Nonplanar Ring Resonators Research Articles

Polarisation compensation in non-planar image-rotating OPO ring resonators.

Non-planar image-rotating OPO ring resonators necessitate polarisation compensation in contrast to their planar counterparts. This is essential for maintaining phase matching conditions for non-linear optical conversion in the resonator during each cavity round trip. In this study, we examine the polarisation compensation and its impact on the performance of two types of non-planar resonators: RISTRA with a π2 image rotation and FIRE with a fractional image rotation (π2 fraction). The RISTRA is insensitive to mirror phase shifts, while the FIRE has a more complex dependence of polarisation rotation on mirror phase shifts. There has been debate over whether a single birefringent element can provide adequate polarisation compensation for non-planar resonators beyond RISTRA-type. Our results show that under certain experimentally feasible conditions, even FIRE resonators can achieve adequate polarisation compensation with a single half-wave plate. We validate our theoretical analysis through numerical simulations and experimental studies of OPO output beam polarisation using ZnGeP2 non-linear crystals.

Beam quality and efficiency of ns-pulsed high-power mid-IR ZGP OPOs compared in linear and non-planar ring resonators.

We compare the performance of ns-pulsed mid-infrared optical parametric oscillators (OPOs) based on ZGP crystals in a simple linear cavity and two non-planar image-rotating resonators. Our 2 μm pump source is a 68 W 10 kHz diffraction limited Ho:LLF MOPA system. In a linear cavity, it allows us to generate up to 38 W of the total average power with M2<2.2 from the ZGP OPO in the 3-5 μm range. Beam quality and stability are significantly improved in both types of non-planar ring resonators (M2<1.8 in RISTRA and M2<1.4 in FIRE), while the total average power is above 21 W. Factors influencing the beam quality such as average power and pump repetition rate are studied in detail.

Design and analysis of 90° image rotating four-mirror non-planar ring resonator based on mid-infrared optical parametric oscillator beam quality optimization

Mid-infrared optical parametric oscillator (OPO) operating in the mid-infrared transmission window (3—5 μm wavelength range) is one of hot issues in the field of laser system. It has many applications in environmental detection, remote sensing, and medicine. Besides, this laser system is used as a key component of infrared countermeasures. The optical damage limit of nonlinear crystal is a great challenge to the mid-infrared OPO which is pumped by a nanosecond laser source. Therefore, the pump beam diameter should be appropriately increased to avoid damaging the crystal when scaling a nanosecond OPO to high pulse energy. The result of this design is that the Fresnel number in the cavity is increased and the beam quality is deteriorated. In order to improve the beam quality of mid-infrared OPO laser, a 90&lt;sup&gt;°&lt;/sup&gt; image-rotating four-mirror non-planar ring resonator structure is designed. The advantages of this design include the general ring resonators, such as greatly reduced feedback into the pump laser and the avoidance of optical damage caused by standing wave cavity structure. Most importantly, the image rotating cavity can uniform the beam in the cavity and improve the beam quality. In this paper, the equivalent sphere representation of a four-mirror nonplanar ring resonator is established, and the image rotation angle of this special cavity structure is calculated. Based on this method, the parameters related to the 90&lt;sup&gt;°&lt;/sup&gt; image rotating resonator structure suitable for mid-infrared OPO operation are designed. The self-reproduction of the transverse mode in the axially-asymmetric resonator is further established. It is found that the transverse mode in the resonator is gradually uniformed as the rotation angle of the image changes from 0&lt;sup&gt;°&lt;/sup&gt; to 90&lt;sup&gt;°&lt;/sup&gt;. When the rotation angle is 90&lt;sup&gt;°&lt;/sup&gt;, the fundamental mode and the high-order mode both exhibit very good central symmetry. Finally, the mid-infrared ZnGeP2 OPO laser with the 90&lt;sup&gt;°&lt;/sup&gt; image rotating resonator structure is used to verify the improvement of beam quality. The beam quality of &lt;inline-formula&gt;&lt;tex-math id="Z-20190909022329-2"&gt;\begin{document}$M_X^2=1.81 $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20182001_Z-20190909022329-2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20182001_Z-20190909022329-2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt;&lt;tex-math id="Z-20190909022441-3"&gt;\begin{document}$M_Y^2=1.61$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20182001_Z-20190909022441-3.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20182001_Z-20190909022441-3.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; are achieved. It can be proved that the 90&lt;sup&gt;°&lt;/sup&gt; rotating four-mirror non-planar ring resonator has a significant effect on the optimization of the output beam quality of the mid-infrared OPO laser system.

Analysis of Misalignment Sensitivity of Generalized Ring Resonator for the Trace Gas Concentration Detection Instrument Based on CRDS

Cavity Ring-Down Spectrometer (CRDS) (Romanini et al., 1997) has been widely used in the fields of atmospheric chemistry, meteorology, air pollution and greenhouse gas emission, ecological environment and ecological hydrology research and public safety assurance. However, in order to maximize the measurement sensitivity of the target analyte of the cavity ring down spectrometer, the absorption measurement should be selected at the target line absorption peak (Kevin K. Lehmann et al., 1996). In addition, it should be noted that the interference of absorption lines of the same or other species should be reduced, in order to achieve a higher accuracy detection of the instrument that improving the spectral accuracy become more critical (Altshuler et al., 1977). In the paper, we have considered the existence of the self-conjugate rays in the resonator which is consisted of a number of mirrors and including spherical mirrors, the effect of spherical mirror misalignment in ring resonators was investigated. Then by utilizing the optical path turning reflection matrix, and the influence that caused by both the displacements of a spherical mirror and plane mirror in a nonplanar ring resonator have been obtained, and given the relation of the error transmission in both azimuth and pitch direction.

Characterization of the eigenmode frequency spectrum influenced by the polarization states and light field distribution in a nonplanar ring resonator.

We present the evolution of the eigenmode frequency spectrum in a nonplanar ring resonator based on the Jones matrix and the Fresnel-Kirchhoff diffraction integral. Taking the modes TEM(q+1)01 and TEMq10 with different polarization states as examples, we numerically derive the frequency difference between them versus the folding angles of the resonator by considering the polarization and the light field distribution of the eigenmodes synchronously. It can be found that the extreme values of frequency difference between TEM(q+1)01 and TEMq10 are particularly affected by the polarization states of the eigenmode, and the locations of these consecutive extreme values correspond to the total image rotation angle with values of the integer multiple of 90°. Moreover, the influence of the resonator structure on the frequency difference of eigenmodes with the identical polarization state is also analyzed. The results prove that the frequency difference between the fundamental mode and higher order modes declines with the increase of the spherical mirrors' radius of curvature but increases with the augmentation of the resonator's total length. These interesting findings are important for the mode selection in high-accuracy ring laser gyroscopes with nonplanar structure by modulating the polarization states and the light field distribution of the eigenmodes to control the frequency difference between them.

Influence of the eigenmode polarization deviation on the output Sagnac frequency difference in nonplanar ring resonators.

We present a theoretical model to quantitatively analyze the influence of the eigenmode polarization deviation (described with ellipticity parameter) on the output Sagnac frequency difference in two nonplanar ring resonators with different mirror arrangements. The theoretical and numerical analysis results prove that the deviation of the eigenmode polarization from the ideally circular polarized state will produce a drop of the output Sagnac frequency difference. Furthermore, for the identical ellipticity parameter and incident angles, the decline values along the rotation axis A(2) is more obvious than that along axis A(1). In other words, these results show that the output Sagnac frequency difference can be improved effectively by restraining the eigenmode polarization deviation quantitatively and that these analysis findings are useful for designing and optimizing the structure of laser gyroscopes with super-high precision.

Reanalysis on coordinate system for Gaussian beam reflection

Some problems and confusions related to matrix analysis for Gaussian beam reflection are clarified. We can choose right-handed coordinates before and after mirror reflection which is called the traditional coordinate system in this Letter. We can also choose a coordinate system with chirality inversion which is called a novel coordinate system in this Letter. The matrix describing optical components should coincide with the selected coordinate system; errors or confusions will appear otherwise. Spherical mirror reflection and coordinate rotation in nonplanar ring resonators are used to clarify some confusion in previous publications due to disorder of the coordinate system. This work is significant to both Gaussian beam propagation analysis and ring laser resonator design.

非平面环形谐振腔模式光强分布的数值仿真

非平面环形谐振腔模式光强分布的数值仿真

Analysis on propagation properties of the eigenmodes in nonplanar ring resonators

Combining with the self-consistent condition and extended 5 × 5 matrix, we theoretically analyzed the polarization properties of the eigenmodes throughout the nonplanar ring resonators with different structures. According to the satisfactory cross section size of the eigenmodes, a comparative study of the stability properties of these nonplanar ring resonators is also provided, and the three dimensions stability space of these resonators are presented for the first time as far as our knowledge goes. The results show that the major and minor axes of the cross section change with the propagation distance and have a symmetrical point for resonators with two different structures, and the area of the stable region for these resonators can be extended by changing the incident angles of the laser beam or the radii of mirror surfaces in the resonator. These interesting results are important for designing and arranging the diaphragm in ring resonators with a nonplanar structure, as well as optimizing the structure of the resonators themselves.

Reanalysis of optical-axis perturbation in nonplanar ring resonators in ray matrix approach with appropriate coordinate systems

Ray matrix approach with appropriate coordinate systems has been proposed in this paper. It is employed to analyze the optical-axis perturbation in nonplanar ring resonators. The sensitivities of optical-axis decentration (SD) and optical-axis tilt (ST) in nonplanar resonators with 90° and 270° image rotation are discussed in detail in the region of 0<K<8, where K is the ratio of the total cavity length to the radius of the curvature mirrors. There are both four singular points in the whole region of 0<K<8. On the left of the first singularity, it is found that the longer the mirror radius, the less the optical-axis decentration sensitivity. This is opposite the behavior of planar ring resonators, but the behaviors of optical-axis tilt sensitivity in planar and nonplanar ring resonators are similar. It is worth to note that SD and ST in the nonplanar resonator with certain parameters have the similar singularities. The analysis in this paper is important for the cavity design and alignment of nonplanar ring resonators.

General beam position controlling method for 3D optical systems based on the method of solving ray matrix equations

A general beam position controlling method for 3D optical systems based on the method of solving ray matrix equations has been proposed in this paper. As a typical 3D optical system, nonplanar ring resonator of Zero-Lock Laser Gyroscopes has been chosen as an example to show its application. The total mismatching error induced by Faraday-wedge in nonplanar ring resonator has been defined and eliminated quite accurately with the error less than 1 μm. Compared with the method proposed in Ref. [14] , the precision of the beam position controlling has been improved by two orders of magnitude. The novel method can be used to implement automatic beam position controlling in 3D optical systems with servo circuit. All those results have been confirmed by related alignment experiments. The results in this paper are important for beam controlling, ray tracing, cavity design and alignment in 3D optical systems. • A general beam position controlling method for 3D optical system was proposed. • The total mismatching error in resonator of Zero-Lock Laser Gyroscopes was eliminated. • The precision of the beam position controlling was improved greatly. • The novel method can be used to implement automatic beam position controlling.

Single frequency 1645 nm Er:YAG nonplanar ring oscillator resonantly pumped by a 1470 nm laser diode

A 1645 nm Er:YAG nonplanar ring oscillator, resonantly pumped by a 1470 nm laser diode, is reported. By using a 0.5%-doped Er:YAG nonplanar ring resonator, a 0.284 W single-frequency laser output at 1645 nm was obtained with a slope efficiency of 42.1%. The beam quality in x and y directions were 1.064 and 1.039, respectively.

Reanalysis of generalized sensitivity factors for optical-axis perturbation in nonplanar ring resonators

By utilizing the novel coordinate system for Gaussian beam reflection and the generalized ray matrix for spherical mirror reflection, the generalized sensitivity factors SD1, ST1, SD2 and ST2 influenced by both the radial and axial displacements of a spherical mirror in a nonplanar ring resonator have been obtained. Besides, the singular points of different kinds of non-planar ring resonators under the conditions of incident angle A ranging from 0° to 45° or total coordinate rotation angle ρ ranging from 0° to 360° have also been obtained through the analysis of the determinant of the coefficient matrix of the linear equations. The analysis in this paper is important to the cavity design of non-planar ring resonators and it could be helpful to avoid the violent movement of the optical-axis to small misalignment of the mirrors in non-planar ring resonators.

Beam position controlling method for 3D optical system and its application in non-planar ring resonators

A novel theoretical beam position controlling method for 3D optical system has been proposed in this paper. Non-planar ring resonator, which is a typical 3D optical system, has been chosen as an example to show its application. To the best of our knowledge, the generalized ray matrices, augmented 5 × 5 ray matrices for paraxial dielectric interface transmission and paraxial optical-wedge transmission, and their detailed deducing process have been proposed in this paper for the first time. By utilizing the novel coordinate system for Gaussian beam reflection and the generalized ray matrix of paraxial optical-wedge transmission, the rules and some novel results of the optical-axis perturbations of non-planar ring resonators have been obtained. Wedge angle-induced mismatching errors of non-planar ring resonators have been found out and two experimental beam position controlling methods to effectively eliminate the wedge angle-induced mismatching errors have been proposed. All those results have been confirmed by related alignment experiments and the experimental results have been described with diagrammatic representation. These findings are important to the beam control, cavity design, and cavity alignment of high precision non-planar ring laser gyroscopes. Those generalized ray matrices and their deducing methods are valuable for ray analysis of various kinds of paraxial optical-elements and resonators. This novel theoretical beam position controlling method for 3D optical system is valuable for the controlling of various kinds of 3D optical systems.

Novel coordinate system for Gaussian beam reflection

A novel coordinate system for Gaussian beam reflection has been proposed in this Letter. Reflection from a spherical mirror is used to describe the novel coordinate system. One single segment of a general resonator is chosen to describe coordinate rotation in detail. Nonplanar ring resonators are chosen to show the application of the novel coordinate system. This novel coordinate system has been proved by two simple experiments and the problem existing in using the traditional coordinate system has been pointed out. This novel coordinate system is valuable for not only the designing of laser resonators but also Gaussian beam propagation analysis.

Generalized sensitivity factors for optical-axis perturbation in nonplanar ring resonators

By utilizing the generalized ray matrix for spherical mirror reflection, two new sensitivity factors are introduced considering the perturbation of the optical-axis caused by the radial and axial displacements of a spherical mirror in a nonplanar ring resonator. Based on this, a novel way for finding the location of the singular points of the sensitivity factors is presented. It is found that some nonplanar ring resonators with the effective modes may have the singular points of the sensitivity factors. The unsuitable regions for nonplanar ring resonators are also obtained from the perspective of the sensitivity factors.

Analysis on the polarization property of the eigenmodes in a nonplanar ring resonator

Based on the theory of the Abeles matrix, the reflections from the multilayer dielectric mirrors in a nonplanar ring resonator are discussed in detail considering the imperfect layer thickness and the incident angle errors. The polarization of Gaussian beams in nonplanar ring resonators are analyzed by using a statistical method and the way to analyze the stability of a nonplanar ring resonator in the perspective of polarization is also presented. The results show that a nonlanar ring resonator with a finite mode size may not have the reasonable polarization performances sometimes; the eigenmodes might be right- and left-handed elliptically polarized instead of circularly polarized, and they also have different ellipticity and round trip losses, which are critical for a nonplanar ring resonator. These interesting findings are important to the cavity designs of ring resonators with a nonplanar structure.

激光二极管抽运的单块非平面环形腔可调谐单频激光器

激光二极管抽运的单块非平面环形腔可调谐单频激光器

LD抽运单块非平面环形腔单频激光器

LD抽运单块非平面环形腔单频激光器

Optical-axis perturbation in nonplanar ring resonators

Several findings on the optical-axis perturbation of nonplanar ring resonators have been obtained identical by utilizing the augmented 5×5 matrix formulation and augmented 6×6 matrix formulation, respectively. It has been found out that in the whole region of 0<L/R<2, the longer the mirror radius, the higher the sensitivity of optical-axis decentration, while the total cavity length is L and the radius of the curvature mirrors is R. The sensitivity of optical-axis tilt in the region of 0<L/R<2 has been carried out too. The optical-axis decentration and optical-axis tilt inside the region of L/R>2 have been discussed. The differences of the optical-axis perturbation between planar and nonplanar ring resonators have also been analyzed. These interesting findings are important to the cavity design of nonplanar ring resonators.