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ϚΠΫϩ೾ཧ࿦

1 ͸͡Ίʹ

ϚΠΫϩ೾͸ɺిࢠϨϯδ΍ܞଳి࿩౳Ͱ࢖ΘΕ

͓ͯΓɺݱ୅ਓͷੜ׆ʹͱͬͯඞཁෆՄܽͳଘࡏͰ͋

Δɻ෺ཧతʹ͸ɺϚΠΫϩ೾͸ి࣓೾ͷҰछͰɺप೾

਺ʢ·ͨ͸ɺ೾௕ʣ͕ɺ͓Αͦ300 MHzʢ೾௕1 mʣ

͘Β͍͔Β 300 GHzʢ೾௕ 1 mmʣ͘Β͍ͷؒͷి

࣓೾ͷ͜ͱΛݴ͏ʢݫີͳఆٛ͸ͳ͍Α͏Ͱ͋Δʣɻ ϚΠΫϩ೾Λ࢖ͬͨՙిཻࢠͷՃ଎͸ɺՃ଎ثͱ͠

ͯ࠷΋Ұൠతͳํ๏Ͱ͋ΔɻͦͷՃ଎૷ஔʢߴप೾

Ճ଎ۭಎʣͷେ͖͞͸ɺେࡶ೺ʹݴͬͯͦͷ೾௕͘Β

͍ͷαΠζͱͳΔɻͭ·Γɺ300 MHzΛ࢖͑͹ 1 m ఔ౓ɺ300 GHzΛ࢖͑͹ 1 mm ఔ౓ͷαΠζͰ͋

Δɻ͜Ε͘Β͍ͷαΠζͰ͋Ε͹ɺ੡଄্ɺେ͖ͳ ࠔ೉͸ͳ͍ɻٯʹݴ͑͹ɺՃ଎૷ஔ1୆Ͱ਺ेm΋ ͷେ͖͕͋͞Ε͹ڊେա͗ͯ੡࡞ࠔ೉Ͱ͋Δɻ·ͨɺ

0.1 mmΑΓখ͍͞Ճ଎ۭಎͷ੡࡞͸໺৺తա͗Δɻ

ਤ1ʹɺ࣮ࡍʹ੡଄͞Εͨ509 MHzͱ200 GHzͷ Ճ଎ߏ଄ͷྫΛࣔ͢ɻՃ଎ߏ଄ͷप೾਺͸ɺՃ଎ث ͷ໨తɺͦͷ࣌୅ͷٕज़ɺطଘͷՃ଎ثͰ࢖ΘΕ͍ͯ

Δप೾਺౳ʹΑΓܾ·ΔɻϚΠΫϩ೾͸·ͨɺՃ଎ث ͷϏʔϜ਍அ΍ϏʔϜҐஔܭଌʹ΋࢖ΘΕΔɻ͍ͣ

Ε΋ɺجૅͱͳΔϚΠΫϩ೾ཧ࿦ʹ͸ڞ௨఺͕ଟ͍ɻ ຊॻͰ͸ɺԼهΛ࢖༻ɾԾఆ͢Δɿ

• ^{ࠃࡍ୯Ґܥ}

• ^ڏ਺୯ҐΛiͰදࣔ

• ^{ෳૉྔ͸ଠࣈͰදࣔ}

• ϕΫτϧྔ͸্෦ʹ໼ҹΛ෇͚ͯදࣔ

• ^{೚ҙͷෳૉϕΫτϧΛ}F⃗ ͰදΘ͢

• ϑʔϦΤม׵ʹ͸ԼઢΛ෇͚ͯදࣔ

• ^࣌ؒΛtͰදࣔ

• ഔ࣭͸౳ํతͱ͠ɺ༠ి཰΍ಁ࣓཰͸ςϯιϧ ʹ͸ͳΒͣɺεΧϥʔྔͱͯ͠ѻ͏

ຊॻͷ಺༰͸ɺϚΠΫϩ೾ͷجૅɺٴͼɺՃ଎ثͰ Α͘࢖͏஌ࣝʹݶ͍ͬͯΔɻ·ͨɺஶऀͷઐ໳΍ڵ ຯͷ౎߹Ͱภͬͨ಺༰ʹͳ͍ͬͯΔͱࢥΘΕΔɻϚ ΠΫϩ೾ཧ࿦Λ໢ཏ͍ͯ͠Δ΋ͷͰ͸ͳ͍ͷͰɺͦ

ͷ఺Λྃ͝ঝ͍͖͍ͨͩͨɻ

(a)

(b) _{100 mm}

ਤ1 ࣮ࡍͷՃ଎ߏ଄ͷྫɻ(a) SuperKEKBཅి

ࢠμϯϐϯάϦϯάՃ଎ث༻ͷ509 MHzৗ఻ಋߴ प೾Ճ଎ۭಎɻ(b) SLACͰϏʔϜࢼݧΛߦͬͨ

200 GHzৗ఻ಋՃ଎ߏ଄ʢࢀߟจݙ[1]ʣɻ

2 ৼಈ໰୊ͱෳૉ਺දࣔ

ϚΠΫϩ೾͸ʢͦͷ໊ͷ௨Γʣ೾ʢৼಈʣͰ͋Δɻͦ

͜Ͱɺ؆୯ͷͨΊɺ·ͣ1࣍ݩͷৼಈ໰୊Λߟ͑Δɿ md²x

dt² =−kx (1)

͜Ε͸ɺ࣭ྔm ͷ࣭఺͕ɺ1࣍ݩ࠲ඪ x্Ͱόω ఆ਺kʹΑΔ୯ৼಈΛ͢ΔӡಈํఔࣜͰ͋Δɻ͜Ε

ʹɺ଎౓dx/dtʹൺྫ͢Δݮਰྗʢൺྫఆ਺Λαͱ

͢Δʣɺٴͼɺ֯ৼಈ਺ωͰৼಈ͢Δ֎ྗ͕͋Δͱ͢

Δͱɺӡಈํఔࣜ͸ɺ

md²x

dt² =−kx−αdx

dt +F0cosωt (2) ͱͳΔɻ͜ͷํఔࣜ͸ɺ2֊ͷఆ਺܎਺ඇಉ࣍ઢܗৗ

ඍ෼ํఔࣜͰ͋Γɺ͜͜Ͱ͸ɺҎԼͷΑ͏ʹͯ͠ղ͍

ͯΈΔɻ·ͣɺ্ه֎ྗͷҐ૬Λωtˠ ωt+π/2ͱ

ͯ͠90^◦ ͣΒͨ͠−F0sin(ωt)ʹର͢Δ1࣍ݩ࠲ඪ y্ͷӡಈํఔࣜɿ

md²y

dt² =−ky−αdy

dt −F0sinωt (3)

Λผ్ߟ͑ɺෳૉ਺z =x+iyʹର͢Δӡಈํఔࣜɿ

md²z

dt² =−kz−αdz

dt +F0e^−iωt (4) Λղ͘͜ͱΛߟ͑Δɻ͜͜ͰɺzͱiҎ֎͸࣮਺Ͱ͋

ΓɺΦΠϥʔͷެࣜɿ

e^iθ= cosθ+isinθ (5) Λ࢖ͬͨɻࣜ(4)ͷղͱͯ͠ɺ

z(t) =Ae^−iωt (6) Λߟ͑ΔʢA͸ෳૉఆ਺ʣɻ͜Ε͸ɺࣜ(4)ΛϑʔϦ Τม׵͠ɺ͋Δಛఆͷप೾਺੒෼ͷΈΛߟ͑Δ͜ͱ ʹ૬౰͢Δɻࣜ(6)Λࣜ(4)ʹ୅ೖ͢Δͱɺ

A= (k−mω²) +iωα

(k−mω²)²+ω²α²F0 (7) ΛಘΔɻͦͯ͠ɺࣜ(7)Λࣜ(6)ʹ୅ೖ͢Δͱɺෳૉ

ղz(t)͸ɺ

z(t) = F0

(k−mω²)²+ω²α² [

(k−mω²) cosωt+ωαsinωt +i{

ωαcosωt

−(k−mω²) sinωt}]

(8) ͱͳΔɻ෺ཧղ͸ɺࣜ(8)ͷ࣮਺෦Λͱͬͯɺ

x(t)=ℜ{z(t)} (9)

= F0

(k−mω²)²+ω²α²

[(k−mω²) cosωt+ωαsinωt]

(10) Ͱ͋Δɻ͜ͷΑ͏ʹɺৼಈ໰୊͸ෳૉ਺දࣔʹ͢Δ ͱɺൺֱత؆୯ͳ୅਺ܭࢉͰղ͚Δ͜ͱ͕ଟ͍^*1ɻ·

ͨɺෳૉ਺ͷ଍͠ࢉ͸ෳૉϕΫτϧͷ࿨ɺ͔͚ࢉ͸ৼ ෯ͷੵͱภ֯ͷ࿨ͰදͤΔͷͰɺ෺ཧతඳ૾΋ඳ͖

΍͍͢ɻ͜ͷΑ͏ͳཧ༝͔Βɺి৔΍࣓৔΋ෳૉ਺

Ͱද͢͜ͱ͕͠͹͠͹͋ΔɻຊॻͰ΋ɺి৔ͱ࣓৔

͸ෳૉ਺Ͱද͢ɻ

*1ୠ͠ɺ௨ৗͷి࣓ؾཧ࿦ͷΑ͏ͳઢܗཧ࿦ʹ͔͠ద༻ग़དྷ ͳ͍ɻ

ঘɺࣜ(8)ͷڏ਺ղy(t)͸ɺ

y(t) =ℑ{z(t)} (11)

= F0

(k−mω²)²+ω²α² [{ωαcosωt

−(k−mω²) sinωt}]

(12) Ͱ͋Γɺࣜ(10)ͷ࣮਺ղͱൺ΂ͯҐ૬͕90^◦ͣΕͯ

͍Δ͚ͩͰ͋Δɻैͬͯɺڏ਺ղΛ෺ཧղͱͯ͠΋

໰୊ͳ͍ɻఆٛͷ໰୊Ͱ͋ΔɻຊॻͰ͸ɺಛهͳ͖

৔߹͸ɺ࣮਺෦Λ෺ཧղͱ͢Δɻ

3 ฏ໘೾ͱ܈଎౓

ฏ໘೾ͱ͸ɺۭؒ࠲ඪ⃗xʹ͓͚Δ೾ͷৼ෯Λϕͱ

ͯ͠ɺ

ϕ(⃗x) =Ae^{i(⃗k·⃗x−ωt)} (13) ͷܗͰදΘ͞ΕΔ೾ͷ͜ͱͰ͋Δɻ͜͜Ͱɺω͸೾

ͷ֯प೾਺Ͱ͋Δɻࣜ(13)ͷҐ૬ʢࢦ਺෦ʣ͕Ұఆ ͷ࣌ɿ

⃗k·⃗x−ωt= const. (14)

͜Ε͸3࣍ݩۭؒ಺ͷฏ໘ΛදΘ͢ɻಉҐ૬໘͕ฏ ໘ʹͳΔͷͰɺࣜ(13)ͰදΘ͞ΕΔ೾Λฏ໘೾ͱݴ

͏^*2ɻ͜ͷಉҐ૬໘͸ɺ଎͞ω/|⃗k|^ͰϕΫτϧ⃗k ͷ

ํ޲ʹਐΉɻ·ͨɺ|⃗k|^͸ɺڑ཭2πͷؒʹ͋Δ೾ͷ ݸ਺ͱͳ͓ͬͯΓɺ⃗kΛ೾਺ϕΫτϧͱݴ͏ɻ࣮ۭ

ؒͱ೾਺ۭؒͷؒͷؔ܎Ͱ͋Δ3࣍ݩϑʔϦΤม׵

ͷࣜɿ F(⃗x) =

∫ _∞

−∞

d³⃗k F(⃗k)e^i⃗k·⃗x (15) (

F(⃗x) : ೚ҙͷʢੑ࣭ͷΑ͍ʣෳૉؔ਺)

͔Β΋Θ͔ΔΑ͏ʹɺ೚ҙͷ೾͸ฏ໘೾ͷॏͶ߹Θ

ͤͰදݱग़དྷΔɻ

࣍ʹɺࣜ(15)ʹ͓͍ͯɺੵ෼͢Δ೾਺ͷྖҬ͕⃗k

=⃗k0ͷपΓͷ͘͝খ͍͞ྖҬ∆kͷΈͰ͋Δ৔߹Λ ߟ͑Δɻฏ໘೾Ͱ͸ɺ֯प೾਺ω ͸೾਺ʹൺྫʢω

∝ |⃗k|^{ʣ͢Δ͕ɺ͜͜Ͱ͸ɺ}ω(⃗k)ͱͯ͠೚ҙͷґଘੑ

*2ฏ໘೾ͷଞɺಉҐ૬໘͕ٿ໘ʹͳΔ೾͕͋ΓɺͦΕΛٿ໘

೾ͱ͍͏ɻ

Λผ్ߟ͑ɺෳૉ਺z=x+iyʹର͢Δӡಈํఔࣜɿ

md²z

dt² =−kz−αdz

dt +F0e^−iωt (4) Λղ͘͜ͱΛߟ͑Δɻ͜͜ͰɺzͱiҎ֎͸࣮਺Ͱ͋

ΓɺΦΠϥʔͷެࣜɿ

e^iθ= cosθ+isinθ (5) Λ࢖ͬͨɻࣜ(4)ͷղͱͯ͠ɺ

z(t) =Ae^−iωt (6) Λߟ͑ΔʢA͸ෳૉఆ਺ʣɻ͜Ε͸ɺࣜ(4)ΛϑʔϦ Τม׵͠ɺ͋Δಛఆͷप೾਺੒෼ͷΈΛߟ͑Δ͜ͱ ʹ૬౰͢Δɻࣜ(6)Λࣜ(4)ʹ୅ೖ͢Δͱɺ

A= (k−mω²) +iωα

(k−mω²)²+ω²α²F0 (7) ΛಘΔɻͦͯ͠ɺࣜ(7)Λࣜ(6)ʹ୅ೖ͢Δͱɺෳૉ

ղz(t)͸ɺ

z(t) = F0

(k−mω²)²+ω²α² [

(k−mω²) cosωt+ωαsinωt +i{

ωαcosωt

−(k−mω²) sinωt}]

(8) ͱͳΔɻ෺ཧղ͸ɺࣜ(8)ͷ࣮਺෦Λͱͬͯɺ

x(t)=ℜ{z(t)} (9)

= F0

(k−mω²)²+ω²α²

[(k−mω²) cosωt+ωαsinωt]

(10) Ͱ͋Δɻ͜ͷΑ͏ʹɺৼಈ໰୊͸ෳૉ਺දࣔʹ͢Δ ͱɺൺֱత؆୯ͳ୅਺ܭࢉͰղ͚Δ͜ͱ͕ଟ͍^*1ɻ·

ͨɺෳૉ਺ͷ଍͠ࢉ͸ෳૉϕΫτϧͷ࿨ɺ͔͚ࢉ͸ৼ ෯ͷੵͱภ֯ͷ࿨ͰදͤΔͷͰɺ෺ཧతඳ૾΋ඳ͖

΍͍͢ɻ͜ͷΑ͏ͳཧ༝͔Βɺి৔΍࣓৔΋ෳૉ਺

Ͱද͢͜ͱ͕͠͹͠͹͋ΔɻຊॻͰ΋ɺి৔ͱ࣓৔

͸ෳૉ਺Ͱද͢ɻ

*1ୠ͠ɺ௨ৗͷి࣓ؾཧ࿦ͷΑ͏ͳઢܗཧ࿦ʹ͔͠ద༻ग़དྷ ͳ͍ɻ

ঘɺࣜ(8)ͷڏ਺ղy(t)͸ɺ

y(t) =ℑ{z(t)} (11)

= F0

(k−mω²)²+ω²α² [{ωαcosωt

−(k−mω²) sinωt}]

(12) Ͱ͋Γɺࣜ(10)ͷ࣮਺ղͱൺ΂ͯҐ૬͕90^◦ͣΕͯ

͍Δ͚ͩͰ͋Δɻैͬͯɺڏ਺ղΛ෺ཧղͱͯ͠΋

໰୊ͳ͍ɻఆٛͷ໰୊Ͱ͋ΔɻຊॻͰ͸ɺಛهͳ͖

৔߹͸ɺ࣮਺෦Λ෺ཧղͱ͢Δɻ

3 ฏ໘೾ͱ܈଎౓

ฏ໘೾ͱ͸ɺۭؒ࠲ඪ⃗xʹ͓͚Δ೾ͷৼ෯Λϕͱ

ͯ͠ɺ

ϕ(⃗x) =Ae^{i(⃗k·⃗x−ωt)} (13) ͷܗͰදΘ͞ΕΔ೾ͷ͜ͱͰ͋Δɻ͜͜Ͱɺω ͸೾

ͷ֯प೾਺Ͱ͋Δɻࣜ(13)ͷҐ૬ʢࢦ਺෦ʣ͕Ұఆ ͷ࣌ɿ

⃗k·⃗x−ωt= const. (14)

͜Ε͸3࣍ݩۭؒ಺ͷฏ໘ΛදΘ͢ɻಉҐ૬໘͕ฏ ໘ʹͳΔͷͰɺࣜ(13)ͰදΘ͞ΕΔ೾Λฏ໘೾ͱݴ

͏^*2ɻ͜ͷಉҐ૬໘͸ɺ଎͞ω/|⃗k|^ͰϕΫτϧ⃗k ͷ

ํ޲ʹਐΉɻ·ͨɺ|⃗k|^͸ɺڑ཭2π ͷؒʹ͋Δ೾ͷ ݸ਺ͱͳ͓ͬͯΓɺ⃗k Λ೾਺ϕΫτϧͱݴ͏ɻ࣮ۭ

ؒͱ೾਺ۭؒͷؒͷؔ܎Ͱ͋Δ3࣍ݩϑʔϦΤม׵

ͷࣜɿ F(⃗x) =

∫ _∞

−∞

d³⃗k F(⃗k)e^i⃗k·⃗x (15) (

F(⃗x) : ೚ҙͷʢੑ࣭ͷΑ͍ʣෳૉؔ਺)

͔Β΋Θ͔ΔΑ͏ʹɺ೚ҙͷ೾͸ฏ໘೾ͷॏͶ߹Θ

ͤͰදݱग़དྷΔɻ

࣍ʹɺࣜ(15)ʹ͓͍ͯɺੵ෼͢Δ೾਺ͷྖҬ͕⃗k

=⃗k0ͷपΓͷ͘͝খ͍͞ྖҬ∆kͷΈͰ͋Δ৔߹Λ ߟ͑Δɻฏ໘೾Ͱ͸ɺ֯प೾਺ω ͸೾਺ʹൺྫʢω

∝ |⃗k|^{ʣ͢Δ͕ɺ͜͜Ͱ͸ɺ}ω(⃗k)ͱͯ͠೚ҙͷґଘੑ

*2ฏ໘೾ͷଞɺಉҐ૬໘͕ٿ໘ʹͳΔ೾͕͋ΓɺͦΕΛٿ໘

೾ͱ͍͏ɻ

ͱ͢Δɻ͜Ε͸ɺ෼ࢄੑഔ࣭΍ಋ೾؅಺Λ఻ΘΔϚ ΠΫϩ೾Λ૝ఆ͓ͯ͠Γɺͦͷ৔߹ɺωͱ|⃗k|^͸ઢܗ

ؔ܎ʹ͸ͳΒͳ͍ɻω =ω(⃗k)ͰදΘ͞ΕΔؔ܎Λ෼

ࢄؔ܎ͱݴ͏ʢઢܗͷ৔߹͸෼ࢄແ͠ʣɻ⃗k Λ⃗k0ͷ पΓͰςʔϥʔల։ͯ͠1࣍ͷ߲·ͰऔΔͱɺ

ω(⃗k)≈ω(⃗k0) + ∂ω(⃗k)

∂⃗k

��

��

�_⃗

k=⃗k0

·∆⃗k (16)

⃗k=⃗k0+ ∆⃗k (17)

Ͱ͋Δɻ͜ΕΛɺ࣌ؒґଘ߲e^{−iω(⃗k)t}΋ؚΊͯࣜ(15) ʹ୅ೖ͢Δͱɺ

F(⃗x) =eⁱ(^⃗k0·⃗x−ω(⃗k0)t)

×

∫

∆k

d³⃗kF(⃗k)e^i∆

⃗k·

(

⃗x−^∂ω(_∂⃗k^⃗k)

��

��_⃗ k=⃗k0

t )

(18)

ΛಘΔɻ|∆⃗k| ≪ |⃗k|^{ͱԾఆͨ͠ͷͰɺࣜ}(18)ͷੵ

෼ͷதͷ೾͸ɺੵ෼ͷ֎ͷ೾ΑΓʢۭؒతʹʣͣͬͱ Ώͬ͘ΓมԽ͢Δɻ࣮ࡍɺࣜ(18)͸ɺਤ2ʹ͋ΔΑ

͏ͳ೾ଋΛදΘ͓ͯ͠Γɺੵ෼෦෼͕೾ଋͷแབྷઢ ʹͳΔɻैͬͯɺ೾ଋͷਐΉ଎͞vg͸ͦͷแབྷઢͷ ਐΉ଎͞Ͱ͋Γɺࣜ(18)ΑΓɺ

⃗vg = ∂ω(⃗k)

∂⃗k (19)

Ͱ͋Δɻ͜ΕΛ܈଎౓ͱݴ͏ɻ·ͨɺࣜ(18)ͷੵ෼

ͷ֎ʹ͋Δ೾ͷਐΉ଎͞ ω(⃗k0)/|⃗k0|^{ΛҐ૬଎౓}vp

ͱݴ͏ɻ೾ଋΛߏ੒͢Δ೾͸Ґ૬଎౓v_pͰਐΉ͕ɺ

೾ଋࣗମ͸܈଎౓vgͰਐΉɻ෼ࢄੑഔ࣭΍ಋ೾؅಺

Λ఻ΘΔϚΠΫϩ೾ͷ೾ଋͰ͸ɺҐ૬଎౓͸ޫ଎Λ

௒͑Δ͕ɺ܈଎౓͸ޫ଎ҎԼͰ͋Δɻͭ·ΓɺҐ૬଎

౓͸ݟ͔͚ͷ଎͞Ͱ͋Δɻ࣮ࡍʹΤωϧΪʔ͕఻Θ Δ଎͞͸܈଎౓ͰɺҼՌ཯͸ഁΕͳ͍ɻ͜Ε͸ɺݱ࣮

ͷ೾͕׬શͳ୯৭ͷฏ໘೾Ͱ͸ͳ͘ɺඞͣप೾਺ʹ ෯͕͋Γɺ೾ଋͱͳ͍ͬͯΔࣄ࣮ͱໃ६͠ͳ͍ɻঘɺ

∆⃗k ͕େ͖͍৔߹͸ɺࣜ(16)ͷۙࣅ͸ѱ͘ͳΓɺߴ

࣍ͷ߲·Ͱߟྀ͠ͳ͚Ε͹ͳΒͳ͍ɻ͜ͷ৔߹ɺ܈

଎౓ͷ֓೦͸ෆਖ਼֬ʹͳΔɻ

4 ϚΫε΢Σϧํఔࣜ

ϚΠΫϩ೾͸ి࣓೾Ͱ͋Γɺి࣓೾͸ϚΫε΢Σ ϧํఔࣜͰݫີʹهड़ग़དྷΔɻຊઅͰ͸ɺϚΫε΢Σ ϧํఔࣜΛجʹɺϚΠΫϩ೾ཧ࿦ͷجຊࣄ߲Λղઆ

͢Δɻ

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

0 0.5 1 1.5 2 2.5 3 3.5

位置

振幅

1/∆k

ਤ2 ೾ଋͷྫɻ

4.1 ਅۭதͷϚΠΫϩ೾

ਅۭதͷϚΫε΢Σϧํఔࣜ͸ɺ

∇ ×⃗ E(⃗x, t) +⃗ ∂ ⃗B(⃗x, t)

∂t = 0ɹ (20)

∇ ×⃗ H⃗ (⃗x, t)− ∂ ⃗D(⃗x, t)

∂t = 0 (21)

∇ ·⃗ D(⃗x, t) = 0⃗ (22)

∇ ·⃗ B(⃗x, t) = 0⃗ (23)

Ͱ͋Δɻ͜͜ͰɺE⃗ ͱH⃗ ͸ͦΕͧΕి৔ͱ࣓৔ɺD⃗ ͱB⃗ ͸ͦΕͧΕిଋີ౓ͱ࣓ଋີ౓Ͱ͋Δɻ∇⃗ ^͸φ ϒϥه߸Ͱɺ۩ମతʹ͸ɺ

∇⃗ = ( ∂

∂x, ∂

∂y, ∂

∂z )

(24)

Ͱ͋Γɺ͜Ε΋਺ֶతͳϕΫτϧͰ͋Δɻ͜͜Ͱɺਅ

ۭͷ༠ి཰ͱಁ࣓཰ΛͦΕͧΕɺ

ϵ0= 8.85418782×10⁻¹²F/m (25) µ₀= 1.256637×10⁻⁶H/m (26)

ͱදΘ͢ͱɺ

D(⃗x, t) =⃗ ϵ0E(⃗x, t)⃗ (27) B(⃗x, t) =⃗ µ0H⃗ (⃗x, t) (28)

ͱॻ͚Δ͜ͱ͔Βɺ্هϚΫε΢Σϧํఔࣜ(20)ʙ (23)͸ɺE⃗ ͱH⃗ ͷ࿈ཱඍ෼ํఔࣜɿ

∇ ×⃗ E(⃗x, t) +⃗ µ0

∂ ⃗H(⃗x, t)

∂t = 0ɹ (29)

∇ ×⃗ H(⃗x, t)⃗ −ϵ0

∂ ⃗E(⃗x, t)

∂t = 0 (30)

∇ ·⃗ E(⃗x, t) = 0⃗ (31)

∇ ·⃗ H(⃗x, t) = 0⃗ (32) ͱͳΔɻࣜ(29)ͷճసʢ∇×⃗ ^{ʣΛऔΓɺͦΕʹࣜ}(30) Λ୅ೖͯ͠ɺϕΫτϧղੳͷެࣜɿ

∇ ×⃗ (

∇ ×⃗ F⃗)

(33)

=∇⃗ (

∇ ·⃗ F⃗)

−∇⃗²F⃗ (34) ͱࣜ(31)ɺ(32)Λద༻͢Δͱɺ

(

∇⃗²−ϵ0µ0

∂²

∂t² )

E(⃗x, t) = 0⃗ (35) ΛಘΔɻಉ༷ͷํ๏Ͱɺ

(

∇⃗²−ϵ0µ0

∂²

∂t² )

H⃗ (⃗x, t) = 0 (36)

΋ಘΔɻ͜ΕΒ͸ɺ଎͞ c0 = 1/√ϵ0µ0 ͰਐΉ೾

Λද͢೾ಈํఔࣜͰ͋Γɺc0 ͸ਅۭதͷޫ଎ʢ≈ 299,792,458 m/sʣͰ͋Δɻ

͜͜Ͱɺి৔Λฏ໘೾ʢࣜ(13)ʣͰදΘ͢ͱɺ E(⃗x, t) =⃗ A⃗E(⃗k, ω)e^{i(⃗k·⃗x−ωt)} (37) Ͱ͋Δɻࣜ(37)Λࣜ(31)ʹ୅ೖ͢Δͱɺ

A⃗_E·⃗k = 0 (38) ΛಘΔɻैͬͯɺి৔E⃗ ͷ޲͖A⃗E͸ɺ೾ಈͷਐߦ

ํ޲⃗kʹରͯ͠௚֯Ͱ͋Δɻ͜Ε͸ɺ࣓৔H⃗ ʹ͍ͭ

ͯ΋ಉ༷Ͱ͋Δɻ࣍ʹɺࣜ(37)Λࣜ(29)ʹ୅ೖ͠ɺ

࣓৔͕ɺ

H(⃗x, t) =⃗ A⃗H(⃗k, ω)e^{i(⃗k·⃗x−ωt)} (39) ͱॻ͚Δ͜ͱʹ஫ҙ͢Δͱɺ

H⃗ _H ∥⃗k×E⃗ (40) Ͱ͋Δ͜ͱ͕Θ͔Δɻͭ·Γɺਅۭதͷ೚ҙͷి࣓৔

͸ɺਤ3ʹ͋Δؔ܎Ͱ⃗kͷํ޲ʹ଎͞c0= 1/√ϵ0µ0

ͰਐΉԣ೾ͷॏͶ߹ΘͤͱͳΔɻ

k

E

H

ਤ3 ి৔E⃗ɺ࣓৔H⃗ɺฏ໘೾ͷਐߦํ޲⃗kͷؔ܎ɻ

ঘɺແଛࣦͰඇ෼ࢄੑͷഔ࣭Ͱຬͨ͞ΕͨྖҬͷ

৔߹͸ɺ୯ʹϵ0 → ϵɺµ0 → µ ͱஔ͖׵͑Δ͚ͩͰ

͋Δɻ͜͜Ͱɺϵͱµ͸ɺͦΕͧΕɺͦͷഔ࣭ͷ༠ి

཰ͱಁ࣓཰Ͱ͋Δɻ 4.2 ಋମதͷϚΠΫϩ೾

ϚΠΫϩ೾͕ਅۭྖҬ͔ΒಋମʹೖΔͱͲ͏ͳΔ

͔Λௐ΂Δɻಋମͱ͸ɺ۩ମతʹ͸ಔ΍εςϯϨεͷ Α͏ͳۚଐͰ͋Δɻಋମ಺Ͱ͸ΦʔϜͷ๏ଇʹैͬ

ͯ఻ಋిྲྀ͕ྲྀΕΔɻ఻ಋిྲྀͷେ͖͞͸ి৔ʹൺ

ྫ͢Δɻͦͷൺྫఆ਺͸ిؾ఻ಋ཰σͰ͋ΓɺΦʔ Ϝͷ๏ଇ͸ɺ

⃗J =σ ⃗E (41)

ͱͳΔɻ͜͜Ͱɺ⃗J͸ిྲྀີ౓ϕΫτϧͰ͋Δ^*3ɻಋ ମதͷϚΫε΢Σϧํఔࣜ͸ɺ͜ͷ఻ಋిྲྀ͕มҐ

ిྲྀ∂ ⃗D/∂tʹՃΘΓɺҎԼͷΑ͏ʹͳΔɿ

∇ ×⃗ E(⃗x, t) +⃗ µ∂ ⃗H(⃗x, t)

∂t = 0ɹ(42)

∇ ×⃗ H(⃗x, t)⃗ −ϵ∂ ⃗E(⃗x, t)

∂t −σ ⃗E(⃗x, t) = 0 (43)

∇ ·⃗ E(⃗x, t) = 0⃗ (44)

∇ ·⃗ H(⃗x, t) = 0⃗ (45)

͜͜Ͱɺϵͱµ͸ɺͦΕͧΕɺಋମதͷ༠ి཰ͱಁ࣓

཰Ͱ͋ΔɻҎલͱಉ༷ʹɺࣜ(42)ͷճసʢ∇×⃗ ^ʣΛ

*3ిྲྀີ౓ϕΫτϧΛ໘ੵ෼͢Δͱɺͦͷੵ෼ྖҬΛ௨Δి

ྲྀ஋ʹͳΔɻ

ͱॻ͚Δ͜ͱ͔Βɺ্هϚΫε΢Σϧํఔࣜ(20)ʙ (23)͸ɺE⃗ ͱH⃗ ͷ࿈ཱඍ෼ํఔࣜɿ

∇ ×⃗ E(⃗x, t) +⃗ µ0

∂ ⃗H(⃗x, t)

∂t = 0ɹ (29)

∇ ×⃗ H(⃗x, t)⃗ −ϵ0

∂ ⃗E(⃗x, t)

∂t = 0 (30)

∇ ·⃗ E(⃗x, t) = 0⃗ (31)

∇ ·⃗ H(⃗x, t) = 0⃗ (32) ͱͳΔɻࣜ(29)ͷճసʢ∇×⃗ ^{ʣΛऔΓɺͦΕʹࣜ}(30) Λ୅ೖͯ͠ɺϕΫτϧղੳͷެࣜɿ

∇ ×⃗ (

∇ ×⃗ F⃗)

(33)

=∇⃗ (

∇ ·⃗ F⃗)

−∇⃗²F⃗ (34) ͱࣜ(31)ɺ(32)Λద༻͢Δͱɺ

(

∇⃗²−ϵ0µ0

∂²

∂t² )

E(⃗x, t) = 0⃗ (35) ΛಘΔɻಉ༷ͷํ๏Ͱɺ

(

∇⃗²−ϵ0µ0

∂²

∂t² )

H(⃗x, t) = 0⃗ (36)

΋ಘΔɻ͜ΕΒ͸ɺ଎͞ c0 = 1/√ϵ0µ0 ͰਐΉ೾

Λද͢೾ಈํఔࣜͰ͋Γɺc0 ͸ਅۭதͷޫ଎ʢ≈ 299,792,458 m/sʣͰ͋Δɻ

͜͜Ͱɺి৔Λฏ໘೾ʢࣜ(13)ʣͰදΘ͢ͱɺ E(⃗x, t) =⃗ A⃗E(⃗k, ω)e^{i(⃗k·⃗x−ωt)} (37) Ͱ͋Δɻࣜ(37)Λࣜ(31)ʹ୅ೖ͢Δͱɺ

A⃗_E·⃗k = 0 (38) ΛಘΔɻैͬͯɺి৔E⃗ ͷ޲͖A⃗E͸ɺ೾ಈͷਐߦ

ํ޲⃗kʹରͯ͠௚֯Ͱ͋Δɻ͜Ε͸ɺ࣓৔H⃗ ʹ͍ͭ

ͯ΋ಉ༷Ͱ͋Δɻ࣍ʹɺࣜ(37)Λࣜ(29)ʹ୅ೖ͠ɺ

࣓৔͕ɺ

H(⃗x, t) =⃗ A⃗H(⃗k, ω)e^{i(⃗k·⃗x−ωt)} (39) ͱॻ͚Δ͜ͱʹ஫ҙ͢Δͱɺ

H⃗ _H ∥⃗k×E⃗ (40) Ͱ͋Δ͜ͱ͕Θ͔Δɻͭ·Γɺਅۭதͷ೚ҙͷి࣓৔

͸ɺਤ3ʹ͋Δؔ܎Ͱ⃗kͷํ޲ʹ଎͞c0= 1/√ϵ0µ0

ͰਐΉԣ೾ͷॏͶ߹ΘͤͱͳΔɻ

k

E

H

ਤ3 ి৔E⃗ɺ࣓৔H⃗ɺฏ໘೾ͷਐߦํ޲⃗kͷؔ܎ɻ

ঘɺແଛࣦͰඇ෼ࢄੑͷഔ࣭Ͱຬͨ͞ΕͨྖҬͷ

৔߹͸ɺ୯ʹϵ0 → ϵɺµ0 → µ ͱஔ͖׵͑Δ͚ͩͰ

͋Δɻ͜͜Ͱɺϵͱµ͸ɺͦΕͧΕɺͦͷഔ࣭ͷ༠ి

཰ͱಁ࣓཰Ͱ͋Δɻ 4.2 ಋମதͷϚΠΫϩ೾

ϚΠΫϩ೾͕ਅۭྖҬ͔ΒಋମʹೖΔͱͲ͏ͳΔ

͔Λௐ΂Δɻಋମͱ͸ɺ۩ମతʹ͸ಔ΍εςϯϨεͷ Α͏ͳۚଐͰ͋Δɻಋମ಺Ͱ͸ΦʔϜͷ๏ଇʹैͬ

ͯ఻ಋిྲྀ͕ྲྀΕΔɻ఻ಋిྲྀͷେ͖͞͸ి৔ʹൺ

ྫ͢Δɻͦͷൺྫఆ਺͸ిؾ఻ಋ཰σͰ͋ΓɺΦʔ Ϝͷ๏ଇ͸ɺ

⃗J =σ ⃗E (41)

ͱͳΔɻ͜͜Ͱɺ⃗J͸ిྲྀີ౓ϕΫτϧͰ͋Δ^*3ɻಋ ମதͷϚΫε΢Σϧํఔࣜ͸ɺ͜ͷ఻ಋిྲྀ͕มҐ

ిྲྀ∂ ⃗D/∂tʹՃΘΓɺҎԼͷΑ͏ʹͳΔɿ

∇ ×⃗ E(⃗x, t) +⃗ µ∂ ⃗H(⃗x, t)

∂t = 0ɹ(42)

∇ ×⃗ H(⃗x, t)⃗ −ϵ∂ ⃗E(⃗x, t)

∂t −σ ⃗E(⃗x, t) = 0 (43)

∇ ·⃗ E(⃗x, t) = 0⃗ (44)

∇ ·⃗ H(⃗x, t) = 0⃗ (45)

͜͜Ͱɺϵͱµ͸ɺͦΕͧΕɺಋମதͷ༠ి཰ͱಁ࣓

཰Ͱ͋ΔɻҎલͱಉ༷ʹɺࣜ(42)ͷճసʢ∇×⃗ ^ʣΛ

*3ిྲྀີ౓ϕΫτϧΛ໘ੵ෼͢Δͱɺͦͷੵ෼ྖҬΛ௨Δి

ྲྀ஋ʹͳΔɻ

औΓɺͦΕʹࣜ(43)Λ୅ೖͯ͠ɺϕΫτϧղੳͷެ

ࣜͱࣜ(44)Λద༻͢Δͱɺ (

∇⃗²−µσ ∂

∂t −ϵµ ∂²

∂t² )

E⃗(⃗x, t) = 0 (46) (47) ΛಘΔɻ͜Ε͸ి৴ํఔࣜͰ͋Γɺ࣌ؒͷ1֊ඍ෼

ͷ߲ʢࠨลୈೋ߲ʣ͸೾ʹݮਰΛ༩͑Δɻ؆୯ͷͨ

Ίɺฏ໘೾͕z࣠ͷਖ਼ͷํ޲΁ਐΈɺz= 0Ͱಋମʹ

ೖΔͱ͠Α͏ʢਤ4ࢀরʣɻి৔͸xํ޲੒෼ͷΈͱ

ͯ͠ɺ

Ex(t) =E0e^i(kz−ωt) (48) ͱ͓͘ɻ͜͜Ͱɺk͸ෳૉ਺Ͱ͋Δɻ͜ΕΛࣜ (46) ʹ୅ೖ͢Δͱɺ

k²=ϵµω²+iµσω (49) ΛಘΔɻ௨ৗͷಋମͱϚΠΫϩ೾Ͱ͸ σ/(ϵω) ≫ 1

͕੒ΓཱͭͷͰɺ

k≈ ±(1 +i)

√µσω

2 (50)

Ͱ͋Δɻ͜ΕΛɺࣜ(48)ʹ୅ೖͯ͠ɺ

|Ex(t)| ≈ |E0|e⁻√µσω

2 z (51)

ͱͳΔɻΑͬͯɺϚΠΫϩ೾͕ಋମʹೖΔͱɺͦͷৼ ෯͸ࢦ਺ؔ਺తʹݮਰ͠ɺਂ͕͞

δskin =

√ 2

µσω (52)

ͷͱ͜ΖͰৼ෯͕1/e≈0.37ഒʹݮਰ͢Δɻ͜ͷΑ

͏ͳݱ৅ΛදൽޮՌͱݴ͍ɺ͜ͷδskinΛදൽޮՌͷ

ਂ͞ʢSkin depthʣͱݴ͏ɻਤ5ʹɺϚΠΫϩ೾ྖ

Ҭʹ͓͚ΔಔͷදൽޮՌͷਂ͞Λࣔ͢ɻैͬͯɺແ

ࢎૉಔͰ࡞ΒΕΔৗ఻ಋߴप೾Ճ଎ۭಎͷిؾతͳ

ੑೳ͸ɺۭಎ಺ද໘ͷബൽҰຕʢ਺ϛΫϩϯҎԼʣͰ

ܾ·͍ͬͯΔͷͰ͋Δɻ

ҎԼͰ͸ɺಋମ͸׬શಋମʢσ =∞^{ʣͱͯ͠ి࣓}

৔ΛٻΊΔɻຆͲͷ৔߹ɺಋମʹ༗ݶͷిؾ఻ಋ཰

͕͋Δͱͯ͠ٻΊͨి࣓৔ͱɺ׬શಋମΛԾఆͯ͠

ٻΊͨి࣓৔ͱͰ༗ҙͳࠩ͸ແ͍ɻಋମද໘ʹ͓͚

ΔϚΠΫϩ೾ͷน໘ଛࣦిྗΛٻΊΔ৔߹͸ɺ׬શ ಋମΛԾఆͯ͠ٻΊͨి࣓৔ͷಋମද໘ʹ͓͚Δ࣓

৔͔ΒٻΊΔઁಈ࿦తํ๏Λ࢖͏ͷ͕ҰൠతͰ͋Δɻ

ਤ4 ൒ແݶಋମɻ

Frequency [GHz]

Skin Depth [µm]

0 0.5 1 1.5 2 2.5 3 3.5 4

1 10 10²

ਤ5 ಔͷදൽޮՌͷਂ͞ɻ

4.3 ଛࣦͷ͋ΔઈԑମதͷϚΠΫϩ೾

࣍ʹɺଛࣦͷ͋Δ౳ํత͔ͭҰ༷ͳઈԑମͰۭؒ

͕ຬͨ͞Ε͍ͯΔ৔߹Λߟ͑Δɻ͜Ε͸ɺՃ଎ثͰ

͸ɺϚΠΫϩ೾ٵऩମͷϞσϧͱͯ͠ॏཁͰ͋Δɻ ઈԑମʹ͓͚Δଛࣦ͸ɺ༠ి཰΍ಁ࣓཰ʹෳૉ੒෼

Λಋೖ͢Δ͜ͱͰදݱग़དྷΔɻෳૉൺ༠ి཰ɺٴͼɺ

ෳૉൺಁ࣓཰ΛɺͦΕͧΕɺ

ϵr(ω) =ϵ^′_r(ω) +iϵ^′′_r(ω) (53) µ_r(ω) =µ^′_r(ω) +iµ^′′_r(ω) (54) ͱఆٛ͢Δɻෳૉ༠ి཰ɺٴͼɺෳૉಁ࣓཰͸ɺͦΕ

ͧΕɺ

ϵ(ω) =ϵ0ϵr(ω) (55) µ(ω) =µ0µ_r(ω) (56)

Ͱ͋Δɻϵ^′_r ͱµ^′_r ͸1Ҏ্ʢਅۭͰ͸1ʣɺϵ^′′_r ͱµ^′′_r

͸θϩʢແଛࣦʣ·ͨ͸ਖ਼஋ʢଛࣦ͋ΓʣͰ͋ΔɻҰ ൠతʹ͸ɺ༠ి཰ͱಁ࣓཰͸प೾਺ͷؔ਺Ͱ͋Δͷ Ͱʢ෼ࢄੑഔ࣭ʣɺࣜ(27)΍(28)ͷΑ͏ͳؔ܎͸ਅ

ۭதɺ·ͨ͸ɺඇ෼ࢄੑഔ࣭Ͱ͔͠੒Γཱͨͳ͍ɻͳ

ͥͳΒɺࣜ(27)ͱ(28)͸࣌ؒྖҬʹ͓͚Δ͕ࣜͩɺ प೾਺ʹґଘ͢Δ༠ి཰΍ಁ࣓཰͸प೾਺ྖҬʹ͓

͚Δ֓೦͔ͩΒͰ͋Δɻͦ͜Ͱɺਅిՙ΋ਅిྲྀ΋

ແ͍৔߹ͷϚΫε΢Σϧํఔࣜɿ

∇ ×⃗ E(⃗x, t) +⃗ ∂ ⃗B(⃗x, t)

∂t = 0ɹ (57)

∇ ×⃗ H⃗ (⃗x, t)−∂ ⃗D(⃗x, t)

∂t = 0 (58)

∇ ·⃗ D(⃗x, t) = 0⃗ (59)

∇ ·⃗ B(⃗x, t) = 0⃗ (60) ʹ͓͚Δి࣓৔ʹϑʔϦΤٯม׵ɿ

E(⃗x, t) =⃗

∫ _∞

−∞

dω ⃗E(⃗x, ω)e^−iωt (61) D(⃗x, t) =⃗

∫ _∞

−∞

dω ⃗D(⃗x, ω)e^−iωt (62) H(⃗x, t) =⃗

∫ _∞

−∞

dω ⃗H(⃗x, ω)e^−iωt (63) B(⃗x, t) =⃗

∫ _∞

−∞

dω ⃗B(⃗x, ω)e^−iωt (64) Λ୅ೖ͢Δͱɺ

∇ ×⃗ E(⃗x, ω)⃗ −iω ⃗B(⃗x, ω) = 0ɹ (65)

∇ ×⃗ H⃗ (⃗x, ω) +iω ⃗D(⃗x, ω) = 0 (66)

∇ ·⃗ D(⃗x, ω) = 0⃗ (67)

∇ ·⃗ B(⃗x, ω) = 0⃗ (68) ΛಘΔɻ࣌ؒґଘੑ͸ϑʔϦΤม׵ͷe^−iωt͕୲͍ɺ ϚΫε΢Σϧํఔ͔ࣜΒ࣌ؒඍ෼͕ফ͑ͯগ͠؆୯ ʹͳͬͨɻ͜͜ͰɺϕΫτϧղੳͷެࣜɿ

∇ ·⃗ (

∇ ×⃗ F⃗)

= 0 (69)

ΑΓɺ্هͷࣜ(67)ɺ(68)͸ɺࣜ(65)ɺ(66)ʹؚ·

ΕΔ͜ͱ͕Θ͔ΔͷͰɺࣜ(67)ɺ(68)͸ෆཁͱͳΔɻ

࣍ʹɺࣜ(55)ͱ(56)Λ࢖͍ɺ

D(⃗x, ω) =⃗ ϵ(ω)E(⃗x, ω)⃗ (70) B(⃗x, ω) =⃗ µ(ω)H(⃗x, ω)⃗ (71)

ͱදΘ͢ɻ͜ͷ͔ࣜΒ΋Θ͔ΔΑ͏ʹɺෳૉ༠ి཰ɾ

ෳૉಁ࣓཰͸ɺҹՃ৔ʢEɺHʣͱ༠ಋ৔ʢDɺBʣ ͷൺͰ͋Γɺి࣓৔ʢి৔ɺ࣓৔ʣͱഔ࣭ͷ૬ޓ࡞

༻ΛදΘ͢ʢഔ࣭ͷి࣓৔ʹର͢ΔԠ౴ΛؚΉʣɻࣜ

(70)ͱ(71)ΛϚΫε΢Σϧํఔࣜ(65)ɺ(66)ʹ୅

ೖ͢Δͱɺ

∇ ×⃗ E(⃗x, ω)⃗ −iωµ(ω)H(⃗x, ω) = 0⃗ ɹ (72)

∇ ×⃗ H(⃗x, ω) +⃗ iωϵ(ω)E(⃗x, ω) = 0⃗ (73) ͱͳΔɻ࠶ͼɺࣜ(72)ɺ(73)ͷճసʢ∇×⃗ ^ʣΛऔΔ ͱɺి৔ͱ࣓৔ͦΕͧΕ͕ຬͨ͢΂͖ҎԼͷΑ͏ͳ

ํఔࣜɿ

(∇⃗²+k(ω)²)

E(⃗x, ω) = 0⃗ (74) (∇⃗²+k(ω)²)

H(⃗x, ω) = 0⃗ (75)

͕ಘΒΕΔɻ͜͜Ͱɺk͸ɺ k(ω) =±ω√

ϵ(ω)µ(ω) (76)

=±ω c0

√ϵr(ω)µ_r(ω) (77)

=±ω c₀

√ϵ^′_rµ^′_r−ϵ^′′_rµ^′′_r +i(ϵ^′_rµ^′′_r +ϵ^′′_rµ^′_r) (78)

Ͱ͋Γɺഔ࣭ͷ༠ి཰ͱಁ࣓཰͔Βܾ·ΔෳૉྔͰ͋

Δɻࣜ(74)ɺ(75)͸ɺບ΍Ի೾౳ͷৼಈ໰୊Ͱ΋Α

͘ग़ͯ͘ΔϔϧϜϗϧπํఔࣜͰ͋Δɻ݁ہɺप೾

਺ྖҬͰϚΫε΢ΣϧํఔࣜΛղ͘͜ͱ͸ɺࣜ(74)ɺ (75)ͷݻ༗ํఔࣜΛ༩͑ΒΕͨڥք৚݅Ͱղ͘͜ͱ ʹؼண͢Δɻ͜͜Ͱɺݻ༗஋͸ݻ༗Ϟʔυप೾਺ʹ ରԠ͢Δɻ

༠ ి ཰ ΍ ಁ ࣓ ཰ ͷ ڏ ෦ ͷ ޮ Ռ Λ ݟ ͯ Έ Α ͏ ɻ

؆୯ͷͨΊɺి৔͸ x ੒෼ͷΈ࣋ͪʢE(⃗x, ω) =⃗ (E_x(⃗x, ω),0,0)ʣɺz࣠ͷਖ਼ͷํ޲ʹਐΜͰ͍Δฏ໘

೾Λߟ͑Δͱɺࣜ(74)͸ɺ ( ∂²

∂z² +k(ω)² )

E_x(⃗x, ω) = 0 (79) ͱͳΔɻ֯प೾਺ ω ͷ࣌ؒґଘੑ΋ؚΊͯɺ͜ͷ ղ͸ɺ

E_x(⃗x, ω)e^−iωt ∝e^{i(k(ω)z−ωt)} (80)

=e^{i(ℜ{k(ω)}z−ωt)−ℑ{k(ω)}z}(81) Ͱ͋Δɻෳૉ༠ి཰ɾಁ࣓཰ͷ࣮෦ͱڏ෦͸θϩ·

ͨ͸ਖ਼஋Ͱఆٛͨ͠ͷͰɺ͜ͷฏ໘೾͕z࣠ͷਖ਼ͷ