Optical Tunnelling from One-Dimensional Square-Well Potentials

The authors study a one-dimensional model for optical tunnellingwith a refractive index in the shape of a square well. The relevanceof the model and its limiting cases are discussed. The mainresult is the leading behaviour of the exponentially small imaginarypart of the eigenvalue which determines the radiation loss.The leading behaviour of the imaginary part is calculated usingBerry's formula which controls the asymptotic expansion of theAiry function Bi(z) to better-than-exponential accuracy.     

DOUBLET Stentor DO NOT DISPLAY PHOTODISPERSAL

Normal Stentor, called singlets since they have a single membranellar band and oral groove surrounding their frontal field, swim away from light sources and collect in the darker areas of an unevenly illuminated container (photodispersal). Phenotypic variants, called doublets since they have 2 membranellar bands and 2 oral grooves, do not exhibit this behavior. Doublets produce photophobic responses and contractions when illuminated at the same fluence rates which produce those responses in singlets, hence their sensitivity to light is normal. Illumination of the frontal field of doublets produces a photophobic response at lower fluence rates than does illumination of their side or posterior. This directional sensitivity is quantitatively similar to that observed in singlets. However, doublets do not reorient their swimming direction after a phobic response as extensively as do singlets. This failure in reorientation is the probable reason that doublets fail to show photodispersal. These results imply that the mechanism producing photodispersal in singlets depends on photophobic responses or some other, presently undescribed, response which requires an asymmetric frontal field.     

Eigenfunction Expansions by the Delta Function and Contour Integral Method

The formal identity is sometimes usedin applied mathematics and engineering textbooks in conjunctionwith the contour integral method to obtain eigenfunction expansionsassociated with y'+y = 0 with boundary conditions. This papergives a rigorous application of this method to the more generalequation y'+( – q(x))y = 0 in the regular case.     

The director structure and electroclinic fast optical switching in a grating-coupled ferroelectric smectic liquid crystal cell

Optical excitation of guided modes in a liquid crystal layer using grating-coupling gives sharp features in the angle-dependent reflectivity data. These features are strengthened by using a metallized grating to enhance coupling to the guided modes in the liquid crystal. In the present study the liquid crystal has a smectic A phase which exhibits fast electroclinic switching. Combining the sharp features in the reflectivity together with the electroclinic effect leads to fast, high contrast, optical switching which may open up potential for novel device structures.