   ᢙ )*\ ߩ๟ᵄᢙᏪߦ߅ߌࠆ⽶ߩㅘ⏛₸ࠍ␜ߔ᭴ㅧߩ㐿⊒ߣߘߩᐢᏪၞൻߦ㑐ߔࠆ⎇ⓥ᦭㚍 ථม㧘 ቝ㊁ ੧᧲੩ㄘᎿᄢቇ ᄢቇ㒮 Ꮏቇ⎇ⓥ⑼ 㔚᳇㔚ሶᎿኾ᡹๟ᵄᢙ߇ᢙ )*\ ߩ㔚⏛ᵄߪᵄ㐳߇ᢙච EO ߢ޽ࠅ㧘ߘߩવ៝․ᕈ߿ᵄ㐳߇ࠕࡦ࠹࠽૞ᚑߦㆡߒߡ޿ࠆߎߣߥߤ߆ࠄ㧘៤Ꮺ㔚⹤ࠍߪߓ߼㧘᭽‫↪ߥޘ‬ㅜߦ૶↪ߐࠇࠆ㧚৻ᣇ㧘ߎࠇ߹ߢ⥄ὼ⇇ߦߪሽ࿷ߒߥ޿ߣᕁࠊࠇߡ޿ߚ㔚᳇⊛․ᕈࠍ␜ߔࡔ࠲ࡑ࠹࡝ࠕ࡞ߣ๭߫ࠇࠆ᭴ㅧ߇ᵈ⋡ߐࠇߡ޿ࠆ㧚╩⠪ࠄߪ㧘๟ᵄᢙ߇ᢙ )*\ ߩ㗔ၞߦ߅޿ߡ㧘ߎߩࡔ࠲ࡑ࠹࡝ࠕ࡞ߩ৻⒳ߢ޽ࠆ⽶ߩㅘ⏛₸ࠍ␜ߔ᭴ㅧߩ㐿⊒߅ࠃ߮⽶ߩㅘ⏛₸ࠍ␜ߔᏪၞߩᐢᏪၞൻࠍⴕߞߚ㧚㐿⊒ߒߚ᭴ㅧߪ㧘ࠦߩሼဳߩዉ૕ㄭறߦነ↢⚛ሶࠍઃടߒ㧘ߎࠇࠍ๟ᦼ⊛ߦਗߴߚ߽ߩߢ޽ࠆ㧚㐿⊒ߦߪ FDTD㧔ᤨ㑆㗔ၞ᦭㒢Ꮕಽ㧕
ᴺߦࠃࠆ㔚⏛⇇ࠪࡒࡘ࡟࡯࡚ࠪࡦࠍⴕߞߚ㧚ࠪࡒࡘ࡟࡯࡚ࠪࡦߪߔߴߡ᧲ർᄢቇࠨࠗࡃ࡯ࠨࠗࠛ
ࡦࠬ࠮ࡦ࠲࡯ߩࠬ࡯ࡄ࡯ࠦࡦࡇࡘ࡯࠲ 5: ࠍ↪޿ߚ㧚 ߪߓ߼ߦ⃻࿷㧘ᚒ‫↢ߩޘ‬ᵴߦ߅޿ߡ㧘㔚⏛ᵄߪήߊߡߪߥࠄߥ޿‛ߣߥߞߡ޿ࠆ㧚㔚⏛ᵄߪ๟ᵄᢙߦࠃߞߡ․ᕈ߇⇣ߥࠅ㧘࿾਄࠺ࠫ࠲࡞᡼ㅍߢߪ /*\㨪/*\ ߩ๟ᵄᢙ߇↪޿ࠄࠇ㧘))) ៤Ꮺ㔚⹤ߦ߅޿ߡߪߘࠇߙࠇ )*㨦Ꮺ㧘)*\ Ꮺ㧘)*\ Ꮺߥߤ߇↪޿ࠄࠇߡ޿ࠆ㧚ߐࠄߦ㜞޿๟ᵄᢙᏪߩ )*\㨪)*\ ߩ㔚⏛ᵄߪࡑࠗࠢࡠᵄߣ๭߫ࠇ㧘79$㧔⿥ᐢᏪၞାภ೑↪㧕ㅢା߿࡟࡯࠳ߥߤߦ೑↪ߐࠇߡ޿ࠆ㧚৻ᣇ㧘ߎࠇࠄ๟ᵄᢙߦ߅޿ߡ⥄ὼ⇇ߦߪሽ࿷ߒߥ޿㔚᳇⊛․ᕈࠍ␜ߔࡔ࠲ࡑ࠹࡝ࠕ࡞=?=?ߣ
๭߫ࠇࠆੱᎿᇦ⾰ߩ⎇ⓥ߇ㅴ߼ࠄࠇߡ޿ࠆ㧚ߘߩਛߢ߽⽶ߩዮ᛬₸=?=?=?ࠍታ⃻ߔࠆࡔ࠲ࡑ࠹࡝ࠕ࡞ߩ⎇ⓥ߇ᵈ⋡ࠍ㓸߼ߡ޿ࠆߎߩࡔ࠲ࡑ࠹࡝ࠕ࡞ߪ๟ᦼ᭴ㅧ૕ߢ᭴ᚑߐࠇ㧘⽶ߩዮ᛬₸ࠍ᦭ߔࠆࡔ࠲ࡑ࠹࡝ࠕ࡞ߦ㔚⏛ᵄࠍᒰߡࠆߣ㧘ᣢሽߩᇦ⾰ߣߪㅒߩᣇะ߳ዮ᛬ࠍߔࠆߚ߼㧘ࠕࡦ࠹࠽ߩዊဳൻ߿࡟ࡦ࠭ߩ㜞ᕈ⢻ൻߦነਈߢ߈ࠆߣߐࠇߡ޿ࠆ㧚⽶ߩዮ᛬₸ࠍታ⃻ߔࠆߦߪ⽶ߩ⺃㔚₸ߣ⽶ߩㅘ⏛₸ߩ⚵ߺวࠊߖ߇ᔅⷐߢ޽ࠆ㧚⽶ߩ⺃㔚₸ࠍታ⃻ߔࠆ᭴ㅧߩ㐿⊒ߪ⃻࿷㧘ᄙߊߐࠇߡ޿ࠆ㧚৻ᣇߢ㧘⽶ߩㅘ⏛₸ࠍታ⃻ߔࠆ᭴ㅧߩ㐿⊒ߪ޿߹ߛዋߥߊ㧘߹ߚ⽶ߩㅘ⏛₸ࠍታ⃻ߔࠆ๟ᵄᢙᏪ߇ᣢሽߩ᭴ㅧߛߣ⁜޿ߚ߼㧘ታ↪⊛ߥᛛⴚᔕ↪߇ߐࠇߦߊ޿ߣߐࠇߡ޿ࠆ㧚ߘߎߢᧄ⎇ⓥߪ㧘๟ᵄᢙ߇ᢙ )*\ ߩ㗔ၞߦ߅޿ߡ⽶ߩㅘ⏛₸ࠍታ⃻ߔࠆ᭴ㅧߩ㐿⊒߅ࠃ߮๟ᵄᢙᏪߩᐢᏪၞൻࠍ⋡⊛ߣߔࠆ㧚㐿⊒ߦߪᓸಽᒻߩࡑ࠶ࠢࠬ࠙ࠚ࡞ߩᣇ⒟ᑼࠍⓨ㑆߅ࠃ߮ᤨ㑆ߦߟ޿ߡᏅಽߔࠆ
FDTD ᴺ=?ࠍ↪޿ߚ㔚⏛⇇ࠪࡒࡘ࡟࡯࡚ࠪࡦࠍⴕߞߚ㧚ࠪࡒࡘ࡟࡯࡚ࠪࡦߪߔߴߡ᧲ർᄢቇࠨ
ࠗࡃ࡯ࠨࠗࠛࡦࠬ࠮ࡦ࠲࡯ߩࠬ࡯ࡄ࡯ࠦࡦࡇࡘ࡯࠲ 5: ࠍ↪޿ߚ㧚㧞㧚(&6& ᴺߦࠃࠆታല⺃㔚₸߅ࠃ߮ㅘ⏛₸ߩ⸃ᨆᚻᴺ ᧄ⎇ⓥߪ㧘FDTD ᴺࠍ↪޿ߚࠪࡒࡘ࡟࡯࡚ࠪࡦߦࠃࠅ㧘᭴ㅧߩㅘ⏛₸ࠍ⸃ᨆߒ㧘ㆡߒߚ᭴ㅧߩ⸳⸘ࠍⴕ߁㧚FDTD ᴺߦࠃࠆ᭴ㅧߩ⺃㔚₸ߣㅘ⏛₸ߩ⸃ᨆᣇᴺࠍ␜ߔ㧚⸃ᨆࡕ࠺࡞ࠍ࿑㧝ߦ␜ߔ㧚
࿑ 1 ߪෘߐ d ߩ᭴ㅧ߇ FDTD ᴺߩ⸃ᨆⓨ㑆ਛߦ߅߆ࠇߡ޿ࠆࡕ࠺࡞ߢ޽ࠆ㧚FDTD ᴺߢߪု⋥౉኿ߦࠃࠆᇦ⾰߆ࠄߩㅘㆊᵄߣ෻኿ᵄߦࠃߞߡ⺃㔚₸ߣㅘ⏛₸ߩ⹏ଔ߇ߢ߈ࠆ.   

࿑ 1 ⸃ᨆⓨ㑆ਛߩ᭴ㅧ⺃㔚₸  ߣㅘ⏛₸  ߪ㧘ᇦ⾰ߩዮ᛬₸ n ߣࠗࡦࡇ࡯࠳ࡦࠬ z ࠍ↪޿ߡ㧘ᰴߩࠃ߁ߦ⴫⃻ߢ߈ࠆ.
nH(1)
zP nz
(2)
ߐࠄߦ,ዮ᛬₸ n ߣࠗࡦࡇ࡯࠳ࡦࠬ z ߪ,ᇦ⾰ࠬ࡜ࡉߦኻߔࠆ S ࡄ࡜ࡔ࡯࠲ߣએਅߩ㑐ଥ߇ᚑࠅ┙ߟ.
S11R01 (1  e i 2 nk0d )2 i 2 nk0 d
1  R01e(3)

S122(1  R01)e ink0d
2 i 2 nk0 d
1  R01e(4)z 1z 1(5)ߎߎߢR01ߢ޽ࠆ.ߒߚ߇ߞߡ㧘(3)㧘(4)ࠍ n ߅ࠃ߮ z ߦߟ޿ߡ⸃ߊߎߣߢ㧘ᇦ⾰ߩ⺃㔚₸  ߣㅘ⏛₸  ࠍ᳞߼ࠆߎߣ߇ߢ߈ࠆ㧚ᑼ(3)㧘(4)ࠍࠗࡦࡇ࡯࠳ࡦࠬ z㧘ዮ᛬₸ n ߦߟ޿ߡ⸃ߊߣᰴߩࠃ߁ߦߥࠆ㧚zn^ >2(1  S11 )2  S 21

(6)2(1  S 21 )2  S21@>

1Im e ink0d  2mS  i Re e ink0dk0 d@`

ߎߎߢ m ߪ Re[n]ߩಽጘߩ⇟ภࠍ␜ߔᢛᢙߢ޽ࠅ㧘e ink0d(7)X r i 1 X 2 , X

21 / 2S 21 (1  S112  S 21)ߢ޽ࠆ㧚m ߪዮ᛬₸ n ߇ㅪ⛯⊛ߦߥࠆࠃ߁ߦߒߡㆬ߱㧚ᰴߦ S ࡄ࡜ࡔ࡯࠲ߩ᳞߼ᣇߦߟ޿ߡ⺑᣿ߔࠆ㧚S ࡄ࡜ࡔ࡯࠲ߩ૏⋧ߪᇦ⾰⴫㕙ߦࠃߞߡቯ⟵ߐࠇࠆ㧚৻ᣇߢ FDTD ᴺߢߪ㧘෻኿ᵄߣㅘㆊᵄߪᇦ⾰߆ࠄዋߒ㔌ࠇߚὐߢ⸃ᨆࠍߔࠆߚ߼㧘ߘߩ߹߹ S ࡄ࡜ࡔ࡯࠲ߦㆡ↪ߢ߈ߥ޿㧚ߒߚ߇ߞߡ૏⋧ߩ⵬ఘࠍߔࠆᔅⷐ߇޽ࠆ㧚෻኿₸ R ߣㅘㆊ₸ Tߩ⸘▚ߪ㧘᭴ㅧ૕߇޽ࠆ႐วߣߥ޿႐วߩ㧞࿁ⴕ߁㧚߹ߕ㧘᭴ㅧ૕߇޽ࠆ႐ว㧘x1 ߢ⸥㍳ߐࠇߚ㔚⇇ߪ
V1 (Z )

A(Z )e iE (Z ) x1  B(Z )e  iE (Z ) x1(8) 
!"#$%&'()*+,./0123)"45 ߢਈ߃ࠄࠇࠆ㧚৻ᣇ,᭴ㅧ߇ߥ޿႐วߩ㔚⇇ߪ(9)A(Z )e iE (Z ) x1

V2 (Z )

ߢਈ߃ࠄࠇࠆߩߢ㧘x1 ߦ߅ߌࠆ෻኿₸ R ߪᰴߩᑼߢਈ߃ࠄࠇࠆ㧚
RV1  V2V2B (Z )e  iE (Z ) x1
A(Z )e iE (Z ) x1

B (Z )  2 iE (Z ) x1
eA(Z )(10)ߎߩ R ߩ૏⋧ࠍ x0 ὐࠍၮḰߦߔࠆߎߣߢ㧘S11 ߇ਈ߃ࠄࠇࠆ㧚(11)

Re 2iE (Z ) x1

S11

S21 ߦߟ޿ߡ߽ห᭽ߩ⸘▚ࠍⴕ߁㧚ㅘㆊ₸ T ߪ᭴ㅧ߇ߥ޿႐วߩㅘㆊᵄߣ᭴ㅧ߇ߥ޿႐วߩㅘ
ㆊᵄ߆ࠄਈ߃ࠄࠇࠆ㧚TA' (Z )e  iE (Z ) x 2A(Z )e iE (Z ) x 2

A' (Z )
A(Z )

(12)

ߎߩ T ࠍ↪޿ࠆߣ㧘S21 ߪᰴߩᑼߢਈ߃ࠄࠇࠆ㧚S 21(13)

Te ik0d㧟ឭ᩺ߔࠆ᭴ㅧߣ⸃ᨆ⚿ᨐ㧟 ឭ᩺ߔࠆ᭴ㅧߣ⸃ᨆ⚿ᨐ
ᐢᏪၞߥ⽶ߩㅘ⏛₸ࠍ␜ߔ᭴ㅧߩ㐿⊒ߦ޽ߚࠅ㧘࿑ 2 ߦ␜ߔᣢሽߩࡕ࠺࡞ߦኻߔࠆ⸃ᨆ⚿ᨐࠍ␜ߔ㧚ߎߩ᭴ㅧߪ Split Ring Resonators(SRRs)ߣ๭߫ࠇࠆ㧚2 ▵ߢ⺑᣿ߒߚᣇᴺࠍ↪޿ߡ㧘⽶ߩㅘ⏛₸ࠍ⸃ᨆߒߚ⚿ᨐࠍ࿑ 3 ߦ␜ߔ㧚⸃ᨆ⚿ᨐ߆ࠄࠊ߆ࠆࠃ߁ߦ㧘1.3 GHz ߦ߅޿ߡ⚂ 96 MHzߩ๟ᵄᢙᏪၞߢ⽶ߩㅘ⏛₸ࠍ␜ߒߡ޿ࠆ㧚࿑
ᣢሽߩ Split Ring Resonators
࿑ 2 ᣢሽߩ
Relative permeability

1050

5−5

10−100

1

23

Frequency [GHz]࿑ᣢሽߩ Split Ring Resonators ߩ⸃ᨆ⚿ᨐߩ⸃ᨆ⚿ᨐ࿑ 3 ᣢሽߩ
ᰴߦᐢᏪၞൻࠍታ⃻ߔࠆߚ߼ߦ㧘ᐢᏪၞൻߩℂ⺰⊛⠨ኤࠍⴕ߁㧚߹ߕSRRsߦ߅ߌࠆㅘ⏛₸ߩℂ⺰ᑼߪએਅߢዉ߆ࠇࠆ㧚 

 P1 FZ (Z )i
1LZ
LC Z 21(14)ߎߎߢ㧘Fߪ(KNNKPIHCEVQT㧘Lߪࠗࡦ࠳ࠢ࠲ࡦࠬ㧘Cߪࠠࡖࡄࠪ࠲ࡦࠬߢ޽ࠆ㧚
1(14)߆ࠄ㧘๟ᵄᢙ߇(౒ᝄ๟ᵄᢙ)ߢㅘ⏛₸߇⊒ᢔߒ㧘LCࠆ㧚ߒߚ߇ߞߡ‫ߩ⽶ޔ‬ㅘ⏛₸ࠍ␜ߔ๟ᵄᢙᏪ᏷ߪ

1LC(11 F11LC1 Fߢㅘ⏛₸߇́п߆ࠄ0ߦᚯ 1) ߢ޽ࠆ੐߇ಽ߆ࠆ㧚ߎߩߎߣࠃࠅ⽶ߩㅘ⏛₸ࠍ␜ߔ๟ᵄᢙᏪ᏷ߪ౒ᝄ๟ᵄᢙ߇㜞޿߆㧘(KNNKPIHCEVQT߇ᄢ߈޿㧚ߟ߹ࠅ๟ᦼ㕙Ⓧߦኻߔࠆᇦ⾰ߩࠦࠗ࡞૞↪ࠍߔࠆ㕙Ⓧ߇ᄢ߈޿߶ߤᄢ߈ߊߥࠆ㧚ߎߩߎߣࠍ೨ឭߣߒߡหߓ౒ᝄ๟ᵄᢙߢ⠨߃ߚ႐ว㧘࿑ߦ޽ࠆࠃ߁ߥභ᦭₸߇ᄢ߈޿ฝߩ᭴ㅧߩ߶߁߇㧘๟ᵄᢙᏪ᏷߇ᄢ߈ߊߥࠆߩߪᔅὼߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚߹ߚ㧘࿑ਛߩฝߩ᭴ㅧߦઃ㓐ߔࠆነ↢⚛ሶߪࠦဳߩಾขࠅㇱಽ߆ࠄዋߒ㔌ߒߚ߶߁߇㧘භ᦭㕙Ⓧ߇ᄢ߈ߊߥࠆߩߢℂߦ߆ߥߞߡ޿ࠆߣ޿߃ࠆ㧚ߒ߆ߒ㧘㔌ߒߔ߉ࠆߣࠠࡖࡄࠪ࠲ࡦࠬ߇޽߹ࠅߦዊߐߊߥࠅᄌ૏㔚ᵹ߇ዊߐߊߥࠅߔ߉ࠆߚ߼㧘࡝ࡦࠣ߇ࠦࠗ࡞ߣߒߡߩᓎഀࠍᨐߚߐߥߊߥࠅ㧘⽶ߩㅘ⏛₸ࠍ␜ߐߥߊߥࠆߩߢᵈᗧ߇ᔅⷐߢ޽ࠆ㧚࿑㕙Ⓧභ᦭₸ߩ㆑޿ߎࠇࠄℂ⺰⠨ኤࠍరߦ㧘㐿⊒ࠍⴕߞߚ᭴ㅧࠍ࿑ 5 ߦ␜ߔ㧚ߎߩ᭴ㅧߪࠦࠗ࡞ߣߒߡ௛߆ߖࠆߚ߼㧘ᣇᒻ࡞࡯ࡊ߇ࠞ࠶࠻ߐࠇߡ޿ࠆㇱಽߦነ↢⚛ሶࠍട߃ߚ߽ߩߢ޽ࠆ㧚࿑࿑ 5 ឭ᩺᭴ㅧឭ᩺᭴ㅧ
Relative permeability
permeability
Relative

1010Ordinary
Modelof
Ordinary
Modelof Fig.
Fig. 22
Modelof
Proposed
Modelof Fig.
Fig. 11
11
Proposed

5500

5−5

10−100
011

Frequency [GHz]22࿑࿑ 6 ឭ᩺ࡕ࠺࡞ߩ⸃ᨆ⚿ᨐឭ᩺ࡕ࠺࡞ߩ⸃ᨆ⚿ᨐ33 !"#$%&'()*+,-./012(!34

࿑ 6 ߦㅘ⏛₸ߩ⸃ᨆ⚿ᨐࠍ␜ߔ㧚ߎߩ⸃ᨆ⚿ᨐࠃࠅឭ᩺ࡕ࠺࡞ߪ 1.3 GHz ઃㄭߢ⚂ 544 MHzߩ๟ᵄᢙᏪၞߢ⽶ߩㅘ⏛₸ࠍ␜ߒ㧘ᓥ᧪ߩ SRRs ߦᲧߴᐢᏪၞൻߢ߈ߚߎߣ߇ಽ߆ࠆ㧚㧠 ታ㛎ߦࠃࠆᬌ⸽
ታ㛎ߦࠃࠆᬌ⸽㧠⸃ᨆ⚿ᨐߩᅷᒰᕈࠍ␜ߔߚ߼ߦታ㛎ߦࠃࠆ᷹ቯࠍⴕߞߚ.એਅߦታ㓙ߩࡕ࠺࡞,߅ࠃ߮ㅘㆊᵄߩ⸃ᨆ⚿ᨐࠍ␜ߔ.

࿑77 ታ㛎ࡕ࠺࡞ታ㛎ࡕ࠺࡞࿑

࿑ 8 ታ㛎෸߮⸃ᨆ⚿ᨐߩᲧセታ㛎⚿ᨐ߆ࠄ㧘౒ᝄ๟ᵄᢙ߇⚂ 80 MHz ߕࠇߡ޿ࠆ߽ߩߩ㧘߶߷৻⥌ߒߡ޿ࠆ㧚ߘߩේ࿃ߣߒ
ߡߪ㧘⵾૞⺋Ꮕߦࠃࠆࠪࡒࡘ࡟࡯࡚ࠪࡦࡕ࠺࡞ߣߩߕࠇ㧘߅ࠃ߮ๆ෼૕ߩ⟎߈ᣇ߿ዉᵄ〝߆ࠄ⊒↢ߒߡߒ߹ߞߚࡁࠗ࠭߇ේ࿃ߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚㧡 ߹ߣ߼߹ߣ߼
㧡ᧄ⎇ⓥߢߪ⽶ߩㅘ⏛₸ࠍታ⃻ߔࠆ๟ᵄᢙᏪၞߩᐢᏪၞൻࠍ߅ߎߥߞߚ㧚ᣢሽߩ᭴ㅧߢߪ 1.3GHz ߢ⚂ 96 MHz ߩ๟ᵄᢙᏪၞߢ⽶ߩㅘ⏛₸ࠍ␜ߒߚߩߦኻߒ㧘ឭ᩺᭴ㅧߢߪ⚂ 544 MHz ߩ๟ᵄᢙᏪၞߢ⽶ߩㅘ⏛₸ࠍ␜ߒ㧘ᐢᏪၞൻ߇⏕⹺ߢ߈ߚ㧚߹ߚㅘㆊᵄࠍ᷹ቯߦࠃࠅ᳞߼⸃ᨆ⚿ᨐߣᲧセߔࠆߎߣߦࠃࠅ㧘⸃ᨆ⚿ᨐߩᅷᒰᕈࠍ␜ߒߚ.

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[6] ቝ㊁੧̌FDTD ᴺߦࠃࠆ㔚⏛⇇߅ࠃ߮ࠕࡦ࠹࠽⸃ᨆ̍ࠦࡠ࠽␠㧘