Open Access
Add to BibSonomy
Abstract
We present a SESAM mode locked Yb:CALGO laser with a harmonic repetition rate to the 300th order pumped by a single-mode fiber coupled laser diode. By fine tuning the internal angle between the laser beam and the normal axis through the gain medium, at pump power of 1.2 W, an average output power of 132 mW is achieved with a pulse duration of 777.6 fs and a repetition rate of 22.4 GHz. The amplification effect over several tens of roundtrips induced Fabry-Perot filtering of the anti-reflection (AR) coated gain medium is analyzed. The modulation depth increases and the FWHM of a passband Δυcrystal decreases with increasing roundtrip numbers in the laser crystal. The intra-cavity pulse shaping mechanism with a comb filter caused by the amplified etalon effect of the AR coated laser crystal leads to the overall mode spacing equal to the free spectral range of the gain medium other than the laser cavity and results in the high repetition rate running.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ultrashort laser pulses with repetition rate greater than 10 GHz can be used in the fields of wireless communication [1], telecommunication [2], quantum communication [3], high signal-to-noise ratio measurements [4], photonic switching [5] and large-mode-spacing supercontinuum generation [6]. Harmonic mode locking is a common technique to achieve pulse trains with high repetition rates from long resonators with easy set-up. It is well known from fiber laser technology [7–10], in which harmonic frequencies are obtained by actively intra-cavity phase [11] or amplitude [12] modulation, or passively with the energy quantization effect [13].
Recently, harmonic mode locking in solid state lasers has received more attention due to the development of the high brightness pumps [13,14]. Compared with the low fundamental repetition rate (typically less than 50 MHz) of fiber lasers with long cavity, the shorter cavity length of solid state laser is easy to obtain the higher fundamental repetition rate [13]. Harmonic mode locking in solid state lasers can be realized by either active harmonic mode locking [15] or passive harmonic mode locking [13] techniques. Normally laser diodes with more than several watts output power are necessary to achieve passively harmonic mode locking in solid state lasers. For example, in [16] a 5.5 W distributed Bragg reflector tapered diode-laser (DBR TDL) is used to achieve 4 GHz repetition rate in a SESAM mode locked Yb:KGW laser; in [13] a 8.8 W fiber coupled laser diode is used to acquire 0.98 GHz repetition rate running in a SESAM mode locked Tm:CYA laser; in [14] a fiber-coupled 30 W diode laser is used to obtain 282 MHz repetition rate running in a SESAM mode locked Yb:CALGO laser.
Lasers utilized the intra-cavity pulse shaping mechanism with a comb filter can also be used to help achieving high repetition rate pulses. It has been initially studied in fiber lasers [17–20] by inserting a specially designed fiber grating or an extra etalon in the laser cavity. This technique has also been employed to achieve high repetition rate running in self-mode-locked solid state lasers [21,22]. In these lasers, special crystal coatings of the Yb:YAG laser crystal are applied to form a composite laser cavity, where up to 240 GHz repetition rate pulses can be obtained at 8.3 W absorbed pump power when the optical length of the laser cavity is close to a commensurate ratio of the optical length of the Yb:YAG plate [21]. Still several watts of pump power is needed to achieve high repetition rate lasing.
Tian has found that even high quality antireflection coated optics with parallel surfaces can produce strong spectral modulation [23]. Normally this effect should be avoided to obtain the shortest possible pulses by using wedged optics [24,25]. However in this work, we find that this phenomenon can be employed in a passively SESAM mode locked solid state laser to achieve pulse trains with high repetition rate at low pump power. This is because that the AR coating of the crystal and SESAM helps to maintain the low pump power threshold for mode locking, while the etalon effect helps to shape the intra-cavity pulses to obtain high repetition rate running. Here for the first time, etalon effect directly generated by the anti-reflection coated Yb:CALGO laser crystal is used to achieve high repetition rate running, without extra optical component added in the laser cavity. A SESAM mode locked Yb:CALGO bulk oscillator pumped by a 1.2 W single mode fiber coupled LD has been built to produce femtosecond pulses at 22.4 GHz repetition rate, which corresponds to 300th order harmonic frequency. In this laser system, only 1.1 W pump power is required to achieve such high order harmonic mode locking running. The high repetition rate mode locking can be self-started and was working continuously for over 2 hours. Both experimental results and numerical calculation show that the amplified Fabry-Perot filtering of the gain medium is the key factor that leads to the overall mode spacing equal to the free spectral range of the gain medium other than the laser cavity and results in the high repetition rate running.
2. Experimental setup
The experimental set-up is presented in Fig. 1. In our experiments, an a-cut 5% doped Yb:CALGO crystal of 3.5 mm thickness is used as gain material. The laser transmission surfaces are anti-reflection coated at both pump and lasing wavelengths, shown in Fig. 2 (measured by the crystal manufacture CastechTM). The reflectivity of the AR coating at 1050 nm is about 0.2%. The maximum error of parallelism between these two surfaces is less than 20 seconds, which makes the crystal being considered as an etalon. A single mode fiber coupled 1.2 W laser diode (LD) is used as pump source. OC is a wedged R = 1.5% output coupler. DM is a concave dichroic mirror of radius of curvature 100 mm. M1 and M2 are concave mirrors of radius of curvature 100 mm. M3 and M4 are chirped mirrors offering in total −1200 fs2 GDD. A BatopTM SESAM, which has absorbance of 1%, Δ R of 0.6%, and τ of about 10 ps, is used to help start the mode locking. The Yb:CALGO gain crystal is mounted on a rotation stage to precisely control the internal angle θ between the laser beam and the normal axis through the gain medium.
3. Experimental results
Initially the normal axis through the laser crystal is placed at an angle of larger than 10° to the laser beam. CW (Continuous Wave) mode locking can be obtained at pump power of 300 mW. The mode locked pulse train is detected by the photodiode (Harmoniclaser) and recorded by the oscilloscope (Rohde&Schwarz RTO 1024) and indicates a fundamental repetition rate of around 74.8 MHz, as shown in Fig. 3(a). With increasing pump power, multiple pulsing has been observed. However, no harmonic mode locked pulses can be obtained. Laser spectrum, shown in Fig. 3(b), is recorded by an Optical Spectrum Analyzer (YOKOGAWA AQ6370C), and the Full Width Half Maximum (FWHM) is measured as 9.78 nm. The autocorrelation trace is measured by an autocorrelator (Femtochrome FR-103WS), the FWHM autocorrelation trace width is measured as 366.7 fs. If a Hyperbolic Secant pulse shape is assumed, the FWHM pulse width is calculated as about 238 fs. The time bandwidth product is calculated as 0.629. The time bandwidth product implies us that optimization of total group dispersion delay (GDD) can be expected to further scale down the pulse duration.
Fig. 3 Measured pulse trains (a) and laser emission spectrum (b) in the regime of fundamental mode locking
Then the laser crystal is rotated precisely, we find that stable high repetition rate mode locking can be achieved at a specific angle, where the laser crystal is nearly perpendicular to the laser path. The pump power dependent output power curve is measured and shown in Fig. 4. At low pump power, Q-switching running is firstly obtained. With increasing pump power, laser reaches the Q-switched mode locking operative mode. As long as the pump power is increased to 1.1 W, high repetition rate CW mode locked pulses are produced. Maximum of about 132 mW output power is obtained at 1.2 W pump power. The power fluctuation of the high repetition rate mode locked laser is measured as around 1.6%, which is comparable with a normal mode locking laser. Because of the limited pump power, we only see two data points falling into the harmonic mode-locking regime. However, we think that with increasing pump power, the output power will be scaled up and multipulse bunching harmonic mode locking trains should be expected.
The photodiode and the oscilloscope are initially used to measure the pulse repetition rate and determine the laser working regime. Figure 5(a) shows the pulse train measured by the photodiode and oscilloscope in the HRR mode locking regime. Clearly there is no parasitic pulse train at the fundamental repetition rate shown from the oscilloscope trace. However, due to the low temporal resolution of the photodiode and the oscilloscope, the accurate pulse repetition rate cannot be acquired. The roughly 1 GHz repetition rate shown in Fig. 5(a) corresponds to the 1 GHz response speed of the photodiode used in the experiment. So the autocorrelator is used to measure the repetition rate, as shown in Fig. 5(b). The separation between two pulses is measured as ~44.7 ps, corresponds to the repetition rate of ~22.4 GHz, which is approximately equal to the free spectral range of the gain medium and 300th harmonics of the laser cavity mode spacing. From the autocorrelation trace, it can be seen that there is a pedestal on the trace and pulse-to-pulse amplitudes fluctuate slightly, which might indicate supermodes oscillation exits in the laser. The FWHM autocorrelation trace width of a single pulse is measured as around 1.2 ps, if a Hyperbolic Secant pulse shape is assumed, the FWHM pulse width is calculated as about 777.6 fs. From Fig. 5(b), a relatively large background is seen, which indicates existence of CW components in the laser output. It is believed that the CW components, through which the globe pulse interaction mediated, help to achieve high-order harmonic mode locking [26,27]. The laser spectrum is strongly modulated as presented in Fig. 5(c). The modulation in the spectrum has a period of ~0.084 nm corresponded to the amplified etalon effect of the laser crystal, which will be discussed later in detail. Few irregular deep modulations in the measured spectrum and a spike in the center section of the spectrum have also been observed. We think these deep modulations are probably the sidebands in the spectrum which has already been observed in harmonic mode locked lasers [26,27]. While the center spectrum spike actually confirms the existence of the CW components in the laser output. Unfortunately the RF spectra has not been taken in the experiments due to the lack of RF-spectrum analyzer in our lab.
Fig. 5 Measured pulse trains from oscilloscope (a) and autocorrelator (b), laser emission spectrum (c) in the regime of harmonic mode locking.
From the experiments, we find that the internal angle θ will influence the laser performance, which is checked and recorded in Fig. 6. It is clear that from the defination of θ, θ = 0° means the laser crystal is absolutely perpendicular to the laser light path. We define the critial internal angle where the laser is working under the HRR mode locking condition shown in Fig. 5 as θc. When the angle is rotated away from θc, either Q-switching mode locking (when θ approaches to 0°) or unstable harmonic mode locking (when θ changes farther away from 0°) will be observed as shown in Fig. 6. In our opinion, there might be two reasons for Q-switching mode locking running. Firstly, Q-switching mode locking running happens due to the internal angle θ being too close to be 0°, where reflections from the crystal surfaces will destroy the mode locking. Secondly, the cavity loss caused by the amplified etalon effect in laser crystal will be increased with increasing roundtrips when the normal axis of laser crystal is closer to the laser light path. As a result, the laser output power decreases as can be seen from Fig. 6, hence the intra-cavity pulse energy is not strong enough to start the stable CW mode locking running. When the axis of laser crystal is turning farther away from laser light path, harmonic mode locking running will become more and more unstable, as shown in the inset in Fig. 6. We think this may be due to the decreasing of roundtrip numbers in the laser crystal by increasing the internal angle θ, which weakens the amplified etalon effect. When the internal angle θ is large enough, harmonic mode locking will be no longer observed.
4. Theoretical analysis of amplified etalon effect in laser crystal
It is already known that even less than 0.5% reflectivity could produce strong wavelength modulation in a laser cavity because of the amplification effect over several tens of round trips [23,28]. If we do not consider gain competition, the amplitude of the wavelength modulation can be estimated approximately by Eq. (1):
where Tcrystal is the spectrum transmission curve of the laser crystal which is assumed as an etalon, G is the laser emission spectrum curve and N is the roundtrip numbers for Eq. (2), F is denoted as finesse coefficient and δ is the phase difference. where R = 0.2% is the residual reflectivity of the laser crystal’s AR coating, λ0 = 1053.73 nm is the center wavelength, d = 3.5 mm is the thickness of the laser crystal, and n = 1.85 is the refractive index of Yb:CALGO crystal. For Eq. (3), the laser emission spectrum curve G is assumed as a Gaussian function, where Δλ = 9.78 nm is the FWHM of the laser spectrum.From Eqs. (1)-(5), we find that the modulation spectrum is a function of roundtrip numbers. The simulation results are shown in Fig. 7. If the laser crystal is tilted far enough to the laser light path, the beams reflected from the two faces of the crystal do not overlap, hence the etalon effect can be ignored. Figure 7(a) shows the Gaussian shape laser emission spectrum centered at ~1053.73 nm with FWHM of 9.78 nm without etalon effect. However, if the laser crystal is nearly perpendicular to the laser light path, the etalon effect has to be considered. Figure 7(b) shows the calculated overall transmission spectrum of the laser crystal after 1, 10 and 150 roundtrips respectively. From Fig. 7(b), the amplified etalon effect in laser crystal after 150 roundtrips has produced a modulation in the spectrum with a minimum transmission of about 10% at center wavelength. This modulation has a period of around 0.084 nm at the center wavelength, which corresponds to the thickness of the crystal. The whole spectrum was narrowed compared with the laser spectrum obtained without the etalon effect as shown in Fig. 7(a). Compared with Fig. 5(c), the calculated results are in good agreement with the experimental results.
Fig. 7 Calculated laser emission spectrum (a) without etalon effect; (b) with weak etalon effect: - black curve 1 round-trip, - blue curve 10 round-trips, - red curve 150 round-trips.
FWHM of a passband and modulation depth at center wavelength with varying roundtrips has been solved numerically and presented in Fig. 8. From both Figs. 7(b) and 8, we find that if the roundtrip number increases, the modulation depth increases and the FWHM of a passband Δυcrystal decreases. It is clear that if the modulation depth is too small, the filtering effect is not strong enough to shape the intra-cavity pulses. Hence the stable high repetition rate running cannot be achieved. This explains why harmonic mode locking running will become more and more unstable with increasing internal angle θ. It is also known that the supermode noise intensity is linearly proportional to the number of optical supermodes excited [29], i.e. the supermode noise is proportional to Δυcrystal/υc. Here Δυcrystal is the full width at half maximum of a passband and υc = c/2lcav is the cavity fundamental frequency. So for a 3.5 mm AR coated Yb:CALGO crystal, there is around hundred supermodes beating which causes the fluctuated pulse-to-pulse amplitude, as shown in Fig. 5(b). From the simulation, we know that in order to suppress the supermode noise, longer crystal with slightly higher reflectivity coating, as well as shorter laser cavity can be employed. For example, if a 10 mm laser crystal with R = 0.5% coating running in a ~0.111 m long laser cavity, the laser crystal can be regarded as a narrowband Fabry-Perot which can select only one supermode, as shown in Fig. 9. In this way, the supermode noise may be highly suppressed by actively controlling the laser cavity length, which will be studied later by us.
Fig. 8 Numerically calculated roundtrip number dependent FWHM of a passband (-■ -) and modulation depth (-●-) at center wavelength.
Fig. 9 Laser cavity mode frequencies (blue line) superimposed upon the transmission function of the laser crystal etalon (black line): central laser cavity mode aligned with the peak etalon mode by fine tuning the laser cavity length.
5. Conclusion
Harmonic mode locked solid state lasers have received more attention recently due to its shorter cavity compared with fiber lasers, i.e. it is easier to obtain higher fundamental repetition rate. However high pump power are normally required to achieve passively harmonic mode locking in solid state lasers, which limits its application. In this paper, we find out that by employing the amplified etalon effect of the laser crystal, we can decrease the pump power required to achieve high repetition rate. A SESAM mode locked single mode fiber coupled LD pumped Yb:CALGO laser has been built in this paper. It is experimentally found that the single pulse harmonically mode locked operation can be acquired by adjusting the internal angle between the laser beam and the normal axis through the gain medium. At pump power of 1.2 W, an average output power of 132 mW is achieved with a pulse duration of 777.6 fs and a repetition rate of 22.4 GHz. The high repetition rate mode locking can be self-started and was working continuously for over 2 hours. From the theoretical analysis, we found that the AR coated gain medium is also act as an etalon. With increasing of the roundtrip number, the modulation depth increases and the FWHM of a passband Δυcrystal decreases. The intra-cavity pulse shaping mechanism with a comb filter caused by the amplified etalon effect of the AR coated laser crystal is the key factor that leads to the overall mode spacing equal to the free spectral range of the gain medium other than the laser cavity and results in the high repetition rate running. The system can be easily transferable to other gain media. Based on this technique, sub-picosecond high repetition rate over 10 GHz oscillators with a simply implementable set-up long resonator without additional components are available. In the future, optimization of the reflection coating and the length of the laser crystal, as well as the laser cavity length may be employed to further increase the mode locking repetition rate and suppress the supermode noise.
Funding
National Natural Science Foundation of China (Grant No. 61605133). Sichuan Province International Cooperation Research Program, China (Grant No. 2016 HH0033). Chengdu Science and Technology Program, China (Grant No. 2015-GH02-00021-HZ)
Acknowledgments
We would like to thank Dr. Zongzhi Lin from Castech for measuring the reflectivity of AR coating of Yb:CALGO laser crystal
References and links
1. J. Federici and L. Moeller, “Review of terahertz and subterahertz wireless communications,” J. Appl. Phys. 107(11), 111101 (2010). [CrossRef]
2. T. Tomaru and H. Petek, “Femtosecond Cr4+:YAG laser with an L-fold cavity operating at a 1.2-GHz repetition rate,” Opt. Lett. 25(8), 584–586 (2000). [CrossRef] [PubMed]
3. C. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable Einstein-Podolsky-Rosen entanglement via the Kerr nonlinearity in an optical fiber,” Phys. Rev. Lett. 86(19), 4267–4270 (2001). [CrossRef] [PubMed]
4. A. Bartels, T. Dekorsy, and H. Kurz, “Femtosecond Ti:sapphire ring laser with a 2-GHz repetition rate and its application in time-resolved spectroscopy,” Opt. Lett. 24(14), 996–998 (1999). [CrossRef] [PubMed]
5. D. A. Miller, “Optics for low-energy communication inside digital processors: quantum detectors, sources, and modulators as efficient impedance converters,” Opt. Lett. 14(2), 146–148 (1989). [CrossRef] [PubMed]
6. A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz self-referenced optical frequency comb,” Science 326(5953), 681 (2009). [CrossRef] [PubMed]
7. K. Harako, M. Yoshida, T. Hirooka, and M. Nakazawa, “770 fs Harmonically and Regeneratively FM Mode-Locked Erbium Fiber Laser in L-Band,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2017), paper SM4L.2. [CrossRef]
8. L. Li, Y. Su, Y. Wang, X. Wang, Y. Wang, X. Li, D. Mao, and J. Si, “Femtosecond passively Er-doped mode-locked fiber laser with WS2 solution saturable absorber,” IEEE J. Sel. Top. Quantum Electron. 23(1), 44–49 (2017). [CrossRef]
9. A. B. Grudinin, D. J. Richardson, and D. N. Payne, “Passive harmonic modelocking of a fibre soliton ring laser,” Electron. Lett. 29(21), 1860–1861 (1993). [CrossRef]
10. B. Grudinin and S. Gray, “Passive harmonic mode locking in soliton fiber lasers,” J. Opt. Soc. Am. B 14(1), 144–154 (1997). [CrossRef]
11. C. X. Yu, H. A. Haus, E. P. Ippen, W. S. Wong, and A. Sysoliatin, “Gigahertz-repetition-rate mode-locked fiber laser for continuum generation,” Opt. Lett. 25(19), 1418–1420 (2000). [CrossRef] [PubMed]
12. T. F. Carruthers, I. N. Duling, and M. L. Dennis, “Active-passive modelocking in a single-polarisation erbium fibre laser,” Electron. Lett. 30(13), 1051–1053 (1994). [CrossRef]
13. W. Zhou, X. Fan, H. Xue, R. Xu, Y. Zhao, X. Xu, D. Tang, and D. Shen, “Stable passively harmonic mode-locking dissipative pulses in 2µm solid-state laser,” Opt. Express 25(3), 1815 (2017). [CrossRef]
14. H. M. Bensch, G. Herink, F. Kurtz, and U. Morgner, “Harmonically mode-locked Yb:CALGO laser oscillator,” Opt. Express 25(13), 14164–14172 (2017). [CrossRef] [PubMed]
15. M. F. Becker, D. J. Kuizenga, and E. Siegman, “Harmonic Mode Locking o f the Nd:YAG Laser,” IEEE J. Quantum Electron. 8(8), 687–693 (1972). [CrossRef]
16. S. Pekarek, C. Fiebig, M. C. Stumpf, A. E. H. Oehler, K. Paschke, G. Erbert, T. Südmeyer, and U. Keller, “Diode-pumped gigahertz femtosecond Yb:KGW laser with a peak power of 3.9 kW,” Opt. Express 18(16), 16320–16326 (2010). [CrossRef] [PubMed]
17. D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high-repetition-rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photonics Technol. Lett. 13(3), 221–223 (2001). [CrossRef]
18. J. Schröder, D. Alasia, T. Sylvestre, and S. Coen, “Dynamics of an ultrahigh-repetition-rate passively mode-locked Raman fiber laser,” J. Opt. Soc. Am. B 25(7), 1178–1186 (2008). [CrossRef]
19. J. S. Wey, J. Goldhar, and G. L. Burdge, “Active harmonic modelocking of an erbium fiber laser with intracavity Fabry-Perot filters,” J. Lightwave Technol. 15(7), 1171–1180 (1997). [CrossRef]
20. G. T. Harvey and L. F. Mollenauer, “Harmonically mode-locked fiber ring laser with an internal Fabry-Perot stabilizer for soliton transmission,” Opt. Lett. 18(2), 107–109 (1993). [CrossRef] [PubMed]
21. Y. F. Chen, W. Z. Zhuang, H. C. Liang, G. W. Huang, and K. W. Su, “High-power subpicosecond harmonically mode-locked Yb: YAG laser with pulse repetition rate up to 240 GHz,” Laser Phys. Lett. 10(1), 015803 (2013). [CrossRef]
22. T. W. Wu, C. H. Tsou, C. Y. Tang, H. C. Liang, and Y. F. Chen, “A high-power harmonically self-mode-locked Nd: YVO4 1.34-μm laser with repetition rate up to 32.1 GHz,” Laser Phys. 24(4), 045803 (2014). [CrossRef]
23. C. Tian, S. Goldstein, and E. S. Fry, “On the etalon effect generated by a Pockels cell with high-quality antireflection coatings,” Appl. Opt. 39(10), 1600–1601 (2000). [CrossRef] [PubMed]
24. D. Kuizenga and A. Siegman, “FM and AM mode locking of the homogeneous laser-Part I: Theory,” IEEE J. Quantum Electron. 6(11), 694–708 (1970). [CrossRef]
25. D. Kuizenga and A. Siegman, “FM and AM mode locking of the homogeneous laser-Part II: Experimental results in a Nd: YAG laser with internal FM modulation,” IEEE J. Quantum Electron. 6(11), 709–715 (1970). [CrossRef]
26. Z. X. Zhang, L. Zhan, X. X. Yang, S. Y. Luo, and Y. X. Xia, “Passive harmonically mode-locked erbium-doped fiber laser with scalable repetition rate up to 1.2 GHz,” Laser Phys. Lett. 4(8), 592–596 (2007). [CrossRef]
27. F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, P. Grelu, and F. Sanchez, “Passively mode-locked erbium-doped double-clad fiber laser operating at the 322nd harmonic,” Opt. Lett. 34(14), 2120–2122 (2009). [CrossRef] [PubMed]
28. X. Dangpeng, W. Jianjun, L. Mingzhong, L. Honghuan, Z. Rui, D. Ying, D. Qinghua, H. Xiaodong, W. Mingzhe, D. Lei, and T. Jun, “Weak etalon effect in wave plates can introduce significant FM-to-AM modulations in complex laser systems,” Opt. Express 18(7), 6621–6627 (2010). [CrossRef] [PubMed]
29. S. Gee, F. Quinlan, S. Ozharar, and P. J. Delfyett, “Correlation of supermode noise of harmonically mode-locked lasers,” J. Opt. Soc. Am. B 24(7), 1490–1497 (2007). [CrossRef]
