Benefits of Spectral Property Engineering in Distributed Brillouin Fiber Sensing

As one of the most consolidated distributed fiber sensors based on stimulated Brillouin scattering, the Brillouin optical time-domain analyzer (BOTDA) has been developed for decades. Despite the commercial availability and outstanding progresses which has been achieved, the intrinsic Lorentzian gain spectrum restricts the sensing performance from possible further enhancements and hence limits the field of validity of the technique. In this paper, the novel method of engineering the gain spectral properties of the Brillouin scattering and its application on static and dynamic BOTDA sensors will be reviewed. Such a spectral property engineering has not only provided improvements to BOTDA, but also might open a new way to enhance the performance of all kinds of distributed Brillouin fiber sensors.

On the spectrality of self-affine measures with four digits on ℝ2

In this paper, we study the spectral property of the self-affine measure [Formula: see text] generated by an expanding real matrix [Formula: see text] and the four-element digit set [Formula: see text]. We show that [Formula: see text] is a spectral measure, i.e. there exists a discrete set [Formula: see text] such that the collection of exponential functions [Formula: see text] forms an orthonormal basis for [Formula: see text], if and only if [Formula: see text] for some [Formula: see text]. A similar characterization for Bernoulli convolution is provided by Dai [X.-R. Dai, When does a Bernoulli convolution admit a spectrum? Adv. Math. 231(3) (2012) 1681–1693], over which [Formula: see text]. Furthermore, we provide an equivalent characterization for the maximal bi-zero set of [Formula: see text] by extending the concept of tree-mapping in [X.-R. Dai, X.-G. He and C. K. Lai, Spectral property of Cantor measures with consecutive digits, Adv. Math. 242 (2013) 187–208]. We also extend these results to the more general self-affine measures.