arXiv subjects

Mehmet Çelik

Publications and source records attributed to Mehmet Çelik.

6 recordsLinked to original sources

arXiv2019

Tailored design of mode-locking dynamics for low-noise frequency comb generation

We report on a mode-locked laser design using Yb-doped fiber lasers for low-noise frequency-comb generation. The frequency comb covers the spectral range from $700$ to $1400$ nm. Although this range is more practical for many measurements than that produced by the more commonly used Er-fiber lasers, it has been addressed in only a handful of reports, mainly due to the difficulty of generating a fully coherent supercontinuum at $1\;μ$m. We overcome this difficulty by a tailored design of the mode-locking dynamics that succeeds in generating energetic 33 fs-long pulses without even using higher-order dispersion compensation, while ensuring that the laser operates with net zero cavity dispersion for low-noise supercontinuum generation. After locking to a Cs atomic clock, this frequency comb is used for absolute-frequency measurements of a Nd:YAG-I$_2$ laser to verify its accuracy by comparison with results from the International Committee for Weights and Measures. After this verification, it is further used to measure the absolute frequency of a 543-nm two-mode stabilized He-Ne laser, which is routinely used for length measurements in our institute, thus verifying its practical utility in metrology applications. The entire setup is built with readily available components for easy duplication by other researchers.

physics.optics↗

arXiv2018

CINet: A Learning Based Approach to Incremental Context Modeling in Robots

There have been several attempts at modeling context in robots. However, either these attempts assume a fixed number of contexts or use a rule-based approach to determine when to increment the number of contexts. In this paper, we pose the task of when to increment as a learning problem, which we solve using a Recurrent Neural Network. We show that the network successfully (with 98\% testing accuracy) learns to predict when to increment, and demonstrate, in a scene modeling problem (where the correct number of contexts is not known), that the robot increments the number of contexts in an expected manner (i.e., the entropy of the system is reduced). We also present how the incremental model can be used for various scene reasoning tasks.

cs.RO↗

arXiv2016

Obstructions for Compactness of Hankel Operators: Compactness Multipliers

We establish a connection between compactness of Hankel operators and geometry of the underlying domain through compactness multipliers for the $\overline{\partial}$-Neumann operator. In particular, we prove that any compactness multiplier induces a compact Hankel operator. We also generalize the notion of compactness multipliers to vector fields and matrices and then we use this generalization to generate compact Hankel operators.

math.CV↗

arXiv2014

Nilpotent Toeplitz Operators on Reinhardt Domains

We construct explicit examples of non-trivial nilpotent Toeplitz operators on Bergman spaces of certain Reinhardt domains in $\mathbb{C}^2$.

math.CV↗

arXiv2013

Hilbert-Schmidt Hankel Operators with Anti-holomorphic Symbols on Complex Ellipsoids

On a complex ellipsoid in $\mathbb{C}^n$, we show that there is no nonzero Hankel operator with an anti-holomorphic symbol that is Hilbert-Schmidt.

math.CV↗

arXiv2008

Observations regarding compactness in the $\overline{\partial}$-Neumann problem

We show that compactness of the $\overline{\partial}$-Neumann operator is independent of the metric, and we give a new proof of this independence for subellipticity. We define an abstract obstruction to compactness, namely the common zero set of all the compactness multipliers, and we identify this subset of the boundary for convex domains in $\mathbb{C}^{n}$ and for complete Hartogs domains in $\mathbb{C}^{2}$.

math.CV↗