First of all, the pumping beam was focused right on the optical axis of laser cavity to obtain the maximum output power for fundamental mode. After finely adjusting the cavity alignment, the laser output can be found to display a stable self-mode-locked operation. Subsequently, the modulated mode-locked laser can be generated resulted from transverse modes coupling with off-axis pumping. Note that once the pumped power reaches the lasing threshold, the system instantaneously steps into the stable mode-locked operation. Figure 6.3-1(a) show the experimental pattern with on-axis pumping that was measuring using CCD camera. It can be seen that the laser demonstrates a nearly perfect fundamental mode output beam. The temporal trace for the operation of the single transverse mode is shown in Fig. 6.3-1(b). As shown in the figure, with time span of 50ns, the pulse trains display stable output, and the complete mode-locking is achieved. With off-axis pumping, the output transverse mode was not a fundamental mode but a superposition of the TEM00 as well as TEM10
modes, as shown in Fig. 6.3-1(c). When the laser excited not only the fundamental mode but also the nearly high-order mode, the stable mode-locked pulse trains were modulated. Figure 6.3-1(d) shows the pulse trains with time span 50 ns, demonstrating the modulated mode-locked pulses. Although the laser output was found to display a modulated pulse train, the pulse repetition rate corresponded to the longitudinal frequency spacing was confirmed and the modulated frequency was checked to come
Fig. 6.3-1. Transverse patterns and pulse trains observed in the stable and modulated mode-locked operation. (a) Transverse pattern of pure fundamental mode. (b) Time span of 50 ns, demonstrating stable cw mode-locked pulses.
(c) Transverse patterns of coupling TEM00 and TEM10 modes. (d) Time span of
(c) (d) 5ns/div
(a) (b) 5ns/div
(c) (d) 5ns/div
(a) (b) 5ns/div
141
from the beat of the TEM00 and TEM10 modes. The corresponding power spectrum is depicted in Fig. 6.3-2. With a pumping power of 1.1W, the center frequency is measured around 3.3GHz which corresponding to the pulse repletion rate. Beside the canter frequency, the transverse beat frequencies are also detected with a frequency separation of 288 MHz. The relative frequency deviation, , is experimentally found to be significantly small than 10-4, where the is the center frequency of the power spectrum and is the frequency deviation of full width at half maximum.
The average output power of the modulated mode-locked laser is found approximately 95% of the stable cw mode-locked laser. Figure 6.3-3(a) depicts the average output powers versus the pumped power obtained at modulated mode-locked operation. The slope efficiency for the modulated mode-locked operation can be seen to be approximately up to 56% with respect to the incident pumped power, corresponding to an optical-optical efficiency of 50%. As shown in Fig. 6.3-3(b), the transverse beat frequencies versus the pumped powers are found in the range of 275-336 MHz. It can be seen that, even the weak thermal lensing resulted from low pumped power, the transverse beat frequencies are also can be experimentally measured.
In order to determination the focal power of thermal lens using the transverse beat frequencies method, the concept of the equivalent g-parameters are applied. An optical resonator with an internal thermal lens can be replaced by the empty cavity with the equivalent g-parameters g* and the equivalent cavity length L* which are given by [28]:
i i j 1 mirrors. Because of the internal thermal lens, the Gaussian propagated with wavelength in the cavity exhibits two waists whose position and radius are a function of the focal length of thermal lens. By using the equivalent cavity parameter, the beam waists and their positions are given by
With the conventional model [29], the transverse beat frequencies of the adjacent modes can obtain from the Guoy phase shifts which are related to the Gaussian beam
143
Fig. 6.3-2. Power spectrum in the modulated mode-locked operation.
Fig. 6.3-3. (a) Average output powers versus the pumped powers for the modulated mode locking. (b) Transverse beat frequencies versus the pumped powers in the modulated mode-locked operation.
Absorbed power (W)
145
where Zo 0 is the Rayleigh range. After some algebra, the transverse beat frequencies can be expressed as
1 tan 1 1 1 tan 1 1 tan 1 2 2 tan 1 2
where Tr is the round trip time. For modulated mode-locked at a beat frequency, the focal power are determined from the Eq. (6.3.7). The parameters used in the calculation are as follows: d114.3 mm, d213.3 mm, R1504 mm, R2 . Figure 6.3-4 shows the experimental results of the focal powers versus the pumped powers in the range of 0.45-1.66 m-1. It can be seen that in Fig. 6.3-4, the focal powers of thermal lens can be determined precisely even for very weak thermal lens.
Fig. 6.3-4. The focal powers versus pumped powers in the modulated mode-locked laser.
Absorbed power (W)
0.0 0.5 1.0 1.5 2.0 2.5
Focal power (m-1 )
0.0 0.5 1.0 1.5 2.0
147
6.4 Conclusion
In summary, we have demonstrated a modulated mode-locked Nd:YVO4 laser with the combination of HG TEM0,0 and TEM1,0 modes. The modulated frequency was checked to come from the beat frequency of the TEM00 and TEM10 modes. By using the transverse beat frequency method [23], the focal powers of thermal lens can determined precisely. The transverse beat frequencies were experimentally found in the range of 275-336 MHz at the pumped power from 0.7 to 2.3 W. Corresponding to the beat frequencies, the focal power of thermal lens were obtained in the range of 0.45-1.66 m-1.
[1] A. K. Cousins, “Temperature and thermal stress scaling in finite- length end- pumped laser rods,” IEEE J. Quantum Electron. 28, 1057 (1992)
[2] W. Koechner, Solid-State Laser Engineering, 6th ed. (Springer, New York, 2006), Chap. 7.
[3] Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “ Optimization in scaling fiber-coupling laser-diode end-pumped lasers to high power: influence of thermal effect,” IEEE Quantum Electron. 33, 1424 (1997).
[4] Y. F. Chen, C. F. kao, T. M. Huang, C. L. Wang, and S. C. Wang, “Influence of thermal effect on output power optimization in fiber-coupled laser-diode end-pumped lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 29 (1997).
[5] W. A. Clarkson, “Thermal effects and their mitigation in end-pumped solid-state lasers,” J. Phys. D 34, 2381 (2001).
[6] W. Koechner, “Thermal lensing in a Nd:YAG laser rod,” Appl. Opt. 9, 2548 (1970).
[7] D. C. Burnham, “Simple measurement of thermal lensing effects in laser rods,”
Appl. Opt. 20, 1727 (1970).
[8] D. C. Burnham, “Simple measurement of thermal lensing effects in laser rods,”
149
[9] H. P. Kortz, R. Iffländer, and H. Weber, “Stability and beam div- ergence of multimode lasers with internal variable lenses,” Appl. Opt. 20, 4124 (1981).
[10] K. P. Driedger, W. Krause, and H. Weber, “Average refractive powers of an alexandrite rod,” Opt. Commun. 57, 403 (1986).
[11] D. S. Sumida, D. A. Rockwell, and M. S. Mangiv, “Energy storage and heating measurements in flashlamp-pumped Cr:Nd:GSGG and Nd:YAG,” IEEE J.
Quantum Electron. 24, 98 (1988).
[12] R. Paugstadt and M. Bass, ‘‘A new technique for spatially resolved thermal lensing measurements,’’ Opt. Laser Technol. 24, 151 (1992).
[13] T. S. Chen, V. L. Anderson, and O. Kahan, ‘‘Measurements of heating and energy storage in diode pumped Nd:YAG,’’ IEEE J. Quantum Electron. 26, 6 (1990).
[14] S. C. Tidwell, j. F. Seamans, M. S. Bowers, and A. K. Cousins, “Scaling CW diode-end-pumped Nd:YAG lasers to high average powers,’’ IEEE J. Quantum Electron. 28, 997 (1992).
[15] C. Phstner, R. Weber, H. P. Weber, S. Merazzi, and R. Gruber, ‘‘Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,’’ IEEE J.
Quantum Electron. 30, 1605 (1994).
[16] T. Omatsu, Y. kato, M. Shimosegawa, A. Hasegawa, and I. Ogura, ‘‘Thermal effects in laser diode pumped self-frequency-doubled NdxY1-xAl3(BO3)4(NYAB) microchip laser,’’ Opt. Commun. 118, 302 (1995).
[17] J. L. Blows, J. M. Dawes, and T. Omatsu, ‘‘Thermal lensing measurements in line-focus end-pumped neodymium yttrium aluminium garnet using holographic
lens in solid-state lasers with stable cavity,’’ IEEE J. Quantum Electron. 31, 1082 (1995).
[19] D. G. Lancaster and J. M. Dawes, “Thermal-lens measurement of a quasi steady-state repetitively flashlamp-pumped Cr, Tm, Ho:YAG laser,” Opt. Laser Technol. 30, 103 (1998).
[20] F. Song, C. Zhang, X. Ding, . Xu, G. Zhang, M. Leigh, and N. Peyghambarian,
“Determination of thermal focal length and pumping radius in gain medium in laser-diode-pumped Nd:YVO4 lasers,” Appl. Phys. Lett. 81, 2145 (2002).
[21] Y. T. Chang, Y. P. Huang, K. W. Su, and Y. F. Chen, “Comparison of thermal lensing effects betweem single-end and doubl-end diffusion-bonded Nd:YVO4 crystals for 4F3/2→4I11/2 and 4F3/2→4I13/2 transitions,” Opt. Express 16, 21155 (2008).
[22] B. Ozygus, and Q. Zhang, “Thermal lens determination of end- pumped solid-state lasers using primary degeneration modes,” Appl. Phys. Lett. 71, 2590 (1997).
[23] B. Ozygus and . Erhard, “ Thermal lens determination of end- pumped solid-state lasers with transverse beat frequencies,”Appl. Phys. Lett. 67, 1361 (1995).
[24] H. C. Liang, Ross C. C. Chen, Y. J. Huang, K. W. Su, and Y. F. Chen, “Compact efficient multi-GHz Kerr-lens mode-locked diode-pumped Nd:YVO4 laser,” Opt.
151
Express 16, 21149 (2008).
[25] H. C. Liang, Y. J. Huang, Y. C. Lin, T. H. Lu, Y. F. Chen, and K. F. Huang,
“Picosecond optical vortex converted from multigigahertz self-mode-locked high-order Hermite-Gaussian Nd:GdVO4 lasers,” Opt. Lett. 34, 3842 (2009).
[26] Y. F. Chen, T. M. Huang, C.F. Kao, C. L. Wang, and S. C. Wang, “Generation of Hermite-Gaussian modes in fiber-coupled laser-diode end-pumped lasers,” IEEE.
J. Quantum Electron. 33, 1025 (1997).
[27] H. Laabs and B. Ozygus, “Excitation of Hermite Gaussian modes in end- pumped solid-state lasers via off-axis pumping,” Opt. Laser Technol. 28, 213 (1996).
[28] N. Hodgson and H. Weber, Laser Resonators and Beam Propagation, Second ed.
(Springer, New York, 2005), Chap. 13.
[29] A. E. Siegman, Lasers, (Mill Valley, California, 1986), Chap. 19.
Chapter 7
Summary and Future Work
153