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Abstract
The stable condition for π-polarization emission in an a-cut Nd:YLF laser is numerical analyzed to find the critical pump power for generating the orthogonally polarized emission. With the numerical analysis, an orthogonally polarized SML lasers at wavelength of 1047 nm and 1053 nm is experimentally achieved in a simple concave-plano cavity without any additional optical element. It is experimentally observed that the polarization switching and coexistence was successfully demonstrated by introducing gain competition and anisotropic thermal lens effect. In the orthogonal polarization mode-locked operation, the pulse durations are found to be 19.1 and 18.8 ps for π- and σ-polarization with pulse repetition rates of 3.85 and 3.89 GHz, respectively.
© 2017 Optical Society of America
1. Introduction
Over the past few decades, orthogonally polarized dual-wavelength lasers have attracted much attention for applications such as material processing, precision measurement, biomedical instrumentation, optical navigation, and laser interferometry [1–3]. The indispensable criterion for generating the orthogonally polarized dual-wavelength lasers is the balance of gain-to-loss for two orthogonally polarized states. Various schemes have been exploited to generate the orthogonally polarized laser output by incorporating an additional birefringence element into the cavity or using an optical bifurcated fiber to pump birefringence laser crystals [4–8]. On the other hand, the realization of orthogonally polarized dual-wavelength mode-locked lasers [9–14] has aroused considerable interests for the applications including asynchronous optical sampling, control of magnetization, laser spectroscopy, and optical communication [15–19]. Recently, the reliable self-mode-locked (SML) operations in both of Nd-doped and Yb-doped gain media [20–24] have been successfully demonstrated with a repetition rate of up to several GHz by increasing the longitudinal mode spacing to reduce the intensity needed for self-starting. The SML operation without using active elements or saturable absorbers is a feasible way to achieve compact mode-locked lasers.
The Nd:YLF crystal is specifically recognized as a promising laser medium for achieving high-power lasers with excellent beam quality. Practically, the a-cut Nd:YLF crystal has two Stark levels within the 4F3/2→4I11/2 transition which can generate two main output emissions at wavelengths of 1047 nm and 1053 nm, corresponding to π and σ polarizations, respectively. In addition, the biaxial anisotropic features of Nd:YLF crystals, such as the different thermo-optical coefficient and thermo-expansion along a and c axes, enable the Nd:YLF crystals to exhibit a quite different thermal lens effect for a and c direction. Both experimental and theoretical results have demonstrated that the focal lengths of thermal lens along a and c axes are positive and negative, respectively [25,26]. In the previous studies, the Nd:YLF lasers were mainly focused on performance at the emission line either 1047 nm or 1053 nm. Recently, by equalizing the emission cross-section at 1047 and 1053 nm, respectively, the two wavelength pulsed Nd:YLF lasers have been successfully demonstrated [27]. However, the dual-wavelength simultaneously mode-locked Nd: YLF lasers at 1047 nm and 1053 nm have not been explored so far.
In this work, we demonstrate a diode-pumped SML Nd:YLF laser with orthogonally polarized simultaneous emission at 1047 nm and 1053 nm in a simple concave-plano cavity without any additional optical element. We numerically analyze the stable criterion for the π-polarization emission which influenced by the internal thermal lens to explore the gain-to-loss balance for achieving orthogonally polarized emission. It is attractively found that the critical pump power is solely determined by the radius of curvature (ROC) of the input mirror. Based on the numerical analysis, we systematically investigate the influences of the ROC of input mirror on the average output power for the orthogonal π- and σ-polarization. It is found that the experimental results agree very well with numerical calculations for all cases. The excellent agreement between experimental and theoretical results not only confirms that the polarization switching and coexistence was realized by gain competition and anisotropic thermal lens effect but also validates the present model. When the laser mode locked simultaneously at π- and σ-polarization, the pulse durations are found to be 19.1 ps and 18.8 ps respectively, with pulse repetition rates of 3.85 GHz and 3.89 GHz.
2. Numerical analysis
In general, the stimulated-emission cross section at 1047 nm (1.8 × 10−19 cm2) is higher than that at 1053 nm (1.2 × 10−19 cm2). As a result, in order to achieve 1053-nm laser operation, the 1047-nm transition line has to be suppressed. Due to the specifically negative dependence of the refractive index on temperature at π-polarization, there exists a critical power Pcri which the thermal lens will cause the resonator to be unstable and induces a diffraction loss for 1047-nm emission. To analyze the stable criterion for concave-plano cavity, the optical resonator with an internal thermal lens can be replaced by the equivalent g*-parameter and the equivalent cavity length L* which are expressed as [28]
where , D is the effective focal power of the thermal lens, d1 and d2 are the optical path length between the mirrors and the incident end of the gain crystal, and ρi is the ROC of mirror. Considering a concave-plano cavity for ρ1 = ρ and ρ2 → ∞, the equivalent g*-parameters can be given by and . Substituting Eq. (1) into the stable condition of 0 ≤ g1*g2* ≤ 1, the quadratic equations can be expressed as:Here we only consider condition of g1*g2* ≥ 0 because it plays more critical condition to determine the stability of concave-plano cavity under the negative thermal lens effect. After some algebra, the roots of Eq. (2) can be solved asIn the plano-concave resonator, the separation d1 was extremely small that can be neglected and d2 was smaller than the ROC of input mirror. As a results, considering the thermal lens to be negative and setting the separations d1 ≈0, d2 < ρ, the critical focal power Dcri can be obtained asOn the other hand, the theoretical thermal modeling of end-pumped solid-state laser presented by Innocenzi et al., the effective focal length can be approximately expressed by [29]where Kc is the thermal conductivity, ωp is the pump-beam radius in the laser crystal, ξ is the fractional thermal loading, Pin is the pump power, dn/dT is the temperature dependence of the refractive index, and α is the absorption coefficient. From Eqs. (4) and (5), the relationship between the critical pump power and the ROC of input mirror can be given byEquation (6) indicates that the larger ROC of input mirror will decrease the critical pump power which leads the cavity to be unstable for π polarization. In other words, it is possible to suppress the 1047-nm emission and achieve the simultaneous dual-wavelength laser operation with two orthogonal polarizations by controlling the pump power and choosing a suitable ROC of input mirror. In the following, we experimentally demonstrated an orthogonally polarized dual-wavelength laser to confirm this analysis.3. Experimental setup
Figure 1 depicts a schematic of the laser experiment for the Nd:YLF laser. The cavity configuration is a simple concave-flat cavity. The laser gain medium is an a-cut 0.8 at.% Nd:YLF crystal with dimensions of 3 x 3 x 20 mm3. Both the surfaces of gain medium were coated to be anti-reflectance (AR, R < 0.1%) at 806 nm and 1050 nm. The laser crystal was wrapped with indium foil and mounted in a water-cooled cooper holder. The water temperature was maintained at 16 °C to ensure stable laser output. Several concave mirrors with the ROC ranging from 200 to 500 mm were used as the input mirrors to explore the variation of critical pump power for achieving polarization switching. These input mirrors were coated with high-transmittance (HT, T > 95%) at 806 nm and with high-reflectance (HR, R > 99.9%) at 1050 nm. The separations d1 and d2 were fixed to be 2 mm and 27.6 mm to satisfy the resonator stable condition for positive thermal lensing effect. With the refractive indices of nπ = 1.47 and nσ = 1.448, the optical path length can be found to be approximately 39 mm and 38.56 mm for π- and σ-polarization, respectively. A wedged output coupler was coated with partial reflectance (PR, R = 85%) at 1050 nm. The pump source was a 16-W, 806 nm fiber-coupled laser diode with a core diameter of 400 μm and a numerical aperture of 0.16. The average pump diameter with beam radius of 240 μm was reimaged into the laser crystal with a focusing lens with 25-mm focal length and 90% coupling efficiency. A Michelson optical spectrum analyzer (Advantest, Q8347) was employed to monitor the spectrum information with a resolution of 0.003 nm.
Fig. 1 Experimental setup for the dual-wavelength orthogonally polarized self-mode-locked Nd:YLF lasers.
4. Experimental results and discussion
First of all, we explore the average output power of Nd:YLF laser with orthogonal polarizations versus the absorption power with different concave input mirror by placing a polarization beam splitter after the output coupler. The measured output power for the π- andσ-polarized states and the total output power versus the pump powers are shown in Fig. 2. Experimental results revealed that the maximum total output power is nearly the same for all input mirrors and is found to be 3.1 W at the pump power of 9.6 W. In the all input mirrors, it can be seen that the lasing with π-polarization is prior to the lasing with σ-polarization in the vicinity of threshold pump power and the polarization state maintained linear π-polarization until reached its maximum output power. For the case of ROC = 200 mm input mirror, as shown in Fig. 2(a), the output power for π-polarization initially increases linearly with the pump power until the pump power was increased to 7 W, which corresponding to the Pcri. When the pump power exceeded the Pcri, the output power of σ-polarization rose with higher slope efficiency in comparison with the π-polarization and the maximum output power of 1.9 W can be obtained at a pump power of 9.6 W. Similar laser performances with polarization switching and coexistence could also be observed for other three other input mirrors, where the polarization coexistence is also specified by the critical pump power Pcri, as shown in Fig. 2(b)-(d). The polarization-resolved output beam profiles of the two orthogonal outputs were experimentally observed to be near TEM00 fundamental mode, as shown in Fig. 3. By the knife edge method, the beam quality better than 1.3 was calculated under dual-polarized operation.
Fig. 2 Experimental results for the average output power for π- and σ-polarization states and the total output power versus the pump power obtained with different ROC of input mirror: (a)ROC = 200mm, (b) ROC = 300 mm, (c) ROC = 400 mm, (d) ROC = 500 mm.
Fig. 3 Experimental results of laser beam profiles under dual-polarized operation. (a) π-polarization, (b) σ-polarization.
The observed polarization switching and coexistence of the π- and σ-polarization was contributed to the thermal lens effect and gain competition. From the Eq. (6), the relationship between the critical pump power and the ROC of input mirror can be numerically calculated with the following parameters: Kc = 6.3 W/m, ωp = 240 μm, ξ = 0.18 was derived from the quantum defect value and can be expressed as ξ = (1-λp/λl)ηaηc, where λl = 1047 nm, λp = 806 nm, ηa = 0.85 is the absorption efficiency, and ηc = 0.9 is the coupling efficiency of coupling lens, dn/dT = −4.3 × 10−6 K−1, lc = 20 mm, α = 0.18 mm−1. Figure 3 shows the calculated results for the Pcri versus the ROC of input mirrors. For comparison, experimental data are also plotted in Fig. 4. It can be seen that experimental data agree very well with the numerical results. The excellent agreement not only indicates that the orthogonally polarized laser could be achieved by exploiting suitable ROC of input mirror but also validates the present analysis. The evolution of lasing spectra with pump power for a ROC = 300 mm input mirror is shown in Fig. 5(a). The central wavelengths for each polarization state locate at 1047 nm and 1053 nm, respectively. Figure 5(b) and 5(c) show the detailed characteristic of the emission spectrum for the two polarization states. The optical spectral widths can be estimated to be approximately 0.09 nm for both orthogonally polarized states. As depicted in the polarized-resolved output power, the polarization switching and coexistence of π- and σ-polarized modes were observed with the increase of pump power. It is confirmed that orthogonally polarized dual-wavelength lasing can be obtained in a simple cavity without any additional optical component.
Fig. 4 Theoretical and experimental results of the critical pump power as a function of ROC of input mirror for π-polarization emission.
Fig. 5 (a)The lasing spectra at different pump power for ROC = 300 mm input mirror; the detailed characteristic of the emission spectrum for (b)π- polarization, (c) σ-polarization.
The orthogonally polarized mode-locked pulses were detected by a high-speed InGaAs photodetector with rise time of 35 ps (Electro-optics Technology, ET-3500) and the recorded signal was connected to a digital oscilloscope (Agilent, DSO8500) with 12 GHz electrical bandwidth and the maximum sampling intervals of 25 ps. The oscilloscope traces of the mode-locked lasers at wavelength of 1047 nm and 1053 nm are demonstrated in Fig. 6 with two different timescales at the pump power of 5.6 W. It can be seen that the pulse trains display full modulation with amplitude fluctuation better than 2% and the complete mode locking is achieved. The pulse repetition rate is experimentally found to be 3.85 GHz and 3.89 GHz for the laser outputs of π- and σ-polarization, respectively. The physical mechanism of SML is speculated to be associated with the combined effect of the nonlinear optical effect (Kerr-lensing) and thermal lensing.
Fig. 6 The oscilloscope trace of the mode-locked pulses for π-polarization with the time span of: (a) 2 μs and (b) 2 ns; The oscilloscope trace of the mode-locked pulses for σ-polarization with the time span of: (c) 2 μs and (d) 2 ns.
The second-order autocorrelation traces were performed with a commercial autocorrelator (APE GmbH, PulseCheck). Figure 7 shows the full width at half maximum widths of the single pulses in second-order autocorrelation trace for two orthogonal polarizations at pump power of 5.6 W. Assuming the Gaussian-shaped temporal profile, the pulse durations were estimate to be 19.1 ps for π-polarization and 18.8 ps for σ-polarization. Note that the pulse duration for different ROC were experimentally found to be nearly the same of 19 ps for both π- and σ-polarizations. As a result, the time-bandwidth products of mode-locked pulses were estimated to be 0.47 and 0.458 for the π- and σ-polarization, respectively. Both values are slightly larger than the Fourier-limited value of 0.441 and indicate the present pulses to be frequency chirped.
5. Conclusions
In conclusion, we have theoretical analyzed the stable condition for the π-polarization emission with negative thermal lens for achieving orthogonally polarized emission in an a-cut Nd:YLF laser. Based on the numerical analysis, we have employed a simple concave-plano cavity without any additional optical element to generate an orthogonally polarized SML lasers at wavelength of 1047 nm and 1053 nm. It is experimentally found that the polarization switching and coexistence was realized by introducing gain competition and anisotropic thermal lens effect. In the orthogonal polarization mode-locked operation, the pulse repetition rate and the pulse duration are found to be 3.85 (3.89) GHz and 19.1 (18.8) ps for π (σ)-polarization.
Funding
Ministry of Science and Technology of Taiwan (Contract No. MOST 105-2112-M-019-002 -).
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