Gap-type dark localized modes in a Bose-Einstein condensate with optical lattices

Bose-Einstein condensate(BEC)exhibits a variety of fascinating and unexpected macroscopic phenomena,and has attracted sustained attention in recent years-particularly in the field of solitons and associated nonlinear phenomena.Meanwhile,optical lattices have emerged as a versatile toolbox for understanding the properties and controlling the dynamics of BEC,among which the realization of bright gap solitons is an iconic result.However,the dark gap solitons are still experimentally unproven,and their properties in more than one dimension remain unknown.In light of this,we describe,numerically and theoretically,the formation and stability properties of gap-type dark localized modes in the context of ultracold atoms trapped in optical lattices.Two kinds of stable dark localized modes-gap solitons and soliton clusters-are predicted in both the one-and two-dimensional geometries.The vortical counterparts of both modes are also constructed in two dimensions.A unique feature is the existence of a nonlinear Bloch-wave background on which all above gap modes are situated.By employing linear-stability analysis and direct simulations,stability regions of the predicted modes are obtained.Our results offer the possibility of observing dark gap localized structures with cutting-edge techniques in ultracold atoms experiments and beyond,including in optics with photonic crystals and lattices.

Image encryption using spatial nonlinear optics

Optical technologies have been widely used in information security owing to its parallel and high-speed processing capability.However,the most critical problem with current optical encryption techniques is that the cyphertext is linearly related with the plaintext,leading to the possibility that one can crack the system by solving a set of linear equations with only two cyphertext from the same encryption machine.Many efforts have been taken in the last decade to resolve the linearity issue,but none of these offers a true nonlinear solution.Inspired by the recent advance in spatial nonlinear optics,here we demonstrate a true nonlinear optical encryption technique.We show that,owing to the self-phase modulation effect of the photorefractive crystal,the proposed nonlinear optical image encryption technique is robust against the known plaintext attack based on phase retrieval.This opens up a new avenue for optical encryption in the spatial nonlinear domain.

Third-order Optical Nonlinearities of a Series of Compounds Derived from a Keplerate Type Molybdenum-oxide-based Polyoxometalate

Abstract By reacting the unique Keplerate type molybdenum-oxide based polyoxometalate （NH4）42·[MoI320372·（CH3COO）30（H2O）y2]·ca.300H2·ca. 10CH3COONH4（1） with tetramethylammonium bromide, a new derivative （NH4）26[TMA]16{MoI32O372（H2O）72（CH3COO）30}·ca.7NH4CH3COO·ca.189H2O（2, TMA=tetramethylammonium） was prepared. Compound 2 was characterized by Fourier transform infrared spectroscopy（FTIR）, UV-Vis, elemental and thermogravimetric analyses. By the well-established Z-scan technique, investigations on the nonlinear opti- cal（NLO） properties of the series of compounds derived from the Keplerate type molybdenum-oxide-based poly- oxometalate, namely, the newly prepared compound 2, the three previously reported compounds, included compound 1, （NH4hs（TBA）24{Mo132O372（H2O）72（CH3COO）30}·ca.7NH4CH3COO·ca. 173H2O（3, TBA=tetrabutylammonium） and （DODA）40（NH4）2[（H2O）nMo132O372（CH3COO）3o（H20）72]（4, DODA=dimethyldioctadecylammonium）, reveal that the third-order nonlinearity[x（3）] values of compounds 1, 2 and 3 in the DMF/H2O solution and compound 4 in chloro- form are almost the same, which indicates that the counter cations with different length of alkyl chains show ignora- ble impacts on the NLO susceptibility. In other words, the remarkable third-order nonlinearities[x（3）≈10 19 m2/V2] mainly come from the [MoI32O372（CH3COO）30（H2O）72]42 anions. This fact reveals that the applications of the NLO active polyoxometalates in various environments（such as hydrophilic, hydrophobic, polar, apolar, etc.） can be achieved by simply varying cations to meet the demands in the design of diverse devices. Keywords Keplerate type polyoxometalate; Nonlinear optical property; Z-Scan technique; Self-defocusing; Reverse saturable absorption