Objective  By constructing a resonant cavity model, the theoretical calculations reveal the spot singularity feature after coherent superposition of two intrinsic modes in an isotropic solid-state laser. And it is experimentally verified for the first time that the polarization state of the 1.6 μm output laser can be effectively manipulated in diode-pumped quasi-continuous c-cut Er,Yb: YAl₃(BO₃)₄ lasers without using any specific intracavity optical polarization selector element. The transformation from a partially polarized state to a stable line-polarized state with a switchable orthogonal special case of line polarization direction is achieved, all with a polarization extinction ratio of 21 dB. It is also verified that the line-polarized output of the laser originates from the coherent superposition of two orthogonal eigenmodes by spot comparison. This thesis provides a reliable scheme for the direct output of line-polarized light from c-cut Er,Yb: YAl₃(BO₃)₄ lasers with the modulation of polarization states.

  Methods  The resonant cavity model is shown (Fig.1), where θ is denoted as the angle between the coordinate systems of the intracavity loss anisotropy ∆φ and the phase anisotropy ∆t. The experimental principle diagram of the c-cut Er,Yb: YAl₃(BO₃)₄ polarization controlled laser is shown (Fig.3). The laser cavity has a length of approximately 32 mm, and the laser crystal is mounted on a water-cooled copper heat sink at 288.1 K. The output laser beam is split into two paths using a beam splitter (Splitter). In one of these paths, a Glan-Laser prism is employed as a polarizer, and a laser power meter (Thorlabs, Inc.) is used to measure the laser power after passing through the polarizer. Both measurements are utilized to determine the polarization state of the laser output. The other output laser uses an infrared camera and a spectrometer to detect the beam quality and emission wavelength of the output laser with different polarization states. In the experiment, by re-aligning the resonator, the output coupling mirror is slightly tilted, and the polarization state of the output laser is transformed from unbiased to linear polarization state, and the maximum polarization extinction ratio of linear polarization output is up to 21 dB.

  Results and Discussions  By re-aligning the resonator, the output coupling mirror is slightly inclined, and the output laser polarization state is linearly polarized, and the polarization direction can be a set of orthogonal directions, and the polarization extinction ratio can reach 21 dB (Fig.4). Measurement of output laser wavelengths in different polarization states is carried out by spectrometer. When the polarization state changes, the center wavelength of the output laser fluctuates around 1 602 nm, with a maximum variation of less than 1 nm (Fig.6). The laser spot is detected after passing through the analyzer. When the angle of the Glan-prism is 0°, the laser power through the Grand prism is minimum. And when it is rotated and shifted by 0°, the line polarized light passes through the Glan-prism and the spot shows an elliptical distribution. And when the offsets are equal but in opposite directions, the ellipsoid-like spots can be observed, whose long axes are orthogonal to each other. The essence is that two orthogonally polarized eigenmodes undergo coherent superposition to produce a linearly polarized light output (Fig.7). Measurement of the beam quality factor M² of different polarization states of the output laser is carried out by beam quality analyzer. The beam quality factor M² of the partially polarized laser output when the laser is running freely and the linearly polarized laser output in two different polarization directions is maintained at about 2.0, and there is no obvious difference in beam quality degradation when the laser output linearly polarized laser (Fig.8),

  Conclusions  In this study, theoretical calculations are performed by constructing a resonant cavity model to simulate the singular features of the spot profile after coherent synthesis of the intrinsic mode. And it is experimentally verified for the first time that in a quasi-continuously pumped c-cut Er,Yb: YAl₃ (BO₃)₄ laser operated at 1.6 μm, the polarization state of the output laser can be switched from a partially polarized state to a stable linearly polarized state by adjusting the degree of tilt of the output coupling mirror, and the polarization extinction ratio reaches 21 dB, with a pair of orthogonal linear polarization directions that can be switched. In the process of adjusting the angle of the output coupling mirror, the output band of the output light is not changed, and the loss of output power of the generated linearly polarized beam is around 7%, while the quality of the beam in different polarization states does not change significantly. By spot comparison, it is verified that the direct output of line-polarized light from the laser is achieved by coherent synthesis of two orthogonal eigenmodes. This method provides a reliable solution for the direct output and modulation of line polarization of c-cut Er,Yb: YAl₃ (BO₃)₄ and other isotropic lasers.