Simple interferometric technique for generation of a radially polarized light beam

We present a theoretical and experimental investigation of an interferometric technique for converting a linearly polarized Gaussian beam into a radially polarized doughnut beam. The experimental setup accomplishes the coherent summation of two orthogonally polarized TEM01 and TEM10 beams that are obtained from the transformation of a TEM00 beam by use of a simple binary diffractive optical element. We have shown that the degree of radial polarization is maximum at a given distance from the interferometer output port that depends on the diameter of the incident beam at the interferometer input port.     

Optical throughput of the Sagnac interferometer with a modified large optical path difference

The basic principle of Sagnac interferometer with modified large optical path difference is expounded on in this paper. According to the Fresnel formula, electromagnetic field energy, and energy flux, the transmittance and reflectance of each interface of a Sagnac interferometer are calculated, respectively, and then the exact expressions of the optical throughput changing with the incident angle, the angle of the incident plane, and paper plane (the bottom plane of Sagnac interferometer) and Sagnac interferometer acute angles are given. Furthermore, we analyze the effects of various parameters on the optical throughput by computer simulation, and some important conclusions are obtained. This work is of great scientific significance to the static, real-time simultaneous detection of upper atmospheric wind field.     

Axial separation of orthogonally polarized focal field components due to a radially polarized beam

In this paper, we investigate the field distribution in the focal volume of an aberrated radially polarized beam. Using two different forms of the vectorial diffraction theory, we show that the presence of defocus in the beam displaces both the axially and the radially polarized fields parallel to the optical axis of the focusing lens, while the presence of spherical aberration primarily shifts the longitudinally polarized field only. This facilitates axial separation of the two orthogonally polarized field components, resulting in a significant boost to the ratio of the peak longitudinally polarized field to the peak laterally polarized field in the focal plane. We further show that with an appropriate combination of oppositely signed defocus and spherical aberration, the energy density in the focal volume due to the longitudinally polarized field can be caused to peak at the focal plane. The results obtained are expected to be beneficial to the applications requiring a stronger longitudinally polarized focal field relative to the laterally polarized focal field component.     

Description of the propagation of a radially polarized beam with the scalar Kirchhoff diffraction

Since radially polarized beams have only one magnetic field component, the azimuthal component, a scalar Kirchhoff diffraction integral can be used to describe the propagation of the magnetic field. In the far-field zone, this diffraction formula gives an analytic expression for the magnetic field from which the electric field component expressions are derived by the Faraday relation. Numerical results from these expressions correctly reflect the properties of a radially polarized beam.     

Precision stabilization of the optical frequency in a large ring laser gyroscope

Pressure-induced fractional changes of 10(-7) in the geometry of a large He-Ne ring laser gyroscope induce backscatter phase changes and thus a fractional pulling of the Sagnac frequency of ~5 x 10(-3). To counter this, the optical frequency was stabilized against an iodine-stabilized laser with a high-finesse Fabry-Perot interferometer and piezoelectric control of the ring perimeter. This scheme, although limited in principle by residual geometric asymmetry and in practice by low beam powers (10 pW), stabilized the perimeter to 2.4 nm (6 x 10(-10) or 300 kHz for the optical frequency) and the Sagnac frequency to 100 parts per million over several days.     

Focusing of radially polarized Lorentz–Gauss beams with the power–exponent–phase vortex

Using the vector diffraction theory, the optical field of the focusing radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex is derived. The normalized intensity distributions of the focusing radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex are numerically demonstrated. The influences of the power order n and the topological charge m on the normalized intensity distribution are examined. The beam centre and the effective beam size, which are defined by the first- and the second-order moments of the intensity distribution, are the important parameters for focus. Therefore, the quantitative effects of the power order n and the topological charge m on the beam centre and the effective beam size are further investigated. This research is beneficial to the optical manipulation which is involved in the radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex.     

Vector propagation of radially polarized Gaussian beams diffracted by an axicon

On the basis of the vectorial Rayleigh diffraction integrals and stationary-phase method, the analytic expression describing the vectorial field distribution of radially polarized Gaussian beams diffracted by an axicon is derived. The theoretical analysis and simulation calculation show that the radial component of the diffraction field is the propagation-invariant first-order Bessel beam when the radially polarized Gaussian beam illuminates the axicon. However, the longitudinal component possesses no such behavior because of its intrinsic r dependence, and its central intensity is the maximum. The longitudinal component is related to the open angle and index of the axicon, which has to be considered when the open angle and index are large. For a small open angle and index, the longitudinal component can be neglected, and the scalar approximation is valid.     

Sharper focal spot formed by higher-order radially polarized laser beams

The intensity distributions near the focal point for radially polarized laser beams including higher-order transverse modes are calculated based on vector diffraction theory. For higher-order radially polarized mode beams as well as a fundamental mode (R-TEM01*) beam, the strong longitudinal component forms a sharper spot at the focal point under a high-NA focusing condition. In particular, double-ring-shaped radially polarized mode (R-TEM11*) beams can effectively reduce the focal spot size because of destructive interference between the inner and the outer rings with pi phase shift. Compared with an R-TEM01* beam focusing in a limit of NA=1, the full width at half-maximum values of the focal spot for an R-TEM11* beam are decreased by 13.6% for the longitudinal component and 25.8% for the total intensity.     

High-visibility interferometric measurement of the diffraction phase

We obtain the absolute phase in Fresnel diffraction for Gaussian beams by using a modified polarization Sagnac interferometer in which counterpropagating paths are spatially separated and labeled according to polarization. By erasing the polarization "which-path" information with an analyzing polarizer situated after the modified interferometer, we are able to regain interference and to precisely control the relative intensities of the diffracted and the reference beams. The resulting optimized visibility allows for a precise phase determination. This setup is very stable, requiring no active elements.     

Robust and environmental insensitive fiber optic Sagnac interferometer for microwave photonic applications

A technique that allows a fiber optic Sagnac interferometer based microwave photonic device to be implemented using non-polarization maintaining components inside the Sagnac loop while still obtaining an output that is insensitive to changes in environmental conditions is presented. It is based on inserting the non-polarization maintaining components in between a polarization beam combiner and a Faraday rotator mirror inside the loop. The technique also introduces a phase bias to the light propagating inside the loop. Experimental results demonstrate that the discretely and continuously tunable Sagnac loop based signal processors implemented using non-polarization maintaining components have an environmentally insensitive frequency response.     

Generation of radially polarized beams with an image-rotating resonator

We show how a passive image-rotating optical resonator can be used to convert a linearly polarised, lowest-order Gaussian beam into a radially polarized beam. The image and polarization rotation of the cavity removes the frequency degeneracy of the modes, making it possible to select the radially polarized mode by cavity tuning. With the addition of gain, the same cavity should operate as a radially polarized laser when injection seeded at the proper wavelength.     

Modified white-light Mach-Zehnder interferometer for direct group-delay measurements

A modified white-light Mach-Zehnder interferometer based on a single beam splitter is described for direct group-delay measurements. The arms of the interferometer are folded in such a manner that a single beam splitter can be used to split the incoming beam and combine the outgoing beams. This method offers a twofold advantage: The measuring range of the interferometer is twice as large as that of the Michelson interferometer, and the systematic error that is associated with the beam splitter is minimized because of the configuration. We report the results of measurements on various optical components performed in the 555-630-nm spectral region and propose a scheme for the processing of the experimental data. We present a comparison of the data analyzed by the proposed processing scheme along with the theoretical calculations.     

Reflection and transmission of strongly focused light beams at a dielectric interface

The reflection and transmission of tightly focused azimuthally, radially and linearly polarized electromagnetic wave beams with subwavelength spot size and wavefront curvature at a dielectric interface are investigated. For a given wavefront radius, the existence of the optimal radius of beam spot corresponding to a minimal reflectance and maximal transmittance is shown. Significant lateral shift in the transmitted intensity peak is revealed for strongly focused azimuthally and radially polarized beams that are normally incident to an interface. The reflection and transmission of transverse-electric- and transverse-magnetic- polarized extremely narrow wave beams which are obliquely incident on the dielectric interface is analysed. Disappearance of the Brewster angle and total internal reflection effects for the strongly focused beams are predicted. The change in beam profile after reflection and transmission for different polarizations, incident beam spots and incidence angles are analysed.     

Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer

This paper describes a fiber optic sensor suitable for noncontact detection of ultrasonic waves. This sensor is based on the fiber optic Sagnac interferometer, which has a path-matched configuration and does not require active stabilization. Quadrature phase bias between two interfering laser beams in the Sagnac loop is applied by controlling the birefringence using a fiber polarization controller. A stable quadrature phase bias can be confirmed by observing the interferometer output according to the change of phase bias. Additional signal processing is not needed for the detection of ultrasonic waves using the Sagnac interferometer. Ultrasonic oscillations produced by conventional ultrasonic piezoelectric transducers were successfully detected, and the performance of this interferometer was investigated by a power spectrum analysis of the output signal. Based on the validation of the fiber optic Sagnac interferometer, noncontact detection of laser-generated surface waves was performed. The configured Sagnac interferometer is very effective for the detection of small displacement with high frequency, such as ultrasonic waves used in conventional nondestructive testing (NDT)     

Radiation forces of highly focused radially polarized hollow sinh-Gaussian beams on a Rayleigh metallic particle

Based on the vector diffraction theory, the tight focusing properties of radially polarized hollow sinh-Gaussian (HsG) beams are theoretically studied. It is found that the radially polarized HsG beams can form a longitudinally polarized sub-wavelength focal spot. Moreover, the radiation forces acting on a Rayleigh metallic particle are calculated for the case where the radially polarized HsG beams are applied. Compared with the use of conventional Gaussian beams, the high-order radially polarized HsG beams can largely enhance the radial trap stiffness and broaden the axial trap distance. The influence of the beam order m on the focusing properties and trap stiffness is investigated in detail.     

Focusing of radially and azimuthally polarized beams through a uniaxial crystal

We calculated and measured the difference between focal positions of radially and azimuthally polarized beams after passing through a uniaxial crystal. Calculations were carried out on the basis of the ray optics and the vector diffraction theory. The results of the calculations were in good agreement with those of the experiment. In addition, we discussed the polarization selection in a hemispherical laser cavity that was used for the generation of a radially polarized beam by use of the birefringence of a c-cut Nd:YVO4 laser crystal [Opt. Lett. 31, 2151 (2006)]. The stability range of the laser cavity length for the generation of a radially polarized beam was also in good agreement with the differences mentioned above.     

Statistical properties of a radially polarized twisted Gaussian Schell-model beam in a uniaxial crystal

We derive the analytical formulas for the elements of the cross-spectral density matrix of a radially polarized partially coherent beam with a twist phase named radially polarized twisted Gaussian Schell-model (RPTGSM) beam propagating in a uniaxial crystal, and explore the statistical properties, such as the intensity distribution, the degree of polarization (DOP) and the state of polarization (SOP) of such beam in a uniaxial crystal with the help of the derived formulas. It is found that the statistical properties of a RPTGSM beam are closely related with the twist phase and the anisotropy of the uniaxial crystal, e.g. the twist phase leads to the rotation of the intensity, DOP and SOP distributions, and the anisotropy of the uniaxial crystal leads to the asymmetry distributions of these statistical properties. Our results will be useful for designing light field with prescribed intensity, DOP and SOP distributions, and may be useful in optical manipulations and free-space optical communications.     

Focal shift in focused radially polarized ultrashort pulsed laser beams

Beginning with a beam coherence polarization (BCP) matrix, we obtain an analytical intensity expression for radially polarized ultrashort pulsed laser beams that pass through an apertureless aplanatic lens. We also investigate the intensity distribution of radially polarized beams in the vicinity of the focus. The focal shift of these beams is studied in detail. The focal shift depends strongly on Z(F) that coincides with pi times the Fresnel number.     

Experimental demonstration of resonant sideband extraction in a sagnac interferometer

Sagnac interferometers have recently been proposed as a potential alternative to Michelson interferometers for the purpose of large-scale laser interferometric gravitational-wave detectors. We report on an experimental investigation of the Sagnac interferometer in two configurations: with arm cavities, and with resonant sideband extraction. Resonant sideband extraction was shown to increase the signal bandwidth by a factor of 6.5 compared with the arm cavity device, corresponding to an increase in sensitivity of as much as 6 dB for signals outside the arm cavity bandwidth. Moreover, we compare the performance of a Sagnac interferometer with resonant sideband extraction to a Michelson interferometer with resonant sideband extraction.