Optical-axis Perturbation Research Articles

Analysis on the characteristic of the optical axis perturbation in a total reflection prismring resonator.

The deduction of the augmented 5×5 matrix describing all the possible angular and decentration misalignment perturbation sources on a spherical prism plane during the refraction is presented in detail for the first time. Combining the augmented matrices and the condition of eigenmode self-consistency, the optical axis perturbation properties (described with the optical axis perturbation sensitivity factor SD1, ST1, SD2, and ST2) in a total reflection prism ring resonator are also analyzed. The singular points of the optical axis perturbation sensitivity factor are found at L/R=0.417 for the cases where the misalignments may originate from distinguished type of prisms P1 and P4 in the resonator, respectively. It is shown that the small errors of the prism can cause large optical axis disturbance in the position of the perturbed singular point and its nearby area, and the disturbance for the case where the misalignments originate from prism P1 is more violent than that of prism P4. With some upgrades to find and avoid the singularity of the optical axis in the total reflection prism ring resonator structure successfully, we expect this work will have great potential for designing and optimizing the structure of super-high-precision ring laser gyroscopes.

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.

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.

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.

Generalized ray matrix for spherical mirror reflection and its application in square ring resonators and monolithic triaxial ring resonators

To the best of our knowledge, the generalized ray matrix, an augmented 5×5 ray matrix for a spherical mirror reflection with all the possible perturbation sources including three kinds of displacements and its detailed deducing process have been proposed in this paper for the first time. Square ring resonators and monolithic triaxial ring resonators have been chosen as examples to show its application, and some novel results of the optical-axis perturbation have been obtained. A novel method to eliminate the diaphragm mismatching error and the gain capillary mismatching error in monolithic triaxial ring resonators more effectively has also been proposed. Both those results and method have been confirmed by related experiments and the experimental results have been described with diagrammatic representation. This generalized ray matrix is valuable for ray analysis of various kinds of resonators. These results are important for the cavity design, cavity improvement and alignment of high accuracy and super high accuracy ring laser gyroscopes.

Method for eliminating mismatching error in monolithic triaxial ring resonators

Several results on optical-axis perturbation and elimination of the mismatching error C of a monolithic triaxial ring resonator (MTRR) are reported. Based on the augmented 5?5 ray matrix method, by simultaneously considering axial displacement of a mirror and the misalignments in three planar square ring resonators of a MTRR, the rules of optical-axis perturbation are obtained. The mismatching error C of the MTRR is eliminated. The results obtained are important for cavity design, as well as in the improvement and alignment of MTRR.

Optical-axis perturbation in triaxial ring resonator

We report several findings on the optical-axis perturbation of monolithic triaxial ring resonator. A criterion, C, which represents the mismatching error of the monolithic triaxial ring resonator, has been found out and it cannot be decreased by modifying the angles of the terminal surfaces or the terminal mirrors of the resonator. When C not equal 0, an optimization method to share the mismatching error C in some specific directions equally and simultaneously has been proposed. The interesting findings are important to cavity design, cavity improvement, and alignment of the monolithic triaxial ring resonator.

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.

Optical axis perturbation in folded planar ring resonators

A mathematical model of a four-sided folded planar ring resonator is established. The model can be modified into a triangular ring resonator, a square ring resonator, and a four-sided folded ring resonator, all of which are widely used for ring laser gyroscopes by changing certain design parameters such as incident angle Ai and side ratio H. By use of the extended matrix formulation, the optical axis perturbation, including optical axis decentration and optical axis tilt, in those planar ring resonators is analyzed in detail resulting in some novel findings. It has been determined that the longer the mirror radius, the larger the mode volume, the higher the sensitivity of optical axis decentration and the lower the sensitivity of optical axis tilt. The same mirror misalignment value, mostly the misalignment induced by optical axis decentration in the x and y components, has the conventional ratio of 1:[cos(Ai)](2) for the symmetrical points of the resonator. Details of the effect of Ai and H on the optical axis tilt have also been determined. The difference in optical axis tilt between different kinds of ring resonator is disclosed. The sensitivity of optical axis tilt was found to undergo singular rapid change along with the right edge of the second stable area. This singular behavior is useful for those resonators that have a small incident angle, such as Ai=15 degrees , because those resonators have a second stable region. These interesting findings are important for cavity design, cavity improvement, and alignment of planar ring resonators.

Optical-axis perturbation singularity in an out-of-plane ring resonator

I use a matrix approach to determine the optical-axis perturbation sensitivity of an out-of-plane stable ring resonator. It is found to have a singularity for certain design parameters. On one side of the singularity the cavity behaves abnormally: the longer the mirror radius, the larger the mode volume and, surprisingly, the less the perturbation sensitivity. This is opposite the behavior of conventional stable resonators, a finding that is important to the cavity designs of out-of-plane ring lasers.