
145-W fiber-coupled laser diode at 808 nm was employed to pump the Nd:YVO4crystal with the spot radius of 800 μm. The
laser beam emitted from the master oscillator was collimated by a plano-convex lens with the focal length of 80 mm. For the double-pass MOPA configuration shown in Fig. 2(b), the laser beam propagated the amplified medium twice achieved
Fig. 4. (a) Power gains as a function of the input seed power and (b) output powers versus the incident pump power at the amplification stage for both configurations.
by a retro-reflecting mirror with a small inclined angle; while only one trip through the Nd:YVO4 crystal for the laser beam
was adopted in the single-pass MOPA architecture described in Fig. 2(c). It should be point out that the crystal structure used in the amplifier stage was different from that utilized in the oscillator stage. This is because the input seed and ampli-fied radiations pass the same side of the active medium in our double-pass MOPA configuration aimed for single end pumping from the opposite face of the crystal. Moreover, if the Nd:YVO4
crystal with a dimension of 3 mm× 3 mm × 30 mm (as used in the oscillator stage) was adopted, the amplified laser radiation would be easily blocked by the surrounded copper holder, re-sulting in a significant decrease of the output power.
Initially, we varied the input seed power from the master oscillator to systematically compare the amplified abilities for two configurations with the incident pump power at the am-plification stage to be fixed at 136 W. Fig. 4(a) illustrates the power gains for the double- and single-pass MOPA configura-tions versus the incident pump power at the amplification stage. The power gain G is defined as the ratio of the amplified power
Pam p to the input seed power Pseed at 1064 nm. It can be
ob-viously seen that the power gain achieved in the double-pass MOPA architecture is generally larger than that obtained from the single-pass MOPA architecture, especially for the low input seed power. Experimental results also manifestly reveal that the power gain decreases by increasing the input seed power for both configurations, this is a typical behavior for the power am-plifier [13], [15], [16]. When the input seed power is changed from 0.8 to 50 W, the power gains are experimentally found to decrease from 8 to 2.16 for the double-pass MOPA frame and from 2.95 to 1.76 for the single-pass MOPA frame, respectively.
In order to well characterize these two types of power ampli-fier, the gain curves are fitted by a Frantz-Nodvik model for a continuous-wave operation [21], [22]: G =Pam p Pseed = Psat Pseed ln 1 + G0 exp Pseed Psat − 1 (15) where Psatis the saturation parameter and G0is the small-signal
gain. For the single-pass MOPA configuration, the saturation pa-rameter and small-signal gain are characterized by Psat= 45 W
and G0 = 2.9, respectively. On the other hand, Psat = 25 W
and G0= 9 are obtained with the double-pass MOPA
config-uration, confirming the relatively high-gain and low saturation power provided by this amplifier structure.
We further investigated the dependence of the amplified power on the incident pump power at the amplification stage when the input seed power was fixed to be 50 W, as exhibited in Fig. 4(b). Under an incident pump power of 136 W, the ampli-fied power for the single-pass MOPA configuration is acquired to be 88 W. On the other hand, the amplified power as high as 108 W is achieved for the double-pass MOPA frame under an incident pump power of 136 W, which is remarkably larger than that obtained from single-pass MOPA frame. The beam quality factors were generally better than 2.2 and the polariza-tion remained linear after either single- or double-pass MOPA configurations. According to the results demonstrated here, it is believed that employing the multi-segmented crystal combined with the double-pass MOPA configuration is suitable for ac-complishing a reliable, efficient high-power diode-end-pumped laser system.
V. CONCLUSION
In summary, a novel Nd:YVO4 crystal with multiple doping
concentrations has been originally fabricated for constructing a high-power MOPA system. The temperature field inside a rectangular-shaped laser crystal has been precisely calculated by a powerful mathematical model on the basis of the Fourier eigenfunction expansion method. Based on the theoretical analysis, a reliable continuous-wave YVO4/0.1 + 0.3 + 0.1%
Nd:YVO4/YVO4 oscillator is successfully developed to
gener-ate the output power of up to 50 W with dual-end pumping. Moreover, we have designed a double-pass MOPA to remark-ably boost the laser power to reach 108 W under a total incident pump power of 244 W, corresponding to the optical conversion efficiency of 44.3%.
REFERENCES
[1] N. Hodgson, K. Griswold, W. Jordan, S. L. Knapp, A. A. Peirce, C. C. Pohalski, E. Cheng, J. Cole, D. R. Dudley, A. B. Petersen, and W. L. Nighanjr, “High power TEM0 0 mode operation of diode-pumped solid
state lasers,” Proc. SPIE, vol. 3611, pp. 119–131, Jan. 1999.
[2] N. Hodgson, M. Li, A. Held, and A. Krueger, “Diode-pumped TEM0 0
mode solid state lasers and their micromachining applications,” Proc.
SPIE, vol. 4977, pp. 281–294, Jan. 2003.
[3] S. R. Bowman, “High-power diode-pumped solid-state lasers,” Opt. Eng., vol. 52, art. no. 021012, Feb. 2013.
[4] F. Hanson, “Improved laser performance at 946 and 473 nm from a com-posite Nd:Y3Al5O1 2rod,” Appl. Phys. Lett., vol. 66, pp. 3549–3551, Jun.
[5] M. Tsunekane, N. Taguchi, T. Kasamatsu, and H. Inaba, “Analytical and experimental studies on the characteristics of composite solid-state laser rods in diode-end-pumped geometry,” IEEE J. Sel. Topics Quantum
Elec-tron., vol. 3, no. 1, pp. 9–18, Feb. 1997.
[6] X. Li, X. Yu, F. Chen, R. Yan, M. Luo, J. Yu, and D. Chen, “Power scal-ing of directly dual-end-pumped Nd:GdVO4 laser using grown-together
composite crystal,” Opt. Exp., vol. 18, pp. 7407–7414, Mar. 2010. [7] Y. J. Huang, Y. P. Huang, H. C. Liang, K. W. Su, Y. F. Chen, and K. F.
Huang, “Comparative study between conventional and diffusion-bonded Nd-doped vanadate crystals in the passively mode-locked operation,” Opt.
Exp., vol. 18, pp. 9518–9524, Apr. 2010.
[8] R. Wilhelm, D. Freiburg, M. Frede, and D. Kracht, “End-pumped Nd:YAG laser with a longitudinal hyperbolic dopant concentration profile,” Opt.
Exp., vol. 16, pp. 20106–20116, Nov. 2008.
[9] R. Wilhelm, M. Frede, and D. Kracht, “Power scaling of end-pumped solid-state rod lasers by longitudinal dopant concentration gradients,”
IEEE J. Quantum Electron., vol. 44, no. 3, pp. 232–244, Mar. 2008.
[10] Y. Jeong, J. Nilsson, J. K. Sahu, D. B. S. Soh, C. Alegria, P. Dupriez, C. A. Codemard, D. N. Payne, R. Horley, L. M. B. Hickey, L. Wanz-cyk, C. E. Chryssou, J. A. Alvarez-Chavez, and P. W. Turner, “Single-frequency, single-mode, plane-polarized ytterbium-doped fiber master os-cillator power amplifier source with 264 W of output power,” Opt. Lett., vol. 30, pp. 459–461, Mar. 2005.
[11] M. Hildebrandt, M. Frede, P. Kwee, B. Willke, and D. Kracht, “Single-frequency master-oscillator photonic crystal fiber amplifier with 148 W output power,” Opt. Exp., vol. 14, pp. 11071–11076, Nov. 2006. [12] J. W. Kim, M. J. Yarrow, and W. A. Clarkson, “High power
single-frequency continuous-wave Nd:YVO4master-oscillator power amplifier,”
Appl. Phys. B, vol. 85, pp. 539–543, Dec. 2006.
[13] X. Yan, Q. Liu, X. Fu, Y. Wang, L. Huang, D. Wang, and M. Gong, “A 108 W, 500 kHz Q-switching Nd:YVO4 laser with the MOPA
configura-tion,” Opt. Exp., vol. 16, pp. 3356–3361, Mar. 2008.
[14] S. Yan, X. Yan, H. Yu, L. Zhang, L. Guo, W. Sun, W. Hou, and X. Lin, “A high power picosecond Nd:YVO4 master oscillator power amplifier
system pumper by 880 nm diodes,” Laser Phys., vol. 23, art. no. 075302, Jul. 2013.
[15] A. Agnesi, L. Carr`a, R. Piccoli, F. Pirzio, and G. Reali, “Nd:YVO4
am-plifier for ultrafast low-power lasers,” Opt. Lett., vol. 37, pp. 3612–3614, Sep. 2012.
[16] X. D´elen, F. Balembois, and P. Georges, “Direct amplification of a nanosecond laser diode in a high gain diode-pumped Nd:YVO4amplifier,”
Opt. Lett., vol. 39, pp. 997–1000, Feb. 2014.
[17] Z. Xiong, Z. G. Li, N. Moore, W. L. Huang, and G. C. Lim, “Detailed investigation of thermal effects in longitudinally diode-pumped Nd:YVO4
lasers,” IEEE J. Quantum Electron., vol. 39, no. 8, pp. 979–986, Aug. 2003. [18] P. Shi, W. Chen, L. Li, and A. Gan, “Semianalytical thermal analysis on a
Nd:YVO4crystal,” Appl. Opt., vol. 46, pp. 4046–4051, Jul. 2007.
[19] Y. J. Huang and Y. F. Chen, “High-power diode-end-pumped laser with multi-segmented Nd-doped yttrium vanadate,” Opt. Exp., vol. 21, pp. 16063–16068, Jul. 2013.
[20] R. Wilhelm, D. Freiburg, M. Frede, D. Kracht, and C. Fallnich, “Design and comparison of composite rod crystals for power scaling of diode end-pumped Nd:YAG lasers,” Opt. Exp., vol. 17, pp. 8229–8236, May 2009.
[21] L. M. Frantz and J. S. Nodvik, “Theory of pulse propagation in a laser amplifier,” J. Appl. Phys., vol. 34, pp. 2346–2349, Aug. 1963.
[22] W. Koechner, Solid-State Laser Engineering, 6th ed. Berlin, Germary: Springer-Verlag, 2005, ch. 4.
Yu-Jen Huang was born in Hualien, Taiwan, in 1987. He received the B.S. and the Ph.D. degrees in electrophysics from National Chiao Tung Univer-sity, Hsinchu, Taiwan, in 2009 and 2013, respectively. He is currently a Postdoctoral Research Fellow in the Department of Electrophysics, National Chiao Tung University. His research interests include the physics and technology of diode-pumped solid-state lasers and nonlinear frequency conversion. Dr. Huang is a Member of the Optical Society of America.
Wei-Zhe Zhuang was born in Taichung, Taiwan, in 1986. He received the B.S. and Ph.D. degrees in electrophysics from National Chiao Tung University, Hsinchu, Taiwan, in 2008 and 2013, respectively.
He is currently a Postdoctoral Research Fel-low with the Department of Electrophysics, National Chiao Tung University. His research interests include fiber lasers and diode-pumped solid-state lasers.
Kuan-Wei Su was born in Kaohsiung, Taiwan, in 1979. He received the B.S. degree in physics from National Cheng Kung University, Tainan, Taiwan, in 2001, and the M.S. and Ph.D. degrees in elec-trophysics from National Chiao Tung University, Hsinchu, Taiwan, in 2004 and 2007, respectively.
He is currently an Associate Professor in the Department of Electrophysics, National Chiao Tung University. His research interests include fiber lasers, diode-pumped solid-state lasers, and high-speed dy-namics of lasers and matter.
Dr. Su is a Member of the Optical Society of America.
Yung-Fu Chen was born in Lukang, Taiwan, in 1968. He received the B.S. and Ph.D. degrees in electronics engineering from National Chiao Tung University, Hsinchu, Taiwan, in 1990 and 1994, respectively.
Since 1994, he was with Precision Instrument De-velopment Center, National Science Council, Taiwan, where his research mainly concerns the development of diode-pumped solid-state laser as well as quantita-tive analysis in surface electron spectroscopy. Since 1999, he was with National Chiao Tung University (NCTU) as the Associate Professor in the Depart-ment of Electrophysics. Since 2001, he was promoted to be the Professor in NCTU. He had served as the Executive Dean in the College of Science, NCTU, between 2006 and 2007. He had also served as the Chair in the Department of Electrophysics between 2011 and 2013. Since 2011, he has been identified as the Distinguished Professor. He has received several outstanding awards, such as Sun-Yet-Sen academic award for excellent papers in 2008, Outstand-ing Research Award from the National Science Council in 2004 and 2011, and Outstanding Honorary Award from the Ho C.T. Education Foundation in 2011. His main research interests include laser physics, solid-state lasers, Q-switched lasers, mode-locked lasers, and transverse pattern formation in microchip lasers. Dr. Chen is a Member of the Optical Society of America and the IEEE Photon-ics Society. Currently, he serves as the Associate Editor for the OptPhoton-ics Express.
