Abstract — We   propose   a   design   and   two   dimensional   (2D)    simulation of a Photonic Crystals (PhC) slab waveguide laser tip  with triangular lattices for dental treatments. The band diagram  is  computed  in  the  transverse  electric  (TE)  mode  for  triangular   lattices  of  air  holes  in  silicon  su bstrate.  The  power  transmission   efficiencies of 90 and 120 bending structure with different sizes  of   defects   are   measured   and   compared   with   the   straight    waveguide.  The  result  shows   that  for  the  bending  structure,   the  efficiency  depends  relativ ely  on  both  bending  degree   and  defect  size  and  for  this   particular  design,  the  highest   efficiency  is  achieved  using  the  120  structure  with  W2  defect.
Keywords-component;    Photonic    Crystals    slab    waveguide; bending structure; triangular lattices;dental  laser tips;

I. I NTRODUCTION Infrared  lasers  are  widely  used  in  applications  of  dentistry   for  coral  cavity  treatment.  In  a  small  area  operation,  the  tiny   probe  is  employed  to  guide  the  laser  beam  to  the  problematic   area. The laser tip is preferably designed to be sharp with small  spot size and with some bendi ng angle to enable a treatment in  the  difficult  to  reach  area  [1-4].  For  the  insert-type  tip,  loss   increases with the bending angle and the fixed-bending tip with  a radius of 2-3 mm can cause the heat around the tip surface up to  100  C  [1].  For  the  chisel-shaped  fiber  tip  [2]  and  a  fiber- based  desktop  diode  with  ultra-short-pulsed  (1552 nm )  laser   [4],  the  ablation  slows  down  when  the  distance  treatment   increases. The important issue in a small area application is the  ability  to  control  the  light  to  a  specific  location  with  high   accuracy and efficiency.  Photonic Crystals (PhC) is an artificial periodic structure of  dielectrics   possessing   great   potential   for   controlling   and    manipulating the light propagation in nano structures with high  efficiency  [5].  The  possibilities  of  absolute  band  gaps  in  their   band   structures   have   found   several   applications   such   as    waveguides,  filters,  and  splitters  [5-6].  This  paper  focuses  on   the  application  of  a  low  loss  p hotonic  crystals  slab  waveguide   to  be  used  as  the  laser  bending  tip  for  dental  treatment.  The   advantages of the proposed tip compared with the conventional  laser  tip  includes  small  spot  size  [1-4],  high  efficiency  even   with bending geometry, and simple design and fabrication. The  simulation  is  performed  to  evaluate  the  efficiency  of  bending   PhC waveguides at 90   and 120   that will be compared to that of the straight (180  ) waveguide. The size of the guiding path  or  defect  is  varied  by  removing  the  arrays  of  holes.  Section  II   presents the theoretical design and simulation setup. Section III  presents the results and discussion. Conclusions are provided in  Section IV.
The  2D  power  flow  plots  of  the  proposed  PhC  tip  are   shown in Fig. 5. These images show how lights are propagated  inside   the   structure.   It   is   noticed   that   scattering   occurs    distinctively  near  bending  spots  of  90   and  120   structures.  Relatively large scattering is observed for W1 and W2 defects  of  the  90    structure  and  for  the  W3  defect  of  the  12 structure,  respectively.  This  result  suggests  that  the  power   efficiency  depends  certainly  on  the  bending  angle  and  the   defect   size   and   the   correlation   between   these   two   input    variables  can  be  expected.  Fig.  6  illustrates  the  plot  of  the   transmission    efficiency    of    the    photonic    crystals    slab     waveguide  laser  tip.  It  is  first  found  that  the  overall  highest   efficiency   of   around   90%   is   achieved   using   the   straight    waveguide,  as  expected.  The  overall  efficiency  decreases  as   the  bending  angle  decreases  and  in  particular  for  the  bending   structures,  W2  gives  higher  transmission  efficiency  than  W1   and  W3.  It  appears  that  this  W2   defect  is  designed  more   properly for the wave propagation at the studied wavelength.
A  laser  tip  used  in  dentistry  application  is  designed  using   the   Photonic   Crystals   slab   waveguide   with   the   TE   mode    propagation. The simulation results show that the transmission  efficiency  depends  certainly  on  the  bending  angle  and  the   defect  size.  The  overall  efficiency  decreases  as  the  bending   angle  decreases  and  for  our  design,  the  highest  efficiency  of   bending  structures  is  achieved  with  120  bending  and  W2   defect. Based on these results presented in this paper, the future  of  the  laser  tip  PhC  waveguide  for  dental  devices  is  highly   promising. Future work includes 3D simulation of the PhC tip, prototype fabrication and experimental validation.