成蹊大学理工学研究報告
J. Fac. Sci. Tech., Seikei Univ.
Vol.43 No.2 (2006) pp.49-61（研究装置設備紹介・報告）ɹଟॏ൓ࣹ‫ׯ‬ব๏ͷଌఆਫ਼౓վળͱ

LiNbO3 ݁থͷి‫ ਺܎ֶޫؾ‬r22 ͷଌఆɹถ૔ ࿨໵ ∗1 ɼۚ ࿇Ֆ ∗2 ɼୌ୔ ᅳ࣏ ∗3
ɹImprovement of Measurement Accuracy of the Multiple Reflection Interference Method
and Measurement of Electro-Optic Coeﬃcient r22 of LiNbO3 Crystalɹ∗1Kazuya YONEKURA , Lianhua JIN∗2 , Kuniharu TAKIZAWA∗3
ɹ
ABSTRACT: Multiple reflection interferometry obtains electro-optic coeﬃcient from the phase of interference signal between the light, which passes through the sample crystal without internal reflection and the lights which after
proceeding several internal reflection inside the crystal. To simplify the data process, conventional interferometry considered only two beam interference, which results in theoretical systematic error. We have analyze the error caused by
the theory and form tolerance of the EO crystal, furthermore, propose two measurement techniques to minimize theseerrors. EO coeﬃcient r22 of non-doped congruent LiNbO3 crystal was measured with multiple reflection interferometry, and the measurement results was 6.54 ± 0.02pm/V at 632.8nm by null method.
ɹ

KEYWORDS: Elctrooptic coeﬃcient, Dispersion, Electrooptic crystal, interference(Received October 13, 2006)͍ɽͦͷͨΊɼՄࢹޫ͔Β੺֎ޫ·Ͱ EO ܎਺ͷ೾௕ґଘ

1. ɹ͸͡ΊʹੑΛҰ؏ͯ͠ଌఆ͢Δ͜ͱ͕‫ٻ‬ΊΒΕ͍ͯΔɽ
͜͜Ͱ͸ɼEO ܎਺ͷ೾௕ґଘੑଌఆͷ‫ݱ‬ঢ়Λ໌Β͔ʹ‫ ڧ‬༠ ి ੑ LiNbO3 (LN) ݁ থ ͸ ɼ(1) େ ͖ ͳ ి ‫ֶ ޫ ؾ‬

͢Δ͜ͱʹΑΓɼຊ࿦จͷ໨తΛ໌֬ʹ͢Δɽ

(Electro-Optic;EO) ܎਺ɼ(2) େ‫݁ܕ‬থͷ੡଄͕༰қɼ(3) ைղੑͳͲΛ࣋ͨͣ‫ʹڥ؀‬ରͯ҆͠ఆɼ(4) Ճ޻ੑʹ༏ΕΔɼ(5) ൺֱత҆ՁɼͳͲଟ͘ͷ༏Εͨಛ࣭Λ΋ͭɽͦͷͨΊ
LN ݁থ͸੨৭ޫΛ༻͍ΔϗϩάϥϜ‫ه‬࿥σόΠε [1–3]ɼ
ՄࢹޫΛ༻͍Δޫը૾ॲཧσόΠε [4]ɼ੺֎ޫΛ༻͍Δ
ޫ௨৴σόΠε [5, 6] ͳͲଟ͘ͷޫ‫ػ‬ೳੑσόΠεʹར༻͞Ε͍ͯΔɻLN ݁থ͸ɼ͜ͷ༷ʹ෯޿͍೾௕ྖҬͰ༻͍ΒΕ͍ͯΔ͕ EO ܎਺ͱ೾௕ͷؔ܎͸ෆ֬ఆͳͱ͜Ζ͕ଟ∗1੒᪟େֶ޻ֶ‫ڀݚ‬Պ෺ཧ৘ใ޻ֶઐ߈Պֶੜɹ

(Doctor Candidate, Dept. of Applied Physics,
e-mail:dd053501@cc.seikei.ac.jp)∗2੒᪟େֶཧ޻ֶ෦෺࣭ੜ໋ཧ޻ֶՊॿख

(Research Associate, Dept. of Materials and Life Science,∗3੒᪟େֶཧ޻ֶ෦෺࣭ੜ໋ཧ޻ֶՊ‫ڭ‬त(Professor, Dept. of Materials and Life Science

EO ܎ ਺ ଌ ఆ ๏ ʹ ͸ ɼMach-Zehnder ‫ ׯ‬ব ๏ [7–9] ‫ͼ ٴ‬
Michelson ‫ׯ‬ব๏ [10]ɼޫϔςϩμΠϯ๏ [11–13]ɼFabry
Perot ‫ׯ‬ব๏ [14]ɼSenarmont ๏ [15] ͳͲͷํ๏͕͋Δ͕ɼଌఆ͞Εͨ೾௕͸‫ݶ‬ΒΕ͍ͯΔɽ
ਤ 1 ʹࣔ͢ Mach-Zehnder ‫ׯ‬ব๏‫ ͼٴ‬Michelson ‫ׯ‬ব๏͸ೋͭͷޫ࿏ؒͷޫͷҐ૬͔ࠩΒ EO ܎਺Λଌఆ͢Δํ๏Ͱ͋Γɼ2 ޫ࿏‫ׯ‬ব๏ͱ΋‫ݺ‬͹ΕΔɽ͜ΕΒͷํ๏͸௚ઢภޫͨ͠ޫͷిքʹΑΔҐ૬มԽΛଌఆͯ͠ EO ܎਺Λ‫ٻ‬ΊΔํ๏Ͱ͋Γɼ෯޿͍प೾਺ྖҬʹΘͨΓ͢΂ͯͷ EO ܎਺Λߴ‫Ͱ౓ײ‬ଌఆՄೳͰ͋ΔɽMach-Zehnder ‫ׯ‬ব๏ΛԠ༻ͨ͠ EO ܎਺ଌఆ๏ͱͯ͠ɼޫͷిքʹΑΔҐ૬มԽͷ‫ج‬ຊ೾੒෼ͱୈ 2 ߴௐ೾੒෼Λൺֱ͢Δ͜ͱʹΑΓߴਫ਼౓
ʹ EO ܎ ਺ Λ ଌ ఆ ͢ Δ ํ ๏ ͕ ։ ൃ ͞ Ε ͯ ͍ Δ [16]ɽ͠ ͔͠ɼೋͭͷޫ࿏Λ௨Δޫͷ‫ׯ‬বΛར༻ͨ͠ଌఆͰ͋ΔͨΊɼਤ 1 ʹࣔ͢Α͏ʹଟ͘ͷޫֶ෦඼͕ඞཁͰ͋Γɼۭ‫ؾ‬ͷ༳Β͗΍ৼಈʹରͯ͠੬ऑͰ͋Γɼ๷ৼ୆ɼ෩๷ɼ๷ਖ

─ 49 ─

disturbances
Half mirror

MirrorPhoto Detectorਤ 3 ݁থ໘Ͱଟॏ൓ࣹͨ͠ޫͷৼ෯ͱҐ૬ͷؔ܎ɽ
Half mirror Crystal

MirrorPhoto Detector෯޿͍೾௕ྖҬʹΘͨΓ EO ܎਺Λ‫ٻ‬ΊΔ͜ͱ͸೉͍͠ɽͦͷ΄͔ϓϦζϜ‫ܗ‬ঢ়ͷ݁থΛ༻͍ͯϨʔβΛภ޲͠ɼHalfmirrorͦͷภ޲͔֯Β EO ܎਺Λ‫ٻ‬ΊΔํ๏ [12, 17]ɼύϧεిѹ
CrystalMirrorΛ݁থʹҹՃͯ͠࿪ΈҰఆͷঢ়ଶʹ͋Δ݁থͷ EO ܎਺Λଌఆ͢Δํ๏ [18–20]ɼϥϚϯࢄཚͱ݁থʹҹՃ͢Δަྲྀ

disturbances Mirrorిքʹର͢Δୈ 2 ߴௐ೾੒෼Λଌఆ͢Δ͜ͱʹΑΓ EO ܎

ਤ 1 2 ޫ࿏‫ׯ‬ব‫֎ͱܭ‬ཚ (্ʀMach-Zehnder ‫ׯ‬ব‫ܭ‬ɼԼʀ਺Λଌఆ͢Δํ๏ [21, 22] ͳͲ͕ఏҊ͞Ε͍ͯΔ͕ɼߴਫ਼

Michelson ‫ׯ‬ব‫)ܭ‬౓ͷଌఆ͸༰қͰ͸ͳ͘ɼෳࡶͳ࣮‫ݧ‬ઃඋΛඞཁͱ͢Δɽ

FP‫ׯ‬ব๏Λআ͘͢΂ͯͷଌఆํ๏ʹ‫ڞ‬௨͢Δ໰୊఺ͱ͠
ΧόʔͳͲΛඞཁͱ͢Δɽߋʹɼࢵ֎ޫ΍੺֎ޫͷෆՄͯɼ݁থ಺ͷଟॏ൓ࣹޫ͕ EO ܎਺ଌఆ࣌ͷཧ࿦‫ܥ‬౷‫ࠩޡ‬ࢹޫʹ͓͚ΔଌఆͰ͸ɼ҆ఆͨ͠‫ׯ‬ব৴߸ΛಘΔ͜ͱࣗ

ͱͳΔ఺͕‫͛ڍ‬ΒΕΔɽ͜ͷ໰୊͸ EO ݁থͷ྆୺໘ʹ൓ମ͕ࠔ೉Ͱ͋Δɽ

ࣹ๷ࢭບΛࢪ͢͜ͱʹΑΓվળͰ͖Δɽ͔͠͠൓ࣹ๷ࢭບ

ޫϔςϩμΠϯ๏͸Ґ૬มௐ͞Εͨޫͷൖૹ೾৴߸ͱ

ͷ༗ޮ೾௕ଳҬ͸Ұൠʹ‫͍ڱ‬ɽͦͷͨΊɼ෯޿͍೾௕ྖҬଆଳ೾৴߸ͷৼ෯Λൺֱ͢Δํ๏Ͱ͋Δɽ͜ͷํ๏Ͱ͸

Ͱ EO ܎਺Λߴਫ਼౓ʹଌఆ͢Δʹ͸ɼ֤ʑͷ೾௕ʹରԠ͠ߴप೾ͷ EO ܎਺Λଌఆ͢Δ͜ͱ͸Ͱ͖Δ͕ɼ௿प೾ʹ͓ͨ൓ࣹ๷ࢭບ͕ࢪ͞Εͨ EO ݁থΛ༻ҙ͢Δඞཁ͕͋Δɽ͚Δ EO ܎਺Λଌఆ ͢ Δ ͜ ͱ ͸ ࠔ ೉ Ͱ ͋ Δ ɽ

EO ܎਺ͷ೾௕෼ࢄΛଌఆ͢Δࡍʹ͸Ҏ্ͷΑ͏ͳ༷ʑ

Senarmont ๏ ͸ ௚ ઢ ภ ޫ ͠ ͨ ೋ ͭ ͷ ޫ ͷ Ґ ૬ ࠩʢ Ϧ λͳ໰୊ͱࠔ೉͕͋ΔɽͦͷͨΊ‫ܥ‬౷ͩͬͨ೾௕෼ࢄଌఆ

σʔγϣϯʣΛଌఆ͢Δ͜ͱʹΑΓ EO ܎਺Λ‫ٻ‬ΊΔํ๏͸΄ͱΜͲߦΘΕ͍ͯͳ͍ɽLN ݁থͷ৔߹ɼEO ܎਺ͷͰ͋Γɼ‫͔͘ݹ‬ΒΑ͘஌ΒΕͨ EO ܎਺ଌఆ๏ͷҰͭͰ͋೾௕෼ࢄଌఆ͸ɼChirakadze ΒʹΑΔϊϯυʔϓίϯάϧ

Δɽ͜ͷଌఆ๏͸ɼਤ 2 ʹࣔ͢Α͏ʹ௚ަ഑ஔ͞ΕͨภޫΤϯτ LN ݁থͷ೾௕ 420-1150nm ʹ͓͚Δ r22 [22] ͷଌఆࢠͱ‫ࢠޫݕ‬ͷؒʹଌఆର৅ͱͳΔ݁থΛઃஔͯ͠ EO ܎਺΍ɼMéndez ΒʹΑΔϊϯυʔϓίϯάϧΤϯτ‫ͼٴ‬४εΛଌఆ͢Δํ๏Ͱ͋ΓɼLN ݁থ΍ LiTaO3 ݁থͳͲͷ఺‫܈‬τΠΩΦϝτϦ LN ݁থͷ೾௕ 458-632.8nm ‫ ͼٴ‬1.04μm ʹ

3m ͷ݁থͷ r22 ͷଌఆʹద͍ͯ͠Δɽ͔͠͠ Senarmont ๏͓͚Δ r13 ‫ ͼٴ‬r33 [23] ͕ ଌ ఆ ͕ ͋ Δ ͷ Έ Ͱ ͋ Δ ɽ

Ͱ LN ݁থͷ EO ܎਺ r13 ɼr33 ɼr51 Λਖ਼֬ʹଌఆ͢Δ͜ͱ͸Ͱ͖ͳ͍ɽ

2 ޫ࿏‫ׯ‬ব๏΍ FP ‫ׯ‬ব๏ͷ՝୊Λղܾ͠ɼ޿͍೾௕ྖҬʹΘͨͬͯ EO ܎਺ΛଌఆͰ͖Δํ๏ͱͯ͠ଟॏ൓ࣹ‫ׯ‬বFabry-Perot(FP)‫ׯ‬ব๏͸ɼബບՃ޻͞ΕͨLN݁থͷ྆໘๏͕͋Δ [24]ɽ͜ͷଌఆ๏͸ɼਤ3ʹࣔ͢Α͏ʹɼ݁থ಺Ͱ

ʹϛϥʔΛࢪͨ͠ FP ‫ثৼڞ‬ͷޫ‫ৼڞ‬ಛੑ͔Β EO ܎਺Λ‫ٻ‬൓ࣹͤͣʹͦͷ··ಁա͢Δޫͱ݁থ಺Ͱෳ਺ճ൓ࣹͨ͠

ΊΔํ๏Ͱ͋Δɽ͔͠͠ɼ͜ͷํ๏͸‫ڥ؀‬Թ౓มԽʹΑΔ‫݁ʹޙ‬থΛಁա͢Δޫͷ‫ׯ‬বΛར༻ͯ͠ EO ܎਺Λଌఆ͢Ө‫ڹ‬Λඇৗʹ‫͘ڧ‬ड͚Δɽ·ͨ FP ‫ͦثৼڞ‬ͷ΋ͷͷ੡଄

ΔɽFP‫ׯ‬ব‫ث‬ͷಛ௃Ͱ͋Δ‫༻ৼڞ‬ϛϥʔΛऔΓআ͘͜ͱʹ΍ɼ෯޿͍೾௕ҬʹΘͨͬͯ൓ࣹ཰ʹ೾௕ґଘੑΛ࣋ͨͳΑΓFP‫ׯ‬ব๏ͷܽ఺Ͱ͋Δ‫ڱ‬ଳҬੑΛഉআ͢Δͱ‫ʹڞ‬ɼ͍͢ϛϥʔͷ੡଄͕ࠔ೉Ͱ͋ΔɽͦͷͨΊ FP‫ثৼڞ‬Λ༻͍ͯ΂ͯͷଟॏ൓ࣹޫ͕ಉ͡ޫ࿏ΛͨͲΔ୯Ұޫ࿏Λ࣮‫͢ݱ‬Δ͜ͱʹΑΓɼ2 ޫ࿏‫ׯ‬ব‫ܭ‬ͷ΋ͭৼಈ΍ۭ‫ؾ‬ͷΏΒ͗ͳ

Signal GeneratoryzͲͷ֎ཚʹରͯ͠੬ऑͰ͋Δͱ͍͏໰୊Λղܾ͍ͯ͠Δɽ

V͜ͷΑ͏ʹଟॏ൓ࣹ‫ׯ‬ব๏͸༏Εͨಛ௃Λ΋͕ͭɼͦͷ

x

Light
Sourceଌఆਫ਼౓͸ଌఆࢼྉͷ۶ં཰ʹґଘ͢Δͱ͍͏໰୊఺Λ๊

LN

Polarizer
(45°)

Photo
Analyzer Detector

Wavelength
Plate(λ/4) (-45°)

ਤ 2 Senarmont ๏͍͑ͯΔɽຊ࿦จͰ͸ EO ܎਺ͷ೾௕෼ࢄಛੑΛ‫ٻ‬ΊΔ͜ͱΛ໨తͱͯ͠ɼଟॏ൓ࣹ‫ׯ‬ব๏ͷ΋ͭ͜ͷ໰୊Λվળ͢Δ͜ͱʹΑΓɼ༰қͳଌఆͱߴ͍ଌఆਫ਼౓ͷཱ྆ΛਤΔɽ
ຊ࿦จͰ͸෯޿͍೾௕ྖҬʹ͓͍ͯ EO ܎਺ͷਫ਼ີଌఆ─ 50 ─

Մೳͳଟॏ൓ࣹ‫ׯ‬ব๏ʹ͍ͭͯɼ‫݁ڀݚ‬ՌΛ 8 અʹΘͨΓ

r41 T Λଌఆ͠ɼѹిఆ਺ d14 ͱͷ૬ରతූ߸ؔ܎Λ໌Β͔ͱΓ·ͱΊͯ‫ه‬ड़͢Δɽୈ 2 અͰ͸ɼEO ܎਺ͷ೾௕෼ࢄʹͨ͠ [26]ɽ

ಛੑऔಘʹదͨ͠ଟॏ൓ࣹ‫ׯ‬ব๏ʹ͍ͭͯड़΂Δɽୈ 3 અଟॏ൓ࣹ‫ׯ‬ব๏ʹΑΔ EO ܎਺ଌఆʹ͸ɼ2 छྨͷ࣮‫ݧ‬ɾͰ͸ null ๏͕͍࣋ͬͯͨཧ࿦‫ܥ‬౷‫ݕ͍ͯͭʹࠩޡ‬౼͠ɼͦղੳํ๏͕͋Δɽͷ‫ࠩޡ‬Λղফ͢ΔͨΊͷղੳํ๏ʹ͍ͭͯৄࡉʹड़΂ΔɽҰͭ͸ޫ‫ݕ‬ग़‫ث‬৴߸ͷ͏ͪ݁থʹҹՃ͢Δަྲྀిѹͱ

ୈ 4 અͰ͸ৼ෯ൺֱ๏͕͍࣋ͬͯͨཧ࿦‫ܥ‬౷‫͍ͯͭʹࠩޡ‬౳͍֯͠प೾਺Λ΋ͭ৴߸ʢ‫ج‬ຊ೾੒෼ʣͷ‫࠷͕౓ڧ‬খ‫ݕ‬౼͠ɼͦͷ‫ࠩޡ‬Λղফ͢ΔͨΊͷղੳํ๏ʹ͍ͭͯৄʹͳΔిѹ஋͔Β EO ܎਺Λ‫ٻ‬ΊΔํ๏Ͱ͋Δɽ͜͜Ͱ͸ࡉʹड़΂Δɽୈ 5 અͰ͸݁থͷ΋ͭ‫ܗ‬ঢ়‫͕ࠩޡ‬ଌఆ݁Ռʹ͜ΕΛ null ๏ͱ‫͢ʹͱ͜Ϳݺ‬Δɽଞํ͸ɼޫ‫ݕ‬ग़‫ث‬৴߸ͷ༩͑ΔӨ‫͍ͯͭʹڹ‬ड़΂Δɽୈ 6 અͰ͸ଟॏ൓ࣹ‫ׯ‬ব๏ͳ‫ج‬ຊ೾੒෼ͱୈ 3 ߴௐ೾੒෼ͷ৴߸‫౓ڧ‬Λൺֱ͢Δ͜ͱʹΒͼʹ null ๏ɾৼ෯ൺֱ๏ͷಛ௃ʹ͍ͭͯड़΂Δɽୈ 7 અ

ΑΓ EO ܎਺Λ‫ٻ‬ΊΔํ๏Ͱ͋Δɽզʑ͸͜ΕΛৼ෯ൺֱͰ͸ɼཧ࿦‫ܥ‬౷‫ࠩޡ‬Λղফͨ͠ଟॏ൓ࣹ‫ׯ‬ব๏Λ༻͍ͯ๏ͱ‫͢ʹͱ͜Ϳݺ‬Δɽϊ ϯ υ ʔ ϓ ί ϯ ά ϧ Τ ϯ τ LN ݁ থ ͷ EO ܎ ਺ r22 Λ ೾ ௕࣍અҎ߱Ͱ૒ํͷํ๏ʹ͍ͭͯઆ໌Λߦ͍ɼͦΕͧΕͷํ๏ͷར఺ͱܽ఺Λ໌Β͔ʹ͢Δɽ

632.8nm Ͱଌఆͨ݁͠ՌΛใࠂ͢Δɽୈ 8 અ͸ຊ‫ڀݚ‬ͷ੒ՌΛ·ͱΊͰ͋Δɽ

3. ɹ null ๏
2. ɹଟॏ൓ࣹ‫ׯ‬ব๏

3.1 null ๏ͷ‫ݪ‬ཧ݁থ಺ͷଟॏ൓ࣹΛੵ‫ۃ‬తʹར༻͢Δ͜ͱʹΑΓ EO ܎ଟ ॏ ൓ ࣹ ‫ ׯ‬ব ๏ ͷ ଌ ఆ ϒ ϩ ο Ϋ Λ ਤ 4 ʹࣔ͢ɽ࣮‫ܥݧ‬਺Λଌఆ͢Δଟॏ൓ࣹ‫ׯ‬ব๏ [24] ͸ɼ྆୺໘Λฏߦʹ‫ݚ‬ຏ͸ɼ྆୺໘Λฏߦʹ‫ݚ‬ຏͨ݁͠থʹަྲྀిѹ VAC sin(ωθ t)

ͨ͠ EO ݁থʹϨʔβޫΛਨ௚ʹೖࣹͤ͞Δ͚ͩͷඇৗʹΛՃ͑ɼϨʔβޫΛ݁থͷ୺໘͔Βೖࣹͤ͞Δ͚ͩͷ؆γϯϓϧͳޫֶ‫ߏͰܥ‬੒͞ΕΔɽ͜ͷํ๏͸݁থ಺Ͱ൓ࣹ

୯ͳޫֶ‫͔ܥ‬Βߏ੒͞ΕΔɽ͜͜Ͱɼ݁থʹҹՃ͢Δަͤͣʹͦͷ··ಁա͢Δޫͱ݁থ಺Ͱ 2 ճ൓ࣹͨ͋͠ͱʹ
ಁա͢Δޫͱͷ‫ׯ‬বΛར༻ͯ݁͠থͷ EO ܎਺Λଌఆ͢Δɽ
ଟॏ൓ࣹ‫ׯ‬ব๏͸ಁաޫͱ݁থ಺ԟ෮ޫ͕ಉ͡ޫ࿏Λྲྀ ి ѹ ͷ ৼ ෯ Λ VAC ɼަ ྲྀ ి ѹ ͷ ֯ प ೾ ਺ Λ ωθ ͱ͢Δɽ݁থͷ୺໘Ͱ൓ࣹͤͣʹಁա͢Δޫͱ݁থ಺Λ 1.5 ճԟ෮ͨ͠‫ʹޙ‬ಁա͢Δޫͱͷ‫ׯ‬ব৴߸͸ඇৗʹখ͍͕͞ɼޫ

ͨͲΔͨΊɼ

‫ݕ‬ग़‫͔ث‬Βͷ৴߸Λத৺֯प೾਺ ωθ ʹઃఆͨ͠ϩοΫΠ(1) ৼಈ΍ۭ‫ؾ‬ͷ༳Β͗ͷӨ‫ڹ‬Λड͚ͣʹ҆ఆͨ͠‫ׯ‬ϯΞϯϓ΍όϯυύεϑΟϧλʹಋ͚͹ɼࡶԻͷগͳ͍বଌఆ͕Մ ೳ ɼ‫ج‬ຊ೾੒෼ sin ωθ t Λ‫ݕ‬ग़͢Δ͜ͱ͕Ͱ͖Δɽ͜ͷᖤա৴(2) ๷ৼ୆͕ෆ ཁ ɼ߸͕࠷খʹͳΔͱ͖ͷҹՃަྲྀిѹͷৼ෯Λଌఆ͢Δ͜(3) ੺֎ޫ΍ࢵ ֎ ޫ ͳ Ͳ ͷ ෆ Մ ࢹ ޫ ͷ ଌ ఆ ͕ ༰ қ ɼͱʹΑΓ࣮ޮత EO ܎਺Λ‫ٻ‬ΊΔ͜ͱ͕Ͱ͖Δɽ࣍ʹͦͷ‫ݪ‬ཧΛड़΂ΔɽͳͲͷಛ௃Λ΋ͭɽ·ͨɼଟॏ൓ࣹ‫ׯ‬ব๏͸ EO ܎਺Λଌఆ͢Δࡍʹ݁থ಺ͷଟॏ൓ࣹΛੵ‫ۃ‬తʹར༻͢ΔͨΊɼਫ਼ີʹ EO ܎਺Λଌ
ఆ͢Δࡍɼैདྷͷଟ͘ͷ‫ׯ‬ব‫ܭ‬ଌ๏Ͱ͸͔ܽͤͳ͍݁থ
୺໘΁ͷ൓ࣹ๷ࢭບͷৠண͕ෆཁ͋ΔɽߋʹҐ૬มԽΛ

ਤ3ʹࣔ͢Α͏ʹϨʔβޫΛ݁থ୺໘ʹରͯ͠ਨ௚ʹ ೖ ࣹ ͞ ͤ Δ ͱ ͖ ɼϨ ʔ β Ϗ ʔ Ϝ ͸ ݁ থ ͷ ྆ ୺ ໘ ؒ Ͱଟॏ൓ࣹ͢ΔͨΊ݁থ͔Βͷಁաޫ͸༷ʑͳҐ૬Λ΋ͭ ෳ ਺ ͷ Ϗ ʔ Ϝ ͔ Β ͳ Δ ɽ݁ থ ໘ ͷ ύ ϫ ʔ ൓ ࣹ ཰ Λ Rɼ݁ থ ಺ Ͱ ൓ ࣹ ͤ ͣ ʹ ಁ ա ͢ Δ ޫ ͷ ৼ ෯ Λ Aɼަ ྲྀ ి ѹ௚઀ଌఆ͢ΔͨΊɼ

VAC sin ωθ t ʹΑΓ༠‫͞ى‬ΕΔޫͷಈతҐ૬มԽΛ θ sin ωθ tɼ

(1) Ұͭͷ݁থ Ͱ ߴ ਫ਼ ౓ ͳ ೾ ௕ ෼ ࢄ ಛ ੑ Λ Մ ೳ ɼ݁থʹҹՃ͢Δ௚ྲྀిѹΛ VDC ɼVDC ʹΑΓ༠‫͞ى‬ΕΔ(2) ͢΂ͯͷ EO ݁থͷ͢΂ͯͷ EO ܎ ਺ Λ ଌ ఆ Մ ೳ ɼͱ͍͏ಛ௃Λ΋ͭɽஶऀͷ 1 ਓ͸͜ͷํ๏Ͱ LN ݁থͱɼLiTiO3 ݁থͷԠྗҰఆঢ়ଶͰͷ EO ܎਺ r13 T ͱ r33 T Λଌఆͨ͠ [24]ɽ·ͨɼTi
֦ࢄ LN ޫಋ೾࿏ʹ͓͚Δ۶ં཰෼෍ͱಋ೾ޫ෼෍ͷॏͳΓ܎਺ Γ ͱ EO ܎਺ r22 T ͷੵͰද͞ΕΔޫಋ೾࿏ͷ࣮ޮత

ਤ 4 ଟॏ൓ࣹ‫ׯ‬ব๏Λ༻͍ͯ EO ܎਺Λଌఆ͢ΔͨΊͷ

EO ܎਺ Γr22 Λଌఆ͠ɼTi ບްͱ Γr22 ͷؔ܎Λ໌Β͔ʹ࣮‫ݧ‬ϒϩοΫਤɽTT͠ ͨ [25]ɽߋ ʹ NH4 H2 PO4 ݁ থ ΍ KH2 PO4 ݁ থ ͷ EO ܎ ਺─ 51 ─

0.8

· ಁ ա ͢ Δ ޫ ͷ ి ք ͸ A sin[ωt + (θ sin ωθ t + φ)] ͱ ද ͞ Ε

0.6

Δɽ͜͜Ͱ θ sin ωθ t ‫ ͼٴ‬φ ͸݁থ΁ͷҹՃిѹʹΑΓੜ͡

0.4
J1 (2θ )ޫͷ੩తҐ૬Λ φ ͱ͢Δͱɼ݁থ಺Ͱ൓ࣹͤͣʹͦͷ·Δ Ϩ ʔ β ޫ ͷ ಈ త Ґ ૬ ม Խ ‫ ͼ ٴ‬੩ త Ґ ૬ Ͱ ͋ Γ ɼͦ ΕͧΕ݁থ಺Λ1ճ఻ൖ͢Δ͜ͱʹΑΓੜ͡Δେ͖͞Ͱθ =1.9159

0.20͋ Δ ɽ݁ থ ಺ Ͱ 1.5 ճ ԟ ෮ʢ ݁ থ ୺ ໘ Ͱ 2 ճ ൓ ࣹ ʣ͠ ͨ

-0.2

͋ ͱ ʹ ಁ ա ͢ Δ ޫ ͸ ɼ݁ থ ಺ Ͱ ൓ ࣹ ͤ ͣ ʹ ಁ ա ͢ Δ ޫ-0.4

ʹ ൺ ΂ ɼ3 ഒ ͷ ‫ ཭ ڑ‬Λ ఻ ൖ ͢ Δ ͜ ͱ ʹ ͳ Δ ɽΑ ͬ ͯ ಈ

0

0.5

1

1.5

2

2.5

3

θ

త Ґ ૬ ‫ ͼ ٴ‬੩ త Ґ ૬ ͷ ม Խ ྔ ͸ 3(θ sin ωθ t + φ) ͱ ͳ Δ ɽ݁ থ ͔ Β ಁ ա ͢ Δ Ϩ ʔ β ޫ ͷ Ґ ૬ ͸ ɼৼ ෯ A ʹ ৼ ෯ ൓

ਤ5√
ࣹ཰ R Λ 2 ճ৐ͯ͡ AR sin[ωt + 3(θ sin ωθ t + φ)] ͱද͞ΕJ1 (2θ) = 0 Λຬ଍͢Δ θɽ

Δ ɽಉ ༷ ʹ ݁ থ ಺ Λ 2.5 ճ ԟ ෮ ͠ ͨ ͋ ͱ ಁ ա ͢ Δ ޫ ͸ ɼͱද͞ΕΔɽ͜͜Ͱ੩తҐ૬ φ ͱಈతҐ૬ θ ͸ະ஌਺Ͱ͋

AR sin[ωt + 3(θ sin ωθ t + φ)] Ͱද͞ΕΔɽ

Δ͕ɼJ1 (2θ) = 0 ͷ஋Λຬ଍͢Δ θ ͷ஋͸ਤ 5 ΑΓ໌Β͔Ͱ୯ҰॎϞʔυϨʔβޫʢҎ‫ޙ‬ɼղੳ΋‫ؚ‬ΊͯԣϞʔυ͋Δɽ·ͨಈతҐ૬ θ ΍ҹՃަྲྀిѹ VAC ʹର͢ΔԠྗҰ͸ৗʹ TEM00 ʣ͕݁থ಺෦Λ (m + 0.5) ճԟ෮͢ΔͱԾఆ͢ఆঢ়ଶʹ͓͚Δ LN ݁থͷ EO ܎਺ r22 ͷؔ܎͸ҎԼͷࣜͰΔͱɼ(m + 1) ຊͷϨʔβޫͷ‫ׯ‬বʹΑΓੜ͡Δޫ‫౓ڧ‬৴ද͞ΕΔɽ

߸ I ͸ࣜ (1) Ͱ༩͑ΒΕΔɽ

⎫2
⎧ m
⎪
⎪
⎪ k

⎪
⎬
2⎨
I=A ⎪
R sin ωt + (2k + 1) (θ sin ωθ t + φ) ⎪
(1)
⎪
⎪
⎭
⎩
k=0

Αͬͯ T Λ 2π/ωθ ( 2π/ω) Ͱ༩͑ΒΕΔޫ‫ݕ‬஌‫ث‬ͷੵ෼࣌ؒͱ͢Ε͹ɼࣜ (1) ΑΓޫ‫ݕ‬ग़‫ث‬ͷग़ྗ৴߸ P ͸ ɼ
T

A2
P=
T
0

m


2
Rk sin[ωt + (2k + 1)(θ sin ωθ t + φ)] dx (2)θ=πn3o r22 LVAC
λD

(6)

͜͜Ͱ no ͸ LN ݁থͷৗ۶ં཰ɼλ ͸Ϩʔβޫͷ೾௕ɼL ͸
݁থ௕ɼD ͸݁থްͰ͋ΔɽΑͬͯɼҹՃަྲྀిѹΛ 0 ͔Βॱ࣍૿େͯ͠ P1F = 0 ͱͳΔిѹΛଌఆ͢Ε͹ɼ੩తҐ૬ φ ΍ύϫʔ൓ࣹ཰ R ʹ͔͔ΘΒͣࣜ (6) Λ༻͍࣮ͯޮత

EO ܎਺Λ‫ٻ‬ΊΔ͜ͱ͕Ͱ͖Δɽ
Ҏ্͕ɼैདྷͷଟॏ൓ࣹ‫ׯ‬ব๏ͷଌఆ‫ݪ‬ཧͰ͋Δɽຊ

k=0

અͰ͸ 2 ຊͷޫϏʔϜͷ‫ׯ‬বʢm = 1 ͷ৔߹ʣʹ͍ͭͯ‫ݕ‬

ͱͳΔɽࣜ (2) Λల։ͯ͠ੵ෼‫ࢉܭ‬Λ͢ΔͱɼP ͸౼͕ͨ͠ɼ࣮ࡍʹ͸݁থ಺Λෳ਺ճԟ෮ͨ͠ͷͪʹಁա
A2  2kP=
R + A2Rk+2l cos 2k (θ sin ωθ t+φ)2 k=0
l=0 k=1m

m−1 m−l

m
2 

m−l
m−1 


͢ΔޫͷӨ‫ڹ‬΋ߟྀ͢Δඞཁ͕͋Δɽ࣍খઅͰ͸൓ࣹճ਺ m ͷ‫ݕ‬౼Λߦ͏ɽ

A
R2k + A2
Rk+2l
2 k=0
l=0 k=1
 ⎫

⎧
∞

⎪
⎪
⎪
⎪
⎪
⎪
(2θ)
(2kθ)
(2hω
J
t)
+
2
cos
cos(2kφ)
J
⎪
⎪
0
2h
θ
⎪
⎪
⎬
⎨
h=1
⎪
⎪
∞
⎪
⎪

⎪
⎪
⎪
⎪
⎪
(2kφ)
(2kθ)
sin [(2h + 1) ωθ t] ⎪J2h+1⎭
⎩ −2 sin=

3.2 ൓ࣹճ਺ m ͷ‫ݕ‬౼
m → ∞ ͷ࣌ʹࣜ (3) ͸Α͘஌ΒΕΔ Fabry-Perot ͷࣜʹͳΓ ɼ݁ থ ௕ ͕ Ϗ ʔ Ϝ அ ໘ ‫ ʹ ܘ‬ൺ ΂ ͯ े ෼ ୹ ͍ ৔ ߹ ʹ ͸

h=0

(3)

Fabry-Perot ͷ͕ࣜ੒ཱ͢Δɽ͔͠͠ɼਤ 3 ͷԣ‫ޫܕ‬มௐ‫ث‬Ͱ͸ɼm ͸༗‫ݶ‬ͷ஋ʹ੍‫͞ݶ‬ΕΔɽຊখઅͰ͸Ψ΢γΞϯ

Ͱ༩͑ΒΕΔɽͨͩ ͠ Jh ͸ h ࣍ͷ ϕ ο η ϧ ؔ ਺ Ͱ ͋ Δ ɽόϯυύεϑΟϧλΛ༻͍ͯҹՃిѹͷ‫ج‬ຊ೾੒෼ϏʔϜͰ͋ΔϨʔβޫ͕ɼԣ‫ܕ‬มௐ‫͍͓ͯʹ಺ث‬൓ࣹՄೳͳճ਺ʹ͍ͭͯ‫ݕ‬౼Λ͢Δɽ

sin ωθ t Λબ୒͢Δ ͱ ɼ‫ج‬ຊ ೾ ੒ ෼ ৴ ߸ PmF ͸
PmF = −2A2

m−1 
m−l


Rk+2l sin (2kφ) J1 (2kθ) sin ωθ t྆୺໘Λฏߦʹ‫ݚ‬ຏͨ͠ LN ݁থʹϨʔβޫΛਨ௚ʹೖ

(4)

l=0 k=1ࣹͤͨ͞৔߹ɼ݁থ಺Λಁա͢ΔϨʔβޫ͕౳Ґ૬໘Λ
อͬͨ··ແ‫ݶ‬ճ൓ࣹ͢Δࣄ͸Ͱ͖ͳ͍ɽͦΕ͸Ψ΢γ
ΞϯϏʔϜ͕ճં‫ݱ‬৅ʹΑΔϏʔϜ֦͕Γ֯Λ΋ͭͨΊɼͱͳΔɽ͜͜Ͱ݁থ಺Ͱ൓ࣹͤͣʹಁա͢Δޫͱ݁থ಺Λ 1.5 ճ͋ΔҰఆҎ্ͷ‫཭ڑ‬Λ఻ൖͨ͠ϨʔβޫͷϏʔϜ‫͕݁ܘ‬ԟ෮ͨ͠‫ʹޙ‬ಁա͢Δޫͱͷ‫ׯ‬বʢm = 1 ͷ৔߹ʣ͚ͩΛথްΛ௒͑ͯ͠·͏ͨΊͰ͋Δɽ݁থ಺Λ఻ൖ͢ΔϨʔ

ߟྀ͢Δͱޫ‫ݕ‬ग़৴ ߸ ͸ ߋ ʹ ؆ ୯ ʹ ͳ Γ ɼβޫ͕౳Ґ૬໘Λอͬͨ··ΤωϧΪʔଛࣦແ͠ʹ఻ൖ

P1F = −2A2 R sin (2φ) J1 (2θ) sin ωθ t(5)

─ 52 ─

Ͱ͖Δ‫཭ڑ‬͸ҎԼ ͷ ࣜ Ͱ ද ͞ Ε Δ [11]ɽ

10.00

D
4λ
= S2
nπ
L

Systematic Error (%)(7)

͜͜Ͱ L ͸݁থ௕ɼD ͸݁থްɼn ͸݁থͷ۶ં཰ɼS ͸ηʔϑςΟϑΝΫλͰ͋ΔɽҰൠʹ S ͕ 3 ∼ 6 ΑΓେ͖͚Ε͹ɼճંଛࣦΛແࢹ ͢ Δ ͜ ͱ ͕ Ͱ ͖ Δ ɽ

1.00

0.10

0.01

Ϩʔβޫ͕݁থ಺Λ (2m + 1) ճԟ෮ͨ͠‫݁ʹޙ‬থ͔Βಁա͢Δ৔߹ɼޫͷ࣮ࡍͷ఻ൖ‫཭ڑ‬͸ (2m + 1)L ͱͳΔɽ͜

0.00
1.0

ΕΛࣜ (7) ΁ద༻͢ΔͱɼϨʔβޫ͕ଛࣦແ͠ʹ݁থ͔Βಁա͢Δ m ͸ɼҎԼ ͷ ࣜ Ͱ ࣔ ͞ Ε Δ ɽ

ਤ7
1 no πD2m=−1
2 4λLS 2

1.5

2.0

2.5
R

3.0

3.5

4.0

݁থͷύϫʔ൓ࣹ཰ R ͱैདྷͷଟॏ൓ࣹ‫ׯ‬ব๏͕΋ͭཧ࿦‫ܥ‬౷‫ࠩޡ‬ͷؔ܎ɽ

(8)͜͜ͰϊϯυʔϓίϯάϧΤϯτ݁থͷ೾௕ λ = 632.8nm

ද 1 ཧ࿦‫ܥ‬౷‫ࠩޡ‬ͷ ৗ ۶ ં ཰ no = 2.2868 Λ ༻ ͍ ͯ [27]ɼ݁ থ α Π ζ Λ

Refractive

Power

Wavelength

Systematic

indices

Reflectivity(nm)

Error(%)

KH2 PO4

1.50790.0410

632.8

LiIO3

1.88300.0930

632.8

0.17

LiNbO32.38700.1677441

0.58

LiNbO32.28640.1532

632.8

0.48

LiNbO3

2.23640.14591000

0.43

Material

D = 2mmɼL = 20mm ͱ͢Δͱɼࣜ (8) ͔Β m = 7.383 ͱͳΔɽਤ 6 ʹɼ͜ͷ৚݅ԼͰͷ m ͱ D ͷؔ܎Λࣔ͢ɽΑͬͯɼ͜ͷ৚݅Ͱ࣮‫ݧ‬Λߦ͏৔߹ɼϨʔβޫͷ݁থ಺Ͱͷԟ෮ճ਺͸ m = 7 ͕ҰԠͷ໨҆ͱͳΔɽͨͩ͠ m ≥ 8 Ͱ΋ޫ͸ճંଛࣦΛ൐͍ͳ͕Β݁থΛಁա͢ΔͨΊɼͦͷӨ‫ڹ‬Λߟྀ͠ͳ͚Ε͹ͳΒͳ ͍ ɽ

0.03

BaTiO32.40370.1701

632.8

0.60

InGaAsP

3.4

0.2975

1550

1.62

GaAs

3.45500.3037

1150

2.17

35

ফ‫͖Ͱڈ‬Δ߲͸ i ͕‫਺ح‬ͷ৔߹ͷΈͰ͋Δɽߴ࣍ͷ‫߲਺ۮ‬25

͕ ࢒ Δ ͱ φ = π/4 ʹ ਖ਼ ֬ ʹ ઃ ఆ ͢ Δ ͜ ͱ ͸ ࠔ ೉ ʹ ͳ Δ ɽ

20

ैͬͯୈ2߲Ҏ͕߱ଟॏ൓ࣹ‫ׯ‬ব๏ͷཧ࿦‫ܥ‬౷‫ͳͱࠩޡ‬Δɽ

15

3.2અʹࣔͨ݁͠থαΠζͷ৔߹ɼԣ‫ޫܕ‬มௐ‫͚͓ʹث‬Δ

10ޫͷ൓ࣹճ਺͸ m = 7 Ͱ͋Δ͜ͱΛલઅͰड़΂ͨɽͦ͜Ͱ

5

m = 7ͱͨ͠৔߹ͷ࣮ޮత EO܎਺ͷཧ࿦‫ܥ‬౷‫ͱࠩޡ‬ύϫʔ

m

30

0
0

ਤ6

0.5

1

1.5

2

2.5

3

3.5

൓ࣹ཰ͷؔ܎Λ‫ͨ͠ࢉܭ‬ɽͦͷ݁ՌΛਤ 7 ʹࣔ͢ɽ·֤ͨ4

D (mm)

छ EO ݁থͷ EO ܎਺Λछʑͷ೾௕Ͱଌఆͨ͠৔߹ͷཧ࿦‫ܥ‬൓ࣹճ਺ m ͷ D ґଘੑɽ
ʢL = 20mmɼλ = 632.8nmɼ౷‫ࠩޡ‬Λද 1 ʹࣔ͢ɽKH2 PO4 ݁থͷΑ͏ʹ۶ં཰͕খ͞

n = 2.2868ʣ

͍৔߹ɼͦͷύϫʔ൓ࣹ཰΋খ͘͞ͳΔͨΊɼཧ࿦‫ܥ‬౷‫ࠩޡ‬͸ඇৗʹখ͍͞ɽ͕ͨͬͯ͠ɼKH2 PO4 ݁থͰ͸ɼଟॏ൓ࣹޫ͕ଌఆ݁Ռʹ༩͑ΔӨ‫ڹ‬͸খ͍͞ɽLN ݁থͷΑ

3.3 null ๏ͷଌఆਫ਼౓͏ʹ۶ં཰͕໿ 2.2 લ‫ޙ‬ͷ݁থͷ৔߹ɼཧ࿦‫ܥ‬౷‫ࠩޡ‬͸໿

0.5% ఔ౓ͱͳΓɼEO ܎਺Λਫ਼ີʹଌఆ͢Δࡍʹ͸ɼ͜Εຊઅ͸ଟॏ൓ࣹޫ͕ଌఆਫ਼౓ʹ༩͑ΔӨ‫͍ͯͭʹڹ‬ղΛແࢹ͢Δ͜ͱ͸Ͱ͖ͳ͍ɽߋʹɼGaAs ݁থ΍ InGaAsPੳ͢Δ [24]ɽ

݁থͷΑ͏ʹ۶ં཰͕ 3 Λ௒͑ΔΑ͏ͳ݁থͷ৔߹ɼཧ࿦

݁থ಺Λ 3 ԟ෮൒ͨ͠‫ʹޙ‬ಁա͢ΔޫϏʔϜͱͷ‫ׯ‬ব‫ܥ‬౷‫ࠩޡ‬͸ 1% Λ௒͑ɼଌఆ݁Ռʹେ͖ͳӨ‫ڹ‬Λ༩͑Δɽʢm = 3 ͷ৔߹ʣͷόϯυύεϑΟϧλͷग़ྗ P3F ͸ɼ⎤⎡⎢⎢⎢ 1+R2+R4 sin (2φ) J1 (2θ) ⎥⎥⎥


⎥⎥
⎢
⎢
P3F = −2A2i R sin ωθ t ⎢⎢⎢⎢+ R + R3 sin (4φ) J1 (4θ)⎥⎥⎥⎥
⎢⎣
⎥⎦
i=1
+R2 sin (6φ) J1 (6θ)
q


3.4 null ๏ͷଌఆਫ਼౓ͷվળ(9)ଟॏ൓ࣹ‫ׯ‬ব๏͕͔͔͑Δཧ࿦‫ܥ‬౷‫ࠩޡ‬Λղফ͢ΔͨF= 0 ͱͳΔಈతҐ૬ θ ΛΊʹɼຊઅͰ͸ࣜ (4) ͔Β௚઀ Pm

ͱͳΔɽ

φ = π/4 ʹઃఆ͢Ε͹ୈ 2 ߲Λফ‫͢ڈ‬Δ͜ͱ͕Ͱ͖Δ͕ɼ
ୈ 3 ߲͸࢒Δɽಉ༷ʹɼm > 3 ͷߴ߲࣍Ͱ΋ φ = π/4 ͱͯ͠‫ٻ‬ΊΔํ๏Λ‫ݕ‬౼͢Δɽࣜ (4) ʹ͸ mɼRɼφɼθ ͷ 4 ͭͷະ஌਺͕‫·ؚ‬ΕΔɽ͜ͷ͏ͪ R ͸ଌఆର৅ͱͳΔ݁থͷछྨ

─ 53 ─

ͱଌఆ೾௕ʹΑΓܾఆ͞ΕΔ͔Βɼ͜ͷࣜ͸ 3 ͭͷม਺Λ

ͷ P7F = 0 ۙ๣Λ֦େͨ͠΋ͷͰ͋Δɽθ0 = 1.9251 ʹ͓͍

F΋ͭؔ਺ͱ‫͖Ͱ͕ͱ͜͢ͳݟ‬Δɽ Pm= 0 ͱͳΔ mɼφɼθ ͷ

ͯ P7F = 0 ͱͳΔɽF
= 0 ͔Β௚ͪʹ૊Έ߹Θͤ͸ແ਺ʹଘࡏ͢Δɽ͜Ε͸ Pmैདྷͷଟॏ൓ࣹ‫ׯ‬ব๏Ͱ͸m = 1ͱ͍ͯͨͨ͠Ίɼ

P1F = 0 ͱͳΔ৚݅͸ θ0 = 1.9159 Ͱ͋ͬͨɽຊઅͷํࣜΛ

EO ܎਺Λ‫ٻ‬ΊΔ͜ͱ ͕ Ͱ ͖ ͳ ͍ ͜ ͱ Λ ҙ ຯ ͢ Δ ɽ͜ΕΛղܾ͢ΔͨΊʹ͸ԿΒ͔ͷํ๏ͰmͱφΛ֬ఆ༻͍Δ͜ͱʹΑΓɼࠓճͷղੳ৚݅Ͱ͸໿ 0.5% ͷཧ࿦‫ܥ‬͠ɼࣜ (4) ΛҰͭͷม਺ θ Λ΋ͭؔ਺ʹऩΕΜͤ͞Δඞཁ͕౷‫ࠩޡ‬ΛղফͰ͖Δ͜ͱ͕໌Β͔ͱͳͬͨɽ

͋Δɽ3.2 અͰࣔͨ͠ଌఆ৚݅ͷ৔߹ɼm = 7 ͕ͻͱͭͷ࠷‫ ʹޙ‬m ͱ θ0 ͷؔ܎Λ໌Β͔ʹ͢Δɽલड़ͷ̡̣݁থʹ໨҆Ͱ͋Δ͜ͱ͔Βɼ͜͜Ͱ͸ m = 7 ͱͯ͠ φ Λ֬ఆ͢Δ

ରͯ͠ λ = 632.8nm Ͱଌఆ͢Δ৔߹ͷ m = 1 ∼ 10 ʹ͍ͭͯํ๏Λࣔ͢ɽ

θ0 Λ‫ٻ‬Ίͨɽͦͷ݁ՌΛਤ 11 ʹࣔ͢ɽ͜ͷ݁Ռ͔Β m ≥ 7

m = 7 ͱͯ͠ɼ೚ҙͷ φ ‫ ͼٴ‬θ Λ༩͑ͨ৔߹ͷ P7F (θ, φ) ͷͳΒ θ0 = 1.9251 ʹऩΕΜ͢Δ͜ͱ͕൑ͬͨɽैͬͯɼ݁

‫ڍ‬ಈΛ‫ͨ͠ࢉܭ‬ɽ͜ͷ‫Ͱࢉܭ‬͸ɼύϫʔ൓ࣹ཰ R ͱͯ͠থ಺ͷଟॏ൓ࣹ͸ m = 7 ·Ͱ‫ݕ‬౼͢Ε͹े෼Ͱ͋Δ͜ͱ͕

2no − 1= 1.5328 Λ༻͍ͨɽҰྫͱͯ͠ɼφ ͷॳ‫ظ‬஋ͱ͠no + 1ͯ0.3ɼ0.5ɼ0.9ɼ1.2mradΛ༩͑ɼP7F (θ, φ)͕࠷େʹͳΔΑ͏໌Β͔ʹͳͬͨɽ
0.2

ʹ φ ͱ θ Λަ‫ʹޓ‬ௐ੔͢Δͱɼ͍ͣΕͷ݁Ռ΋ φ = 0.76567ɼ

0.1

θ = 0.90437ʹ͓͍ͯ P7F ͕࠷େͱͳͬͨɽφ͕ॳ‫ظ‬஋ͷ࣌ͷ

0.1

θ=1.9251

P 7 (θ , φ )‫ۂ‬ઢͱ φ = 0.76567 ͷ࣌ͷ‫ۂ‬ઢΛਤ 8 ʹࣔ͢ɽਤͷ P7F (θ, φ)

θ=1.97460.0Fπ͸ɼଠઢͷ࠷େ஋Ͱਖ਼‫ن‬Խ͞Ε͍ͯΔɽ࣍ʹɼ0 < φ <4ͷൣғͰ φ Λࡉ͔͘‫݁ͨ͠ࢉܭ‬ՌΛਤ 9 ʹࣔ͢ɽಉਤ͸ԣ-0.1

ͷਤ͸0 ≤ θ ≤ 2‫ͼٴ‬0 ≤ φ ≤-0.2πͷ ൣ ғ ಺ Ͱ P7F ͕ ། Ұ ͷ ࠷4

θ=1.9571-0.1࣠ʹ θɼॎ࣠ʹ φ Λ༩͑ͨ P7F ʹର͢Δ౳ߴઢਤͰ͋Δɽ͜

1.86

θ=1.8719

θ=1.9074

1.88

1.9

1.92

େ஋Λ΋ͭҰͭͷؔ਺ʹऩΕΜ͢Δ͜ͱΛ͍ࣔͯ͠ΔɽP7F ͕࠷େͱͳΔ φ Λ 0.76567 ʹ‫ݻ‬ఆ͢Ε͹ɼࣜ (4) ͔Βɼ

ਤ 10

1.2

1.94

1.96

1.98

2

φ ΛมԽͤͨ͞৔߹ͷɼθ ʹର͢Δ PmF (θ, φ)ʢθ0 ۙ

1.926
φ = 0.3
φ = 0.5
φ = 0.76421
φ = 0.9
φ = 1.2

0.8
0.6
0.4

1.924
1.922

θ0 (rad)

1.0

0.2

1.920
1.918

0.0

1.916

-0.2
-0.4

1.914

-0.6

1
0

ਤ8

0.5

1

1.5

θ

2

2.5

2

3

4

5

3

high

1.5

6

7

8

9

10

m

ਤ 11

φ ΛมԽͤͨ͞৔߹ͷɼθ ʹର͢Δ P7F (θ, φ)ɽ

m ͱ θ0 ͷؔ܎ɽ

4. ɹৼ෯ൺֱ๏
4.1 ৼ෯ൺֱ๏ͷ‫ݪ‬ཧ

1.0
PF7(θ,φ)㱢(rad)

લઅΑΓɼnull ๏ʹΑΔղੳ͸ɼޫ‫ݕ‬ग़‫ث‬৴߸ͷ‫ج‬ຊ೾੒ ෼ ͕ ࠷ খ ʹ ͳ Δ ి ѹ ஋ ͔ Β EO ܎ ਺ Λ ‫ ٻ‬Ί Δ ํ ๏Ͱ͋

0.5Γɼߴਫ਼౓ͳଌఆ͕ՄೳͰ͋Δ͜ͱ͕ࣔ͞Εͨɻ͔͠͠
0

low

F

θ

๣ͷ֦େਤʣ(m = 7)ɽ

P7F = 0 ͱͳΔ།Ұͷ θ0 ΛಘΔ͜ͱ͕Ͱ͖Δɽਤ 10 ͸ɼਤ 8

P 7 (θ , φ )φ = 0.3
φ = 0.5
φ = 0.76421
φ = 0.9
φ = 1.2

0.5

ਤ9

1.0
㱔(rad)

1.5

P7F (θ, φ) ͷ౳ߴઢਤɽ

2.0

൒೾௕ిѹΑΓେ͖ͳৼ෯Λ΋ͭަྲྀిѹΛ݁থʹҹՃ͢Δඞཁ͕͋Γɼి‫਺܎ֶޫؾ‬ͷখ͞ͳ EO ݁থ΍੺֎ޫʹର͢Δଌఆʹ͸ద͞ͳ͍ɻͦͷܽ఺Λղফ͢ΔͨΊʹৼ෯ൺֱ๏ [28] ͕ ߟ Ҋ ͞ Ε ͨ ɽ

─ 54 ─

ৼ෯ൺֱ๏ͷ࣮‫ܥݧ‬͸ਤ 4 ͱɼ΄΅ಉҰͰ͋ΔɽEO ܎100਺͸ɼޫ‫ݕ‬ग़‫ث‬ͷग़ྗ৴߸͔ΒόϯυύεϑΟϧλΛ༻80
J 1(2θ)/J 3(2θ)͍ͯ‫ج‬ຊ೾੒෼ͱୈ 3 ߴௐ೾੒෼Λൈ͖ग़͠ɼͦΕͧΕͷ৴߸ͷৼ෯Λൺֱ͢Δ͜ͱʹΑΓ‫ٻ‬ΊΒΕΔɽຊ࿦จͷஶऀͷ 1 ਓͰ͋Δ Takizawa ͸ɼ͜ͷํ๏Λ༻͍ͯϊϯυʔϓίϯάϧΤϯτͱ MgO υʔϓ͞ΕͨίϯάϧΤϯτ LN

60
40

α

݁থͷ೾௕ 632.8nm ʹ͓͚Δ r13 ͱ r33 ͷෳ߹తి‫܎ֶޫؾ‬20

਺ rc Λ‫ٻ‬Ίͨ [28]ɽ͜͜Ͱ͸ैདྷͷৼ෯ൺֱ๏ͷ‫ݪ‬ཧͱ0β0ͦͷ‫ࠩޡ‬Λࣔ͢ɽ

Takizawa ͸ LN ݁ থ ͷ ೖ ग़ ྗ ୺ ໘ ʹ ൓ ࣹ ๷ ࢭ ບ Λ ৠ ணਤ 12͠ɼଟॏ൓ࣹޫͷӨ‫ڹ‬Λ௿‫[ ͨ͠ݮ‬28]ɽલड़ͷͱ͓Γɼ͜

0.5

1

θ

1.5

2

ଌఆ͞Εͨ J1 (θ)/J3 (θ) ͔Β θ ͷؔ܎‫ ͼٴ‬EO ܎਺Λ‫ٻ‬ΊΔͨΊͷ α ͷ‫ٻ‬Ίํɽͷํ๏͸ EO ܎਺ͷ೾௕ґଘੑΛଌఆ͢Δʹ͸ద͞ͳ͍ɽ
ଟॏ൓ࣹ‫ׯ‬ব๏ʹΑΔޫ‫ݕ‬ग़৴߸͸ࣜ (3) Ͱද͞ΕΔɽ͠

Λଌఆ͢ΔͨΊʹϩοΫΠϯΞϯϓΛҰ୆௥Ճͨ͠఺Ͱ

͕ͨͬͯɼଟॏ൓ࣹΛߟྀͨ͠‫ׯ‬ব৴߸ͷ‫ج‬ຊ೾੒෼͸

͋Δɽਤ 4 ͷ࣮‫Ͱܥݧ‬΋‫ج‬ຊ೾ͱୈ 3 ߴௐ೾Λผ‫ʹݸ‬ଌఆࣜ (4) ͱͳΔɽಉ༷ʹόϯυύεϑΟϧλͷᖤաத৺֯प

͢Δ͜ͱ͕ՄೳͰ͋Δ͕ φ ͕Թ౓มԽʹ͖ΘΊͯහ‫͋Ͱײ‬೾਺ΛҹՃిѹͷ֯प೾਺ 3ωθ ͱઃఆ͢Δ͜ͱʹΑΓɼ‫ׯ‬Δ͜ͱΛߟྀ͢Δͱɼೋͭͷप೾਺੒෼Λಉ࣌ʹଌఆ͢ব৴߸ͷ͏ͪୈ 3 ߴௐ೾੒෼ sin 3ωθ t Λ༰қʹ‫ݕ‬ग़͢Δ͜

Δ͜ͱ͕๬·͍͠ɽਤ 13 ͷ஫ҙ఺͸ೋͭͷϩοΫΠϯΞͱ͕Ͱ͖Δɽ͕ͨͬͯ͠‫ׯ‬ব৴߸ͷୈ 3 ߴௐ೾੒෼ PTm ͸ϯϓͷೖग़ྗಛੑΛ͋Β͔͡Ίଌఆͯ͠ɼ྆ऀͷརಘิ࣍ͷࣜͰ༩͑ΒΕΔɽਖ਼߲Λ‫ٻ‬Ί͓ͯ͘͜ͱͰ͋Δɽ

PTm=−2A2

m−l
m−1 


Rk+2l sin (2kφ) J3 (2kθ) sin 3ωθ tͦ͜ͰຊઅͰ͸ɼଟॏ൓ࣹ‫ׯ‬ব๏ͱৼ෯ൺֱ๏Λ૊Έ

(10)߹Θͤͯɼ௿ిѹͰ EO ܎ ਺ Λ ଌ ఆ ͢ Δ ํ ๏ Λ ड़ ΂Δɽ

l=0 k=1ैདྷͷৼ෯ൺֱ๏Ͱ͸ɼ݁থ಺Λͦͷ··ಁա͢Δޫͱैདྷͷৼ෯ൺֱ๏͸ɼnull ๏ʹΑΔղੳͱಉ༷ʹɼߴ࣍݁থ಺ΛҰԟ෮൒ͨ͠‫݁ʹޙ‬থ͔Βಁա͢Δޫͷ‫ׯ‬বͷͷଟॏ൓ࣹޫʹΑΔཧ࿦‫ܥ‬౷‫ࠩޡ‬Λ΋ͭɽͦ͜Ͱߴ࣍ͷΈΛߟ͍͑ͯͨ (m = 1 ͷ৔߹)ɽ͜ΕΛࣜ (10) ʹ୅ೖ͢Δ

ଟॏ൓ࣹޫΛ‫ؚ‬Ήࣜ (4) ‫( ࣜͼٴ‬10) ͔Β௚઀ θ ͷؔ਺Λ‫ٻ‬Ίͱɼࣜ (11) ΛಘΔɽΔ͜ͱΛ‫ݕ‬౼͢ΔɽͦΕͧΕͷࣜͷৼ෯ʹ஫໨͢Δͱ θ ͸

PT1 = −2Aɹ R sin (2φ) J3 (2θ) sin 3ωθ tҎԼͷΑ͏ʹࣔ͞ΕΔɽ

(11)

m−1
 m−l
 k+2lRsin (2kφ) J1 (2kθ)
FPm 
l=0 k=1
 =PTm rms m−1
 m−l
 k+2lRsin (2kφ) J3 (2kθ)
l=0 k=1‫ج‬ຊ೾੒෼͸ࣜ (5) Ͱ༩͑ΒΕΔɽΑͬͯࣜ (5)ɼࣜ (11) ΑΓɼ‫ج‬ຊ೾੒෼ͱୈ 3 ߴௐ೾੒෼ͷৼ෯ൺ͸࣍ͷࣜͰ༩͑ΒΕΔɽ


P1F PT √
− 2A2 R sin (2φ) J1 (2θ) J1 (2θ)= √=− 2A2 R sin (2φ) J3 (2θ) J3 (2θ)
1 rms

(13)

(12)

3.2 અͷٞ࿦ʹै͍ m = 7 ͱ͓͍ͯɼnull ๏ͱಉ༷ʹɼP7F ͕
P7F 
࠷େͱͳΔ φ Λ‫ٻ‬ΊΕ͹ɼ T  ΛҰͭͷؔ਺ʹऩΕΜ͞P 

ࣜ (12) ͸ɼޫ‫ׯ‬ব৴߸ͷ‫ج‬ຊ೾੒෼ͱୈ 3 ߴௐ೾੒෼ͷଌ

ͤΔ͜ͱ͕Ͱ͖Δɽ͜ͷؔ਺ͱ࣮‫Ͱݧ‬ಘΒΕͨ‫ׯ‬ব৴߸ఆ஋ͷൺʢӈลʣ͕ɼϕοηϧؔ਺ J1 /J3 Ͱද͞ΕΔ͜ͱͷ‫ج‬ຊ೾੒෼ͱୈ 3 ߴௐ೾੒෼ͷൺΛൺֱ͢Ε͹ಈతҐ૬Λҙຯ͍ͯ͠Δɽ͢ͳΘͪɼਤ 12 ʹࣔ͞ΕΔଌఆ஋ α ͕ಘθ ͕ܾఆ͞ΕɼҹՃͨ͠ VAC ͱࣜ (6) ͔Β EO ܎਺͕‫·ٻ‬ΔɽΒΕΕ͹ɼͦΕʹରԠ͢ΔಈతҐ૬ β ͕Ұҙʹ‫ٻ‬ΊΒΕɼҎ্͔ΒɼϊϯυʔϓίϯάϧΤϯτ LN݁থɼ݁থԹ౓

EO ܎਺͕ܾఆ͞ΕΔ͜ͱʹͳΔɽ͜ͷํ๏͸ඇৗʹγϯϓϧͰ͋Δ͕ɼ݁থ಺ͷଟॏ൓

7 rms

25ˆɼଌఆ೾௕ 632.8nm ͷ৚݅Ͱ‫ࢉܭ‬Λߦ͍ φ = 0.76567 ΛಘͨɽಘΒΕͨ φ Λࣜ (4) ‫( ࣜͼٴ‬10) ʹ୅ೖ͠ɼP7F ɼPT7 ͱ θࣹΛߟྀ͍ͯ͠ͳ͍ɽ3.3 અͰࣔͨ͠Α͏ʹɼ݁থͷ۶ં
Signal Generator + High Power Amp.

཰͕ 2 Λ௒͑Δͱଟॏ൓ࣹޫͷӨ‫ڹ‬Λແࢹ͢Δ͜ͱ͕Ͱ͖

䌾

ͳ͘ͳΔɽ

Laser Beamଌఆਫ਼౓ͷվળ II(ৼ෯ൺֱ๏)Crystal㸢

4.2

VAC sin ωθ t + VDC

Photo Detector
Multi Meterଟॏ൓ࣹ‫ׯ‬ব๏ͱৼ෯ൺֱ๏Λ૊Έ߹Θ࣮ͤͨ‫ܥݧ‬Λ

ਤ 13 ৼ෯ൺֱ๏ͷ࣮‫ܥݧ‬౷ਤɽ

ਤ 13 ʹࣔ͢ɽਤ 4 ͷ࣮‫ͱܥݧ‬ҟͳΔͷ͸ɼୈ 3 ߴௐ೾੒෼

─ 55 ─

Lock-inAmp.
Lock-inAmp.

ͷ ؔ ܎ Λ ‫ ٻ‬Ί ͨ ɽ‫ ݁ ࢉ ܭ‬Ռ Λ ਤ 14 ʹ ࣔ ͢ ɽ· ͨP7F 
PT ɼ࿏௕ࠩΛ΋ͭɽΑۭͬͯ‫ؾ‬ͷ۶ં཰Λ 1 ͱ͢Δͱɼ΢Σοδ֯ʹґଘ͢Δ੩తҐ૬ࠩ Δφ ͸ࣜ (14) Ͱ༩͑ΒΕΔɽ

7 rms

J1 (2θ)ͱಈతҐ૬ θ ͷؔ܎Λਤ 15 ʹࣔ͢ɽ͜ͷਤΛ༻͍ΕJ3 (2θ)͹ɼ࣮‫͔ݧ‬Β‫ٻ‬ΊΒΕͨ‫ج‬ຊ೾੒෼৴߸ͱୈ 3 ߴௐ೾৴߸

Δφ =

2π
(no − 1)W tan ξλ(14)Ұ ྫ ͱ ͠ ͯ ɼW = 1mmɼλ = 632.8nmɼno = 2.2868ɼ

ͷ‫౓ڧ‬ൺ α ͔ΒɼಈతҐ૬ β ͕ ಘ Β Ε Δ ɽ
ਤ 15 ͷ Δβ ͕ m = 1 ͱ m = 7 ͷཧ࿦తͳ‫ܥ‬౷‫ͳͱࠩޡ‬Δɽ

ξ = 0.1mrad ΛԾఆ͢ΔͱɼϨʔβ‫಺ܘ‬ͷ Δφ ͸ 1.277rad ͱͳΓɼnull ๏‫ৼͼٴ‬෯ൺֱ๏ʹ͓͍ͯ͜ͷ੩తҐ૬ࠩ͸ແ

0.1ࢹͰ͖ͳ͍ଌఆ‫ͳͱࠩޡ‬Δɽ

0.08

ͦ͜Ͱ΢Σοδ֯ͷޮՌΛܰ‫ͤ͞ݮ‬ΔͨΊɼਤ 17 ʹࣔ

0.04͢Α͏ʹɼഒ཰ M ͷϏʔϜΤΩεύϯμΛ༻͍ͯϨʔβ0.02ޫΛ֦େ͠ɼͦͷϨʔβޫΛϗʔϧ‫ ܘ‬w ͷϐϯϗʔϧͰൈ

T

P 7(2θ ), P 7(2θ )0.06

͖ ग़ ͠ ͨ ͷ ͪ ʹ ޫ ‫ ݕ‬ग़ ‫ ʹ ث‬ೖ ࣹ ͞ ͤ Δ ɽൈ ͖ ग़ ͞ Ε ͨ

F

0
-0.02

Fundamental wave amplitude(PFϨʔβޫͷ྆୺ؒͷ੩తҐ૬ࠩ͸ࣜ (15) ͱ ͳ Δ ɽ

7)Third harmonic wave amplitude (P T 7)

-0.04

Δφ =

-0.06
0

0.5

ਤ 14

1

θ (rad)

1.5

2

2.5

2π
w
(no − 1) tan ξ
λ
M

(15)

͜͜ͰɼϏʔϜΤΩεύϯμͷഒ཰ M = 20ɼϐϯϗʔϧ‫ ܘ‬w = 0.5mm ͱԾఆ͢ΔͱɼϨʔβ‫಺ܘ‬ͷ Δφ ͸ 0.0319radθ ʹର͢Δ‫ج‬ຊ೾‫ͼٴ‬ୈ 3 ߴௐ೾ͷৼ෯ɽ

ͱͳΔɽ͜ͷ੩తҐ૬ φ ͷ‫͕ࠩޡ‬ಈతҐ૬ʹ༩͑ΔӨ‫ڹ‬͸

0.21% Ҏ Լ Ͱ ͋ Γ ɼແ ࢹ ͢ Δ ͜ ͱ ͕ Ͱ ͖ Δ ɽ100͜ͷΑ͏ʹϨʔβޫΛϏʔϜΤΩεύϯμͰ޿͛ɼͦ
80

J1 ( 2θ )͔͜ΒҰ෦ͷޫΛൈ͖ग़͢͜ͱʹΑΓɼϨʔβ‫಺ܘ‬ͷ੩

P F7 ( 2θ )J 3 ( 2θ )PT7 ( 2θ ) rms

60త Ґ ૬ ࠩ ʹ Α Δ ଌ ఆ ‫ ࠩ ޡ‬Λ ‫ ݮ‬গ ͞ ͤ Δ ͜ ͱ ͕ Ͱ ͖Δɽ

α40

6. ɹଟॏ൓ࣹ‫ׯ‬ব๏ͳΒͼʹ null ๏ɾৼ෯ൺֱ๏

20

ͷಛ௃

Δβ

0
0

ਤ 15

0.5

1

θ

1.5

ଟॏ൓ࣹ‫ׯ‬ব๏Ͱ͸ɼ͢΂ͯͷಁաޫͷޫ࿏͕Ұக͢

2ΔͨΊɼ࣍ͷΑ͏ͳಛ௃Λ࣋ͭɽैདྷͷৼ෯ൺֱ๏ͱཧ࿦‫ܥ‬౷‫ࠩޡ‬Λվળͨ͠ৼ෯

(1) ‫ج‬ຊతͳޫֶ‫ܥ‬͸Ϩʔβޫ‫ݯ‬ɼଌఆର৅ͱͳΔ݁থɼൺֱ๏ͷൺֱɽ

ޫ‫ݕ‬ग़‫ث‬ͷΈͰߏ੒ՄೳͰ͋Γɼ‫ۃ‬Ίͯ؆қͰ͋Δɽξ

5. ɹ݁থͷ‫ܗ‬ঢ়‫ʹࠩޡ‬ΑΔଌఆ΁ͷӨ‫ڹ‬લઅ·Ͱͷٞ࿦͸ɼ݁থͷ྆୺໘͕‫ʹີݫ‬ฏߦͰ͋Δ

W

Laser Beam͜ͱΛલఏͱ͍ͯͨ͠ɽ͔͠͠ɼଌఆࢼྉ͸‫ػ‬ցతՃ޻yΛ‫ͯܦ‬੡଄͞ΕΔͨΊɼ྆୺໘Λ‫ʹີݫ‬ฏߦʹՃ޻͢Δzx͜ͱ͸ෆՄೳͰ͋Γɼ྆୺໘ؒʹ͸΢Σοδ͕֯ੜ͡ΔɽຊઅͰ͸͜ͷ΢Σοδ͕֯ଌఆਫ਼౓ʹ༩͑ΔӨ‫͍ͭʹڹ‬

ਤ 16

LN

Wtanξ

݁থΛಁա͢ΔϨʔβ‫಺ܘ‬ͷޫ࿏ࠩɽ

ͯߟ࡯͢Δɽ
ਤ 16 ʹ݁থΛಁա͢ΔϨʔβޫͷϏʔϜ‫͚͓ʹ಺ܘ‬ΔMW

ޫ࿏ࠩΛࣔ͢ɽ͜͜Ͱ ξ ͸΢Σοδ֯ɼW ͸Ϩʔβޫͷ‫ن‬W

2֨Խ‫ ͕౓ڧ‬1/e ͱͳΔϏʔϜ‫͋Ͱܘ‬Δɽ΢Σοδ֯͸ޫ࣠ʹରͯ͠ਨ௚ۙ๣ͷ֯౓Λ࣋ͭ 2 ͭͷ໘͕ [100] ࣠‫ͼٴ‬w

LN crystal
y[010] ࣠Ͱճసͨ͠৔߹ͷ֯౓ͱ͢Δɽਤ 16 Ͱ͸ɼҰํͷx໘͕ [010] ࣠ʹରͯ͠ ξmrad ճస͢Δ৔߹Λ‫ݕ‬౼ͨ͠ɽ݁
থΛಁա͢ΔϨʔβޫ͸ϏʔϜ‫ܘ‬ͷ྆୺Ͱ no W tan ξ ͷޫ

ਤ 17

─ 56 ─

z

Beam expander

Pinholeഒ཰ M ͷϏʔϜΤΩεύϯμʹΑΔϨʔβޫͷ֦େɽ

(2) Mach-Zehnder ‫ׯ‬ব๏΍ Michelson ‫ׯ‬ব๏ͳͲͷैདྷ

7. ɹ࣮‫݁ͼٴݧ‬ՌͷҐ૬‫ݕ‬ग़๏Ͱ͸ޫֶ‫ܥ‬ͷৼಈΛ཈͑ΔͨΊͷ๷ৼ૷ஔ͕ෆՄܽͰ͋Δ͕ɼຊଌఆ๏Ͱ͸ඞཁͳ͍ɽ

(3) ‫ػ‬ցతৼಈ΍ۭ‫ؾ‬ͷ֧ཚͳͲͷӨ‫ڹ‬ͷͳ͍҆ఆ͠

7.1 ଌఆʹ࢖༻ͨ͠ LN ݁থ‫ͦͼٴ‬ͷੇ๏ɾฏߦੑͷଌఆͨ‫ׯ‬ব৴߸ ͕ ಘ Β Ε Δ ɽ(4) ҆ఆͨ͠‫ׯ‬ব৴߸͕༰қʹಘΒΕΔͨΊɼ୹࣌ؒલઅ·Ͱʹࣔͨ͠ଌఆ๏ͷ༗ޮੑΛ֬ೝ͢ΔͨΊɼϊͰଌఆͰ͖ Δ ར ఺ Λ ΋ ͭ ɽϯυʔϓίϯάϧΤϯτͷ Y ࣠Χοτ Z ࣠఻ൖ LN ݁থͷ(5) ࢵ֎ޫ‫ޫ֎੺ͼٴ‬ͷΑ͏ͳෆՄࢹޫʹΑΔଌఆ΋

EO ܎਺ r22 Λଌఆͨ͠ɽຊઅͰ͸ɼࠓճଌఆͨ݁͠থͷ‫ܗ‬༰қʹߦ͏͜ͱ͕Ͱ͖Δɽैདྷͷ‫ׯ‬ব๏Ͱ͸Մࢹঢ়ͳͲʹ͍ͭͯड़΂ΔɽޫҎ֎ͷޫͰࡶԻͷগͳ͍‫ׯ‬ব৴߸ΛಘΔ͜ͱ͸ຊ࣮‫͍݁ͨ༻Ͱݧ‬থΛਤ 18 ʹࣔ͢ɽ݁থ͸ NEL ΫϦε༰қͰ͸ͳ ͍ ɽλϧ (‫ʹ )ג‬ΑΓ੡଄͞ΕͨɽEO ܎਺ͷଌఆΛਖ਼֬ʹߦ͏(6) ݁থ಺ͷ൓ࣹΛੵ‫ۃ‬తʹར༻ͯ͠ EO ܎਺Λଌఆͨ͢Ίʹ͸ɼ݁থͷੇ๏ɼฏߦੑ‫ͼٴ‬΢Σοδ֯ɼฒͼʹɼ

Δํ๏Ͱ͋ΔͨΊɼ݁থʹ൓ࣹ๷ࢭບΛࢪ͢ඞཁ݁থ୺໘ͱ݁থํҐͷؔ܎Λਖ਼֬ʹଌఆ͢Δඞཁ͕͋Δɽ

͕ͳ͍ɽ͜ͷ͜ͱʹΑΓ EO ܎਺ͷ೾௕෼ࢄಛੑΛ݁থੇ๏ɼฏߦੑ‫ͼٴ‬΢Σοδ֯ʹ͍ͭͯ͸χίϯ੡ը༰қʹଌఆ͢ Δ ͜ ͱ ͕ Ͱ ͖ Δ ɽ૾‫ܭ‬ଌγεςϜ NEXIV VM-150M Ͱଌఆͨ͠ɽ·ͨ݁থ(7) ௿प೾͔Βߴप೾ʹΘͨΓ݁থͷ EO ܎਺Λଌఆ͢ํҐʹ͍ͭͯ͸ϥϜμϓϨγδϣϯࣾʹଌఆΛґཔͨ͠ɽΔ͜ͱ͕Մೳ Ͱ ͋ Δ ɽ݁ থ α Π ζ ‫ ࣠ ͼ ٴ‬ਫ਼ ౓ Λ ද 2 ʹ ࣔ ͢ ɽ· ͨ ݁ থ ͕ ΋ ͭ΢Σοδ֯Λਤ 19 ʹࣔ͢ɽ࣍ʹ null ๏ͱৼ෯ൺ ֱ ๏ ͷ ಛ ௃ Λ Ҏ Լ ʹ · ͱ Ί Δ

݁থ௕ L = 20.01mmɼ݁থް d = 2.00mm Ͱ͋ͬͨɽLN(1) null ๏Ͱ͸ɼEO ܎਺͸ޫ‫ݕ‬ग़৴߸ͷ‫ج‬ຊ೾੒෼͕݁ থ ͷ ݁ থ ໘ (100) ʹ ର ͠ ͯ ݁ থ ޫ ࣠ [100] ͕ ΋ ͭ ֯ ౓࠷খͱͳΔަྲྀిѹͷৼ෯͔Β‫ٻ‬ΊΒΕɼਤ 8ɼਤ

͸ 90 ± 0.1 ౓ ɼ(010) ʹ ର ͢ Δ [010] ͷ ֯ ౓ ͸ 90 ± 0.01 ౓ ɼ

10 ʹࣔ͞ΕΔΑ͏ʹɼ੩తҐ૬ φ ͕େ͖͘มԽͯ͠(001) ʹର͢Δ [001] ͷ ֯ ౓ ͸ 90 ± 0.1 ౓Ͱ͋ͬͨɽ

΋ಈతҐ૬ θ ͷมಈ͸ඇৗʹখ͍͞ɽଌఆճ਺Λ૿

EO ܎ ਺ r22 ͷ ଌ ఆ ࣌ ʹ ͸ ݁ থ ୺ ໘ ؒ ͷ ΢ Σ ο δ ֯ ͕΍ͯ͠‫܁‬Γฦ͠ଌఆΛߦ͑͹‫ۃ‬Ίͯྑ͍ਫ਼౓Ͱ EO

0.05mrad ͷྖҬΛ༻͍ͨɽ܎਺Λ‫ٻ‬Ί Δ ͜ ͱ ͕ Ͱ ͖ Δ ɽ
ද 2 ݁থੇ๏ͱ࣠ਫ਼౓

(2) null ๏Ͱ͸ɼ݁থʹ൒೾௕ిѹΑΓେ͖ͳిѹΛҹՃ͢ΔͨΊɼখ͞ͳ EO ܎਺ͷଌఆʹ͸ద͞ͳ͍ɽ

LN Crystal length (mm)(3) ৼ෯ൺֱ๏Ͱ͸ɼEO ܎਺͸ޫ‫ݕ‬ग़৴߸ͷ‫ج‬ຊ೾੒
෼ͱୈ 3 ߴௐ೾੒෼ͷৼ෯ൺ͔Β‫ٻ‬ΊΒΕΔɽಈత

Axial accuracy (deg)Ld

X AxisY AxisZ Axisɹ 20.01 ɹ

2.00

±0.1

±0.01

±0.1

Ґ૬ͷେ͖͞ʹ͸੍‫͍ͨͳ͕ݶ‬Ίɼnull ๏ʹൺ΂਺෼ͷ 1ʙ10 ෼ͷ 1 ҎԼͷҹՃిѹͰ EO ܎਺ΛଌఆͰ
͖Δɽ͜ͷํ๏͸খ͞ͳ EO ܎਺Λ΋ͭ݁থͷଌఆ

7.2 ଟॏ൓ࣹ‫ׯ‬ব‫ܭ‬ͷߏ੒ʹద͍ͯ͠Δ ɽ

LN ݁থͷ EO ܎਺ r22 Λଌఆ͢Δଟॏ൓ࣹ‫ׯ‬ব‫ܭ‬ͷ࣮‫ݧ‬(4) ৼ෯ൺֱ๏ͷଌఆਫ਼౓͸ɼୈ 3 ߴௐ೾੒෼ʹґଘ͢‫ܥ‬౷ਤΛਤ 20 ʹࣔ͢ɽҎԼʹ࣮‫ܥݧ‬ͷઃஔํ๏Λ‫͢ه‬ɽ

ΔɽಈతҐ૬͕খ͞ͳ৴߸ʹ͸੩తҐ૬ͷ੍‫ޚ‬Λ༻͍ͨ૷ஔ͸ҎԼͷͱ͓ΓͰ͋Δɽ‫ ͏ߦʹີݫ‬ඞ ཁ ͕ ͋ Δ ɽ(5) ݁থ͔Βಁա͢ΔϨʔβޫΛ֦େ͠Ұ෦Λൈ͖ग़͢͜ͱʹΑΓɼ݁থ͕΋ͭ‫ܗ‬ঢ়‫ࠩޡ‬ʢ΢Σοδ֯ʣʹΑ

m
.01m
0
2
L=

Δଌఆ஋΁ͷӨ‫ڹ‬ΛղফͰ͖Δɽ͜Ε͸ null ๏΍ৼ෯ൺֱ๏ʹ‫ݶ‬Βͣɼ͢΂ͯͷ‫ܭ‬ଌ๏ʹద༻Ͱ͖Δɽ

D=2.00mm

y
z
x

ਤ 18

─ 57 ─࣮‫ ͍ͨ༻ʹݧ‬non-doped congruent LN ݁থɽաͨ͠ϨʔβޫΛഒ཰ M = 20 ͷϏʔϜΤΩεύϯμͰ֦0.35
y [010]0.25

େ͠ɼw = 1mm ͷϐϯϗʔϧͰൈ͖ग़ͨ͠ϨʔβޫΛޫ

E
(010)

LN Crystal

CW LaserBeam‫ݕ‬ग़‫ʹث‬ೖࣹͨ͠ɽ

(0
01

0.20

L

)

Wedge Angle (mrad)

0.30

z [001]

0.15

(100)

x [100]

0.10
y

0.00
2

3

4

5

6

7

8

Photo
Detector

Signal(P)x

Laser Source

0.05

1

Beam
expanderND Filter LN CrystalzMultimeter

High Power
Amplifier9⚿᥏䈱Xᣇะᐳᮡ(mm)SignalGenerator

ਤ 19 ޫ࣠ʹରͯ͠ਨ௚ۙ๣ͷ 2 ͭͷ (001) ໘͕ [010] ࣠PinholeOSC.

Ref. Sig.

Band pass
FilterSignal(Pm)Lock-inAmp.(FW)
Lock-inAmp.(THW)ʹରͯ͠ճస͢Δ͜ͱʹΑΓੜ͡Δ ξ ɽਤ 20ৄࡉͳ࣮‫ݧ‬ϒϩοΫਤɽ• He-Ne Ϩʔβޫ‫ݯ‬ɿMELLES GRIOT ੡ 05-LHP-171(೾௕ λ=632.8nmɼ࠷େ ग़ ྗ 15mW)ɼ
• Si-PIN ޫ‫ݕ‬ग़‫ث‬ɿNEOARK ੡ RD-252ɼ

7.3 null ๏ʹΑΔଌఆ

• γάφϧδ Σ ω Ϩ ʔ λɿAgilent ੡ 33220Aɼ
• ϚϧνϝʔλɿAgilent੡34401Aʢ෼ղೳɿ6 1/2ܻʣɼ
• όϯυύεϑΟϧλɿNF ճ࿏ઃ‫ܭ‬ϒϩοΫ੡ 3628

લઅͷଟॏ൓ࣹޫ‫ׯ‬ব‫ܭ‬Λ༻͍ͯɼnull ๏Ͱ EO ܎਺ r22ଌఆΛߦͬͨɽଌఆͰ͸ɼ݁থʹ൒೾௕ిѹҎԼͷ௚ྲྀిѹͱަྲྀిѹΛಉ࣌ʹҹՃ͠ɼͦΕΒͷిѹΛަ‫ʹޓ‬

ʢ1 ΦΫλʔϒ ‫ ݮ‬ਰ ൺ 48dBʣɼ• ϩοΫΠϯΞϯϓɿNF ճ࿏ઃ‫ܭ‬ϒϩοΫ੡ LI5640ɼ
• ύϫʔΞϯϓɿদఆϓϨγδϣϯ੡ HEOPS-3B10ɼ
• Φγϩεί ʔ ϓɿέϯ ΢ ο υ ੡ CS-4125ɽ

F
ͷ৴߸‫࠷͕౓ڧ‬େͱͳΔ VDC ͱ VAC Λ‫ݟ‬ग़͠ௐ੔ͯ͠ Pm

VDC Λ‫ݻ‬ఆͨ͠ɽͦͷঢ়ଶͰ VAC Λঃʑʹ૿Ճͤ͞ A ͕࠷
খͱͳΔ࠷ॳͷ VAC Λଌఆ͠ɼࣜ (6) Λ༻͍ͯ EO ܎਺ r22 Λଌఆͨ͠ɽ͜͜Ͱ no ͸ 2.2868 [27] Λ ༻ ͍ ͨ ɽ࣮‫Ͱݧ‬͸௚ઢภޫͨ͠ He-Ne Ϩʔβޫͷৼಈ໘Λճస͞Ҏ্ΑΓEO܎਺r22 = 6.54 ± 0.02pm/VΛಘͨɽ0.02pm/V

ͤɼਨ௚·ͨ͸ਫฏʹઃఆ͠ɼND ϑΟϧλͰ໿ 100μW ʹ͸ଌఆճ਺ 20 ճʹ͓͚Δඪ४ภࠩͰ͋Δɽ‫ݮ‬ਰͤͨ͞ͷͪʹ݁থ΁ೖࣹͤͨ͞ɽϨʔβޫͷಈతҐ૬ຊଌఆ๏ͱैདྷͷଟॏ൓ࣹ‫ׯ‬ব๏ͷൺֱͷͨΊɼޫ‫ݕ‬ͱ੩తҐ૬Λ੍‫͢ޚ‬ΔͨΊ LN ݁থʹަྲྀిѹ VAC sin(ωθ t)ग़‫ث‬৴߸͔Β‫ج‬ຊ೾੒෼Λநग़͠ɼͦΕ͕࠷খʹͳΔ VAC‫ͼٴ‬௚ྲྀిѹ VDC ΛՃ͑ͨɽޫ‫ݕ‬஌‫͔ث‬Βͷޫ‫ݕ‬஌‫ث‬৴߸͔Β EO ܎਺Λ‫ٻ‬ΊΔैདྷͷଟॏ൓ࣹ‫ׯ‬ব๏Ͱ r22 Λଌఆ͠P Λೋͭʹ෼‫͠ذ‬ɼҰͭ͸த৺֯प೾਺Λ ωθ ʹઃఆͨ͠

6.51pm/V Λಘͨɽຊଌఆ๏Λ༻͍Δ͜ͱʹΑΓैདྷͷଟόϯυύεϑΟϧλʹೖྗ͠ɼόϯυύεϑΟϧλ͔Βॏ൓ࣹ‫ׯ‬ব๏๊͕͍͑ͯͨ໿ 0.5 % ͷཧ࿦‫ܥ‬౷‫ࠩޡ‬Λղফ

FΛΦγϩείʔϓΛ༻͍ͯ‫؍‬ଌͨ͠ɽ΋͏ͷग़ྗ৴߸ Pmͨ͠ɽҰํͷ‫ݕ‬஌‫ث‬৴߸ P ͸ϩοΫΠϯΞϯϓͷҰͭʹೖྗ͠ɼP ͷ‫ج‬ຊ೾੒෼Ͱ͋Δ PmF ͷ৴߸‫౓ڧ‬Λਖ਼֬ʹଌఆͨ͠ɽ

7.4 ৼ෯ൺֱ๏ʹΑΔଌఆ

ϩοΫΠϯΞϯϓʹ͸ϦϑΝϨϯε৴߸ͱͯ͠γάφϧnull ๏ʹΑΔଌఆͱฒߦͯ͠ɼৼ෯ൺֱ๏Ͱ EO ܎਺ r22δΣωϨʔλ͔Βͷ৴߸ sin(ωθ t) ΛՃ͑ͨɽಉ༷ʹɼ‫ج‬ຊΛଌఆͨ͠ɽ೾ ৴ ߸ ͷ ୈ 3 ߴ ௐ ೾ ੒ ෼ Ͱ ͋ Δ PTm ͸ ɼϩ ο Ϋ प ೾ ਺ Λsin(3ωθ t) ʹઃఆͨ͠ϩοΫΠϯΞϯϓΛ༻͍ͯଌఆͨ͠ɽ

null ๏ʹΑΔଌఆʹ͓͍ͯɼP7F ͕࠷େͱͳΔ VDC ͱ VACΛఆΊͨͱ͖ɼ‫ׯ‬ব৴߸ͷୈ 3 ߴௐ೾੒෼Ͱ͋Δ PT7 ΛଌిѹҹՃ༻ͷೋͭͷి‫ʹۃ‬ຒΊࠐΜͩ೤ిରΛ༻͍ͯɼ
P7F ఆ ͠ ɼͦ ͷ ࣌ ͷ VAC Λ ‫ ه‬࿥ ͠ ͨ ɽଌ ఆ ͠ ͨ T  ͔ Β ɼ
P7 rms
4.2 અͷखॱʹै͍ਤ 15 ΑΓಈతҐ૬Λಘͨɽͦͷ݁Ռɼؒ઀తʹଌఆͨ͠ɽଌఆ ஋ ͸ ͦ Ε ͧ Ε 25 ˆͰ͋ͬͨɽ

VAC = 168.0V ʹ ͓ ͍ ͯ P7F ͕ ࠷ େ ͱ ͳ Γ ɼβ = 5.83 Λ ಘ݁থ୺໘͔Βͷ൓ࣹޫ͕Ϩʔβൃৼ෦ʹ໭Δ͜ͱʹΑͨɽࣜ (6) ʹ θ = β Λ୅ೖ͠ɼr22 = 6.50 ± 0.05pm/V Λಘͨɽ݁থԹ౓Λɼ࣮‫૷ݧ‬ஔશମΛଌఆঢ়ଶʢిѹҹՃɾϨʔ
βরࣹɾଌఆงғ‫ ؾ‬25 ˆʣͰे෼ʹΤʔδϯάͨ͠‫ʹޙ‬Γੜ͡ΔॎϞʔυෆ҆ఆΛ๷͙ͨΊɼ݁থ୺໘ͷ๏ઢʹ

0.05pm/V ͸ ଌ ఆ ճ ਺ 20 ճ ʹ ͓ ͚ Δ ඪ ४ ภ ࠩ Ͱ ͋ Δɽର͢ΔϨʔβೖࣹ֯Λ 0.05mrad ͱͨ͠ɽ·ͨɼϏʔϜ‫ܘ‬಺ͷ੩తҐ૬ࠩʹΑΔଌఆ‫ࠩޡ‬Λ‫ۃ‬খԽ͢ΔͨΊʹɼಁ

─ 58 ─

·ಁա͢ΔϨʔβޫ͔Β݁থ಺Λ7.5ԟ෮ͨ͠‫ʹޙ‬ಁ

7.5

ଌఆ݁Ռͷ·ͱΊա͢Δޫ·Ͱͷɼ8 ຊͷϏʔϜʹΑΔ‫ׯ‬ব͍ͭͯ‫ݕ‬౼Λߦ͑͹े෼ͳਫ਼౓ͰଌఆͰ͖Δ͜ͱ͕൑ͬͨɽ

null ๏ʹΑΔଌఆ஋‫ৼͼٴ‬෯ൺֱ๏ʹΑΔଌఆ஋ͱɼ͜

(4) null ๏͸ޫͷ‫ׯ‬ব৴߸ͷ‫ج‬ຊ೾੒෼͕࠷খͱͳΔಈΕ·Ͱͷଌఆ஋Λද 3 ʹ·ͱΊͨɽnull ๏‫ৼͼٴ‬෯ൺֱ๏తҐ૬ θ ͔Β EO ܎਺Λ‫ٻ‬ΊΔ΋ͷͰ͋Δɽຊํࣜ͸ʹΑΔଌఆ஋͸ैདྷͷଌఆ஋ͱΑ͘Ұகͨ͠ɽ·ͨैདྷ• EO ܎਺Λଌఆ͢Δ࣌ͷ੩తҐ૬ φ ͕େ͖͘มԽ

͸ 2 ܻͰ͋ͬͨଌఆਫ਼౓͸ɼnull ๏‫ৼͼٴ‬෯ൺֱ๏Λ༻͍ͯ͠΋ θ ͷมԽ͕গͳ͘ɼߴਫ਼౓ͳଌఆ͕Մೳɼ

Δ͜ͱʹΑΓ 3 ܻ΁޲্ͨ͠ɽ
ද3• খ͞ͳ EO ܎ ਺ ͷ ଌ ఆ ʹ ͸ ద ͞ ͳ ͍ ɼ͜Ε·Ͱͷ r22 ଌఆ஋ͱࠓճͷଌఆ஋ͱ͍͏ಛ௃Λ༗͍ͯ͠Δɽ(5) ৼ෯ൺֱ๏͸ޫͷ‫ׯ‬ব৴߸ͷ‫ج‬ຊ೾੒෼ͱୈ 3 ߴௐ

r22 (pm/V)ଌఆऀ

6.54±0.02

Our group (null ๏)೾੒෼ͷৼ෯Λൺֱ͢Δ͜ͱʹΑΓɼEO ܎਺Λ‫ٻ‬6.50±0.05

Our group (ৼ෯ൺֱ๏)Ί Δ ΋ ͷ Ͱ ͋ Δ ɽຊ ํ ๏ ͸ ɼ

6.3• null ๏ ʹ ൺ ΂ ɼ1 ∼ 10 ෼ ͷ 1 Ҏ Լ ͷ ҹ Ճ ి ѹ Ͱ

Iwasaki [29]Chirakadze [22]ɼ

6.4

EO ܎ ਺ ͷ ଌ ఆ ͕ Մ ೳ ɼAbdi [30]ɼ

• ଌఆਫ਼౓͸ಈతҐ૬มԽʹහ‫ͳײ‬ୈ 3 ߴௐ೾ʹ

Abarkan [31]6.7
6.8

ґଘ͢ΔͨΊɼ੩తҐ૬ͷ੍‫ޚ‬Λ‫͏ߦʹີݫ‬

Lenzo [12]ɼ

ඞཁ͕͋Δɼ

Smakula [32]• খ͞ͳ EO ܎ ਺ ͷ ଌ ఆ ʹ ద ͠ ͯ ͍ Δ ɼ

Smakula [32]ͱ͍͏ಛ௃Λ༗͍ͯ͠Δɽ(6) ݁থͷ΢Σοδ֯ʹΑΔಈతҐ૬͕ࠩଌఆ݁Ռʹେ ͖ ͳ Ө ‫ ڹ‬Λ ༩ ͑ Δ ͜ ͱ Λ ໌ Β ͔ ʹ ͠ ͨ ɽ· ͨ ɼ

8. ɹ݁‫ݴ‬ϏʔϜΤΩεύϯμͱϐϯϗʔϧΛ༻͍ͯ݁থ͔

EO ܎਺ͷ೾௕෼ࢄଌఆʹద͍ͯ͠Δଟॏ൓ࣹ‫ׯ‬ব๏ʹΒಁաͨ͠ϨʔβޫͷҰ෦Λൈ͖ग़͢͜ͱʹΑΓɼͭ ͍ͯৄࡉʹ‫ݕ‬౼͠ ͨ ɽͦͷӨ‫ڹ‬Λ‫ۃ‬খԽͰ͖Δ͜ͱ͕൑ͬͨɽ͜ͷํ๏͸൓ࣹޫ‫ׯ‬ব๏ʹ‫ݶ‬Βͣɼ͢΂ͯͷ‫ׯ‬ব‫ܭ‬ଌ๏ʹ(1) ଟॏ൓ࣹ‫ׯ‬ব๏͸྆୺໘Λฏߦʹ‫ݚ‬ຏͨ͠ EO ݁থద༻ՄೳͰ͋ΔɽʹϨʔβޫΛೖࣹ͠ɼ݁থ಺Ͱ൓ࣹͤͣʹಁա͢Δ(7) ϊ ϯ υ ʔ ϓ ί ϯ ά ϧ Τ ϯ τ LiNbO3 ݁ থ ͷ ೾ ௕ޫͱ݁থ಺Λෳ਺ճԟ෮ͨ͠‫ʹޙ‬ಁա͢Δޫͷ‫ׯ‬ব

632.8nmʹ͓͚ΔEO܎਺r22 Λଌఆͨ͠ɽͦͷ݁Ռ͸ɼ৴߸ΑΓ EO ܎਺Λ‫ٻ‬ΊΔ΋ͷͰ͋Δɽຊํ๏͸ɼ• 6.54 ± 0.02pm/V (null ๏)ɼ• ‫ػ‬ցతৼಈ΍ۭ‫ؾ‬ͷ֧ཚʹӨ‫͞ڹ‬Εͳ͍҆ఆ

• 6.50 ± 0.05pm/V (ৼ෯ൺֱ๏)ɼ

ͨ͠‫ׯ‬ব৴߸ͷଌఆ͕ՄೳɼͰ͋ͬͨɽ• ޫֶ‫ۃ͕ܥ‬Ίͯ؆୯Ͱ͋Γɼ๷ৼ૷ஔ΋ෆཁɼ(8) ଌఆ݁ՌΛैདྷͷଟॏ൓ࣹ‫ׯ‬ব๏ฒͼʹա‫ڈ‬ͷଌ• ௿प೾͔Βߴप೾ʹΘͨΓଌఆ͕Մೳɼఆ ݁ Ռ ͱ ൺ ֱ ͠ ͨ ɽ྆ ऀ ͸ Α ͘ Ұ க ͠ ͯ ͍ ͨɽ

• Մࢹޫ͚ͩͰͳ͘ɼࢵ֎ޫ΍੺֎ޫΛΛ༻͍ͯ΋ଌఆ͕༰қɼࠓ ‫ ޙ‬ɼଟ ॏ ൓ ࣹ ‫ ׯ‬ব ๏ Λ ༻ ͍ ͯ ϊ ϯ υ ʔ ϓ ί ϯ ά ϧ• Ұͭͷ݁থͰશ೾௕ྖҬͷଌఆ͕ՄೳɼΤ ϯ τ LN ݁ থ ɼ5% M ̶ O υ ʔ ϓ ί ϯ ά ϧ Τ ϯ τ LN ݁ͳͲैདྷͷҐ૬‫ݕ‬ग़๏ʹͳ͍ଟ͘ͷಛ௃Λ༗ͯ͠থ ɼ1.8% MgO υ ʔ ϓ ४ ε τ Π Ω Φ ϝ τ Ϧ LN ݁ থ ͷ ੨͍Δɽ৭ (440nm) ͔Βத੺֎ྖҬ (3,39μ m) ʹ͓͚Δ EO ܎਺ r22 ɼ(2) L = 20mmɼD = 2mm ͷϊϯυʔϓίϯάϧΤϯτ

r13 ɼr33 ͷ೾௕෼ࢄಛੑΛଌఆ͢Δɽ

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