In the present paper,we provide an error bound for the learning rates of the regularized Shannon sampling learning scheme when the hypothesis space is a reproducing kernel Hilbert space(RKHS) derived by a Mercer kerne...In the present paper,we provide an error bound for the learning rates of the regularized Shannon sampling learning scheme when the hypothesis space is a reproducing kernel Hilbert space(RKHS) derived by a Mercer kernel and a determined net.We show that if the sample is taken according to the determined set,then,the sample error can be bounded by the Mercer matrix with respect to the samples and the determined net.The regularization error may be bounded by the approximation order of the reproducing kernel Hilbert space interpolation operator.The paper is an investigation on a remark provided by Smale and Zhou.展开更多
The most relevant aspects related to the phase mask dithering/moving method for the fabrication of complex Bragg grating designs are reviewed. Details for experimental implementation of this technique is presented, in...The most relevant aspects related to the phase mask dithering/moving method for the fabrication of complex Bragg grating designs are reviewed. Details for experimental implementation of this technique is presented, including theoretical analysis of the calibration functions for the correct dither/displacement. Results from tailored Bragg grating structures fabricated by this method are shown. Apodized Bragg gratings with modeled spatial profiles were implemented, resulting in side mode suppression levels of more than 20 dB in gratings showing transmission filtering level higher than 30 dB. Chirped gratings with the spectral bandwidth up to 4 nm, π-shift and sampled Bragg gratings with equalized peaks equally spaced by 0.8 nm （100 GHz） were also fabricated.展开更多
In this paper we design a new kind of sinc-sampled fiber Bragg grating which is fabricated in high birefringence fiber (HBF). The sampled grating has two sets of reflection spectra along two perpendicular polarization...In this paper we design a new kind of sinc-sampled fiber Bragg grating which is fabricated in high birefringence fiber (HBF). The sampled grating has two sets of reflection spectra along two perpendicular polarization directions. The grating's channel number can be doubled approximately by designing the refractive index difference between the fast and slow axes of the fiber, which enhances the utilization ratio and reduces the claim for photosensitivity of the fiber. The group delay characteristics are theoretically studied and side-lobes are depressed by apodization as well to get the optimized spectra. The results show that the comb-like spectra of the grating have promising applications in both multi-wavelength polarized fiber lasers and fiber sensing networks.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10871226)Natural Science Foundation of Zhejiang Province (Grant No. Y6100096)
文摘In the present paper,we provide an error bound for the learning rates of the regularized Shannon sampling learning scheme when the hypothesis space is a reproducing kernel Hilbert space(RKHS) derived by a Mercer kernel and a determined net.We show that if the sample is taken according to the determined set,then,the sample error can be bounded by the Mercer matrix with respect to the samples and the determined net.The regularization error may be bounded by the approximation order of the reproducing kernel Hilbert space interpolation operator.The paper is an investigation on a remark provided by Smale and Zhou.
文摘The most relevant aspects related to the phase mask dithering/moving method for the fabrication of complex Bragg grating designs are reviewed. Details for experimental implementation of this technique is presented, including theoretical analysis of the calibration functions for the correct dither/displacement. Results from tailored Bragg grating structures fabricated by this method are shown. Apodized Bragg gratings with modeled spatial profiles were implemented, resulting in side mode suppression levels of more than 20 dB in gratings showing transmission filtering level higher than 30 dB. Chirped gratings with the spectral bandwidth up to 4 nm, π-shift and sampled Bragg gratings with equalized peaks equally spaced by 0.8 nm （100 GHz） were also fabricated.
基金supported by the Natural Science Funds of Shandong Province (No.Q2007G03)the Independent Innovation Fund of Shandong University (No.2010TS014)the Open Fund of Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), Ministry of Education
文摘In this paper we design a new kind of sinc-sampled fiber Bragg grating which is fabricated in high birefringence fiber (HBF). The sampled grating has two sets of reflection spectra along two perpendicular polarization directions. The grating's channel number can be doubled approximately by designing the refractive index difference between the fast and slow axes of the fiber, which enhances the utilization ratio and reduces the claim for photosensitivity of the fiber. The group delay characteristics are theoretically studied and side-lobes are depressed by apodization as well to get the optimized spectra. The results show that the comb-like spectra of the grating have promising applications in both multi-wavelength polarized fiber lasers and fiber sensing networks.
