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1. Main.aux
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1. Main.aux
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\citation{shvartsburg2013}
\citation{Roper2014}
\citation{Roper2014}
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\bibcite{Ramsay1969}{1}
\bibcite{Jackson2004}{2}
\bibcite{Arslan2006}{3}
\bibcite{Begaud2013}{4}
\bibcite{paul2006}{5}
\bibcite{Botello-Perez2005}{6}
\bibcite{james1989}{7}
\bibcite{Shafai2007}{8}
\bibcite{Gao2013}{9}
\bibcite{Balanis2005}{10}
\bibcite{Rumsey1957}{11}
\bibcite{Collin1985}{12}
\@writefile{toc}{\contentsline {chapter}{{Bibliography}}{98}{chapter*.21}}
\bibcite{hansen1946}{13}
\bibcite{Hines1957}{14}
\bibcite{Jackson2008}{15}
\bibcite{Oliner1988}{16}
\bibcite{Alexopoulos1984}{17}
\bibcite{Jackson1985}{18}
\bibcite{Ettorre2010}{19}
\bibcite{Wollitzer1998}{20}
\bibcite{Yang2013}{21}
\bibcite{Antoniades2008}{22}
\bibcite{mirzaei2011}{23}
\bibcite{Neto2003}{24}
\bibcite{Maci2004}{25}
\bibcite{Neto2005}{26}
\bibcite{Bruni2007}{27}
\bibcite{Sievenpiper2011}{28}
\bibcite{Pendry2006}{29}
\bibcite{Leonhardt2009}{30}
\bibcite{Schmied2010}{31}
\bibcite{Rahm2008}{32}
\bibcite{Luo2008}{33}
\bibcite{Chen2009}{34}
\bibcite{Cheng2010}{35}
\bibcite{Narimanov2009}{36}
\bibcite{Kildishev2007}{37}
\bibcite{Tsang2008}{38}
\bibcite{Yaghjian2008}{39}
\bibcite{Jiang2008}{40}
\bibcite{Alu2009}{41}
\bibcite{Campbell2016}{42}
\bibcite{landy2009}{43}
\bibcite{Wu2014}{44}
\bibcite{Lustrac2013}{45}
\bibcite{pozar2009}{46}
\bibcite{Tang2010}{47}
\bibcite{Tang2014}{48}
\bibcite{Aghanejad2012}{49}
\bibcite{hunt2005}{50}
\bibcite{sadiku2001}{51}
\bibcite{IEEE1983}{52}
\bibcite{Stutzman2012}{53}
\bibcite{Kraus2002}{54}
\bibcite{chen2006}{55}
\bibcite{Walter1965}{56}
\bibcite{Tamir1969}{57}
\bibcite{Neto2010}{58}
\bibcite{felsen1994}{59}
\bibcite{Mahmoud2010}{60}
\bibcite{zelinski2005}{61}
\bibcite{Sutinjo2008}{62}
\bibcite{Hessel1969}{63}
\bibcite{Kong1990}{64}
\bibcite{Shigesawa1988}{65}
\bibcite{Galejs1962}{66}
\bibcite{Neto2010_2}{67}
\bibcite{Enoch2002}{68}
\bibcite{Garcia2002}{69}
\bibcite{Mirzaei2015}{70}
\bibcite{Long2014}{71}
\bibcite{Markley2014}{72}
\bibcite{gordon1923}{73}
\bibcite{dyson1920}{74}
\bibcite{Pendry2000}{75}
\bibcite{Leonhardt2008}{76}
\bibcite{Lier2011}{77}
\bibcite{Luo2009}{78}
\bibcite{Popa2009}{79}
\bibcite{Schmiele2010}{80}
\bibcite{Tichit2009}{81}
\bibcite{Ward1996}{82}
\bibcite{ozgun2010}{83}
\bibcite{Saks1952}{84}
\bibcite{nehari1952}{85}
\bibcite{Urzhumov2010}{86}
\bibcite{Ma2010}{87}
\bibcite{Gomez-Reino1987}{88}
\bibcite{zouhdi2012}{89}
\bibcite{Zhang2010}{90}
\bibcite{Smithgall1973}{91}
\bibcite{Marcuse1973}{92}
\bibcite{Bliokh2007}{93}
\bibcite{merchand2012}{94}
\bibcite{Melorose2015}{95}
\bibcite{nieto1991}{96}
\bibcite{Burokur2016}{97}
\bibcite{martio2008}{98}
\bibcite{Thompson2012}{99}
\bibcite{yi2015}{100}
\bibcite{Henrici1986}{101}
\bibcite{aghanejad2016}{102}
\bibcite{AlNoor2016}{103}
\bibcite{chew1995}{104}
\bibcite{pearson1969}{105}
\bibcite{martin1974}{106}
\bibcite{shvartsburg2013}{107}
\bibcite{Roper2014}{108}