Orthogonally Polarized Dual-Wavelength Pr:LLF Green Laser at 546 nm and 550 nm with the Balanced Output Powers at All Pump Power Level

Abstract

A continuous-wave (CW) orthogonally polarized dual-wavelength (OPDW) Pr³⁺:LiLuF₄ (Pr:LLF) green laser with a balanced output power on the ³P₀→³H₅ transition was demonstrated for the first time. We theoretically analyzed the conditions for achieving equal output power in the OPDW laser operation using two intracavity etalons and experimentally realized the OPDW green laser in a Pr:LLF crystal. Under pumping with a frequency-doubled optically pumped semiconductor laser (2ω-OPSL) generating 10 W at 479 nm, an OPDW green laser at 546 nm in π-polarization and 550 nm in σ-polarization was obtained with a total output power of 1.68 W. The output powers of the two wavelengths were equal for all the pump power levels. Further, a CW ultraviolet (UV) laser at 274 nm by intracavity sum-frequency mixing was also achieved with a maximum output power of 386 mW. The OPDW Pr:LLF green lasers with the balanced output power were desirable for medical detection and the generation of UV lasers.

1. Introduction

Dual-wavelength (DW) lasers in the visible region are pivotal in biomedical diagnostics and environmental sensing. For instance, in non-invasive blood glucose monitoring, simultaneous DW laser emission in the green region enables differential absorption measurements of hemoglobin derivatives, enhancing the measurement accuracy by compensating for tissue scattering artifacts [1]. Additionally, DW lasers are employed in LiDAR-based atmospheric pollutant detection, where DW lasers in the orange-red region allow real-time discrimination of aerosols and trace gases like nitrogen dioxide, through wavelength-dependent backscattering analysis [2]. In particular, OPDW lasers have found extensive applications in advanced photonic systems, including differential interference imaging for high-resolution surface profiling, LiDAR-based 3D reconstruction, CW terahertz (THz) generation through optical parametric oscillation, and ultra-precision metrology with sub-nanometer displacement sensitivity. Their inherent polarization diversity enables noise suppression in coherent detection schemes, while facilitating wavelength-division multiplexing (WDM) for dual-channel signal processing [3,4,5,6,7]. At present, OPDW operation in solid-state lasers can be achieved either by two Stark energy level transitions of the gain medium [8,9,10,11,12] or by two laser crystals with perpendicular optical axes [13,14,15]. However, the output powers of the two emission wavelengths generated by these two methods cannot always be maintained in balance, which severely limits their application. For example, only equal fundamental powers can guarantee efficient nonlinear sum- or difference-frequency generation. The main reason for the power imbalance was that the first method was due to gain competition between the two transition lines in a single crystal [8], and the second method was due to the competition of pump power in the composite crystals [13]. Although the OPDW laser may occasionally exhibit balanced output powers, it does so only at a certain pump power level, and this is not the optimal balance power. To address this challenge, we introduce a novel method that can balance the output powers of the two wavelengths at each pump power level. Host materials doped with trivalent rare-earth (RE) ions (Pr³⁺, Dy³⁺, Sm³⁺, Er³⁺, and Eu³⁺) enable visible wavelength generation. Pr³⁺-based gain media exhibits enhanced visible emission efficiencies compared to other RE³⁺ [16,17,18,19,20,21,22]. The power scaling of Pr³⁺-doped laser systems has been significantly enhanced by advancements in high-power blue laser diodes (LDs) [23,24,25,26,27,28,29]. However, Pr³⁺-doped lasers have mainly focused on single-wavelength generation, while DW lasers in Pr³⁺-doped laser crystals have rarely been reported. For instance, we realized the first visible OPDW laser emission in a Pr:YLF crystal in 2015, and the output powers of the two wavelengths were 184 mW (546 nm) and 158 mW (550 nm), respectively. In 2023, Jin et al. reported an OPDW single-longitudinal-mode Pr:YLF orange laser at 607 nm and 604 nm, with corresponding output powers of 201 mW and 81 mW, respectively [30].

LiLuF₄ (LLF) shares the same crystal structure as uniaxial LiYF₄ (YLF) [31]. The crystal permits the substitution of Lu³⁺ ions with other trivalent rare-earth ions without requiring additional charge carriers or structural adjustments. Similar to YLF, its refractive index exhibits a negative temperature coefficient, minimizing the thermal lensing effects while maintaining a closer alignment of the thermal expansion coefficients and thermal conductivities across different crystallographic axes [32]. Notably, LLF undergoes completely congruent crystallization, in contrast to the incongruent solidification of YLF. This characteristic eliminates the need for excess LiF during growth, preventing the formation of micro-inclusions that compromise optical quality. These advantages have enabled successful laser operations in various rare-earth-doped LLF variants, including Sm³⁺, Nd³⁺, Ho³⁺, Tm³⁺, and Yb³⁺ dopants [33,34,35,36,37]. Cornacchia et al. first reported on the spectral properties of the Pr:LLF crystal, and the single-wavelength laser emissions at 523 nm, 607 nm, 640 nm and 722 nm have been obtained [38]. However, to the best of our knowledge, DW lasers in Pr:LLF crystals have not been reported to date. Figure 1 presents the emission cross-sections of an a-cut Pr:LLF crystal in the two polarized directions in the 510–560 nm spectral range, which was calculated using the Fuchtbauer-Ladenburg (F-L) formalism [39]. It can be seen in Figure 1, the maximum emission peak of the Pr:LLF crystal was 523 nm in the π-polarization on the ³P₁→³H₅ transition. Emission spectrla analysis demonstrates that the Pr:LLF crystal exhibits nearly identical emission cross-sections for π- and σ-polarizations, measured at 546 nm (0.90 × 10⁻²⁰ cm²) and 550 nm (1.1 × 10⁻²⁰ cm²), corresponding to the ³P₀→³H₅ transition energy transition. Therefore, the Pr:LLF crystal was suitable for producing OPDW green laser emission via the ³P₀→³H₅ transition. In this work, a CW OPDW Pr:LLF green laser at 546 nm and 550 nm with balanced output power was achieved, which is desirable for medical detection and the generation of UV lasers. For instance, carboxyhemoglobin (COHb) concentration can be quantitatively assessed via differential absorbance measurements at 546 nm and 550 nm in the green spectral region, enabling precise determination of carbon monoxide (CO) poisoning severity [40] and UV laser generation via type-II critical phase matching sum-frequency mixing. At an absorbed pump power of 9.0 W, the total output power obtained at 546 and 550 nm was 1.68 W with equal output power. In addition, a CW UV laser at 274 nm by intracavity sum-frequency mixing was also achieved with a maximum output power of 386 mW. CW UV lasers in the 250–300 nm range have garnered significant attention due to their emerging technological capabilities and wide-ranging applicability across multiple high-impact domains. These UV lasers are particularly promising for advancing spectral analysis precision, enabling ultrafine microfabrication at nanoscale resolutions, enhancing sensitive chemical detection, and revolutionizing biomedical research through advanced imaging and diagnostics [41,42,43].

2. Theoretical Analysis

The 546 and 550 nm transition lines of the Pr:LLF crystal produce gain competition because of the different emission cross-sections, and the OPDW green laser oscillation cannot be generated simultaneously. To achieve OPDW green laser operation, the first uncoated etalon (E₁) was placed in the cavity. The a-axis of the Pr:LLF crystal was set to the vertical direction, and the inclined angle of E₁ was relative to the cavity axis, with the incident plane in the horizontal direction, as shown in Figure 2a. The results showed that the π- (P-wave) and σ- (S-wave) polarizations were parallel and perpendicular to the incident plane.

The inclined angle (θ₁) of the laser beam was the same as that of E₁. The cavity round-trip losses, L_i (θ₁), caused by the Fresnel equation for the two orthogonally polarized waves can be written by [44]

$$L_i\left({\theta }_1\right)=R_i+\left(1-R_i\right)R_i$$

(1)

where the subscripts i = S and P represent the S- and P-waves, respectively, and R_i is the reflectivity of E₁, which depends on the inclined angle θ₁ of E₁. R_s = sin²(θ₁−θ_t)/sin²(θ₁ + θ_t), R_p(θ₁) = tan²(θ₁−θ_t)/tan²(θ₁ + θ_t), sinθ₁ = nsinθ_t, and n =1.5 is the refractive index of the E₁. The losses in the two polarized directions were calculated as a function of the inclined angle θ₁, as shown in Figure 3. As can be seen from Figure 3, as the inclined angle increases, the two losses are separated.

For the four-level system, the absorbed pump threshold of laser transition wavelength in an OPDW laser operation is described by [45]

$$P_{tha,j}={\displaystyle \frac{-\ln (1-T_{oc})+L_i}{2f_j{\eta }_{q,j}}}{\displaystyle \frac{\pi h{\nu }_p}{{\sigma }_j{\tau }_j}}{\displaystyle \frac{{\omega }_p^2}{1-\exp \left(-2{\omega }_p^2/{\omega }_j^2\right)}}$$

(2)

where the subscript j = 546, 550 represents the 546 nm and 550 nm wavelengths, respectively; T_oc is the transmittance of M₂; f is the fraction of the population of the upper energy level; η_q is the quantum efficiency; hν_p is the pump photon energy; σ is the stimulated emission cross-section; τ is the fluorescence lifetime at the upper level; ω_p is the pump spot radius; and ω is the laser spot radius, which was determined by the thermal lens of the Pr:LLF crystal and can be computed using the ABCD matrix. The focal lengths of the thermal lens for the gain medium can be calculated as [46]

$$f_{th,j}={\displaystyle \frac{\pi K_{c,j}{\omega }_p^2}{{\xi }_j{P}_{abs}{\left(dn/dT\right)}_j}}$$

(3)

where K_c is the thermal conductivity, ξ is the heat conversion coefficient, and dn/dT is the thermal chromatic dispersion coefficient. Using Equations (2) and (3) and the experimental parameters: T_oc = 0.01, η_q, 546 ≈ η_q,550 = 0.74, σ₅₄₆ = 0.90 × 10⁻²⁰ cm², σ₅₅₀ = 1.1 × 10⁻²⁰ cm², hν_p = 4.18 × 10⁻¹⁹ J, τ₅₄₆ = τ₅₅₀ = 48 μs, and ω_p = 100 μm, the laser thresholds were calculated as a function of the inclined angle of E₁, as shown in the inset of Figure 3. It can be seen in Figure 3, the laser thresholds of the two wavelengths have an intersection point at θ₁ ≈ 15°. At an inclined angle of less than 15°, the threshold for the stronger transition line (550 nm) is larger than that for the weaker line (546 nm), and the weaker 546 nm line cannot be obtained due to gain competition between the two transitions. Therefore, in order to realize the OPDW laser output simultaneously, the inclined angle of E₁ must be greater than or equal to 15°.

To make the gain-to-loss balancing at each pump power level and beyond P_tha,i more intuitive, we recall the output power (P_out,j), which is given by [47]

$$P_{out,j}={\displaystyle \frac{-\ln (1-T_{oc}){\eta }_j}{-\ln (1-T_{oc})+L_i\left({\theta }_1\right)}}\left(P_{abs}-P_{tha,j}\right)$$

(4)

Equation (4) also shows the expanded form of the slope efficiency with respect to the absorbed pump power (η_sa,j) of a given laser system η_sa,j = P_out,j/(P_abs − P_tha,j), so the slope efficiency can be written

$${\eta }_{sa,j}={\displaystyle \frac{-\ln (1-T_{oc}){\eta }_j}{-\ln (1-T_{oc})+L_i\left({\theta }_1\right)}}$$

(5)

It can be seen in Equation (5), η_sa,546 > η_sa, 550 when L₅₅₀ (θ₁) > L₅₄₆(θ₁). To more intuitively understand the relationship between the two slope efficiencies, we use Figure 4 to illustrate the slope efficiencies of the 546 and 550 nm wavelengths. Figure 4a shows the slope efficiencies of the two wavelengths at P_tha,546 = P_tha,550, which are similar. As shown in Figure 4a, there is no intersection between the two slope efficiencies; therefore, the output powers of the two wavelengths cannot be balanced at all pump levels. Similarly, the output powers of the two wavelengths cannot be balanced at P_tha,550 > P_tha,546, as shown in Figure 4b. To solve this problem, a second etalon (E₂) was placed inside the cavity. The inclination of E₂ was relative to the vertical direction of the cavity, and the plane of incidence was in the vertical direction, as shown in Figure 2b. The result was that the σ- (P-wave) and π- (S-wave) polarizations were parallel to and perpendicular to the incident plane, which was exactly opposite to the two polarization directions corresponding to E₁. Therefore, L (θ₂) < L′_p (θ₂) when E₂ is placed, as shown in Figure 2b. L (θ₂) and L′_p (θ₂) were reflective losses of 550 nm and 546 nm, respectively, which were caused by E₂. The newly introduced loss from E₂ reduces the slope efficiency and increases the laser oscillation threshold for S- and P-waves. Importantly, by properly adjusting E₂, the laser oscillation threshold of 546 nm can be shifted to a higher value than that of 550 nm. The slope efficiencies of the two wavelengths were different, and the slope efficiencies must have an intersection point; therefore, the 546 and 550 nm wavelengths can obtain equal output power, and the effect is shown in Figure 4c. We fixed the incident angle of E₁ at 15°, and then adjusted E₂.

The losses at 550 and 546 nm were L′₅₅₀ (θ₂) = 0.085 + L′_p(θ₂) and L′₅₄₆ (θ₂) = 0.071 + L′_s(θ₂), respectively. When the output power of the 546 nm and 550 nm wavelengths was equal, it could be obtained according to Equation (4)

$${\displaystyle \frac{{\eta }_{550}\left(P_{abs}-P_{tha,550}\right)}{-\ln (1-T_{oc})+{L^{\prime }}_{550}\left({\theta }_2\right)}}={\displaystyle \frac{{\eta }_{546}\left(P_{abs}-P_{tha,546}\right)}{-\ln (1-T_{oc})+{L^{\prime }}_{546}\left({\theta }_2\right)}}$$

(6)

According to Equation (6), the inclined angle of E₂ was calculated as a function of the absorbed pump power, as shown in Figure 5. As can be seen from Figure 5, when the inclined angle of E₂ and the absorbed pump power meet the relationship of the curve, the balanced output power of 546 nm and 550 nm can be realized.

Using Equations (4) and (6), the relationship between the balanced output power of the two wavelengths, the absorbed pump power, and the inclined angle of E₂ was calculated, as shown in Figure 6. It can be seen in Figure 6, the balanced output power increases monotonically with an increase in the absorbed pump power and the inclined angle of E₂. In fact, the output power increases linearly with the pump power, as shown in Figure 5. Note that to change the absorption pump power level, the inclined angle of E₂ must be adjusted accordingly, according to the curve in Figure 5.

3. Experimental Setup

A schematic of the OPDW Pr:LLF green laser is shown in Figure 7. The optical pumping system employed a 2ω-OPSL delivering a maximum output power of 10 Watts at 479 nm with a beam quality factor of M² = 3.5. A collimating lens assembly (L₁) was integrated within the laser module to ensure uniform beam profile propagation, followed by a 50 mm focal-length lens (L₂) positioned to precisely focus the pump radiation onto the Pr:LLF crystal. The plane mirror (M₁) functioned as the input coupler, which was antireflection (AR) coated (479 and 523 nm) while exhibiting high-reflectivity (HR) performance across the 545–555 and 274 nm spectral ranges.

The concave mirror (M₂) functioned as the output coupler, with a radius of curvature of −200 mm and a transmittance of 1.0% at 545–555 nm. Three different output couplers (0.5, 1.0, and 2.0%) were used in the experiments, and the performance was best when the output coupler was 1.0%. The laser gain medium was an a-cut Pr:LLF crystal 5 mm long and 0.2 at. % doped Pr³⁺, which was AR coated at 274 nm and 545–555 nm. The Pr:LLF crystal was thermally encapsulated using indium foil to enhance the thermal contact and mounted onto precision water-cooled copper mounts maintained at 16 °C to mitigate thermal lensing effects and ensure stable optical performance under continuous-wave pumping conditions. Two identical etalons, each with a thickness of 0.15 mm, were employed to separate the wavelength losses of the two polarized directions.

4. Results and Discussion

First, a single-wavelength operation was performed in the absence of E₁ and E₂ to investigate the green laser output performance of the Pr:LLF crystal. Figure 8 shows the relationship between the 550 nm output power and the 479 nm pump power. The laser threshold was set to 1.21 W. The output power reached 2.6 W at an absorbed pump power of 9.5 W (equivalent to an incident pump power of 10 W). The corresponding slope and optical-to-optical conversion efficiencies with respect to the absorbed pump power were 31.1% and 27.4%, respectively. The laser output at 550 nm was along the σ-polarized direction of the Pr:LLF crystal.

Then, to obtain the OPDW green laser operation, only E₁ was inserted into the laser cavity to balance the gain-to-loss between the 546 and 550 nm wavelengths. We controlled the inclined angle of E₁ to about 15° to obtain P_tha,550 > P_tha,546 and successfully achieved green OPDW lasing. The green OPDW laser output was separated using a polarizing beam splitter (PBS), with simultaneous measurement of the individual wavelength powers. Figure 8 shows the recorded output power for each lasing wavelength as a function of the 479 nm absorbed pump power. It was observed that the 546 nm wavelength achieved lasing prior to the 550 nm wavelength as a result of the σ-polarization being initially suppressed by the inclined E₁. The thresholds of the absorbed pump power were 1.85 W at 546 nm and 2.30 W at 550 nm, which were consistent with the calculation in the insert of Figure 3. At an absorbed pump power of 9.5 W, a CW total output power of 2.1 W (1.3 W at 546 nm and 0.8 W at 550 nm) was obtained. The total optical-to-optical conversion efficiency of the absorbed pump power was 22.1%.

Finally, to achieve OPDW green laser operation with equal output powers, both E₁ and E₂ were placed in the cavity. The equal output powers at 546 and 550 nm versus the absorbed pump power and the inclined angle of E₂ are shown in Figure 9. The dual output powers of the OPDW green laser were sensitive to changes in the pumping and inclination of E₂; however, the equal output powers at each absorbed pump power level could be achieved by adjusting E₂. The inclination of E₂ was mainly between 0° and 13°. At an absorbed pump power of 9.5 W, a CW total output power of 1.68 W was obtained. Figure 10 shows the relationship between the total output power and the absorbed pump power for the OPDW green laser operation with equal output powers. The total slope and optical-to-optical conversion efficiencies of the absorbed pump power were 23.1% and 17.7%, respectively. The spectrum of the OPDW green laser at the maximum output power is shown in Figure 10a. The peak wavelengths were 546.12 and 550.32 nm, with spectral linewidths (FWHM) of 0.32 and 0.27 nm, respectively.

The stability of the OPDW green laser was measured using a power meter, and the power fluctuation at the maximum output power was 2.3% (RMS) in 1 h, as shown in Figure 11. The green OPDW beam profile is shown in Figure 11a, which exhibits an approximate Gaussian function distribution along the x- and y-axes. Figure 11a also shows the measured beam radii and profiles of the OPDW green laser, and the M² factors of both polarized directions were less than 1.12 using the knife-edge technique at the maximum output power.

A V-shaped cavity was used to achieve the SHG UV laser output, as shown in Figure 7b. The angle of the V-shaped cavity was about 30°. The other components were the same as those shown in Figure 7a, except for M₃ and M₄. The concave mirror (M₃) with a radius of curvature of −50 mm was HR coated at 274 nm and 545–555 nm. The concave mirror (M₄) with a radius of curvature of −50 mm was the output coupler, which was AR-coated at 274 nm and HR coated at 545–555 nm. A β-BaB₂O₄ (BBO) cut for type-II critical phase matching (θ = 45.7° with d_eff = 1.79 pm/V) was used as the nonlinear sum-frequency mixing crystal. The output performance of the UV laser at 274 nm is also presented in Figure 10. At an absorbed pump power of 9.5 W, a CW second-harmonic generating (SHG) UV laser at 274 nm with an oscillation threshold of 2.61 W and an output power of 386 mW was obtained. The UV laser spectrum at 274 nm is shown in Figure 10b. The peak wavelength of the UV laser was 274.14 nm, with a line width of 0.26 nm. The stability of the UV laser output was 2.4%, as also shown in Figure 11. The beam profile at 274 nm is shown in Figure 11b. The UV beam radii were measured in the x- and y-directions, as shown in Figure 11b. The M² factors in the two directions were 1.25 (${\mathrm{M}}_x^2$) and 1.16 (${\mathrm{M}}_y^2$).

5. Conclusions

A 2ω-OPSL-end-pumped CW OPDW Pr:LLF green laser with balanced output powers on the ³P₀→³H₅ transition was demonstrated. We theoretically analyzed the conditions for achieving equal output power of the OPDW laser operation using two intracavity etalons, and experimentally realized the OPDW green laser in the Pr:LLF crystal. Under pumping with a 2ω-OPSL generating 10 W at 479 nm, an OPDW green laser at 546 nm in π-polarization and 550 nm in σ-polarization was obtained with a total output power of 1.68 W. The output powers of the two wavelengths were equal at all pump power levels. The total slope efficiency and optical-to-optical conversion efficiency relative to the absorbed pump power were 23.1% and 17.7%, respectively. Further, a CW UV laser at 274 nm by intracavity sum-frequency mixing was also achieved with a maximum output power of 386 mW and an optical-to-optical conversion efficiency of 4.1% with respect to the absorbed pump power. This paper demonstrates that the proposed methodology can be extended to other laser crystals to achieve OPDW lasers with equal output power.