Tatsushi Tanaka

Proposal of optical mode switch

Here, we propose a novel optical mode switch, which is a new concept of the optical switch. It can overcome the matrix size limitation issue, which has been a general issue for the waveguide optical space switch, because of its simple fiber coupling configuration. In addition, it contributes to the lossless mux/demux function such as wavelength multiplexing with powerless mode conversion unlike wavelength conversion. In this paper, we propose the principle of the optical mode switch. The simulation results showed less than −30 dB mode crosstalk, with less than only 0.1 dB excess loss for a two-mode optical switch. Moreover, the scalable configuration up to four modes is also proposed in this paper.

The Bowman-Bradley theorem for multiple zeta-star values

Abstract Text The Bowman–Bradley theorem asserts that the multiple zeta values at the sequences obtained by inserting a fixed number of twos between 3 , 1 , … , 3 , 1 add up to a rational multiple of a power of π. We establish its counterpart for multiple zeta-star values by showing an identity in a non-commutative polynomial algebra introduced by Hoffman. Video For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=LpqA2OJ6vP8 .

Electrically controlled optical-mode switch for fundamental mode and first order mode

We have proposed an optical mode switch, the principle of which is based on the partial phase shift of injected light; therefore, one important issue is to clarify the proper design criteria for the mode combiner section. We focused on the bending radius of the S-bend waveguide issue that is connected to the multi mode waveguide in the Y-junction section that acts as mode combiner. Long radius leads to undesired mode coupling before the Y-junction section, whereas a short radius causes radiation loss. Thus, we simulated this mode combiner by the beam-propagation method to obtain the proper radius. In addition, we used a trench pin structure to simplify the fabrication process into a single-step dry-etching process. As a result, we successfully fabricated an optical-mode switch with the bending radius R = 610 µm. It showed the successful electrical mode switching and the achieved mode crosstalk was approximately −10 dB for 1550 nm wavelength with the injection current of 60 mA (5.7 V).

Mode crosstalk evaluation on optical mode switch

We show the mode crosstalk between the fundamental mode and the 1st order mode based on the optical mode switch to investigate the performance experimentally for the first time. In order to evaluate the mode crosstalk, we fabricated and integrated multimode interference (MMI) mode filter with the optical mode switch. The crosstalk of approximately -10 dB between modes has been evaluated by using this mode filter.

Rooted tree maps and the derivation relation for multiple zeta values

Rooted tree maps assign to an element of the Connes-Kreimer Hopf algebra of rooted trees a linear map on the noncommutative polynomial algebra in two letters. Evaluated at any admissible word these maps induce linear relations between multiple zeta values. In this note we show that the derivation relations for multiple zeta values are contained in this class of linear relations.