Optimal direct coupling from single-mode fibers to Ti:LiNbO₃, channel waveguides

Utilizing the Shift-or-Shrink Algorithm to Optimize the Direct Coupling from Laser Diodes to Diffused Channel Waveguides

“…And the notation c denotes the vertical distance from the center of LD's active region to the top surface of the diffused channel waveguide. On the other hand, for improving the direct coupling efficiency, there may exist a tiny lens or lens-like medium for converging the laser For either cases in sub-figures 1(a) or (b), the direct coupling efficiency between LD's optical beam and the diffused channel waveguide can be calculated by a normalized overlapped integral [8], [9], [14],…”

“…On the other hand, some mathematical models have been proposed for approximating the guided modes of the diffused channel waveguides since their exact analytical solutions are hardly obtained [7], [9], [14]- [16]. One type of approximate model (Type-1 waveguiding mode, W1) has a Gaussian profile in the horizontal direction but two asymmetric half-Gaussian profiles in the vertical direction.…”

“…Afterwards, we search for their optimal coupling conditions by a heuristic shift-or-shrink (SOS) algorithm. SOS algorithm has been proposed for seeking the extrema of a function comprising a few variables, finding the complex solutions of an equation, obtaining the stationary solution in the calculus of variation, and optimizing the photonic device's structures [9], [19], [20]. Among them, the authors have presented an example of searching for the extreme value of a multi-variable paraboloid function by SOS algorithm in [20].…”

Utilizing Shift-or-Shrink Method to Optimize Multisegment Structures of Bent Optical Waveguides

“…In PSO, each particle is stochastically accelerated toward its own extremum locations, that is, global or local extrema. Moreover, the present authors proposed the shift-or-shrink (SOS) method to obtain the optimal directional coupling efficiency from an optical fiber to a diffused waveguide [4] and attempted to find the solution of a calculus-of-variation equation by maximizing the propagation constant of the fundamental mode in an optical waveguide [5]. The proposed SOS algorithm performs the shift or the shrink operation in each round of the procedure.…”

A Comparison of Commonly-used Trial Functions in the Variational Analysis of Ti:LiNbO3 Channel Waveguides

“…For example, a circular Gaussian function is the most popular candidate for modeling the fundamental mode of the fiber due to its simplicity [7][8][9]. However, the Gaussian mode has poor accuracy at low V value (the normalization frequency) and fails to give the correct expression for the evanescent fields [10].…”