In optics, Zernike polynomials are widely used in testing, wavefront sensing, and aberration theory. This unique set of radial polynomials is orthogonal over the unit circle and finite on its boundary. This Letter presents a recursive formula to compute Zernike radial polynomials using a relationship between radial polynomials and Chebyshev polynomials of the second kind. Unlike the previous algorithms, the derived recurrence relation depends neither on the degree nor on the azimuthal order of the radial polynomials. This leads to a reduction in the computational complexity.
An all-optical generation of a microwave carrier at 21 GHz that incorporates a double-Brillouin frequency shifter is presented. The frequency shift of approximately 21 GHz is achieved by generating the second-order Brillouin Stokes signal from the Brillouin pump. This is accomplished through the circulation and isolation of its first-order Stokes signal in the optical fiber. The Brillouin pump signal is heterodyned with its second-order Brillouin Stokes signal at a high-speed photodetector, and the output beating frequency is equal to the offset between these two signals. The generated microwave carrier is measured at 21.3968 GHz, and the carrier phase noise as low as -58.67 dBc/Hz is achieved.
To overcome astigmatism has always been a great challenge in designing a heliostat capable of focusing the sunlight on a small receiver throughout the year. In this Letter, a nonimaging focusing heliostat with a dynamic adjustment of facet mirrors in a group manner has been analyzed for optimizing the astigmatic correction in a wide range of incident angles. This what is to the author's knowledge a new heliostat is not only designed to serve the purpose of concentrating sunlight to several hundreds of suns, but also to significantly reduce the variation of the solar flux distribution with the incident angle.
A single-wavelength Brillouin fiber laser (BFL) is demonstrated at the extended L-band region using bismuth-based erbium-doped fiber (Bi-EDF) for the first time to the best of our knowledge. A 2.15-m-long Bi-EDF is used to provide both nonlinear and linear gains to generate a stimulated Brillouin scattering (SBS) and to amplify the generated SBS, respectively. The BFL operates at 1613.93 nm, which is upshifted by 0.09 nm from the Brillouin pump with a peak power of 2 dBm and a side-mode suppression ratio of more than 22 dB. The generated BFL has a narrow linewidth and many potential applications, such as in optical communication and sensors.
A configuration for linear cavity Brillouin fiber laser (BFL) generation is demonstrated using a standard single-mode fiber, two optical circulators, a 3 dB coupler, and a 95/5 coupler to allow high efficiency. With a Brillouin pump (BP) power of 13 dBm, the laser peak power is 12.3 dB higher than a conventional linear cavity BFL at an upshifted wavelength of 0.086 nm from the BP wavelength. In addition, it is revealed that the BFL peak power can be higher than the transmitted BP peak power when the BP power exceeds the second Brillouin Stokes threshold power.
We demonstrate a multiple-wavelength Brillouin comb laser with cooperative Rayleigh scattering that uses Raman amplification in dispersion-compensating fiber. The laser resonator is a linear cavity formed by reflector at each end of the dispersion-compensating fiber to improve the reflectivity of the Brillouin Stokes comb. Multiple Brillouin Stokes generation has been improved in terms of optical signal-to-noise ratio and power-level fluctuation between neighboring channels. Furthermore, the linewidth of the Brillouin Stokes is uniform within the laser output bandwidth.