Orthogonally Polarized Green Dual-Wavelength Pr³⁺:LiLuF₄ Laser at 523 and 538 nm with the Power Ratio of 1:1

Abstract

An orthogonally polarized green dual-wavelength (OPGDW) laser output in a Pr³⁺:LiLuF₄ (Pr:LLF) crystal with the power ratio of 1:1 was realized for the first time. We calculated the condition for obtaining the identical power of the two output wavelengths and achieved the OPGDW laser by adjusting the tilt angle of the intracavity etalon and optimizing the output coupling transmittance. Using a frequency-doubled (2ω) optically pumped semiconductor (OPS) laser of 10 W at 479 nm, a continuous wave (CW) OPGDW laser output at 523 nm (π-polarized) and 538 nm (σ-polarized) was achieved with a combined power of 1.83 W. In addition, by type-II critical phase-matched (CPM) β-BaB₂O₄ (BBO) nonlinear crystal, a 57 mW, 265 nm CW UV laser was also realized by sum-frequency generation (SFG) of 523 nm and 538 nm wavelengths. CW OPGDW lasers with identical power output were ideal for both medical detection and generating UV lasers.

1. Introduction

Visible dual-wavelength (DW) laser emissions demonstrate critical functionality in environmental sensing applications and biomedical diagnostics. For example, in non-invasive blood glucose monitoring, synchronized green-emitting DW lasers facilitate differential hemoglobin derivative analysis through tissue-scattering compensation, improving measurement precision by mitigating tissue-induced artifacts [1]. These DW laser systems are further deployed in LiDAR-driven atmospheric monitoring, where their orange-red counterparts achieve real-time aerosol–gas differentiation via wavelength-resolved backscattering analysis [2]. Especially, orthogonally polarized DW emissions show particular efficacy in photonic platforms, supporting interference imaging of nanometric surface characterization, LiDAR-based three-dimensional tomography and terahertz generation via parametric frequency conversion. The inherent polarization-diverse design facilitates concurrent noise suppression during coherent signal processing and allows for dual-channel signal steering via wavelength-division multiplexing [3,4,5,6,7]. Current implementations of the orthogonally polarized DW laser utilizes two different mechanisms: stark split of the same transition or two different transitions in the single active medium [8,9,10,11,12], and two active mediums with mutually perpendicular crystal axes [13,14,15]. Nevertheless, a stable equilibrium of orthogonal output powers remains unachievable through these two approaches, significantly restricting practical application. For instance, equivalent fundamental power outputs are prerequisite for efficient nonlinear frequency conversion. The primary instability stems from competing stimulated emission processes between the two transitions in the single active medium [8], whereas another reason arises from pump power distribution conflicts in composite active mediums [13]. An innovative methodology was developed to overcome this challenge, which can keep the power ratio of the two output wavelengths at 1:1 at all pump powers.

Doping host materials with trivalent rare earth ions (Pr³⁺, Eu³⁺, Sm³⁺, Er³⁺, Dy³⁺) could produce visible emissions. Pr³⁺-doped active mediums demonstrate higher visible emission efficiency than other RE³⁺ dopants [16,17,18,19,20,21,22]. Improvements in power scaling for Pr³⁺-based laser systems result from advances in blue laser diode (LD) technology [23,24,25,26,27,28,29]. However, Pr³⁺-doped laser emissions have been predominantly investigated for single-wavelength operation, whereas DW configurations in Pr³⁺-doped active mediums were seldom reported. In 2015, we generated the first orthogonally polarized visible DW laser in the Pr:YLF, obtaining power outputs of 158 mW (550 nm) and 184 mW (546 nm), respectively [1]. Jin et al. presented an orthogonally polarized orange DW laser at 607 and 604 nm in the Pr:YLF, achieving power outputs of 81 mW and 201 mW for these wavelengths in 2023 [30]. In 2025, we achieved a CW OPGDW laser at 550 and 546 nm in the Pr:LLF, attaining an output power of 1.68 W [31]. While this work has attained balanced DW power output control, the requirement for exact adjustment of two loss elements in cavity at every pump level had compromised system stability to some degree and heightened the complexity of DW laser operation. Cornacchia et al. characterized the optical spectrum properties of Pr:LLF crystals, achieving single-wavelength emissions at 523, 607, 640, and 722 nm [32]. Figure 1 shows the green emission cross-section of the Pr:LLF cut along the a-axis, which was calculated by the Füchtbauer-Ladenburg equation [33]. The green emission spectra analysis demonstrates that the emission peaks were 523 nm in the π-direction and 538 nm in the σ-direction, respectively. As a result, the Pr:LLF was ideal for generating the OPGDW laser, which utilizes inbiomedical imaging and spectroscopic diagnostics, particularly for non-invasive tissue analysis and real-time monitoring of metabolic processes through their distinct absorption and fluorescence characteristics in biological tissues [1,31].

In this study, an OPGDW laser at 523 and 538 nm in the Pr:LLF with a power ratio of 1:1 was achieved. At an absorption pump power of 9.5 W, a combined power of 1.83 W was realized. In addition, a 57 mW, 265 nm CW UV laser was also produced by SFG of 523 and 538 nm wavelengths, which demonstrated unique potential for enhancing spectral analysis precision, facilitating nanoscale microfabrication, improving sensitivity of chemical detection, and transforming biomedical study through imaging diagnostics [34,35,36].

2. Theoretical Analysis

To make the power output ratio of 1:1 for both wavelengths, we reviewed the output power (P_out,i) of the solid-state laser [37] as follows:

$$P_{out,i}={\displaystyle \frac{-\ln (1-T_{oc,i}){\eta }_{q,i}}{-\ln (1-T_{oc,i})+L_{0i}+L_i}}\left(P_{abs}-P_{tha,i}\right)$$

(1)

where i = 523, 538 represents the 523 and 538 nm, respectively; η_q,i is the quantum efficiency; T_oc,i is the cavity mirror transmittance; L_0i is the round trip passive loss of the cavity; L_i is the loss caused by the reflection of the etalon; P_abs is the absorption pump power; and P_tha,i is the oscillation threshold of the emission wavelength. The slope efficiency (η_sa,i) with the P_abs can be obtained according to Equation (1):

$${\eta }_{sa,i}={\displaystyle \frac{-\ln (1-T_{oc,i}){\eta }_{q,i}}{-\ln (1-T_{oc,i})+L_{0i}+L_i}}$$

(2)

From Equation (2), the η_sa,523 = η_sa,538 can be written as follows:

$${\displaystyle \frac{\ln (1-T_{oc,523}){\eta }_{523}}{\ln (1-T_{oc,523})-L_{523}}}={\displaystyle \frac{\ln (1-T_{oc,538}){\eta }_{538}}{\ln (1-T_{oc,538})-L_{538}}}$$

(3)

While observing the simultaneous Equations (2) and (3), it can be seen that to achieve η_sa,523 = η_sa,538, both T_oc,i and L_i need to be changed simultaneously, because adjusting either parameter alone is not feasible, for example, when L₅₂₃ > L₅₃₈ and P_tha,523 = P_tha,538, η_sa,538 > η_sa,523 was obtained. To understand the power output performance of the two wavelengths more intuitively, Figure 2 is used to explain the variation relationship between the η_sa,538 and η_sa,523. Figure 2a shows the η_sa,538 and η_sa,523 at P_tha,523 = P_tha,538, T_oc,523 = T_oc,538 and L₅₂₃ > L₅₃₈. Figure 2a demonstrates that the two slope efficiencies do not intersect, meaning the output powers of the 523 nm and 538 nm fail to achieve equilibrium at each pump power, as reported in reference [38] for such output characteristic. Similarly, the η_sa,523 and η_sa,538 could not be balanced when P_tha,523 > P_tha,538, T_oc,523 = T_oc,538 and L₅₂₃ > L₅₃₈, as shown in Figure 2b, as demonstrated in reference [8]. By the same token, only the T_oc,i was changed, the η_sa,538 and η_sa,523 could not be balanced, as achieved in references [39,40].

In addition, when the transmittance of the two output wavelengths (λ₁ and λ₂) was same (T_oc,1 = T_oc,2) and both the loss-inducing components were inserted inside the resonator, our experimental effects shown in Figure 2c [11]. Although the η_sa,1 ≠ η_sa,2, the same power could be generated by dynamically adjusting the loss components. However, the occurrence of changes in pump power requires accurate adjustments of associated loss elements for power balance maintenance, yet such rigorous control specifications inherently generate technical barriers that restrict the applicability of DW lasers. Therefore, the T_oc,i and L_i of 523 nm and 538 nm need to be controlled simultaneously to maintain the equivalent slope efficiency.

To achieve different cavity losses in orthogonal polarization directions, an etalon was integrated into the linear cavity. Ensure the c axis of the laser crystal is set vertically, as illustrated in Figure 3a. The inclination angle of the etalon is adjusted relative to the laser beam orientation, with the incidence plane maintained horizontally, as shown in Figure 3b. As shown in the results, π-polarized (S-wave) and σ-polarized (P-wave) directions maintained perpendicularly and parallel with the incident plane, respectively. The angle of inclination of the etalon was equal to the incident angle (θ) of the laser beam. The cavity round-trip losses, L_s and L_p, can be given by the following [8]:

$$L_s=R_s+\left(1-R_s\right)R_s\mathrm{and}{L}_p=R_p+\left(1-R_p\right)R_p$$

(4)

where R_s and R_p are the reflectance of the etalon for the S-wave and the P-wave, respectively, and R_s and R_p can be given by the Fresnel equation [41]:

$$R_s={\displaystyle \frac{{\sin }^2\left(\theta -{\theta }_t\right)}{{\sin }^2\left(\theta +{\theta }_t\right)}}\mathrm{and}{R}_p={\displaystyle \frac{{\tan }^2\left(\theta -{\theta }_t\right)}{{\tan }^2\left(\theta +{\theta }_t\right)}}$$

(5)

where θ_t is the refractive angle, and sinθ = nsinθ_t, n is the refractive index of the glass. When both the powers of the 523 and 538 nm are equal at each pump power level, both the thresholds for the 523 and 538 nm must also be equal. The condition of the laser oscillation threshold for each transition wavelength was described by [42] as follows:

$$P_{tha,i}={\displaystyle \frac{L_i-\ln (1-T_{oc,i})}{2{\eta }_i{l}_c}}{\displaystyle \frac{h{\nu }_p}{{\tau }_i{\sigma }_i}}{\displaystyle \frac{1}{{\displaystyle \iiint r_p\left(r,z\right)s_i\left(r,z\right)d\upsilon }}}$$

(6)

where l_c is the length of the laser crystal, h is the Planck constant, ν_p is the frequency of pump photon, σ_i is the emission cross-section of the emission wavelength, τ_i is the fluorescence lifetime, and r_p(r,z) is the pump beam distribution of the normalized intensity in the resonant cavity, which can be calculated by [43], $s_i\left(r,z\right)=2\exp \left(-2r^2/{\omega }_i^2\right)/\pi {\omega }_i^2{l}_c$ is the cavity mode distribution of the normalized intensity for the emission wavelength, ω_i is the radius of the laser beam waist, which was affected by the focal length of the thermal lens of the laser crystal and can be calculated by ABCD matrix. The thermal focal lengths of laser crystal can be expressed as [44]:

$${\displaystyle \frac{1}{f_{th,i}}}={\displaystyle \frac{P_{abs}{\xi }_i{\left(dn/dT\right)}_i}{K_{c,i}\pi {\omega }_p^2}}$$

(7)

With Equations (1)–(7) and the parameters in the experiment: σ₅₂₃ = 3.0 × 10⁻²⁰ cm², σ₅₃₈ = 1.2 × 10⁻²⁰ cm², η₅₂₃ = 0.92, η₅₃₈ = 0.89, ω_p = 100 μm, ξ₅₂₃ = 8.4%, ξ₅₃₈ = 11.0%, L_0i = 0.4% was measured using the Findlay-Clay method [45], the T_oc,538 and θ were calculated as a function of the T_oc,523, as shown in Figure 4. It can be seen that when the η_sa,523 = η_sa,538 and P_tha,523 = P_tha,538, there exists a fixed correspondence between the T_oc,523, T_oc,538 and θ. For example, when given T_oc,523 = 2.0%, T_oc,538 = 0.8% and θ = 14.4° could be calculated.

3. Experimental Setup

The schematic diagram for the OPGDW laser was displayed in Figure 5a. The pumping source was a 2ωOPS laser, providing a linearly polarized beam at 479 nm and an output power of 10 W with a M² of 3.5. The pump light emitted from the 2ωOPS laser was collimated with a convex lens (L₁). A convex lens (L₂) with a focal length of 50 mm and anti-reflection (AR) film for the pump wavelength was used to focus collimated pump light into the Pr:LLF. The cavity input coupler was a planar mirror (M₁) with AR for 479 nm and high reflectivity (HR) at 523–538 nm and 265 nm. The cavity output coupler was a concave mirror (M₂) with the radius of curvature (R_c) = −200 mm and T_oc,523 = 2.0%, T_oc,528 = 0.8%, AR at 545–700 nm. Two other couplers (1.1% at 523 nm and 0.2% at 538 nm and 3.3% at 523 nm and 1.3% at 538 nm) were also carried out, with the M₂ demonstrated the optimal output performance. An a-axis-oriented Pr:LLF (0.2 at.% Pr³⁺ doping, 5 mm length) functioned as the active medium with AR at 265 nm and 523–538 nm, which was sealed in indium foil and affixed to red copper mounts equipped with water cooling, maintained at 15 °C. A 0.15 mm thick uncoated etalon was utilized to adjust the losses in both polarized directions.

4. Results and Discussion

First of all, the single-wavelength laser emission at 523 nm was conducted without the etalon to investigate Pr:LLF green laser performance. Figure 6 shows the input and output performance of the single-wavelength laser. The laser oscillation threshold was determined to be 0.72 W. The green laser at 523 nm delivered a power output of 2.97 W with a η_sa,523 = 33.8% and an optical conversion efficiency (η_oa,523) = 31.3%, corresponding to 10 W incident pump power (or 9.5 W absorbed pump power). Note that the wavelength output at 523 nm was linearly polarized along the π-polarization. The green spectrum of the 523 nm emission at the maximum pumping, as displayed in the inset of Figure 6. The linewidth was 0.43 nm (FWHM) with a central wavelength of 522.8 nm.

Then, to realize the OPGDW laser emission with the power output ratio of 1:1, the tilt angle θ was controlled at around 15°, the combined output at 523 and 538 nm versus 479 nm pump power was presented in Figure 7. Both the powers of the 523 and 538 nm were sensitive to the change in the angle of inclination of the etalon, but it could reach the power ratio of 1:1 at each pump power by fine-tuning the etalon around 15°. The OPGDW laser was separated into two orthogonally polarized beams with a polarizing beam splitter, and the output powers for individual wavelengths were measured. The output powers of the two wavelengths were approximately equal at all pump power levels. A total combined power of 1.83 W with η_sa,523 + η_sa,538 = 25.4% and η_oa,523 + η_oa,538 = 19.2% was obtained at maximum pumping. The spectrum of the OPGDW is displayed in Figure 7a. The central wavelengths were 522.8 nm and 538.1 nm, with corresponding linewidths of 0.38 and 0.39 nm, respectively. The power stability of the OPGDW laser was measured with a precision power meter, demonstrating < 1.6% over a 1 h (Figure 8). The stabilities of individual wavelengths were also measured, and the power stabilities at 523 and 538 nm were 1.58 and 1.62%, respectively. The beam radii along the x and y axes of the OPGDW laser were measured as displayed in Figure 8a. The M² factor of the OPGDW laser was also measured by the knife-edge technique, and the values of ${\mathrm{M}}_2^{\mathrm{x}}$ and ${\mathrm{M}}_2^{\mathrm{y}}$ were 1.14 and 1.17, respectively. The profile of OPGDW laser beam is also displayed in Figure 8a, which was approximately the Gaussian distribution.

Finally, to realize the UV laser operation, a folding cavity was employed, as displayed in Figure 5b. The cavity reflector was a concave lens (M₃) with R_c = –200 mm and HR at 523–538 nm and AR at 265 nm. The cavity output coupler was a concave lens (M₄) with R_c = –50 mm; HR at 523–538 nm; and AR at 265 nm. A type-II CPM cut BBO (θ = 80.1° with d_eff = 0.058 pm/V) was served as the nonlinear optical medium for SFG. The output characteristic of the 265 nm UV SFG was also displayed in Figure 7. The maximum UV SFG output power at 265 nm reached 57 mW with a threshold of 2.1 W. The laser spectrum at 265 nm was displayed in Figure 7b. The linewidth was 0.37 nm with a central wavelength of 265.2 nm. The power stability of the 265.2 nm UV laser was approximately 1.9% over 1 h (Figure 8). The beam radii along the x and y axes of the 265 nm UV SFG laser were measured with M² values of 1.25 (x-axis) and 1.21 (y-axis), as displayed in Figure 8b. The profile of the UV beam was also displayed in Figure 8b.

5. Conclusions

A 2ωOPS laser-end-pumped CW OPGDW Pr:LLF laser output at 523 nm and 538 nm with the power ratio of 1:1 is demonstrated. The condition for obtaining identical power of the two output wavelengths was analyzed, and the OPGDW laser was achieved through adjustment of the tilt angle of the intracavity etalon and optimization of the output coupling transmittance. Using a 10 W 2ωOPS laser at 479 nm, a CW OPGDW laser output at 523 nm (π- polarized) and 538 nm (σ-polarized) was realized with a total power of 1.83 W. The power outputs in the two polarized directions were the same at each pump level. The total slope efficiency and optical conversion efficiency with respect to the absorbed pump power were 25.4% and 19.2%, respectively. In addition, using type-II CPM BBO crystal, a CW UV SFG at 265 nm was also realized with a maximum power output of 57 mW by 523 and 538 nm intracavity SFG. We believe that the method presented in this paper has the potential to be extended to other laser crystals for obtaining OPGDW lasers with the same slope efficiency.