deletions | additions       diff --git a/Another_topic_is_how_graphene__.tex b/Another_topic_is_how_graphene__.tex  index da84229..1b37888 100644  --- a/Another_topic_is_how_graphene__.tex  +++ b/Another_topic_is_how_graphene__.tex 
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Another topic is how graphene can be implemented into waveguides. An understanding of plasmons and surface plasmon polaritons or SPPs are needed to understand Consider  the modes and properties for types of waves that  graphene integrated can support,  in hopes to integrate this into  waveguides. Plasmons are high-frequency, collective density oscillations of an electron liquid and occur in many metals and semiconductors [3]. Surface plasmons areare  the collective oscillations of charges at the surface of plasmonic materials and SPs coupled with photons form composite particles of surface plasmon polaritons. polaritons [4]. It is found that two types of electromagnetic surface waves can exist in graphene, TE and TM modes [4]. The TE mode should come as a surprise. It is know that SPPs can exist at an interface between a dielectric and a metal for TM modes but TE modes don't exist since they don't satisfy boundary conditions at the interface [5]. Mikhailov, S., and K. Ziegler. "New Electromagnetic Mode in Graphene." Physical Review Letters 99.1 (2007): n. pag. Web. It is predicted that TE modes exist in graphene, a mode that does not exist in systems with parabolic electron dispersion [6]. Further it is shown that TE modes lie in the range $1.667 <\frac{\hbar\omega}{\mu}<2$ [6].