An analysis of waveguiding in hBN for studying the optical properties of 2D semiconductors

The van der Waals layering and dielectric properties of hexagonal boron nitride (hBN) have made it an essential component in studying the transport and optoelectronic properties of layered materials, especially graphene and transition metal dichalcogenides (TMDs).  Importantly, hBN’s wide band gap and uniform dielectric environment reduce emission line broadening due to charge fluctuations in TMDs.  At optical frequencies, hBN is yet again imbued with advantageous properties with an absorption-free in-plane near-IR index of refraction of <!--[if gte msEquation 12]> style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'>n _{style='mso-bidi-font-style:normal'>o} n_o= 2.25, and out-of-plane index of refraction of <!--[if gte msEquation 12]>n style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'>­_e style='mso-bidi-font-style:normal'>  n_e= 1.59, yielding a positive uniaxial birefringence of Δn=0.66<!--[if gte msEquation 12]> style='font-size:11.0pt;line-height:107%;font-family:"Cambria Math",serif;
mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-family:
"Times New Roman";mso-bidi-theme-font:minor-bidi;mso-ansi-language:EN-US;
mso-fareast-language:EN-US;mso-bidi-language:AR-SA'> m:val="p"/>?n style='mso-bidi-font-style:normal'>=0.66, more than doubling both calcite (-0.172) and rutile (0.287).  With the ubiquity of hBN employed in layered material stacks, in this work we computationally explore routes to in-couple and out-couple light to and from TMD films either embedded within, or supported by, hBN films ranging from a few monolayers to hundreds of nanometers.  In particular, we identify the wavelength-dependent cut-off thicknesses for transverse electric (TE) and transverse magnetic (TM) guided-modes, and investigate the mode coupling for in-plane (bright excitons) and out-of-plane (dark excitons) electric dipoles, thereby simulating luminescence. We will also discuss strategies to exploit the birefringence and control polarization via edge-orientated coupling. We will conclude by comparing the findings with experimental results spanning a range of TMD test structures.