Original Text © Astro, Ltd., 2012.
1
1. INTRODUCTION
Highpeakpower, linearlypolarized lasers with pulse repetition rates up to several tens of kilohertz have a wide variety of applications in range finding, nonlinear wavelength conversion, and material pro cessing [1–3]. The thermally induced distortion is the main hindrance for power scaleup in solidstate crys tal lasers [4]. The masteroscillator fiber powerampli fier (MOFA) that collects the advantages of good beam quality, high efficiency, compactness, and supe rior heat dissipations has been identified as a promis ing light source [5–9]. To achieve the highpeak power pulses with singlestage amplification, diode pumped actively Qswitched (AQS) [10, 11] or pas
sively Qswitched (PQS) [12–14] Nddoped lasers are often used as the seed lasers of the Ybdoped MOFAs. Compared to the active Qswitching, the PQS laser with a saturable absorber offers the advantages of com pactness, robustness, and low cost. Since Cr4+:YAG crystals possess the advantages of high absorption cross section near the infrared region, high damage threshold, and low temperaturesensitive properties [15–21], they have been proved to be reliable saturable absorbers for Nd3+doped lasers. Nevertheless, the Cr4+:YAG crystal is usually not convenient for the Nd doped vanadate crystal lasers due to the mismatch between the stimulated emission cross section of the gain medium and the absorption cross section of the absorber. Several methods, including the threeele ment resonator with the intracavity focusing [15, 20, 22] or the employment of a ccut crystal as the gain
medium [23–25], have been proposed to overcome 1The article is published in the original.
this mismatch. The threeelement resonators, how ever, not only increase the complexity of the cavities but also lead to relatively long pulse durations owing to the long cavity lengths. On the other hand, the employ ment of a ccut crystal inevitably raises the pumping
threshold and loses the characteristic of linear polar ization. Therefore, it is highly useful for the seed laser of MOFA to develop highpeakpower PQS lasers with
acut vanadate crystals in a simple compact cavity.
In this work, we systematically consider the sec ond threshold criterion and the thermal lensing effect to develop compact and highpeakpower Nd:YVO4/Cr4+:YAG PQS lasers with nearly hemi spherical cavities. We further exploit several Cr4+:YAG crystals with different initial transmissions (T0) to real ize the designed PQS laser. Experimental results reveal that at a pump power of 5.4 W the output pulse energy increases from 22 to 36 μJ and the pulse repetition rate decreases from 50 to 25 kHz for the initial transmis sion of the Cr4+:YAG crystal decreasing form 70% to 40%. Injecting the seed laser obtained with T0 = 70% into a polarization maintained Ybdoped fiber, the pulse energy and peak power at a pump power of 16 W are enhanced up to 178 μJ and 37 kW, respectively. Excellent amplification confirms the PQS perfor mance. Employing the seed laser obtained with T0 = 40%, we find that the surface damage of the fiber limits the maximum pulse energy and peak power to be 192μJ and 120 kW, respectively. The polarization extinction ratio is approximately 100:1 for both MOFAs in the whole pump power. To the best of our knowledge, this is the first time to realize highpeak power, singlestage, linearlypolarized MOFAs with the compact Nd:YVO4/Cr4+:YAG PQS lasers as seed oscillators.
>100kW Linearly Polarized Pulse Fiber Amplifier Seeded
by a Compact Efficient Passively
Qswitched Nd:YVO
4Laser
1W. Z. Zhuang, W. C. Huang, C. Y. Cho, Y. P. Huang, J. Y. Huang, and Y. F. Chen*
Department of Electrophysics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, 30010, Taiwan
*email: [email protected]
Received December 21, 2012; in final form, December 28, 2012; published online October 1, 2012
Abstract—We thoroughly develop compact highpeakpower Nd:YVO4/Cr4+:YAG passively Qswitched lasers (PQS) as the seed source of the fiber amplifier. We exploit a nearly hemispherical cavity to reach the second threshold criterion and systematically consider the thermal lensing effect and the modesize matching in the overall optimization. Employing a Cr4+:YAG absorber with 70% initial transmission, we obtain a 50kHz seed pulse train with the pulse duration of 4.8 ns and the pulse energy of 22 μJ at a pump power of 5.4 W. Injecting this seed laser into a polarization maintained Ybdoped fiber, the pulse energy and peak power at a pump power of 16 W are enhanced up to 178 μJ and 37 kW, respectively. We also use an absorber with 40% initial transmission to generate a 25 kHz pulse train with the pulse duration of 1.6 ns and the pulse energy of 36 μJ at a pump power of 5.4 W. With this seed laser, we find that the surface damage of the fiber limits the maximum pulse energy and peak power to be 192 μJ and 120 kW, respectively.
DOI: 10.1134/S1054660X12110205
2. ANALYSIS AND OPTIMIZATION OF THE PQS LASER
To achieve good passive Qswitching, absorption
saturation in the absorber must occur before gain sat uration in the laser crystal [22]. From the analysis of the coupled rate equation, the good passively Q
switching criterion which is also called second thresh old condition is given by:
(1)
where R is the reflectivity of the output coupler, σ is
the stimulated emission crosssection of the gain medium, σgsa is the groundstate absorption crosssec tion of the saturable absorber with the initial transmis sion T0, L is the nonsaturable intracavity roundtrip dissipative optical loss, A/As is the ratio of the effective area in the gain medium to that in the saturable absorber, γ is the inversion reduction factor with a value between 0 and 2 [26], and β is the ratio of the excitedstate absorption crosssection to that of the groundstate absorption in the saturable absorber. The challenge of obtaining a compact and stable Nd:YVO4/Cr4+:YAG PQS laser results from which the emission crosssection of Nd:YVO4 crystals (~2.5 × 10–18 cm2) [15] is comparable with the groundstate absorption crosssection of Cr4+:YAG crystals (~(2.0 ± 0.5) × 10–18 cm2) [27]. It was found that unstable pulse trains with satellite pulses would occur when the good
Qswitching criterion is not achieved [28, 29]. To ful
fill the good passive Qswitching criterion in
Nd:YVO4/Cr4+:YAG PQS lasers, the ratio A/As gener ally needs to be greater than 10 [29].
Even though the threeelement resonator can be used to achieve the requirement of the ratio A/As ≥ 10, the long cavity usually leads to a wide pulse dura tion. Here we utilize the nearly hemispherical reso nator to develop compact highpeakpower Nd:YVO4/Cr4+:YAG PQS lasers to be seed oscillators. In terms of the gparameters, the beam radii ω1 and ω2
1/T02 ( ) ln 1/T02 ( ) ln +ln(1/R)+L σgsa σ A As γ 1–β , >
on the rear and front mirrors are given by [30]: (2)
(3)
where L is the cavity length, λ is the wavelength of laser mode, and ρ1 and ρ2 are the radii of curvature of the rear and front mirrors, respectively. For a simple planoconcave resonator, as depicted in Fig. 1a, g1 = 1 – L/ρ1 and g2 = 1. Given that the gain medium and the saturable absorber are as close as possible to the rear mirror and the flat output coupler, the ratio of the effective area in the gain medium to that in the satura ble absorber A/As can be found to be
(4)
Equation (4) reveals that the ratio A/As can be up to 10 under the circumstance of a nearly hemispherical cav ity with L = 0.9ρ1. A smaller ρ1 consequently corre sponds to a shorter cavity length that is beneficial for the generation of Qswitched pulses with narrower
pulse duration. Nevertheless, the geometrical sizes of the gain medium, the saturable absorber, and the heat sinks limit the minimum cavity length. Therefore, ρ1 = 25 mm is chosen for further optimizing the compact highpeakpower Nd:YVO4/Cr4+:YAG PQS laser.
The next design parameter is the pump size that needs to be optimized to reach the good mode match ing for the fundamental transverse mode. Since the thermal lensing effect in the gain medium always affects the cavity mode size, it is practically important to consider the thermal lensing effect for determining the optimum pump size. For an endpumped crystal laser, the thermal lens is given by [31]:
(5) gi 1 L ρi , – = ωi λL π gj gi(1–g1g2) ; i j, 1 2;, i≠j, = = A As ω1 2 ω2 2 ρ1 ρ1–L . = = 1 fth = ξPin πKc αe αz – 1–e–αl 1 ωp 2 z ( ) 1 2 dn T d (n–1)αT ωp( )z l + dz, 0 l
∫
(a) (b) S1 S2 Cr4+:YAG Nd:YVO4 ρ1 d1 d2 ρ1 Lwhere
(6)
z0 is the focal plane of the pump beam in the laser crys tal, is the pump beam quality factor, ωpo is the pump beam radius, n is the refractive index of along the caxis of the laser crystal, λp is the wavelength of the pump laser diode, ξ is the fractional thermal load ing, Kc is the thermal conductivity, Pin is the incident pump power, α is the absorption coefficient of the gain medium, l is the crystal length, dn/dT is the thermal optic coefficient of n, and αT is the thermal expansion coefficient along the aaxis.
Figure 1b depicts the configuration of a nearly hemi spherical resonator for a Nd:YVO4/Cr4+:YAG PQS laser. Considering the thermal lens effect and taking S1 as the reference plane, the ray transfer matrix from S1 to
S2 of the cavity configuration can be presented as [32]:
(7) (8) (9) (10) ωp( )z ωpo 1 λpMp 2 z–zo ( ) nπωpo2 2 + , = Mp 2 MD g1* L* g1*g2*–1 L* g2* ⎝ ⎠ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎛ ⎞ , = gi* gi dj fth 1 di ρi – ⎝ ⎠ ⎛ ⎞ , – = gi 1 d1+d2 ρi ; i – ,j 1 2; i, ≠j, = = L* d1 d2 d1d2 fth . – + =
Here d1 and d2 are the optical path length between the cavity mirrors and the principal planes of the laser crystal, and fth is the effective focal length of the ther mal lens. With the following parameters: ξ = 0.24,
Kc= 5.23 W/K m, d1 = 2 mm, d2 = 0.9ρ1 – d1, ρ2 = ∞,
n = 2.165, l = 12 mm, dn/dT = 3.0 × 10–6 K–1, = 80, α = 0.6 mm–1, α
T = 4.43 × 10–6 K–1, and λp = 808 nm, the effective focal length of the thermal lens effect and g*parameters of the resonator can be cal
culated as functions of the incident pump power. In terms of the g*parameters for the thermal lensing effect, the beam radii ω1 and ω2 on the rear and front mirrors can be expressed as [32]:
(11)
Figure 2 shows the modetopump size ratio ω1/ωpa of different pumping spot radii as a function of the pump power with the radius of curvature of the rear mirror of 25 mm, where the averaged pump size along the gain medium is given by [33]:
(12)
According to the optimal mode matching condition [33], the ratio of ω1/ωpa should be in the range of 0.8 to 1.2 for Pin < 10 W. In our design, the maximum pump power is approximately 5.5 W. As can be seen from the Fig. 2, the optimum pump radius is in the region of 100 μm.
With ωpo = 100 μm and ρ1 = 25 mm, we consider the thermal lensing effect to calculate the effective mode area ratio of A/As as a function of the pump power. Fig
Mp2 ωi λL* π gj* gi* 1( –g1*g2*) ; i j, 1 2;, i≠j. = = ωpa ωp( )ez αz – z/ e–αzdz. 0 l
∫
d 0 l∫
= 6 5 4 3 2 1 0Launched pump power, W 1.1 0.5 1.0 0.9 0.8 0.7 0.6
Mode size ratio of ω1 to ωpa
ωpo = 50 μm
100 μm
150 μm
200 μm
Fig. 2. Dependence of the modetopump size ratio ω1/ωpa on the pump power for different pumping spot radii.
60 50 40 30 20 10
Mode area ratio of A to As
6 5 4 3 2 1 0
Launched pump power, W
Fig. 3. Effective mode area ratio of A/As as a function of the
pump power in the Nd:YVO4/Cr4+:YAG PQS laser with L = 0.9ρ1, ρ1 = 25 mm, ωp = 100 μm.
ure 3 shows the calculated result for the dependence of the effective mode area ratio of A/As on the pump power. It can be seen that the effective mode area ratio
of A/As is generally greater than 10 for the pump power less than 5.5 W. To be brief, we choose a nearly hemi spherical cavity with the radius of curvature of the rear
Fibercoupled LD Nd:YVO4 Cr4+:YAG Output coupler R = 60% @ 1064 nm Rear mirror HR @ 1064 nm, HT @ 808 nm Focusing lens
Fig. 4. Schematic diagram of a diodepumped Nd:YVO4 laser PQS with a Cr4+:YAG as a saturable absorber. HR—high reflec tion. HT—high transmission.
70 60
50 40
Initial transmission of Cr4+:YAG, % 60 0 50 40 30 20 10 Repetition rate, kHz (a) 40 0 35 30 25 20 15 10 5 Pulse energy, µ J
Pulse repetition rate Pulse energy 25 0 20 15 10 5 Peak power, kW 6 0 5 4 3 2 1 70 60 50 40
Initial transmission of Cr4+:YAG, % Pulse width Peak power
Pulse width, ns
(b)
Fig. 5. (a) Dependence of the pulse repetition rate and the pulse energy on the initial transmission of Cr4+:YAG at the pump power of 5.4 W. (b) Dependence of the pulse width and the peak power on the initial transmission of Cr4+:YAG at the pump power of 5.4 W.
(a)
10 ns/div 10 ns/div
(b)
mirror of 25 mm and the pumping spot radius of 100 μm to simultaneously satisfy the optimal mode matching condition and the good Qswitching criterion.
3. EXPERIMENTAL RESULTS FOR THE PQS LASER
We followed the theoretical analysis to construct a nearly hemispherical cavity for realizing the compact highpeakpower Nd:YVO4/Cr4+:YAG PQS laser, as
shown in Fig. 4 for the experimental setup. The rear mirror was a concave mirror with a radiusofcurva ture of 25 mm with hightransmission coating at 808 nm (T ~ 95%) and highreflection at 1064 nm
(R > 99.8%). The output coupler was a flat mirror with
partially reflection at 1064 nm (R = 60%). The pump
ing source was a 7W 808nm fibercoupled laser diode with a core diameter of 200 μm and a numerical aperture of 0.22. The focusing lens with 25 mm focal length and 80% coupling efficiency was used to re
Fiber coupled LD @976 nm
3 m, PM, Yb doped doubleclad fiber HT@976 nm HR@1030–1100 nm Coupling lens Coupling lens Nd:YVO4 PQS seed laser (a) (b)
Fig. 7. (a) Scheme of the MOFA setup. HT: high transmission HR: high reflection. (b) Cross section of the PM Ybdoped fiber.
18 16 14 12 10 8 6 4 2 0
Launched pump power, W 10
8
6
4
2
Averaged output power, W
(a)
MOPA with the seed of repetition rate of 50 kHz Averaged power Peak power 50 40 30 20 10 0 Peak power, kW (b) 10 ns/div (c) C2 20 μs/div
Fig. 8. (a) Average output power and peak power of MOFA with the seed of repetition rate of 50 kHz as a function of the launched
pump power. (b) Oscilloscope traces of a single pulse of the output pulse of the amplifier. (c) Oscilloscope traces of a train of amplified pulses.
image the pump beam into the laser crystal. The gain medium was an acut 12mmlong Nd:YVO4 crystal with 0.3 at % Nd3+ concentration. Several Cr4+:YAG absorbers with T0 of 70, 60, 50%, and 40% were used to investigate the performance. The Cr4+:YAG crystals were all 2 mm in thickness. Both sides of the Nd:YVO4 and the Cr:YAG crystals were coated for antireflection at 1064 nm. All the laser crystal were wrapped within indium foils and mounted in the water cooled heat sinks that keep at 19°C. The Nd:YVO4 crystal and Cr4+:YAG crystals were placed as close as possible to the rear mirror and the output coupler respectively. The effective cavity length was set to be 22.5 mm based on the design rule of L = 0.9ρ1. The pulse temporal behavior was recorded by Leroy digital oscilloscope (Wavepro 7100; 10G samples/s; 4 GHz bandwidth) with a fast InGaAs photodiode.
Figure 5a shows the output pulse energies and pulse repetition rates for Cr4+:YAG saturable absorbers with different initial transmissions T0 at the pump power of 5.4 W. It can be seen that for the initial transmission T0 decreasing form 70 to 40% the output pulse energy increases from 22 to 36 μJ; at the same time, the pulse repetition rate decreases from 50 to 25 kHz. Figure 5b
depicts the pulse widths and peak powers for saturable absorbers with different initial transmissions T0 at the pump power of 5.4 W. For the initial transmission T0 decreasing form 70 to 40% the pulse width can be seen to decrease from 4.8 ns to 1.6 ns; consequently, the peak power was enhanced from 4.5 to 22.5 kW. Fig ures 6a and 6b show typical oscilloscope traces for a single pulse at the maximum output powers of the seeds with T0 = 70 and 40%, respectively. Experimen tal results reveal that the characteristics of the output pulse in the present PQS laser display a simple pulse train without the satellite pulses phenomenon. It is worth mentioning that the satellite pulses phenomena such as two pulses oscillate simultaneously or one giant pulse followed by a weak pulse are often observed when the laser cavity does not properly comply with the second threshold criterion in Eq. (1). The spectral spectrum was measured by an optical spectrum ana lyzer with 0.1nm resolution (Advantest Q8381A). The spectral linewidths for all the present PQS lasers were nearly the same to be 0.5 nm. In the next section, we will employ these highpeakpower PQS lasers to realize a single stage, linearpolarized fiber amplifier.
12 0
Launched pump power, W 6
Averaged output power, W
(a)
MOPA with the seed of repetition rate of 25 kHz Averaged power Peak power 120 0 Peak power, kW (b) 10 ns/div (c) C2 4 2
Fiber facet damage threshold
100 80 60 40 20 10 8 6 4 2 50 μs/div
Fig. 9. (a) Average output power and peak power of MOFA with the seed of repetition rate of 25 kHz as a function of the launched
pump power. (b) Oscilloscope traces of a single pulse of the output pulse of the amplifier. (c) Oscilloscope traces of a train of amplified pulses.
4. EXPERIMENTAL RESULTS FOR THE MOFA SYSTEM
The experimental architecture for the MOFA sys tem is shown in Fig. 7a. The gain fiber was a 3mlong Ybdoped Pandastyle PM double clad fiber (Nufern) with a core diameter of 30 μm (N.A. = 0.06) and an inner clad diameter of 250 μm (N.A. = 0.46) with pump absorption of 6.6 dB/m at 975 nm. The Panda style stress applying parts around the core generate a birefringence of 1.5 × 10–4. A microscope image of the fiber crosssection is depicted in Fig. 7b. Both ends of the fiber were polished at an angle of 8° to eliminate the end facet reflection. The pump source was a 20W 976nm fibercoupled laser diode with a core diameter of 200 μm and a numerical aperture of 0.2. A focusing lens with 25mm focal length was used to reimage the pump beam into the fiber through a dichroic mirror with high transmission (HT, T > 90%) at 976 nm and
high reflectivity (HR, R > 99.8%) within 1030– 1100 nm. The pump spot radius was approximately 100μm, and the pump coupling efficiency was esti mated to be nearly 80%. The seed laser was coupled through a focusing lens into the core of the fiber. A half wave plate was used to control the polarization direction of the seed laser to match the fastaxis of the PM fiber.
Figure 8a shows the average output power of the MOFA injected by the seed laser with T0 = 70% as a function of launched pump power at a repetition rate of 50 kHz. Under the launched pump power of 16 W, the output power of the amplifier was 8.9 W, corre
sponding to the pulse energy of 178 μJ. The slope effi ciency was approximately 54%. Figure 8b shows the typical oscilloscope trace for a single pulse at the max imum output power of amplifier. The pulse duration was 4.8 ns and the corresponding peak power was 37 kW. The oscilloscope trace of a train of output pulses of the amplifier is shown in Fig. 8c. The pulse topulse amplitude fluctuation was generally less than 1.5% in root mean square (rms).
Figure 9a shows the average output power of the MOFA injected by the seed laser with T0 = 40% as a function of launched pump power at a repetition rate of 25 kHz. It was found that the end facet damage of the fiber limited the maximum average output power to be approximately 4.8 W under the pump power of 10 W. As a result, the maximum pulse energy was restricted to 192 μJ. Figure 10 depicts the microscope image of the damaged end view and the side view of the fiber. Figure 9b shows the typical oscilloscope trace for a single pulse at the maximum output powers of amplifier. The pulse duration was 1.6 ns and the corre sponding peak power was 120 kW. The calculated opti cal intensity on the end facet of the fiber was 27.2 J/cm2 which agrees with the surface damage threshold of fused silica at 1064 nm [34]. The oscillo scope trace of a train of output pulses of the amplifier is shown in Fig. 9c. The pulsetopulse amplitude fluctuation was generally less than 4.0% in rms.
The timing jitters for both the amplifiers shown in Figs. 8 and 9 were generally less than 2% in rms. The
M2 factors were found to be smaller than 1.3 over the entire output power range. Furthermore, the polariza tion extinction ratios for both the amplifiers were mea sured to be about 100:1. Figures 11a and 11b show the optical spectra of the MOFAs at the maximum output powers injected by the seed lasers with T0 = 70 and
T0= 40%, respectively. It can be seen that the peak levels of the amplified spontaneous emission (ASE) around 1040 nm shown in Figs. 11a and 11b were approximately 30 and 40 dB below the signal peak intensity, respectively. The power levels of the whole ASE intensities at the maximum output powers shown
Fig. 10. End view and side view of the damaged fiber.
10 −70 0 −10 −20 −30 −40 −50 −60 Intensity, dBm (a) 1120 1100 1080 1060 1040 1020 1000 Wavelength, nm 20 −60 Intensity, dBm (b) 1120 1100 1080 1060 1040 1020 1000 Wavelength, nm 0 −20 −40
in Figs. 8a and 9a were measured to be less than 2% and 0.5%, respectively.
5. CONCLUSIONS
In conclusion, we have developed compact Nd:YVO4/Cr4+:YAG PQS lasers as seed oscillators for highpeakpower, singlestage, linearpolarized MOFAs. Compact and highpeakpower Nd:YVO4/Cr4+:YAG PQS lasers were theoretically optimized by considering the second threshold crite rion and the thermal lensing effect in a nearly hemi spherical cavity. Several Cr4+:YAG crystals with differ ent initial transmissions (T0) have been used to con firm the performance of the designed PQS laser. It was experimentally found that at a pump power of 5.4 W the output pulse energy increases from 22 to 36 μJ and the pulse repetition rate decreases from 50 to 25 kHz for the initial transmission of the Cr4+:YAG crystal decreasing form 70 to 40%. Injecting the seed laser obtained with T0 = 70% into a polarization main tained Ybdoped fiber, the pulse energy and peak power at a pump power of 16 W were found to be 178μJ and 37 kW, respectively. Employing the seed laser obtained with T0 = 40%, it was found that the surface damage of the fiber limited the maximum pulse energy and peak power to be 192 μJ and 120 kW, respectively. The polarization extinction ratio was approximately 100:1 for both MOFAs in the whole pump power. It is believed that the high peakpower and high polarizationextinctionratio suggest further applications such as industrial material processing and nonlinear optics researches.
ACKNOWLEDGMENTS
The authors thank the National Science Council for the financial support of this research under Con tract no. NSC1002628M009001MY3.
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