❚♦♠♦❣r❛✜❛ ❞❡ ❍❡♠á❝✐❛s ●✐✉s❡♣♣❡ ●❧✐♦♥♥❛
❚♦♠♦❣r❛✜❛ ❞❡ ❍❡♠á❝✐❛s
●✐✉s❡♣♣❡ ●❧✐♦♥♥❛
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❖s❝❛r ◆❛ss✐❢ ❞❡ ▼❡sq✉✐t❛
❆❣r❛❞❡❝✐♠❡♥t♦s
❈♦♥s✐❞❡r♦ q✉❡ ❛ ❡❧❛❜♦r❛çã♦ ❞❡ ✉♠❛ t❡s❡ ❞❡ ❞♦✉t♦r❛❞♦ é ✉♠ ♣r♦❞✉t♦ ❝♦❧❡t✐✈♦ ❡♠❜♦r❛ s✉❛ r❡❞❛çã♦✱ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❡ str❡ss s❡❥❛ ♣r❡❞♦♠✐♥❛♥t❡♠❡♥t❡ ✐♥❞✐✈✐❞✉❛❧✳ ❱ár✐❛s ♣❡ss♦❛s ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ q✉❡ ❡st❡ tr❛❜❛❧❤♦ ❝❤❡❣❛ss❡ ❛♦ t❡r♠♦✳ ❆ t♦❞❛s ❡❧❛s r❡❣✐str♦ ♠✐♥❤❛ ❣r❛t✐❞ã♦✳
❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r Pr♦❢✳ ❖s❝❛r ◆❛ss✐❢ ❞❡ ▼❡sq✉✐t❛ ♥❛ s✉❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ✐rr❡str✐t❛✱ ♥❛ s✉❛ ❢♦r♠❛ ❡①✐❣❡♥t❡✱ ❝rít✐❝❛ ❡ ❝r✐❛t✐✈❛ ❞❡ ❛r❣ü✐r ❛s ✐❞é✐❛s ❛♣r❡s❡♥t❛❞❛s✱ t❡♥❤♦ ❝❡rt❡③❛ q✉❡ ❞❡r❛♠ ♥♦rt❡ ❛ ❡st❡ tr❛❜❛❧❤♦✱ ❢❛❝✐❧✐t❛♥❞♦ ♦ ❛❧❝❛♥❝❡ ❞❡ s❡✉s ♦❜❥❡t✐✈♦s✳ ❆♦s ❛♠✐❣♦s ❡ ❝♦❧❡❣❛s ❞♦ ❧❛❜♦r❛tór✐♦ ❇✐r❛✱ ▼❛r❝✐♦✱ ❍❡♥r✐q✉❡✱ ❈❛♠✐❧❧❛✱ ▲✐✈✐❛✱ ▼❛r✐❛ ❈❧❛r❛ ❡ ▼❛②✉♠✐ ♣❡❧❛ ❛❥✉❞❛ ♣r❡st❛❞❛ ❡♠ t♦❞❛s ♦s ♠♦♠❡♥t♦s q✉❡ ♣r❡❝✐s❡✐✳
❆♦ Pr♦❢✳ ▼♦♥❦❡♥ ♣❡❧♦ s✉♣♦rt❡ ❡ s✉❣❡stõ❡s ❞❡ ó♣t✐❝❛✳
❙✉♠ár✐♦
❆❣r❛❞❡❝✐♠❡♥t♦s ✶
❘❊❙❯▼❖ ①✐
❆❇❙❚❘❆❈❚ ①✐✐✐
✶ ■♥tr♦❞✉çã♦ ✶
✷ ▼✐❝r♦s❝♦♣✐❛ ❞❡ ❉❡s❢♦❝❛❧✐③❛çã♦ ✽
✷✳✶ ▼✐❝r♦s❝♦♣✐❛ ❞❡ ❈♦♥tr❛st❡ ❞❡ ❋❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✷ ❊s♣❡❝tr♦ ❆♥❣✉❧❛r ❞♦ ❈❛♠♣♦ ❊❧étr✐❝♦ ❞❛ ▲✉③ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✷✳✶ ❆ ❊q✉❛çã♦ ❞❡ ❍❡❧♠❤♦❧t③ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✷✳✷ Pr♦♣❛❣❛çã♦ ▲✐✈r❡ ❞♦ ❊s♣❡❝tr♦ ❆♥❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✷✳✸ Pr♦♣❛❣❛çã♦ ❞♦ ❊s♣❡❝tr♦ ❆♥❣✉❧❛r ❛tr❛✈és ❞❡ ✉♠❛ ▲❡♥t❡ ❉❡❧❣❛❞❛ ✶✾ ✷✳✸ Pr♦♣❛❣❛çã♦ ❞♦ ❊s♣❡❝tr♦ ❆♥❣✉❧❛r ❛tr❛✈és ❞♦ ▼✐❝r♦s❝ó♣✐♦ ❉❡s❢♦❝❛❧✐③❛❞♦ ✷✹ ✷✳✹ ❈❛♠♣♦ ❊❧étr✐❝♦ ♣❛r❛ ▼✐❝r♦s❝ó♣✐♦ ❉❡s❢♦❝❛❧✐③❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✺ ❈❛♠♣♦ ❊❧étr✐❝♦ ♣❛r❛ ▼✐❝r♦s❝ó♣✐♦ ❉❡s❢♦❝❛❧✐③❛❞♦ ❛tr❛✈és ❞❡ ✉♠ ❖❜❥❡t♦
❞❡ ❋❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✺✳✶ ❈♦♥tr❛st❡ ❞❛ ■♥t❡♥s✐❞❛❞❡ ❞❡ ▲✉③ ❞❛ ■♠❛❣❡♠ C(ρ~) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵
✷✳✺✳✷ ❈♦rr❡❧❛çã♦ ❞❛s ❋❧✉t✉❛çõ❡s ❞♦ ❈♦♥tr❛st❡h∆C(0,0)∆C(~r, t)i ✳ ✸✺
✷✳✺✳✸ ❋❧✉t✉❛çã♦ ◗✉❛❞rát✐❝❛ ▼é❞✐❛ ❞♦ ❈♦♥tr❛st❡ h∆C2(zf)i ✳ ✳ ✳ ✳ ✳ ✸✽
✷✳✺✳✹ ❊s♣❡❝tr♦ ❞❡ P♦tê♥❝✐❛ ❊s♣❛❝✐❛❧ ❞❛s ❋❧✉t✉❛çõ❡s ❞♦ ❈♦♥tr❛st❡ ✉s❛♥❞♦ h∆C2(zf)i ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✷✳✻ ❈❛♠♣♦ ❊❧étr✐❝♦ ♣❛r❛ ▼✐❝r♦s❝ó♣✐♦ ❉❡s❢♦❝❛❧✐③❛❞♦ ❛tr❛✈és ❞❡ ✉♠ ❖❜❥❡t♦ ❞❡ ❋❛s❡ ❝♦♠ ❞✉❛s ■♥t❡r❢❛❝❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✷✳✻✳✶ ❈♦♥tr❛st❡ ❞❛ ■♥t❡♥s✐❞❛❞❡ ❞❡ ▲✉③ ❞❛ ■♠❛❣❡♠ C(ρ~) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
✷✳✻✳✷ ❈♦rr❡❧❛çã♦ ❞❛s ❋❧✉t✉❛çõ❡s ❞♦ ❈♦♥tr❛st❡h∆C(0,0)∆C(~r, t)i ✳ ✺✵
✷✳✻✳✸ ❋❧✉t✉❛çã♦ ◗✉❛❞rát✐❝❛ ▼é❞✐❛ ❞♦ ❈♦♥tr❛st❡ h∆C2(zf)i ✳ ✳ ✳ ✳ ✳ ✺✶
✷✳✻✳✹ ❊s♣❡❝tr♦ ❞❡ P♦tê♥❝✐❛ ❊s♣❛❝✐❛❧ ❞❛s ❋❧✉t✉❛çõ❡s ❞♦ ❈♦♥tr❛st❡ ✉s❛♥❞♦ h∆C2(zf)i ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
✸ ❊str✉t✉r❛ ❞❛ ▼❡♠❜r❛♥❛ ❡ ❈✐t♦❡sq✉❡❧❡t♦ ❞❡ ❍❡♠á❝✐❛s ❡ ▼♦❞❡❧♦s
❞❡ ❊❧❛st✐❝✐❞❛❞❡ ✺✽
✸✳✶ ❆ ❇✐❝❛♠❛❞❛ ▲✐♣í❞✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✸✳✷ Pr♦t❡í♥❛s ❞❛ ▼❡♠❜r❛♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✸✳✸ ❖ ❈♦rt❡① ❞❛ ▼❡♠❜r❛♥❛ P❧❛s♠át✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✸✳✹ ❆s ❍❡♠á❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✸✳✺ ◆♦çõ❡s ❇ás✐❝❛s s♦❜r❡ ❊❧❛st✐❝✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✸✳✻ ❋❧✉t✉❛çõ❡s ❡♠ ❋✐❧❛♠❡♥t♦s ❡ ▼❡♠❜r❛♥❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼
✸✳✻✳✶ ❋❧✉t✉❛çõ❡s ❚ér♠✐❝❛s ❞❛ ❋♦r♠❛ ❞❡ ❋✐❧❛♠❡♥t♦s ❡ ❈♦♠♣r✐♠❡♥t♦ ❞❡ P❡rs✐stê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✸✳✻✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ▼♦♥❣❡ ♣❛r❛ ❙✉♣❡r❢í❝✐❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✸✳✻✳✸ ❋❧✉t✉❛çõ❡s ❚ér♠✐❝❛s ❞❛ ➪r❡❛ ❞❡ ■♥t❡r❢❛❝❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✸✳✻✳✹ P♦t❡♥❝✐❛❧ ❞❡ ❈♦♥✜♥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✸✳✻✳✺ ❈✉r✈❛t✉r❛ ❞❡ ❙✉♣❡r❢í❝✐❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✸✳✻✳✻ ❊♥❡r❣✐❛ ▲✐✈r❡ ❞❡ ❍❡❧❢r✐❝❤ ❝♦♠ ❈✉r✈❛t✉r❛ ❊s♣♦♥tâ♥❡❛ ✳ ✳ ✳ ✳ ✳ ✾✷ ✸✳✼ ▼♦❞❡❧♦s ❞❡ ❊❧❛st✐❝✐❞❛❞❡ ❞❡ ❍❡♠á❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻
✹ ▼❡t♦❞♦❧♦❣✐❛ ❊①♣❡r✐♠❡♥t❛❧ ❡ ❆♥á❧✐s❡ ❞❡ ❉❛❞♦s ✶✵✸
✹✳✶ ▼♦♥t❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺ ✹✳✶✳✶ ❆♠♦str❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✹✳✶✳✷ ❈❛❧✐❜r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✹✳✷ ❚é❝♥✐❝❛s ❞❡ Pr♦❝❡ss❛♠❡♥t♦ ❞❡ ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾
✺ ❘❡s✉❧t❛❞♦s ❡ ❉✐s❝✉ssõ❡s ✶✶✶
✺✳✶ ■♥t❡r♣r❡t❛çã♦ ♣❛r❛ ♦ ❈♦♥tr❛st❡ ▼é❞✐♦ hCi ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸ ✺✳✷ ■♥t❡r♣r❡t❛çã♦ ♣❛r❛ ❛ ❋❧✉t✉❛çã♦ ◗✉❛❞rát✐❝❛ ▼é❞✐❛h∆C2i ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼
✺✳✸ ■♥t❡r♣r❡t❛çã♦ ♣❛r❛ ❛ ❋✉♥çã♦ ❞❡ ❆✉t♦✲❈♦rr❡❧❛çã♦h∆C(0,0)∆C(0, t)i ✳ ✶✷✶
✺✳✹ ❖❜t❡♥çã♦ ❞♦ ❊s♣❡❝tr♦ ❞❡ P♦tê♥❝✐❛ ❊s♣❛❝✐❛❧ ✉s❛♥❞♦h∆C2(zf)i ✳ ✳ ✳ ✳ ✶✷✸
✻ ❈♦♥❝❧✉sõ❡s ❡ P❡rs♣❡❝t✐✈❛s ✶✷✺
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✶✸✷
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ■♠❛❣❡♠ ❞❡s❢♦❝❛❧✐③❛❞❛ ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❝❛♠♣♦✲❝❧❛r♦ ❞❡ ✉♠ ♠❛❝r♦❢á❣♦✳ ✸ ✶✳✷ ■♠❛❣❡♠ ❞❡s❢♦❝❛❧✐③❛❞❛ ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❝❛♠♣♦✲❝❧❛r♦ ❞❡ ✉♠❛ ❤❡♠á❝✐❛✳ ✹ ✷✳✶ ✭❆✮ P❡r✜❧ ❞♦ ♦❜❥❡t♦ ❞❡ ❢❛s❡ ✭❝é❧✉❧❛ ❛❞❡r✐❞❛ ❡♠ ✉♠❛ ❧â♠✐♥❛ ❞❡ ✈✐❞r♦✮❀
✭❇✮ ❞✐❢❡r❡♥ç❛s ❞❡ ❢❛s❡ ♥❛ ❛❜s♦rçã♦ ❞❛ ❧✉③ ♣♦r ♣❛rt❡ ❞♦ ♦❜❥❡t♦ ❞❡ ❢❛s❡✳ ✾ ✷✳✷ ■♠❛❣❡♥s ❝♦♠ ♠✐❝r♦s❝ó♣✐♦ ✭❆✮ ♥♦r♠❛❧ ❡ ✭❇✮ ❝♦♠ ❝♦♥tr❛st❡ ❞❡ ❢❛s❡✳ ✳ ✳ ✶✵ ✷✳✸ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ s✐st❡♠❛ ót✐❝♦ ♣❛r❛ ✉♠ ♠✐❝r♦s❝ó♣✐♦ ❞❡
❝♦♥tr❛st❡ ❞❡ ❢❛s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✹ ❈♦♦r❞❡♥❛❞❛s ❞♦ s✐st❡♠❛ ❞❡ r❡❢❡rê♥❝✐❛✿ ✭❆✮ ♥♦ ❡s♣❛ç♦ r❡❛❧❀ ✭❇✮ ♥♦
❡s♣❛ç♦ ❞❡ ❋♦✉r✐❡r ❞♦s ✈❡t♦r❡s ❞❡ ♦♥❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✺ ❘❡♣r❡s❡♥t❛çã♦ ❞❛s ❝♦♦r❞❡♥❛❞❛s ❡ ❡s♣❡ss✉r❛ ❞❛ ❧❡♥t❡ ❞❡❧❣❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✻ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ t❛♠❛♥❤♦ ❞❛s s❡çõ❡s ❞❡ ❝❛❞❛ s❡❣♠❡♥t♦ ❞❛ ❧❡♥t❡✳ ✭❆✮
❡ ✭❈✮ sã♦ ♦s s❡❣♠❡♥t♦s ❧❛t❡r❛✐s✱ ✭❇✮ ❞♦ s❡❣♠❡♥t♦ ❝❡♥tr❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✼ ❊sq✉❡♠❛ ó♣t✐❝♦ ❞♦ ♥♦ss♦ ♠✐❝r♦s❝ó♣✐♦✿ S é ❛ ❢♦♥t❡ ❞❡ ❧✉③ ✭❧â♠♣❛❞❛
❤❛❧ó❣❡♥❛ ❞❡ t✉♥❣stê♥✐♦✮✱ C é ❛ ❧❡♥t❡ ❞♦ ❝♦♥❞❡♥s❛❞♦r✱ L1 é ❛ ❧❡♥t❡
♦❜❥❡t✐✈❛✱ L2 é ❛ ❧❡♥t❡ ❞❡ t✉❜♦✱ f1 ❡ f2 sã♦ ❛s ❞✐stâ♥❝✐❛s ❢♦❝❛✐s✱ O é
♦❜❥❡t♦ q✉❡ ❡st❛ ♥♦ ❢♦❝♦ ❞❡L1✱d é ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛s ❧❡♥t❡s ❡ ♦ ♣❧❛♥♦
✐♠❛❣❡♠I ❡stá ♥♦ ♣❧❛♥♦ ❢♦❝❛❧ ❞❡ L2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✷✳✽ ❊sq✉❡♠❛ ❞♦ ♠✐❝r♦s❝ó♣✐♦ ❞❡s❢♦❝❛❧✐③❛❞♦✿ ♦❜❥❡t♦ ❡stá ❞❡s❢♦❝❛❧✐③❛❞♦ ❞❡ ✉♠❛ ♣❡q✉❡♥❛ ❞✐stâ♥❝✐❛ ∆f❀ ❛s ❧❡♥t❡s ❡stã♦ s❡♣❛r❛❞❛s ♣♦r ✉♠❛ ❞✐s✲ tâ♥❝✐❛ d ❡ ❛ ✐♠❛❣❡♠ é ❢♦r♠❛❞❛ ❞❡s❢♦❝❛❧✐③❛❞❛ ♥♦ ♣❧❛♥♦ ■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✷✳✾ ●❡♦♠❡tr✐❛ ❞❛ ♣r♦♣❛❣❛çã♦ ❞♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ❛tr❛✈és ❞❡ ✉♠❛ ✐♥t❡r❢❛❝❡ ♦♥❞✉❧❛❞❛✿ E0 é ♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ✐♥❝✐❞❡♥t❡❀ h(~ξ) é ❛ ❛♠♣❧✐t✉❞❡ ❞❛
♦♥❞✉❧❛çã♦ ❞❛ ✐♥t❡r❢❛❝❡ ♦♥❞✉❧❛❞❛❀ n1 ❡ n2 sã♦ ♦s í♥❞✐❝❡s ❞❡ r❡❢r❛çã♦
❞♦ ♠❡✐♦ ❛♥t❡s ❡ ❞❡♣♦✐s ❞❛ ✐♥t❡r❢❛❝❡ ♦♥❞❡ ♦ ❝❛♠♣♦ ❡❧étr✐❝♦ s❡ ♣r♦✲ ♣❛❣❛❀ξ~é ♦ ✈❡t♦r ♣♦s✐çã♦ ♥♦ ♣❧❛♥♦(x, y)♣❡r♣❡♥❞✐❝✉❧❛r à ❞✐r❡çã♦ z ❞❡ ♣r♦♣❛❣❛çã♦ ❞♦ ❝❛♠♣♦ ❡❧étr✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✶✵ ❈✉r✈❛s ❞❡ h∆C2(zf)i ❝♦♠ (∆nk0)2
π = 1✱ R = 4,9µm ❡ k = 9,3µm
−1✱
✉s❛♥❞♦ ♥♦ ❡s♣❡❝tr♦ |u(q)|2 ❞❛ ❡q✉❛çã♦ ✷✳✶✵✺ ♦s ♣❛râ♠❡tr♦s a = 7,6✱
b = 212µm−2 ❡ c = 4680µm−4✿ ❧✐♥❤❛ ❛③✉❧ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ ❡q✉❛çã♦
✷✳✶✵✷❀ ❧✐♥❤❛ ✈❡r♠❡❧❤❛ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ ❡q✉❛çã♦ ✷✳✶✵✸❀ ❧✐♥❤❛ ✈❡r❞❡ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛♦ ❧✐♠✐t❡ h∆C2(∞)i ♣❛r❛ zf → ∞ ❞❛ ❡q✉❛çã♦ ✷✳✶✵✹✳ ✳ ✹✶
✷✳✶✶ ❊s♣❡❝tr♦ ❡s♣❛❝✐❛❧ ❞❛s ✢✉t✉❛çõ❡s ❣❡r❛❞♦ ♣❡❧❛ ❡q✉❛çã♦ ✷✳✶✵✺ ✭❧✐♥❤❛ ❝♦♥tí♥✉❛✮ ❡ ❣❡r❛❞♦ ♣❡❧❛ ❡q✉❛çã♦ ✷✳✶✶✶ ✭❧✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✷✳✶✷ ●❡♦♠❡tr✐❛ ❞❛ ♣r♦♣❛❣❛çã♦ ❞♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ❛tr❛✈és ❞❡ ❞✉❛s ✐♥t❡r❢❛❝❡s
tr❛♥s♣❛r❡♥t❡s ✜♥❛s✳ ◆❛ r❡❣✐ã♦ ❡♥tr❡ ❛s ✐♥t❡r❢❛❝❡s ♦ í♥❞✐❝❡ ❞❡ r❡❢r❛çã♦ é n+ ∆n ❡ ❢♦r❛ é n✱ ❝♦♥s✐❞❡r❛❞♦s ❤♦♠♦❣❡♥❡♦✉s ❡ ✐s♦tró♣✐❝♦s✳ E0 é
♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ✐♥✐❝✐❛❧ q✉❡ ✐♥❝✐❞❡ ♥❛ ✐♥t❡r❢❛❝❡ ✶ ❝♦❧♦❝❛❞❛ ♥❛ ♣♦s✐çã♦ p1❀E1′ é ♦ ❝❛♠♣♦ ❡❧étr✐❝♦ q✉❡ ❞✐❢r❛t❛❞♦ ♣❡❧❛ ✐♥t❡r❢❛❝❡ ✶ s❡ ♣r♦♣❛❣❛ ❛té
à ✐♥t❡r❢❛❝❡ ✷ ❝♦❧♦❝❛❞❛ ♥❛ ♣♦s✐çã♦p2❀ E2 é ♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ❞✐❢r❛t❛❞♦
❧♦❣♦ ❛♣ós ❛ ✐♥t❡r❢❛❝❡ ✷✱ q✉❡ s❡rá ♣r♦♣❛❣❛❞♦ ❛té à ♣♦s✐çã♦zf ❞♦ ♣❧❛♥♦ ❢♦❝❛❧ ❞❛ ♦❜❥❡t✐✈❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✷✳✶✸ ❈✉r✈❛s ❞❡ h∆C2(zf)i ❝♦♠ R = 4,9µm✱ k = 9,3µm−1 ❡ (∆nk0)2
2π =
1✱ ✉s❛♥❞♦ ♥♦s ❡s♣❡❝tr♦s |u1(q)|2 ❡ |u2(q)|2 ❞❛s ❡q✉❛çõ❡s ✷✳✶✸✺❛ ♦s
♣❛râ♠❡tr♦s a1 = a2 = 7,6✱ b1 = b2 = 212µm−2 ❡ c1 = 4680µm−4✿
❧✐♥❤❛ ❛③✉❧ ❝♦♠c2 = 2c1 ❝❤❛♠❛❞❛ ❞❡ ❛ss✐♠étr✐❝♦❀ ❧✐♥❤❛ ✈❡r♠❡❧❤❛ ❝♦♠
c2 =c1 ❝❤❛♠❛❞❛ ❞❡ s✐♠étr✐❝❛❀ p1 =−0,5µm ❡p2 = 0,5µm✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✷✳✶✹ ❈✉r✈❛s ❞❡h∆C2(zf)i ❝♦♠ ♦s ♣❛râ♠❡tr♦s ✉t✐❧✐③❛❞♦s ♥❛ ✜❣✉r❛ ✷✳✶✸ ♥♦
❝❛s♦ s✐♠étr✐❝♦✿ ❧✐♥❤❛ ❛③✉❧ ❡ ❞❛ ❡q✉❛çã♦ ✷✳✶✸✸❀ ❧✐♥❤❛ ❛③✉❧ ❡ ❞❛ ❡q✉❛çã♦ ✷✳✶✸✹❀ ❧✐♥❤❛ ✈❡r❞❡ ❡ ♥♦ ❧✐♠✐t❡ ♣❛r❛ zf → ∞ ❞❛ ❡q✉❛çã♦ ✷✳✶✸✻✳ ✳ ✳ ✳ ✳ ✺✹ ✸✳✶ ✭❆✮ ❈é❧✉❧❛ Pr♦❝❛r✐♦♥t❡✿ ❖r❣❛♥✐③❛çã♦ ❝❡❧✉❧❛r s✐♠♣❧❡s✱ s❡♠ ♥ú❝❧❡♦ ♥❡♠
♦r❣❛♥❡❧❛s ♦✉ ♦r❣â♥✉❧♦s ❝✐t♦♣❧❛s♠át✐❝♦s❀ ✭❇✮ ❈é❧✉❧❛ ❊✉❝❛r✐♦♥t❡✿ ♦r❣❛✲ ♥✐③❛çã♦ ❝❡❧✉❧❛r ♠❛✐s ❝♦♠♣❧❡①❛ ❬✷✾❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✸✳✷ ❊str✉t✉r❛ ❞❛ ▼❡♠❜r❛♥❛✿ ✭❆✮ ✐♠❛❣❡♠ ❝♦♠ ♠✐❝r♦s❝ó♣✐♦ ❡❧❡trô♥✐❝♦ ❞❛ ♠❡♠❜r❛♥❛ ♣❧❛s♠át✐❝❛ ❡♠ s❡çã♦ tr❛♥s✈❡rs❛❧❀ ✭❇✮ ❡ ✭❈✮ ❞❡s❡♥❤♦s q✉❡ ♠♦str❛♠ ♦s ♠♦❞❡❧♦s ❜✐✲❞✐♠❡♥s✐♦♥❛❧ ❡ tr✐❞✐♠❡♥s✐♦♥❛❧ ❞❡ ✉♠❛ ♠❡♠✲ ❜r❛♥❛ ❝❡❧✉❧❛r ❬✷✾❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✸✳✸ ❆s ♣❛rt❡s ❞❡ ✉♠❛ ♠♦❧é❝✉❧❛ ❞❡ ❢♦s❢♦❧✐♣í❞✐♦✿ ✭❆✮ ❋♦s❢❛t✐❞✐❧❝♦❧✐♥❛✱ r❡✲
♣r❡s❡♥t❛❞❛ ❡sq✉❡♠❛t✐❝❛♠❡♥t❡❀ ✭❇✮ ❝♦♠♦ ♠♦❞❡❧♦ ❡s♣❛❝✐❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✸✳✹ ▼♦❧é❝✉❧❛s ❧✐♣í❞✐❝❛s ❡♠ á❣✉❛✿ ✭❆✮ ❛ ❢♦r♠❛ ❞❛ ♠♦❧é❝✉❧❛ ❧✐♣í❞✐❝❛ ❞❡✜♥❡
q✉❛❧ ❡str✉t✉r❛ é ❞❡t❡r♠✐♥❛❞❛✳ ❯♠❛ ❢♦r♠❛ ❝✉♥❡✐❢♦r♠❡ ❢♦r♠❛ ♠✐❝❡❧❛s ✭✜❣✉r❛ ❞❡ ❝✐♠❛✮✱ ❡♥q✉❛♥t♦ ❝✐❧✐♥❞r✐❢♦r♠❡ ❢♦r♠❛ ❜✐❝❛♠❛❞❛s ✭✜❣✉r❛ ❞❡ ❜❛✐①♦✮❀ ✭❇✮ ✈✐sã♦ tr✐❞✐♠❡♥s✐♦♥❛❧ ❞❛ ❜✐❝❛♠❛❞❛ ❧✐♣í❞✐❝❛ ❝♦♠ s✉❛ s✐♠✉✲ ❧❛çã♦ ❡♠ ❝♦♠♣✉t❛❞♦r ❬✷✾❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✸✳✺ ▼♦❜✐❧✐❞❛❞❡ ❞❡ ❢♦s❢♦❧✐♣í❞✐♦s✿ ♦s t✐♣♦s ❞❡ ♠♦✈✐♠❡♥t♦s ♣♦ssí✈❡✐s ♣❛r❛
♠♦❧é❝✉❧❛s ❞❡ ❢♦s❢♦❧✐♣í❞✐♦s ❡♠ ✉♠❛ ❜✐❝❛♠❛❞❛ ❧✐♣í❞✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✸✳✻ ▼♦❞♦s ♣❡❧♦s q✉❛✐s ❛s ♣r♦t❡í♥❛s ❞❛ ♠❡♠❜r❛♥❛ ❛ss♦❝✐❛♠✲s❡ ❝♦♠ ❛ ❜✐❝❛✲
♠❛❞❛ ❧✐♣í❞✐❝❛✿ ✭❆✮ ♠✉✐t❛s ♣r♦t❡í♥❛s ❞❛ ♠❡♠❜r❛♥❛ ❡st❡♥❞❡♠✲s❡ ❛tr❛✲ ✈és ❞❛ ❜✐❝❛♠❛❞❛✱ ❝♦♠♦ ♣❛rt❡ ❞❡ s✉❛s ♠❛ss❛s ❡♠ ❛♠❜♦s ♦s ❧❛❞♦s✿ ❛tr❛✈és ❞❡ ✉♠❛ ú♥✐❝❛α✲❤é❧✐❝❡ ♦✉ ❝♦♠ ♠ú❧t✐♣❧❛sα✲❤é❧✐❝❡✳ ✭❇✮ ❖✉tr❛s ♣r♦t❡í♥❛s ❞❛ ♠❡♠❜r❛♥❛ ❡stã♦ ❧♦❝❛❧✐③❛❞❛s ✐♥t❡r✐♦r♠❡♥t❡ ♥♦ ❝✐t♦s♦❧ ❡ sã♦ ❛ss♦❝✐❛❞❛s ❝♦♠ ❛ ❜✐❝❛♠❛❞❛ ♥♦ ❧❛❞♦ ❞❛ ♠❡♠❜r❛♥❛ ✐♥t❡r♥♦ ❛tr❛✈és ❞❡ ✉♠❛ ú♥✐❝❛ α✲❤é❧✐❝❡ ❛♥✜♣át✐❝❛ ❡①♣♦st❛ ❛ s✉♣❡r❢í❝✐❡ ❞❛ ♠♦❧é❝✉❧❛✳ ✭❈✮ ❖✉tr❛s ♣r♦t❡í♥❛s ❞❛ ♠❡♠❜r❛♥❛ sã♦ t♦t❛❧♠❡♥t❡ ❡①♣♦st❛s ♥❛ s✉✲ ♣❡r❢í❝✐❡ ❡①t❡r♥❛✱ s❡♥❞♦ ❧✐❣❛❞❛s ❛ ❜✐❝❛♠❛❞❛ s♦♠❡♥t❡ ♣♦r ✉♠❛ ❧✐❣❛çã♦ ❝♦✈❛❧❡♥t❡ ❛ ✉♠ ♦✉ ♠❛✐s ❣r✉♣♦s ❧✐♣í❞✐❝♦s✳ ✭❉✮ ❆❧❣✉♠❛s ♣r♦t❡í♥❛s✱ ❞❛s q✉❛✐s ♥❡♥❤✉♠❛ ❞❛s ♣❛rt❡s ♣❡♥❡tr❛♠ ♥♦ ✐♥t❡r✐♦r ❞❛ ❜✐❝❛♠❛❞❛✱ sã♦ ❧✐✲ ❣❛❞❛s ♠♦❧❡❝✉❧❛r♠❡♥t❡ ❛ ✉♠❛ ♦✉ ♦✉tr❛ ❞❛s ❢❛❝❡s ❞❛ ♠❡♠❜r❛♥❛ ♣♦r ✐♥t❡r❛çõ❡s ♥ã♦✲❝♦✈❛❧❡♥t❡s ❝♦♠ ♦✉tr❛s ♣r♦t❡í♥❛s ❞❛ ♠❡♠❜r❛♥❛✳ ✳ ✳ ✳ ✳ ✻✹ ✸✳✼ ❊sq✉❡♠❛ ❞❛ ❡str✉t✉r❛ ❞♦ ❝✐t♦❡sq✉❡❧❡t♦ s♦❜r❡ ❞♦ ❧❛❞♦ ❝✐t♦♣❧❛s♠át✐❝♦
❞❛ ♠❡♠❜r❛♥❛ ❞♦ ❡r✐tró❝✐t♦ ❤✉♠❛♥♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✸✳✽ ❍❡♠á❝✐❛s ❍✉♠❛♥❛s✿ ✭❆✮ ✐♠❛❣❡♠ ❝♦♠ ♦ ♠✐❝r♦s❝ó♣✐♦ ❡❧❡trô♥✐❝♦❀ ✭❇✮
♣❡r✜❧ ❤♦r✐③♦♥t❛❧ ❡ s❡çã♦ ❞❡ ✉♠❛ ú♥✐❝❛ ❤❡♠á❝✐❛✳ ❋♦t♦✿ ❉❛✈❡ ▼❝❈❛rt❤② ❛♥❞ ❆♥♥✐❡ ❈❛✈❛♥❛❣❤✴❲❡❧❧❝♦♠❡ ❚r✉st✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✸✳✾ ❊sq✉❡♠❛ ❞❛ ♠♦❧é❝✉❧❛s ❞❡ ❡s♣❡❝tr✐♥❛ ❞❛s ❤❡♠á❝✐❛s ❤✉♠❛♥❛s✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✸✳✶✵ ❈♦♠♣♦s✐çã♦ ♣r♦té✐❝❛ ❞♦ ❝♦rt❡① ❝❡❧✉❧❛r ❞❡ ❤❡♠á❝✐❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
✸✳✶✶ ❋♦rç❛s s✉♣❡r✜❝✐❛✐s s♦❜r❡ ✉♠ ❡❧❡♠❡♥t♦ ❞❡ ✈♦❧✉♠❡ ❞♦ ♠❛t❡r✐❛❧ ✳ ✳ ✳ ✳ ✳ ✼✶ ✸✳✶✷ ✭❆✮ ❉❡s❧♦❝❛♠❡♥t♦ ✉♥✐❛①✐❛❧∆uxx❀ ✭❇✮ ❉❡s❧♦❝❛♠❡♥t♦ ❞❡ ❝✐s❛❧❤❛♠❡♥t♦
∆uxy✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
✸✳✶✸ ❋♦rç❛s s✉♣❡r✜❝✐❛✐s ❡♠ ✉♠❛ ❧á♠✐♥❛ ❞❡ ❡s♣❡ss✉r❛d✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✸✳✶✹ ✭❆✮ ❋❧❡①ã♦ ❞❡ ✉♠❛ ❤❛st❡ ❞❡ ❝♦♠♣r✐♠❡♥t♦ L✱ ❧❛r❣✉r❛ b ❡ ❡s♣❡ss✉r❛
a✳ ❆ ❧✐♥❤❛ ♣♦♥t✐❧❤❛❞❛ ✐♥❞✐❝❛ ♦ ♣❧❛♥♦ ♥❡✉tr♦✳ ✭❇✮ ❙❡❝çã♦ r❡t❛ ❞❛ ❤❛st❡ ❡ s✐st❡♠❛ ❞❡ r❡❢❡rê♥❝✐❛ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ♠♦♠❡♥t♦ ❞❡ ✐♥ér❝✐❛ ❣❡♦♠étr✐❝♦ I✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✸✳✶✺ ▲✐♥❤❛ ❣❡♥ér✐❝❛s ❝✉❥❛ ♣♦s✐çã♦ ♥♦ ❡s♣❛ç♦ é ❞❛❞❛ ♣❡❧♦ ✈❡t♦r~r(s)✳ ✳ ✳ ✳ ✳ ✼✽
✸✳✶✻ ❱❡t♦r❡s t❛♥❣❡♥t❡s ♥♦ ♣♦♥t♦ ③❡r♦ ❡ ♥♦ ♣♦♥t♦s ❞❡ ✉♠ ✜❧❛♠❡♥t♦ ❝✉r✈♦✳ ✼✾ ✸✳✶✼ P♦❧í♠❡r♦s ❝♦♠ ❞✐❢❡r❡♥t❡s r❛③õ❡s ❡♥tr❡ ξp ❡ Lc✳ ◗✉❛♥t♦ ♠❡♥♦r ξp
❝♦♠♣❛r❛❞♦ ❝♦♠ Lc✱ ♠❛✐s ❡♥♦✈❡❧❛❞♦ ✜❝❛ ♦ ♣♦❧í♠❡r♦ ❡ ♠❛✐s ♣ró①✐♠♦s ✜❝❛♠ s✉❛s ❡①tr❡♠✐❞❛❞❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✸✳✶✽ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ✈❡t♦rR~ ❡♥tr❡ ❛s ❡①tr❡♠✐❞❛❞❡s ❞♦ ✜❧❛♠❡♥t♦✳ ✳ ✳ ✳ ✳ ✽✷ ✸✳✶✾ ✭❆✮ ❋✐❣✉r❛ ❞❡ ✉♠❛ s✉♣❡r❢í❝✐❡ ❝♦♠ ✉♠❛ ❞♦❜r❛✱ ♦♥❞❡ ❛ ❢✉♥çã♦h(x, y)
♥ã♦ é s✐♥❣❧❡✲✈❛❧✉❡❞✳ ✭❇✮ ❋✐❣✉r❛ ❞❡ ✉♠❛ s✉♣❡r❢í❝✐❡ ❝✉r✈❛✱ ♦♥❞❡ ❛ ❢✉♥çã♦ h(x, y) é s✐♥❣❧❡✲✈❛❧✉❡❞✳ ▼♦str❛✲s❡ ♦ ❞❡s❧♦❝❛♠❡♥t♦ ✉♥✐tár✐♦ ❛♦ ❧♦♥❣♦
❞❡x q✉❡ ❣❡r❛ ♦ ✈❡t♦r t❛♥❣❡♥t❡ rx✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺~ ✸✳✷✵ ❈❛♠❛❞❛ ❛♥✜❢í❧✐❝❛ ❛ss✐♠étr✐❝❛ q✉❡ ❝❛✉s❛ ✉♠❛ ❝♦♥✜❣✉r❛çã♦ ❞❡ ❡q✉✐❧í✲
❜r✐♦ ♥ã♦ ♣❧❛♥❛r ✭❝♦♠ ❝✉r✈❛t✉r❛ ❡s♣♦♥tâ♥❡❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ✸✳✷✶ ✭❆✮ ▼♦❞❡❧♦ ❞❡ ❛❝♦♣❧❛♠❡♥t♦ ❞❡ ❝✐t♦❡sq✉❡❧❡t♦ ♣❛r❛ ❤❡♠á❝✐❛s❀ ✭❇✮ ❘✉♣✲
t✉r❛ ❞❛ ❧✐❣❛çã♦ ❞❡ ❡s♣❡❝tr✐♥❛ ❛t✐✈❛❞❛ ♣♦r ❆❚P✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✸✳✷✷ ■❧✉str❛çã♦ ❞♦ ❛❝♦♣❧❛♠❡♥t♦ ❞♦s ♠♦❞♦s ❞❡ ❝✐s❛❧❤❛♠❡♥t♦ ❞♦ ❝✐t♦❡sq✉❡✲
❧❡t♦ ❡ ❞❡ ❝✉r✈❛t✉r❛ ❞❛ ♠❡♠❜r❛♥❛ ✐♥❞✐❝❛♥❞♦ q✉❡ ♣❛r❛ ❣r❛♥❞❡s ❝♦♠✲ ♣r✐♠❡♥t♦s ❞❡ ♦♥❞❛ ❛s ❞✉❛s ❝❛♠❛❞❛s ✢✉t✉❛♠ ❥✉♥t❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ✸✳✷✸ ✭❆✮ ■❧✉str❛çã♦ ❞❛ ❜✐❝❛♠❛❞❛ ❡ ❝✐t♦❡sq✉❡❧❡t♦ ♥ã♦ t❡♥s✐♦♥❛❞♦s✱ s✉♣❡r✲
❢í❝✐❡ ♣❧❛♥❛❀ ✭❇✮ ■❧✉str❛çã♦ ❞♦ ❛✉♠❡♥t♦ ❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❝♦♥✜♥❛♠❡♥t♦ ❝❛✉s❛❞♦ ♣❡❧❛ ❝✉r✈❛t✉r❛ ❧♦❝❛❧ ❞❛ ❜✐❝❛♠❛❞❛✲❝✐t♦❡sq✉❡❧❡t♦✳ ❆ ❝✉r✈❛t✉r❛ ❧♦❝❛❧ ❡st✐❝❛ ❛s ♠♦❧❛s ❡♥tró♣✐❝❛s t❡♥s✐♦♥❛♥❞♦ ❛ ❡str✉t✉r❛ ❡ ❝♦♥✜♥❛♥❞♦ ❛s ✢✉t✉❛çõ❡s ❞❛ ❜✐❝❛♠❛❞❛ ❧✐♣í❞✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵
✹✳✶ ✭❆✮ ❋✐❣✉r❛ ❡sq✉❡♠át✐❝❛ ❞❡ ✉♠❛ ❤❡♠á❝✐❛ ❞✐s❝ót✐❝❛✱ s✐st❡♠❛ ❞❡ r❡❢❡✲ rê♥❝✐❛ ❡ sí♠❜♦❧♦s ✉t✐❧✐③❛❞♦s✳ ✭❇✮ ■♠❛❣❡♥s ❞❡ ✉♠❛ ❤❡♠á❝✐❛ ♣❛r❛ três ❞❡s❢♦❝❛❧✐③❛çõ❡s ✭zf✮ ❞✐❢❡r❡♥t❡s r❡❧❛t✐✈❛s ❛♦ ♣❧❛♥♦ ♠é❞✐♦ ❞❡ s✐♠❡tr✐❛✳ ❆ ❛ss✐♥❛t✉r❛ ❞❡st❛ té❝♥✐❝❛ é ❛ ✐♥✈❡rsã♦ ❞♦ ❝♦♥tr❛st❡ ❡♠ t♦r♥♦ ❞♦ ♣❧❛♥♦ ❞❡ s✐♠❡tr✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✹✳✷ ❋♦t♦ ❞♦ ♠✐❝r♦s❝ó♣✐♦ ❞♦ ▲❛❜♦r❛tór✐♦ ❞❡ ❇✐♦❢ís✐❝❛ ❞❛ ❯❋▼●✴■❈❊❳✳ ✳ ✳ ✶✵✺ ✹✳✸ ❊sq✉❡♠❛ ❞❛ ♠♦♥t❛❣❡♠ ❡①♣❡r✐♠❡♥t❛❧ ✉t✐❧✐③❛❞❛ ♥♦s ❡①♣❡r✐♠❡♥t♦s✳ ✳ ✳ ✳ ✶✵✻ ✹✳✹ P♦rt❛ ❛♠♦str❛s✿ ❝♦♥s✐st❡ ❞❡ ✉♠ ❖✲r✐♥❣ ❞❡ ❞✐â♠❡tr♦ ❞❡ ❝❡r❝❛ 1,5cm
❝♦❧❛❞♦ ❝♦♠ ♣❛r❛✜♥❛✱ ❡♠ ✉♠❛ ❧❛♠í♥✉❧❛ ❞❡ ✈✐❞r♦ ✭❈♦r♥✐♥❣✮ ❞❡ 0,17
mm ❞❡ ❡s♣❡ss✉r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✹✳✺ ◆í✈❡❧ ❞❡ ❝✐♥③❛ N ❡♠ ❢✉♥çã♦ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❧✉♠✐♥♦s❛ I ♠❡❞✐❞❛ ♣❡❧♦
❝♦♥t❛❞♦r ❞❡ ❢ót♦♥s✳ P❛r❛ ❡st❡ ❛❥✉st❡ ♣❛rt✐❝✉❧❛r ❞❛ ❝â♠❡r❛✱ N = −36,7 + 7,3I✳ ❖ ♣❛râ♠❡tr♦ ✐♠♣♦rt❛♥t❡ ♣❛r❛ ❝❛❧✐❜r❛çã♦ ❞♦ ❝♦♥tr❛st❡ é B = −36,7✱ q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛♦ ♥í✈❡❧ ❞❡ ❝✐♥③❛ ♣❛r❛ ♦ ✈❛❧♦r ❞❛
✐♥t❡♥s✐❞❛❞❡ ❧✉♠✐♥♦s❛ ✐❣✉❛❧ ❛ ③❡r♦✱ ❞❛ ❡①tr❛♣♦❧❛çã♦ ❧✐♥❡❛r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✹✳✻ ▼❡♥✉ ❞♦ s♦❢t✇❛r❡ ■♠❛❣❡❏✳ ◆❛ ❤❡♠á❝✐❛ ❛ s❡r ❛♥❛❧✐s❛❞❛ ✭♥♦ ❛❧t♦ ❛
❡sq✉❡r❞❛ ❞❛ ✜❣✉r❛✮ tr❛ç❛♥❞♦ ✉♠❛ ❧✐♥❤❛ ✭❡♠ ❛♠❛r❡❧♦✮ s❡ ♣♦❞❡ ♦❜s❡r✈❛r ✭❛❜❛✐①♦ ❛ ❡sq✉❡r❞❛✮ ♦ s❡✉ ♣❡r✜❧ ❝♦rr❡s♣♦♥❞❡♥t❡✱ ❡♠ ♥í✈❡✐s ❞❡ ❝✐♥③❛✳ ◆♦ ❧❛❞♦ ❞✐r❡✐t♦✱ s❡ ♣♦❞❡ ♦❜s❡r✈❛r ❛ s✉♣❡r❢í❝✐❡ ❡♠ ♥í✈❡✐s ❞❡ ❝✐♥③❛ ❞❛ ✐♠❛❣❡♠ ✐♥t❡✐r❛✳ ❈♦♠ ♦s ♥í✈❡✐s ❞❡ ❝✐♥③❛ ♣❛r❛ ❝❛❞❛ ♣✐①❡❧ ❡♠ ❝❛❞❛ ✐♠❛❣❡♠ ♣♦❞❡♠♦s ❢❛③❡r ✉♠❛ sér✐❡ t❡♠♣♦r❛❧ q✉❡ ♥♦s ♣❡r♠✐t❡ ❝❛❧❝✉❧❛r ❛ ✢✉t✉❛çã♦ q✉❛❞rát✐❝❛ ♠é❞✐❛ ❡ ❢✉♥çõ❡s ❞❡ ❝♦rr❡❧❛çã♦ ❞♦ ❝♦♥tr❛st❡✳ ✳ ✳ ✶✶✵ ✺✳✶ ✭❆✮ ✐♠❛❣❡♠ ❞❡ ✉♠❛ ❤❡♠á❝✐❛ ❞❡s❢♦❝❛❧✐③❛❞❛ ❝♦♠ ∆f = −2µm❀ ✭❇✮
●rá✜❝♦s ❞❡ hCi ✭q✉❛❞r❛❞♦✮ ❡ h∆C2i ✭❝ír❝✉❧♦s✮ ❡♠ ❢✉♥çã♦ ❞❛ ♣♦s✐çã♦
❛♦ ❧♦♥❣♦ ❞♦ ❡✐①♦ ❤♦r✐③♦♥t❛❧ x✐♥❞✐❝❛❞♦ ❡♠ ✜❣✉r❛ ✭❆✮❀ ✭❈✮ ●rá✜❝♦s ❞❡ κ2 ✭q✉❛❞r❛❞♦✮ ❡ h∆C2i ✭❝ír❝✉❧♦s✮ ❡♠ ❢✉♥çã♦ ❞❛ ♣♦s✐çã♦ ❤♦r✐③♦♥t❛❧✳
◆♦t❛✲s❡ ❛ ❛♥t✐❝♦rr❡❧❛çã♦ ❡♥tr❡ κ2 ❡h∆C2i ♦ ❧♦♥❣♦ ❞❛ ♣♦s✐çã♦ x✳ ✳ ✳ ✳ ✶✶✷
✺✳✷ ❉✐❢❡r❡♥t❡s ♦r✐❡♥t❛çõ❡s ♣❛r❛ ♦ ♣❡r✜❧ ✸✲❉ ❞❛ ❤❡♠á❝✐❛ ❞❛ ✜❣✉r❛ ✺✳✶ ✭❆✮ ♦❜t✐❞♦ ✉s❛♥❞♦ ❛ ❡q✉❛çã♦ ✺✳✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺ ✺✳✸ ●rá✜❝♦s ❞❛s ♠é❞✐❛s ❛♥❣✉❧❛r❡s ❞❡ ❝✉r✈❛t✉r❛sκ2
1(ρ)✭q✉❛❞r❛❞♦s✮ ❡κ22(ρ)
✭❝ír❝✉❧♦s✮ ❡♠ ❢✉♥çã♦ ❞❡ρ♣❛r❛ ❛ ❤❡♠á❝✐❛ ❞❡ ✜❣✉r❛ ✺✳✶ ✭❆✮✳ ❆s ❧✐♥❤❛s ❝♦♥tí♥✉❛s sã♦ ❣✉✐❛s ♣❛r❛ ♦s ♦❧❤♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✻
✺✳✹ ✭❆✮ ▼♦❞❡❧♦ ó♣t✐❝♦ q✉❡ ✉s❛♠♦s ♣❛r❛ ❛ ♣❛rt❡ ❝❡♥tr❛❧ ❞❛ ❤❡♠á❝✐❛✱ ♦♥❞❡ ❛s s✉♣❡r❢í❝✐❡s sã♦ ♠♦❞❡❧❛❞❛s ❝♦♠♦ r❡❞❡s ❞❡ ❞✐❢r❛çã♦ ❞❡ ❢❛s❡ ♣❧❛♥❛s❀ ✭❇✮ ❋❧✉t✉❛çã♦ q✉❛❞rát✐❝❛ ♠é❞✐❛ ❞♦ ❝♦♥tr❛st❡ ❞❛ ❤❡♠á❝✐❛ ❡♠ ❢✉♥çã♦ ❞❛ ❞❡s❢♦❝❛❧✐③❛çã♦ ✭❝ír❝✉❧♦s✮✳ ❖s ♠í♥✐♠♦s ♦❝♦rr❡♠ q✉❛♥❞♦ ♦ ♣❧❛♥♦ ❢♦❝❛❧ ❞❛ ♦❜❥❡t✐✈❛ ❝♦✐♥❝✐❞❡ ❝♦♠ ❛s ✐♥t❡r❢❛❝❡s❀ ✭❈✮ ❋✉♥çã♦ ❞❡ ❛✉t♦✲ ❝♦rr❡❧❛çã♦ ❞♦ ❝♦♥tr❛st❡ ❡♠ ❢✉♥çã♦ ❞❛ ❞❡s❢♦❝❛❧✐③❛çã♦ ✭❝ír❝✉❧♦s✮✱ ♣❛r❛ ✉♠ t❡♠♣♦ ❞❡ ❛tr❛s♦ ✜①♦ ❞❡ 1/30 s❡❣✉♥❞♦s✳ ❖s ♠í♥✐♠♦s ♥ã♦ sã♦
♠❛✐s r❡s♦❧✈✐❞♦s✱ ♣♦rq✉❡ ♦s ♠❛✐♦r❡s ✈❡t♦r❡s ❞❡ ♦♥❞❛ ❞❛s ✢✉t✉❛çõ❡s ❥á ❞❡❝❛ír❛♠✱ ✐❧✉str❛♥❞♦ ❛ ❝♦♥❡①ã♦ ❡♥tr❡ r❡s♦❧✉çã♦ ó♣t✐❝❛ ❧❛t❡r❛❧ ❡ ❧♦♥❣✐✲ t✉❞✐♥❛❧✳ ❆s ❧✐♥❤❛ ❝♦♥tí♥✉❛s ♥❛s ✜❣✉r❛s ✭❇✮ ❡ ✭❈✮ ❝♦rr❡s♣♦♥❞❡♠ ❛♦s ❛❥✉st❡ ❛♦s ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ✉s❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ❆✉t❤✳ ❛❧✳ ✳ ✳ ✳ ✳ ✶✷✵ ✺✳✺ ❊s♣❡❝tr♦ ❞❡ ♣♦tê♥❝✐❛ ❡s♣❛❝✐❛❧ ♦♥❞❡ ♦s ❝ír❝✉❧♦s sã♦ ❞❛❞♦s ❡①♣❡r✐♠❡♥✲
t❛✐s r❡s✉❧t❛♥t❡s ❞❛ ✐♥t❡❣r❛çã♦ ♥✉♠ér✐❝❛ ❞❛ ✢✉t✉❛çã♦ q✉❛❞rát✐❝❛ ♠é❞✐❛ ❞♦ ❝♦♥tr❛st❡✱ ❝♦♠♦ ♥❛ ❡q✉❛çã♦ ✷✳✶✹✶✳ ❆ ❧✐♥❤❛ ❝♦♥tí♥✉❛ é ♦ ❛❥✉st❡ ❞❡ f(q)✉s❛♥❞♦ ❛ ❡q✉❛çã♦ ✺✳✶✷✱ q✉❡ r❡t♦r♥❛ ♦s ✈❛❧♦r❡s kc
kTef = (6,8±2,0)
❡ µ
kTef = (8,9±0,6)×10
3µm−2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ❚❡♠♣♦ ❞❡ ✈✐❞❛ ❞❡ ❤❡♠á❝✐❛s ♥❛ ❝✐r❝✉❧❛çã♦ ♣❛r❛ ✈ár✐❛s ❡s♣é❝✐❡s✳ ✳ ✳ ✳ ✳ ✻✽
❘❡s✉♠♦
❖❜❥❡t♦s tr❛♥s♣❛r❡♥t❡s ✭♦❜❥❡t♦s ❞❡ ❢❛s❡✮ s❡ t♦r♥❛♠ ✈✐sí✈❡✐s ❡♠ ✉♠ ♠✐❝r♦s❝ó♣✐♦ ó♣t✐❝♦ ♦♣❡r❛♥❞♦ ❡♠ ❝❛♠♣♦✲❝❧❛r♦✱ s❡ ♦ ♠✐❝r♦s❝ó♣✐♦ ❡st✐✈❡r ❞❡s❢♦❝❛❧✐③❛❞♦✳ ◆❛ ✈❡r✲ ❞❛❞❡✱ ✉♠ ♠✐❝r♦s❝ó♣✐♦ ó♣t✐❝♦ ❞❡s❢♦❝❛❧✐③❛❞♦ ♦♣❡r❛♥❞♦ ❡♠ ❝❛♠♣♦✲❝❧❛r♦ é ❡q✉✐✈❛❧❡♥t❡ ❛ ✉♠ ♠✐❝r♦s❝ó♣✐♦ ❞❡ ❝♦♥tr❛st❡ ❞❡ ❢❛s❡✱ ❛♣r❡s❡♥t❛♥❞♦ ✈❛♥t❛❣❡♥s q✉❡ s❡rã♦ ❞✐s❝✉t✐❞❛s ♥❡st❛ t❡s❡✱ ❡♠ r❡❧❛çã♦ ❛♦ ♠✐❝r♦s❝ó♣✐♦ ❞❡ ❝♦♥tr❛st❡ ❞❡ ❢❛s❡ ❝♦♥✈❡♥❝✐♦♥❛❧✳ ❆ ❞❡s❢♦❝❛❧✐✲ ③❛çã♦ ✐♥tr♦❞✉③ ✉♠❛ ❞✐❢❡r❡♥ç❛ ❞❡ ❢❛s❡ ❡♥tr❡ ❛ ❧✉③ tr❛♥s♠✐t✐❞❛ ✭♥ã♦✲❞✐❢r❛t❛❞❛✮ ❡ ❛ ❧✉③ ❞✐❢r❛t❛❞❛ ♣❡❧♦ ♦❜❥❡t♦✱ q✉❡ ❛♦ s❡r❡♠ r❡❝♦♠❜✐♥❛❞❛s ♥♦ ♣❧❛♥♦ ❞❡ ❞❡t❡çã♦ ❡ ❞❡✈✐❞♦ à ✐♥✲ t❡r❢❡rê♥❝✐❛ ❡♥tr❡ ❡st❛s ❧✉③❡s✱ ❢❛③ ❝♦♠ q✉❡ ♦ ♦❜❥❡t♦ tr❛♥s♣❛r❡♥t❡ s❡ t♦r♥❡ ✈✐sí✈❡❧✱ ❝♦♠ ✉♠ ❝♦♥tr❛st❡ ❞❛ ✐♠❛❣❡♠ ❞✐❢❡r❡♥t❡ ❞❡ ③❡r♦✳ ■st♦ ❢♦✐ ❞❡♠♦♥str❛❞♦ ❡♠ ♥♦ss♦ ❧❛❜♦r❛tó✲ r✐♦ ❡ ♣✉❜❧✐❝❛❞♦ ❡♠ ❛rt✐❣♦s ❡ t❡s❡s ❛♥t❡r✐♦r❡s ❬✶✕✼❪✳ ◆❡st❛ t❡s❡✱ ♠❡❧❤♦r❛♠♦s ♦ ♠♦❞❡❧♦ ó♣t✐❝♦ ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❞❡s❢♦❝❛❧✐③❛çã♦✱ ♣❛r❛ q✉❡ ❡❧❡ ❢♦ss❡ ✈á❧✐❞♦ ♣❛r❛ q✉❛❧q✉❡r ❞❡s❢♦❝❛❧✐③❛çã♦✱ ✐♥❝❧✉s✐✈❡ ♥♦ ❧✐♠✐t❡ ❛ss✐♥tót✐❝♦ ❞❡ ❣r❛♥❞❡s ❞❡s❢♦❝❛❧✐③❛çõ❡s✱ ❡ ♣❛r❛ ♥ú✲ ♠❡r♦s ❞❡ ♦♥❞❛ ❞❡ ❞✐❢r❛çã♦ ♠❛✐♦r❡s✳ ❖❜t✐✈❡♠♦s ❡①♣r❡ssõ❡s t❡ór✐❝❛s ♣❛r❛ ♦ ❝♦♥tr❛st❡ ❞❡ ♦❜❥❡t♦s ❞❡ ❢❛s❡ ❝♦♠♣♦st♦s ♣♦r ✉♠❛ ❡ ♣♦r ❞✉❛s ✐♥t❡r❢❛❝❡s ♣❛r❛❧❡❧❛s✳ ◆♦ ❧✐♠✐t❡ ❞❡ ♣❡q✉❡♥❛s ❞❡s❢♦❝❛❧✐③❛çõ❡s ❡ ♥ú♠❡r♦s ❞❡ ♦♥❞❛ ❞❡ ❞✐❢r❛çã♦ ♣❡q✉❡♥♦s✱ ❛tr❛✈és ❞❛ ♠é✲ ❞✐❛ t❡♠♣♦r❛❧ ❞♦ ❝♦♥tr❛st❡✱ ♣♦❞❡♠♦s ♦❜t❡r ❛ ❢♦r♠❛ ❞❡ ❡q✉✐❧í❜r✐♦ ❞❡ ❤❡♠á❝✐❛s✱ ❝♦♠♦ ❞❡♠♦♥str❛❞♦ ❡♠ ♣✉❜❧✐❝❛çã♦ ❛♥t❡r✐♦r ❞❡st❡ ❧❛❜♦r❛tór✐♦ ❬✹❪✳ ◆♦ss❛ ♥♦✈❛ ❡①♣r❡ssã♦ é ✐♠♣♦rt❛♥t❡ ♣❛r❛ ❡st❛❜❡❧❡❝❡r ✉♠❛ r❡❧❛çã♦ ❡♥tr❡ ✢✉t✉❛çõ❡s ❞❡ ❝♦♥tr❛st❡ ❡ ✢✉t✉❛çõ❡s ♥❛ ❛❧t✉r❛ ❞❛s s✉♣❡r❢í❝✐❡s ❞❛ ❤❡♠á❝✐❛✳ ❈♦♠ ❡st❡ ♥♦✈♦ ♠♦❞❡❧♦ ó♣t✐❝♦✱ ♥ós ♠♦str❛♠♦s q✉❡ ❛♦ ❢❛③❡r ✉♠❛ ✈❛rr❡❞✉r❛ ♥❛ ♣♦s✐çã♦ ❞♦ ♣❧❛♥♦ ❢♦❝❛❧ ❞❛ ♦❜❥❡t✐✈❛ ✭zf✮✱ ❝♦♠♦ ❛s s✉♣❡r❢í❝✐❡s ❞❛s ❤❡♠á❝✐❛s ❡stã♦ ❡♠ ♣♦s✐çõ❡s ❞✐❢❡r❡♥t❡s ❡♠ r❡❧❛çã♦ à ③✱ ❛ ❧✉③ ❞✐❢r❛t❛❞❛ ♣❡❧❛s s✉♣❡r✜❝✐❡s t❡♠ ❢❛s❡s ❞✐❢❡r❡♥t❡s ❡✱ ♣♦rt❛♥t♦✱ ♣♦❞❡♠ s❡r ❞✐st✐♥❣✉✐❞❛s ♥❡st❛ té❝✲ ♥✐❝❛ ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❞❡s❢♦❝❛❧✐③❛çã♦✳ ❊st❡ ❢❛t♦ ♥♦s ♣❡r♠✐t❡ ❡st✉❞❛r ❛s ♣r♦♣r✐❡❞❛❞❡s
❞❡ ❝❛❞❛ s✉♣❡r❢í❝✐❡ s❡♣❛r❛❞❛♠❡♥t❡✳ P❛r❛ ✢✉t✉❛çõ❡s ❝♦♠ ♥ú♠❡r♦s ❞❡ ♦♥❞❛ ♠❛✐♦r❡s q✉❡ ✶ µm−1✱ ♣♦❞❡♠♦s ❛♣r♦①✐♠❛r ❛ r❡❣✐ã♦ ❝❡♥tr❛❧ ❞❛ ❤❡♠á❝✐❛ ♣♦r ♣❧❛♥♦s ♣❛r❛❧❡❧♦s
❡ ❛♣❧✐❝❛r ♦ ♠♦❞❡❧♦ ó♣t✐❝♦ ♣❛r❛ ♦❜❥❡t♦s ❞❡ ❢❛s❡ ❝♦♠ ❞✉❛s ✐♥t❡r❢❛❝❡s ❞❡s❡♥✈♦❧✈✐❞♦s ♥❡st❛ t❡s❡✳ ❯s❛♥❞♦ ♦ ♠♦❞❡❧♦ ❡❧ást✐❝♦ r❡❝❡♥t❡ ❞❡ ❆✉t❤ ❡t ❛❧✳ ❬✽❪✱ q✉❡ ❧❡✈❛ ❡♠ ❝♦♥t❛ ♦ ❛❝♦♣❧❛♠❡♥t♦ ❡♥tr❡ ❛ ❜✐❝❛♠❛❞❛ ❧✐♣í❞✐❝❛ ❡ ♦ ❝✐t♦❡sq✉❡❧❡t♦ ❞❡ ❡s♣❡❝tr✐♥❛ ✭q✉❡ t❛♠❜é♠ ❝♦♥s✐❞❡r❛ ❛s s✉♣❡r❢í❝✐❡s ❞❡ ❤❡♠á❝✐❛s ❝♦♠♦ ♣❧❛♥♦s ♣❛r❛❧❡❧♦s✮ ❡ ♥♦ss♦ ♠♦❞❡❧♦ ó♣t✐❝♦✱ ♦❜t✐✈❡♠♦s ✉♠ ót✐♠♦ ❛❥✉st❡ ♣❛r❛ ♦s ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s✳ ❉❡st❡ ❛❥✉st❡ ♦❜t✐✈❡♠♦s ♦s ✈❛❧♦r❡s ♣❛r❛ ♦ ♠ó❞✉❧♦ ❞❡ ❝✉r✈❛t✉r❛ ❞❛ ❜✐❝❛♠❛❞❛✱ ♦ ♠ó❞✉❧♦ ❞❡ ❝✐s❛❧❤❛♠❡♥t♦ ❞♦ ❝✐t♦❡sq✉❡❧❡t♦ ❡ ♣❛r❛ ❛ t❡♠♣❡r❛t✉r❛ ❡❢❡t✐✈❛✳ ❆s ✢✉t✉❛çõ❡s ❞❡ ❛❧t✉r❛ ♥❛ ❤❡♠á❝✐❛ ♥ã♦ sã♦ s♦♠❡♥t❡ ❞❡ ♦r✐❣❡♠ tér♠✐❝❛✳ ❖✉tr❛ ❝♦♥tr✐❜✉✐çã♦ ✈❡♠ ❞❛ ❝♦♥✈❡rsã♦ ❞❡ ❡♥❡r❣✐❛ q✉í♠✐❝❛ ❡♠ tr❛❜❛❧❤♦ ♠❡❝â♥✐❝♦ ♥❛s s✉♣❡r❢í❝✐❡s✱ ♠❡❞✐❛❞❛ ♣♦r ❆❚P ✭❛❞❡♥♦s✐♥❛ tr✐❢♦s✲ ❢❛t♦✱ ♦ ❝♦♠❜✉stí✈❡❧ ❞❛s ❝é❧✉❧❛s✮ ❬✾✱✶✵❪✳ ❊st❡s ❡❢❡✐t♦s ❢♦r❛✲❞♦✲❡q✉✐❧í❜r✐♦ sã♦ r❡❞✉③✐❞♦s ❛ ✉♠ ú♥✐❝♦ ♣❛râ♠❡tr♦✱ q✉❛❧ s❡❥❛ ❛ t❡♠♣❡r❛t✉r❛ ❡❢❡t✐✈❛ ✐♥tr♦❞✉③✐❞❛ ❞❡ ✉♠❛ ♠❛♥❡✐r❛ ❛❞✲❤♦❝✳ ❊st❡ ❡❢❡✐t♦ ❛✐♥❞❛ é ♠♦t✐✈♦ ❞❡ ❝♦♥tr♦✈érs✐❛ ♥❛ ❧✐t❡r❛t✉r❛ ❬✶✶❪✳ ❊st✉❞❛♠♦s t❛♠❜é♠ ❛ r❡❧❛①❛çã♦ ❞❡st❛s ✢✉t✉❛çõ❡s ❛♥❛❧✐s❛♥❞♦ ❛ ❢✉♥çã♦ ❞❡ ❛✉t♦✲❝♦rr❡❧❛çã♦ t❡♠✲ ♣♦r❛❧ ❞♦ ❝♦♥tr❛st❡✳ ❊st❛ r❡❧❛①❛çã♦ ❞❡♣❡♥❞❡ ❞❛ ❡❧❛st✐❝✐❞❛❞❡ ❞❛ ❜✐❝❛♠❛❞❛ ❧✐♣í❞✐❝❛ ❡ ❝✐t♦❡sq✉❡❧❡t♦ ❞❡ ❡s♣❡❝tr✐♥❛✱ ❡ ❞♦ ❡s❝♦❛♠❡♥t♦ ❞♦ ❝✐t♦♣❧❛s♠❛ ❛tr❛✈és ❞♦ ❝❛♥❛❧ ❡str❡✐t♦✱ ❞❡ ❡s♣❡ss✉r❛ d ❞❛ ♦r❞❡♠ ❞❡ ✷✵ ❛ ✸✵ nm✱ ❡♥tr❡ ❛ ❜✐❝❛♠❛❞❛ ❡ ♦ ❝✐t♦❡sq✉❡❧❡t♦✳ ❉♦ ❛❥✉st❡ ❞❛ t❡♦r✐❛ ❛♦s ♥♦ss♦s ❞❛❞♦s ♦❜t✐✈❡♠♦sd= 21±1nm✳ ▼♦str❛♠♦s q✉❡ ❛ té❝♥✐❝❛
❞❡ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❞❡s❢♦❝❛❧✐③❛çã♦ é ✉♠❛ té❝♥✐❝❛ ❞❡ ♠✐❝r♦s❝♦♣✐❛ ó♣t✐❝❛ ❜❛st❛♥t❡ út✐❧ ❡ ❝♦♥✜á✈❡❧ ♣❛r❛ ♦ ❡st✉❞♦ ❞♦ ♣❡r✜❧ ❡ r✉❣♦s✐❞❛❞❡s ❞✐♥â♠✐❝❛ ❡ ❡stát✐❝❛ ❞❡ ✐♥t❡r❢❛❝❡s ❡♠ ✉♠ ♠❛t❡r✐❛❧ tr❛♥s♣❛r❡♥t❡ ❡♠ ♠✉❧t✐❝❛♠❛❞❛s✱ ❝♦♠♦ ♠❡♠❜r❛♥❛s ❞❡ ❝é❧✉❧❛s ❜✐♦❧ó❣✐❝❛s✳
❆❜str❛❝t
❚r❛♥s♣❛r❡♥t ♦❜❥❡❝ts ✭♣❤❛s❡ ♦❜❥❡❝ts✮ r❡♥❞❡r ✈✐s✐❜❧❡ ✐♥ ❛ ❜r✐❣❤t✲✜❡❧❞ ♦♣t✐❝❛❧ ♠✐✲ ❝r♦s❝♦♣❡✱ ✐❢ t❤❡ ♠✐❝r♦s❝♦♣❡ ✐s ❞❡❢♦❝✉s❡❞✳ ■♥ ❢❛❝t✱ ❛ ❞❡❢♦❝✉s❡❞ ❜r✐❣❤t✲✜❡❧❞ ♦♣t✐❝❛❧ ♠✐❝r♦s❝♦♣❡ ✐s ❡q✉✐✈❛❧❡♥t t♦ ❛ ♣❤❛s❡ ❝♦♥tr❛st ♠✐❝r♦s❝♦♣❡✱ ♣r❡s❡♥t✐♥❣ ❛❞✈❛♥t❛❣❡s ♦✈❡r t❤❡ ❝♦♥✈❡♥t✐♦♥❛❧ ♦♥❡✱ ❛s ✐t ✇✐❧❧ ❜❡ ❞✐s❝✉ss❡❞ ✐♥ t❤✐s t❤❡s✐s✳ ❉❡❢♦❝✉s✐♥❣ ❝❛✉s❡s ❛ ♣❤❛s❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ tr❛♥s♠✐tt❡❞ ❧✐❣❤t ✭♥♦♥✲❞✐✛r❛❝t❡❞✮ ❛♥❞ t❤❡ ❧✐❣❤t ❞✐✛r❛❝t❡❞ ❜② t❤❡ ♣❤❛s❡ ♦❜❥❡❝t✱ ✇❤✐❝❤ ✇❤❡♥ ❝♦♠❜✐♥❡❞ ❛t t❤❡ ❞❡t❡❝t✐♦♥ ♣❧❛♥❡ ❞✉❡ t♦ ❧✐❣❤t ✐♥t❡r❢❡✲ r❡♥❝❡✱ r❡♥❞❡rs t❤❡ ♦❜❥❡❝t ✈✐s✐❜❧❡✱ ✇✐t❤ ❛♥ ✐♠❛❣❡ ❝♦♥tr❛st ❞✐✛❡r❡♥t t❤❛♥ ③❡r♦✳ ❚❤✐s ❡✛❡❝t ✇❛s ❞❡♠♦♥str❛t❡❞ ✐♥ ♦✉r ❧❛❜♦r❛t♦r② ✐♥ s❡✈❡r❛❧ ❛rt✐❝❧❡s ❛♥❞ ♣r❡✈✐♦✉s t❤❡s✐s ❬✶✕✼❪✳ ■♥ t❤✐s t❤❡s✐s✱ ✇❡ ✐♠♣r♦✈❡❞ ♦✉r ♦♣t✐❝❛❧ ♠♦❞❡❧ ♦❢ ❞❡❢♦❝✉s✐♥❣ ♠✐❝r♦s❝♦♣②✱ s✉❝❤ t❤❛t ✐ts ✈❛❧✐❞✐t② ✇❛s ❡①t❡♥❞❡❞ t♦ ❛♥② ❞❡❢♦❝✉s✐♥❣✱ ✐♥❝❧✉❞✐♥❣ ❛s②♠♣t♦t✐❝❛❧❧② ❧❛r❣❡ ❞❡❢♦❝✉s✐♥❣✱ ❛♥❞ ❢♦r ❧❛r❣❡r ❞✐✛r❛❝t✐♦♥ ✇❛✈❡♥✉♠❜❡rs✳ ❲❡ ♦❜t❛✐♥ t❤❡♦r❡t✐❝❛❧ ❡①♣r❡ss✐♦♥s ❢♦r t❤❡ ❝♦♥tr❛s ♦❢ ♣❤❛s❡ ♦❜❥❡❝ts ❝♦♠♣♦s❡❞ ❜② ♦♥❡ ❛♥❞ ❜② t✇♦ ♣❛r❛❧❧❡❧ ✐♥t❡r❢❛❝❡s✳ ■♥ t❤❡ ❧✐♠✐t ♦❢ s♠❛❧❧ ❞❡❢♦❝✉s✐♥❣ ❛♥❞ s♠❛❧❧ ❞✐✛r❛❝t✐♦♥ ✇❛✈❡♥✉♠❜❡rs✱ ❢r♦♠ t❤❡ t✐♠❡ ❛✈❡r❛✲ ❣❡❞ ❝♦♥tr❛st✱ ✇❡ ❝❛♥ ♦❜t❛✐♥ ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t t❤❡ ❡q✉✐❧✐❜r✐✉♠ s❤❛♣❡ ♦❢ ✭❘❇❈✮ r❡❞ ❜❧♦♦❞ ❝❡❧❧s ✭❡r②t❤r♦❝②t❡s✮✱ ❛s ♣r❡✈✐♦✉s❧② ❞❡♠♦♥str❛t❡❞ ❬✹❪✳ ❖✉r ♥❡✇ ❡①♣r❡ss✐♦♥s ❛r❡ ✐♠♣♦rt❛♥t t♦ ❡st❛❜❧✐s❤ ❛ r❡❧❛t✐♦♥s❤✐♣ ❜❡t✇❡❡♥ ❞❡❢♦❝✉s❡❞ ✐♠❛❣❡ ❝♦♥tr❛st ✢✉❝t✉❛t✐♦♥s ❛♥❞ s✉r❢❛❝❡ ❤❡✐❣❤t ✢✉❝t✉❛t✐♦♥s ♦♥ ❘❇❈s✳ ❲✐t❤ ♦✉r ♥❡✇ ♦♣t✐❝❛❧ ♠♦❞❡❧ ✇❡ s❤♦✇ t❤❛t ❜② s❝❛♥♥✐♥❣ t❤❡ ♠✐❝r♦s❝♦♣❡ ♦❜❥❡❝t✐✈❡ ❢♦❝❛❧ ♣❧❛♥❡ ♣♦s✐t✐♦♥ ✭zf✮✱ ❛♥❞ s✐♥❝❡ t❤❡ ❘❇❈ s✉r❢❛❝❡s ❛r❡ ❛t ❞✐✛❡r❡♥t ♣♦s✐t✐♦♥s ✐♥ r❡❧❛t✐♦♥ t♦ t❤❡ ③✲❛①✐s✱ t❤❡r❡ ❞✐✛r❛❝t❡❞ ❧✐❣❤t ❛r❡ ❛✛❡❝t❡❞ ❜② ❞✐✛❡r❡♥t ♣❤❛s❡ ❞✐✛❡r❡♥❝❡s✱ s✉❝❤ t❤❛t ✐t s✉r❢❛❝❡ ❝❛♥ ❜❡ ❞✐st✐♥❣✉✐s❤❡❞ ❜② ✉s✐♥❣ ❞❡❢♦❝✉s✐♥❣ ♠✐❝r♦s❝♦♣②✳ ❚❤✐s ❢❛❝t ❛❧❧♦✇s ✉s t♦ st✉❞② t❤❡ ♣r♦♣❡rt✐❡s ♦❢ ❡❛❝❤ ✐♥t❡r❢❛❝❡ s❡♣❛r❛t❡❧②✳ ❋♦r ✢✉❝t✉❛t✐♦♥s ✇✐t❤ ✇❛✈❡♥✉♠❜❡rs ❧❛r❣❡r t❤❛♥ ✶ µm−1✱ ♦♥❡
❝❛♥ ❛♣♣r♦①✐♠❛t❡ t❤❡ ❘❇❈ ❝❡♥tr❛❧ r❡❣✐♦♥ ❜② ♣❛r❛❧❧❡❧ ♣❧❛♥❡s✱ ❛♥❞ ❛♣♣❧② t❤❡ ♦♣t✐❝❛❧ ♠♦❞❡❧ ❢♦r t✇♦ ✐♥t❡r❢❛❝❡s ❞❡✈❡❧♦♣❡❞ ✐♥ t❤✐s t❤❡s✐s✳ ❇② ✉s✐♥❣ t❤❡ r❡❝❡♥t❧② ❞❡✈❡❧♦♣❡❞ ❡❧❛st✐❝ ♠♦❞❡❧ ❜② ❆✉t❤ ❡t ❛❧✳ ❬✽❪✱ ✇❤✐❝❤ t❛❦❡s ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ❝♦✉♣❧✐♥❣ ❜❡t✇❡❡♥ t❤❡ ❧✐♣✐❞ ❜✐❧❛②❡r ❛♥❞ t❤❡ s♣❡❝tr✐♥ ❝②t♦s❦❡❧❡t♦♥ ✭❛♥❞ ❛❧s♦ ✉s❡s t❤❡ ❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ ♣❛✲ r❛❧❧❡❧ ♣❧❛♥❡s ❢♦r t❤❡ ❘❇❈ s✉r❢❛❝❡s✮ ❛♥❞ ♦✉r ♦♣t✐❝❛❧ ♠♦❞❡❧✱ ✇❡ ❤❛✈❡ ♦❜t❛✐♥❡❞ ❛ ✈❡r② ❣♦♦❞ ✜t ❢♦r t❤❡ ❡①♣❡r✐♠❡♥t❛❧ ❞❛t❛✳ ❋r♦♠ t❤✐s ✜t ✇❡ ❤❛✈❡ ♦❜t❛✐♥❡❞ t❤❡ ✈❛❧✉❡s ❢♦r t❤❡ ❧✐♣✐❞ ❜✐❧❛②❡r ❝✉r✈❛t✉r❡ ♠♦❞✉❧✉s✱ ❢♦r t❤❡ ❝②t♦s❦❡❧❡t♦♥ s❤❡❛r ♠♦❞✉❧✉s ❛♥❞ ❢♦r t❤❡ ❡✛❡❝t✐✈❡ t❡♠♣❡r❛t✉r❡✳ ❚❤❡ ❘❇❈ ❤❡✐❣❤t ✢✉❝t✉❛t✐♦♥s ❛r❡ ♥♦t ♦♥❧② ♦❢ t❤❡r♠❛❧ ♦r✐❣✐♥✳ ❆♥♦t❤❡r ❝♦♥tr✐❜✉t✐♦♥ ❝♦♠❡s ❢r♦♠ t❤❡ ❝♦♥✈❡rs✐♦♥ ♦❢ ❝❤❡♠✐❝❛❧ ❡♥❡r❣② ✐♥t♦ ♠❡❝❤❛♥✐❝❛❧ ✇♦r❦ ❞r✐✈❡♥ ❜② ❆❚P ✭❛❞❡♥♦s✐♥❡ tr✐♣❤♦s♣❤❛t❡✱ t❤❡ ❝❡❧❧✬s ❝♦♠❜✉st✐❜❧❡✮ ❬✾✱✶✵❪✳ ❚❤❡s❡ ♥♦♥✲❡q✉✐❧✐❜r✐✉♠ ❡✛❡❝ts ❛r❡ ❧✉♠♣❡❞ ✐♥t♦ ❛ s✐♥❣❧❡ ♣❛r❛♠❡t❡r✱ ♥❛♠❡❧② t❤❡ ❡✛❡❝t✐✈❡ t❡♠♣❡r❛t✉r❡ ✐♥tr♦❞✉❝❡❞ ✐♥ ❛♥ ❛❞✲❤♦❝ ♠❛♥♥❡r✳ ❚❤✐s ❡✛❡❝t ✐s st✐❧❧ ❝♦♥t♦✈❡rs✐❛❧ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡ ❬✶✶❪✳ ❲❡ ❛❧s♦ st✉❞✐❡❞ t❤❡ r❡❧❛①❛t✐♦♥ ♦❢ ❘❇❈ ❤❡✐❣❤t ✢✉❝t✉❛t✐♦♥s t❤r♦✉❣❤ t❤❡ t✐♠❡ ❛✉t♦❝♦rr❡❧❛t✐♦♥ ❢✉♥❝t✐♦♥ ♦❢ ❝♦♥tr❛st ✢✉❝t✉❛t✐♦♥s✳ ❚❤✐s r❡❧❛①❛t✐♦♥ ✐s ❞✐❝t❛✲ t❡❞ ❜② t❤❡ ❡❧❛st✐❝✐t② ♦❢ t❤❡ ❧✐♣✐❞ ❜✐❧❛②❡r ❛♥❞ t❤❡ s♣❡❝tr✐♥ ❝②t♦s❦❡❧❡t♦♥✱ ❛♥❞ ❜② t❤❡ ✢♦✇ ♦❢ t❤❡ ❝②t♦♣❧❛s♠ t❤r♦✉❣❤ t❤❡ ♥❛rr♦✇ ❣❛♣ ♦❢ ✇✐❞t❤ ❞ ∼ ✷✵ t♦ ✸✵ nm✱ ❜❡t✇❡❡♥ t❤❡ ❜✐❧❛②❡r ❛♥❞ t❤❡ ❝②t♦s❦❡❧❡t♦♥✳ ❋r♦♠ t❤❡ ✜t ♦❢ t❤✐s t❤❡♦r② t♦ ♦✉r ❞❛t❛✱ ✇❡ ♦❜t❛✐♥❡❞ ❛ ❣❛♣✲✇✐❞t❤ d = 21±1 nm✳ ❲❡ s❤♦✇❡❞ t❤❛t ❞❡❢♦❝✉s✐♥❣ ♠✐❝r♦s❝♦♣② ✐s ❛♥ ✉s❡❢✉❧
❛♥❞ tr✉st❛❜❧❡ t❡❝❤♥✐q✉❡ t♦ st✉❞② ❤❡✐❣❤t ♣r♦✜❧❡s ❛♥❞ st❛t✐❝ ❛♥❞ ❞②♥❛♠✐❝ r♦✉❣❤♥❡ss ♦❢ ✐♥t❡r❢❛❝❡s ✐♥ ❛ tr❛♥s♣❛r❡♥t ♠✉❧t✐❧❛②❡r❡❞ ♠❛t❡r✐❛❧✱ ❧✐❦❡ ♠❡♠❜r❛♥❡s ♦❢ ❧✐✈✐♥❣ ❝❡❧❧s✳
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❖ ❡st✉❞♦ ❞❡ s✐st❡♠❛s ❜✐♦❧ó❣✐❝♦s ❞❡s❞❡ ❛ ❡s❝❛❧❛ ❞❡ t❛♠❛♥❤♦s ♠♦❧❡❝✉❧❛r❡s (nm)
❛té ❛ ❡s❝❛❧❛ ❞❡ t❛♠❛♥❤♦s ❞❛s ❝é❧✉❧❛s (µm) t❡♠ s❡ ❜❡♥❡✜❝✐❛❞♦ ❞❛s ✈ár✐❛s té❝♥✐❝❛s
❞❡ ♠✐❝r♦s❝♦♣✐❛✱ ❝♦♠♦ ❛ ♠✐❝r♦s❝♦♣✐❛ ❡❧❡trô♥✐❝❛ ✭❡s❝❛❧❛ nm✮ ❡ ❛s ✈ár✐❛s té❝♥✐❝❛s ❞❡ ♠✐❝r♦s❝♦♣✐❛ ó♣t✐❝❛ ✭❡s❝❛❧❛ µm✮✳ ❆ ❧✐♥❤❛ ❞❡ ♣❡sq✉✐s❛ ❞♦ ♥♦ss♦ ❧❛❜♦r❛tór✐♦ ♥❛ ár❡❛ ❞❡ ❋ís✐❝❛ ❞❡ ❙✐st❡♠❛s ❇✐♦❧ó❣✐❝♦s t❡♠ s❡ ❞❡❞✐❝❛❞♦ ❛♦ ❡st✉❞♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ❡❧ás✲ t✐❝❛s ❡ ♠♦t✐❧✐❞❛❞❡ ❞❡ ❝é❧✉❧❛s✱ ❛tr❛✈és ❞❛ ♠❡❞✐❞❛ ❞❛s ✢✉t✉❛çõ❡s ❞✐♥â♠✐❝❛s ❡♠ s✉❛s s✉♣❡r❢í❝✐❡s✱ ❝✉❥♦s ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♦♥❞❛ ❞❡ ✐♥t❡r❡ss❡ s❡ ❡♥❝♦♥tr❛♠ ♥❛ ❡s❝❛❧❛ ❞❡ µm ❡✱ ♣♦rt❛♥t♦✱ ♣♦❞❡♠ s❡r ❡st✉❞❛❞❛s ❝♦♠ ♠✐❝r♦s❝♦♣✐❛ ó♣t✐❝❛✳ ◆♦ ❝❛s♦ ❞❡ ♠✐❝r♦✲ s❝♦♣✐❛ ó♣t✐❝❛ ❞❡st❛❝❛♠✲s❡ ❛s té❝♥✐❝❛s ❞❡ ✢✉♦r❡s❝ê♥❝✐❛ ✭❡s♣❡❝✐❛❧♠❡♥t❡ ♠✐❝r♦s❝♦♣✐❛ ❝♦♥❢♦❝❛❧✮✱ ❝♦♥tr❛st❡ ❞❡ ❢❛s❡ ❡ ❉■❈ ✭❞✐✛❡r❡♥t✐❛❧ ❝♦♥tr❛st ♠✐❝r♦s❝♦♣②✱ ♦✉ ♠✐❝r♦s❝♦✲ ♣✐❛ ❞❡ ❝♦♥tr❛st❡ ❞✐❢❡r❡♥❝✐❛❧✮✱ q✉❡ sã♦ ❜❛st❛♥t❡ ✉s❛❞❛s ♣❛r❛ ♦ ❡st✉❞♦ ❞❡ ❜✐♦❧♦❣✐❛ ❝❡❧✉❧❛r ❬✶✷✱✶✸❪✳ ❍♦❥❡ ❥á ❡①✐st❡ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❣r❛♥❞❡ ❞❡ ❝♦r❛♥t❡s ✢✉♦r❡s❝❡♥t❡s q✉❡ s❡ ❧✐❣❛♠ ❡s♣❡❝✐✜❝❛♠❡♥t❡ ♥❛s ✈ár✐❛s ♣r♦t❡í♥❛s ❞❛s ❝é❧✉❧❛s q✉❡ s❡ q✉❡r ❡st✉❞❛r✱ q✉❡ ♣❡r♠✐t❡ ❛ ✈✐s✉❛❧✐③❛çã♦ ❞❡ ♣❛rt❡s ❡s♣❡❝í✜❝❛s ❞❛s ❝é❧✉❧❛s ♦♥❞❡ ❛q✉❡❧❛s ♣r♦t❡í♥❛s s❡ ❧♦❝❛❧✐③❛♠ ❬✶✸❪✳ P❛r❛ ♠✐❝r♦s❝ó♣✐♦s ❝♦♥✈❡♥❝✐♦♥❛✐s ❞❡ ✢✉♦r❡s❝ê♥❝✐❛✱ ✉♠❛ ❣r❛♥❞❡ q✉❛♥✲ t✐❞❛❞❡ ❞❡ ❝♦r❛♥t❡s ❞❡✈❡ s❡r ❛❞✐❝✐♦♥❛❞❛ às ❝é❧✉❧❛s ♣❛r❛ ✈✐s✉❛❧✐③❛çã♦✱ ❡ t❛❧ ❢❛t♦ ♣♦❞❡ ❛❧t❡r❛r ❛❧❣✉♠❛s ❞❛s ♣r♦♣r✐❡❞❛❞❡s ❞❛ ❝é❧✉❧❛✳ ❆s ♠✐❝r♦s❝♦♣✐❛s ó♣t✐❝❛s q✉❡ ✉s❛♠ ❡❢❡✐t♦s ó♣t✐❝♦s ♥ã♦✲❧✐♥❡❛r❡s✱ ❝♦♠♦ ❛ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ✷✲❢ót♦♥s ♣♦r ❡①❡♠♣❧♦✱ ♦❢❡r❡❝❡♠ ❣r❛♥❞❡ ♣♦t❡♥❝✐❛❧ ❞❡ ❡st✉❞♦ ✉♠❛ ✈❡③ q✉❡ s❡ ♣♦❞❡ ✉s❛r ❧✉③ ✐♥❢r❛✲✈❡r♠❡❧❤❛✱ q✉❡ ❞❛♥✐✜❝❛ ♠❡✲ ♥♦s ❛s ❝é❧✉❧❛s ❬✶✸❪✳ ◆♦ ❡♥t❛♥t♦✱ ❝♦r❛♥t❡s ✢✉♦r❡s❝❡♥t❡s sã♦ ❛✐♥❞❛ ♥❡❝❡ssár✐♦s ♣❛r❛ ✈✐s✉❛❧✐③❛çã♦✳ P❛r❛ ✈✐s✉❛❧✐③❛çã♦ ❞❛s ♠❡♠❜r❛♥❛s ❞❛s ❝é❧✉❧❛s ❛s té❝♥✐❝❛s ❞❡ ❝♦♥tr❛st❡ ❞❡ ❢❛s❡ ❡ ❉■❈ sã♦ ❜❛st❛♥t❡ ♣♦♣✉❧❛r❡s ❡ ❢❛③❡♠ ♣❛rt❡ ❞❛ ❣r❛♥❞❡ ♠❛✐♦r✐❛ ❞♦s ♠✐❝r♦s❝ó✲
♣✐♦s ✉s❛❞♦s ♣♦r ❜✐ó❧♦❣♦s ❝❡❧✉❧❛r❡s✳ ❊st❛s té❝♥✐❝❛s sã♦ r❡q✉❡r✐❞❛s ✉♠❛ ✈❡③ q✉❡ ❛ ❛❜s♦rçã♦ ❞❛ ❧✉③ ✈✐sí✈❡❧ ♣❡❧❛s ♠❡♠❜r❛♥❛s ❞❛s ❝é❧✉❧❛s é ♠✉✐t♦ ♣❡q✉❡♥❛✱ ✐♠♣♦ss✐❜✐❧✐✲ t❛♥❞♦ s✉❛ ✈✐s✉❛❧✐③❛çã♦ ♣♦r ✉♠ ♠✐❝r♦s❝ó♣✐♦ ❝♦♥✈❡♥❝✐♦♥❛❧ ♦♣❡r❛♥❞♦ ❡♠ ❝❛♠♣♦✲❝❧❛r♦✳ ❆❧é♠ ❞✐st♦✱ ❛ ❞✐❢❡r❡♥ç❛ ❞❡ í♥❞✐❝❡ ❞❡ r❡❢r❛çã♦ ❡♥tr❡ ❛s ♠❡♠❜r❛♥❛s ❡ ♦ ♠❡✐♦ é ♠✉✐t♦ ♣❡q✉❡♥❛ ✭❞❛ ♦r❞❡♠ ❞❡ 5%✮ ❡ s♦♠❡♥t❡ té❝♥✐❝❛s ❞❡ ✐♥t❡r❢❡rê♥❝✐❛ ❧✉♠✐♥♦s❛✱ s❡r✐❛♠ ❝❛✲
♣❛③❡s ❞❡ tr❛♥s❢♦r♠❛r ♣❡q✉❡♥❛s ✈❛r✐❛çõ❡s ♥❛ ❢❛s❡ ❞❛ ❧✉③ ❡♠ ✈❛r✐❛çõ❡s ♠❡♥s✉rá✈❡✐s ❞❡ ✐♥t❡♥s✐❞❛❞❡ ❧✉♠✐♥♦s❛✳ ❊st❛s ♠❡♠❜r❛♥❛s s❡r✐❛♠ ❡♠ ♣r✐♥❝í♣✐♦ ✐♠♣♦ssí✈❡✐s ❞❡ s❡r❡♠ ♦❜s❡r✈❛❞❛s ❝♦♠ ✉♠ ♠✐❝r♦s❝ó♣✐♦ ❝♦♥✈❡♥❝✐♦♥❛❧ ♦♣❡r❛♥❞♦ ❡♠ ❝❛♠♣♦✲❝❧❛r♦✳ ◆❛ ár❡❛ ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♥♦✈❛s ♠✐❝r♦s❝♦♣✐❛s ó♣t✐❝❛s t❡♠✲s❡ ❞❛❞♦ ê♥❢❛s❡ ❡s♣❡❝✐❛❧ àq✉❡✲ ❧❛s q✉❡ ♣♦❞❡♠ ♠❡❧❤♦r❛r ❛ r❡s♦❧✉çã♦ ó♣t✐❝❛ ✭✈❡♥❝❡♥❞♦ ♦ ❧✐♠✐t❡ ❞❡ ❞✐❢r❛çã♦✮ ❝♦♠♦ ❛s ♣r♦♣♦r❝✐♦♥❛❞❛s ♣❡❧♦s ♠✐❝r♦s❝ó♣✐♦s ❞❡ ❝❛♠♣♦✲♣ró①✐♠♦ ✭♥❡❛r✲✜❡❧❞ ♠✐❝r♦s❝♦♣❡s✮✱ q✉❡ ❝♦♥s❡❣✉❡♠ ✉♠❛ r❡s♦❧✉çã♦ ❝♦♠ ❧✉③ ✈✐sí✈❡❧ ❞❡ ❛té ✺✵ nm✳ ❆ss✐♠✱ ♣❛r❡❝❡ q✉❡ ❡♠ t❡r♠♦s ❞❡ ♠✐❝r♦s❝♦♣✐❛ ó♣t✐❝❛✱ ❝♦♥tr❛st❡ ❞❡ ❢❛s❡ ❡ ❉■❈ ❡stã♦ ❜❡♠ ❡st❛❜❡❧❡❝✐❞❛s ❡ ❛t✐♥❣✐r❛♠ s❡✉s ❧✐♠✐t❡s✱ ❡♥q✉❛♥t♦ q✉❡ ♣r♦❣r❡ss♦s tê♠ s✐❞♦ ❢❡✐t♦s ❝♦♠ ❛s ♠✐❝r♦s❝♦♣✐❛s ❝♦♥❢♦❝❛✐s✱ ❞❡ ❝❛♠♣♦✲♣ró①✐♠♦ ❡ ❛s ♥ã♦✲❧✐♥❡❛r❡s ❞❡ ♠✉❧t✐✲❢ót♦♥✳ ■r❡♠♦s ♠♦str❛r q✉❡ ❛ ♥♦ss❛ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❞❡s❢♦❝❛❧✐③❛çã♦ é t❛♠❜é♠ ✉♠❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❝♦♠♣❡t✐t✐✈❛ ♥❡st❛ ár❡❛✳ ❈❛❞❛ té❝♥✐❝❛ ❞❡ ♠✐❝r♦s❝♦♣✐❛ s❡ ❛❞❛♣t❛ ♠❡❧❤♦r ❛ ✉♠ ❞❛❞♦ t✐♣♦ ❞❡ ❛♣❧✐❝❛✲ çã♦✳ ❊♠ tr❛❜❛❧❤♦s r❡❝❡♥t❡s ♦ ♥♦ss♦ ❣r✉♣♦ ♠♦str♦✉ q✉❡ é ♣♦ssí✈❡❧ ♦❜s❡r✈❛r ♦❜❥❡t♦s tr❛♥s♣❛r❡♥t❡s ✉s❛♥❞♦ ✉♠ ♠✐❝r♦s❝ó♣✐♦ ♦♣❡r❛♥❞♦ ❡♠ ❝❛♠♣♦ ❝❧❛r♦✱ s❡ ❡st❡ ♠✐❝r♦s❝ó✲ ♣✐♦ ❡st✐✈❡r ❞❡s❢♦❝❛❧✐③❛❞♦ ❬✶✕✺❪✳ ➱ s✉r♣r❡❡♥❞❡♥t❡ ♦ ❝♦♥tr❛st❡ q✉❡ ♣♦❞❡ s❡r ♦❜t✐❞♦ ❞❡ ❞❡❢♦r♠❛çõ❡s ♥❛ s✉♣❡r❢í❝✐❡ ❞❡ ♠❡♠❜r❛♥❛s tã♦ ✜♥❛s q✉❛♥t♦ ✶ µm ❡ ❝♦♠ ❞✐❢❡r❡♥✲ ç❛s ❞❡ í♥❞✐❝❡ ❞❡ r❡❢r❛çã♦ ❞❡ 0,05✱ ❝♦♠♦ ♠♦str❛❞♦ ♥❛ ✜❣✉r❛ ✶✳✶✱ q✉❡ é ❛ ✐♠❛❣❡♠
❞❡ ✉♠ ♠❛❝ró❢❛❣♦ ❧✐❣❡✐r❛♠❡♥t❡ ❞❡s❢♦❝❛❧✐③❛❞♦✳ ◆❛ ✜❣✉r❛ ✶✳✷ ❡stá ❛ ✐♠❛❣❡♠ ❞❡ ✉♠❛ ❤❡♠á❝✐❛✱ q✉❡ ❞❡✈❡r✐❛ s❡r ✐♥✈✐sí✈❡❧ ✭♣❛r❛ ❛ ❧✉③ ✈❡r♠❡❧❤❛ q✉❡ ❡stá s❡♥❞♦ ✉s❛❞❛ ♥❛ ✐❧✉♠✐♥❛çã♦✮ s❡ ♥ã♦ ❢♦ss❡ ♦ ❡❢❡✐t♦ ❞❡ ❞❡s❢♦❝❛❧✐③❛çã♦✳ ❆ ❋ís✐❝❛ ❜ás✐❝❛ ❡♥✈♦❧✈✐❞❛ é ❛ s❡❣✉✐♥t❡✿ ❛ ❧✉③ ❛♦ ❛tr❛✈❡ss❛r ♦ ♦❜❥❡t♦ tr❛♥s♣❛r❡♥t❡ é ❞✐❢r❛t❛❞❛ ♣❡❧❛s ❞❡❢♦r♠❛çõ❡s ♥❛ ♠❡♠❜r❛♥❛✳ ❆ ❞❡s❢♦❝❛❧✐③❛çã♦ ✐♥tr♦❞✉③ ✉♠❛ ❞✐❢❡r❡♥ç❛ ❞❡ ❢❛s❡ ❡♥tr❡ ❛ ❧✉③ ❞✐❢r❛t❛❞❛ ❡ ❛ ❧✉③ tr❛♥s♠✐t✐❞❛ ✭♥ã♦ ❞✐❢r❛t❛❞❛✮✱ q✉❡ ❞❡♣❡♥❞❡ ❞❛ ❞❡s❢♦❝❛❧✐③❛çã♦✳ ❆ ❧✉③ ❞✐❢r❛t❛❞❛ ❡ ❛ tr❛♥s♠✐t✐❞❛✱ ✈✐♥❞❛ ❞❡ ✉♠ ♦❜❥❡t♦ ❞❡s❢♦❝❛❧✐③❛❞♦✱ ❛♦ s❡ r❡❝♦♠❜✐♥❛r❡♠ ♥♦ ♣❧❛♥♦ ❞❡ ❞❡t❡çã♦ ✭♥♦ ❝❛s♦ ♥❛ ❝â♠❡r❛ ❞❡ ✈í❞❡♦✮✱ ✐♥t❡r❢❡r❡♠ ❞❛♥❞♦ ♦r✐❣❡♠ às ✈❛r✐❛çõ❡s ♥♦ ❝♦♥tr❛st❡ ❞❛ ✐♠❛❣❡♠ ♦❜s❡r✈❛❞❛✳ P❛r❛ ♦ ♦❜❥❡t♦ ❡♠ ❢♦❝♦✱ ♥❡♥❤✉♠❛ ❞✐❢❡r❡♥ç❛ ❞❡ ❢❛s❡ ❡♥tr❡ ❛ ❧✉③ ❞✐❢r❛t❛❞❛ ❡ tr❛♥s♠✐t✐❞❛ é ✐♥tr♦❞✉③✐❞❛✱ ❡ ♦ ♦❜❥❡t♦ ♣❡r♠❛♥❡❝❡ ✐♥✈✐sí✈❡❧✳ ❆ss✐♠ ♦ ♠✐❝r♦s❝ó♣✐♦ ❞❡s❢♦❝❛❧✐③❛❞♦ ♦♣❡r❛♥❞♦ ❡♠ ❝❛♠♣♦ ❝❧❛r♦ é ✉♠❛ ❢♦r♠❛ ❞❡ ♠✐✲
❝r♦s❝ó♣✐♦ ❞❡ ❝♦♥tr❛st❡ ❞❡ ❢❛s❡✳ ❖ ♠♦❞❡❧♦ ó♣t✐❝♦ ❞♦ ♠✐❝r♦s❝ó♣✐♦ ❞❡s❢♦❝❛❧✐③❛❞♦ ✉s❛❞♦ ♥❛s t❡s❡s ❬✻✱✼❪ ❡ tr❛❜❛❧❤♦s ❛♥t❡r✐♦r❡s ❬✶✕✺❪ ❞♦ ♥♦ss♦ ❣r✉♣♦ é ✈á❧✐❞♦ ♣❛r❛ ♣❡q✉❡♥❛s ❞❡s❢♦❝❛❧✐③❛çõ❡s✳ ◆❡st❛ t❡s❡ ♠❡❧❤♦r❛♠♦s ❡st❡ ♠♦❞❡❧♦ ❡ ♦❜t✐✈❡♠♦s ❡①♣r❡ssõ❡s t❡ór✐❝❛s q✉❡ ♥♦s ♣❡r♠✐t❡♠ ✐♥t❡r♣r❡t❛r ❛s ✐♠❛❣❡♥s ❞❡ ♦❜❥❡t♦s ❛r❜✐tr❛r✐❛♠❡♥t❡ ❞❡s❢♦❝❛❧✐③❛❞♦s✳ ❈♦♠ ❡st❡ ♥♦✈♦ ♠♦❞❡❧♦ t❡ór✐❝♦✱ ♥ós ♠♦str❛r❡♠♦s ❝❧❛r❛♠❡♥t❡ q✉❡ ❡①✐st❡♠ ✈❛♥t❛❣❡♥s ♥♦ ✉s♦ ❞❛ ♥♦ss❛ té❝♥✐❝❛ ❞❡”♠✐❝r♦s❝♦♣✐❛ ❞❡ ❞❡s❢♦❝❛❧✐③❛çã♦”q✉❛♥❞♦ ❝♦♠♣❛r❛❞❛ ❝♦♠
❛s ♠✐❝r♦s❝♦♣✐❛s ❞❡ ❝♦♥tr❛st❡ ❞❡ ❢❛s❡ ❡ ❉■❈✳ ❯♠❛ ❞❛s ❣r❛♥❞❡s ✈❛♥t❛❣❡♥s é q✉❡ ❡♠ ✉♠ ♠❛t❡r✐❛❧ tr❛♥s♣❛r❡♥t❡ ❡♠ ♠✉❧t✐❝❛♠❛❞❛s✱ ❝♦♥s❡qü❡♥t❡♠❡♥t❡ ❝♦♠ ♠ú❧t✐♣❧❛s ✐♥t❡r✲ ❢❛❝❡s✱ ♣♦❞❡♠♦s ❞✐s❝r✐♠✐♥❛r ❛ ❝♦♥tr✐❜✉✐çã♦ ✭r✉❣♦s✐❞❛❞❡ ❡stát✐❝❛ ❡ ❞✐♥â♠✐❝❛✮ ❞❡ ❝❛❞❛ ✐♥t❡r❢❛❝❡ s❡♣❛r❛❞❛♠❡♥t❡ ♥♦ ❝♦♥tr❛st❡ ❞❛ ✐♠❛❣❡♠✱ ❢❛③❡♥❞♦ ✉♠❛ ✈❛rr❡❞✉r❛ ❞❛ ♣♦s✐çã♦ ❞♦ ♣❧❛♥♦ ❢♦❝❛❧ ❛tr❛✈és ❞❛ ❛♠♦str❛✳ ❈♦♠♦ ❛s ❞✐stâ♥❝✐❛s ❞♦ ♣❧❛♥♦ ❢♦❝❛❧ ❞❛ ♦❜❥❡t✐✈❛ às ✐♥t❡r❢❛❝❡s sã♦ ❞✐❢❡r❡♥t❡s✱ ❛ ❧✉③ ❞✐❢r❛t❛❞❛ ♣♦r ❡st❛s ✐♥t❡r❢❛❝❡s ❡st❛rã♦ ❛❢❡t❛❞❛s ♣♦r ❢❛s❡s ❞✐❢❡r❡♥t❡s ❡ ❡♥tã♦ ♣♦ssí✈❡✐s ❞❡ s❡r❡♠ ❞✐s❝r✐♠✐♥❛❞❛s✳
❋✐❣✉r❛ ✶✳✶✿ ■♠❛❣❡♠ ❞❡s❢♦❝❛❧✐③❛❞❛ ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❝❛♠♣♦✲❝❧❛r♦ ❞❡ ✉♠ ♠❛❝r♦❢á❣♦✳
❋✐❣✉r❛ ✶✳✷✿ ■♠❛❣❡♠ ❞❡s❢♦❝❛❧✐③❛❞❛ ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❝❛♠♣♦✲❝❧❛r♦ ❞❡ ✉♠❛ ❤❡♠á❝✐❛✳
❆ té❝♥✐❝❛ ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❞❡s❢♦❝❛❧✐③❛çã♦ s❡rá ❡♥tã♦ ❛♣❧✐❝❛❞❛ ❛♦ ❡st✉❞♦ ❞❛s ✢✉t✉❛çõ❡s ♥❛s s✉♣❡r❢í❝✐❡s ❞❡ ❤❡♠á❝✐❛s✳ ❱ár✐♦s ♠♦❞❡❧♦s ❡❧ást✐❝♦s ♣❛r❛ ❤❡♠á❝✐❛s ❡①✐s✲ t❡♠ ♥❛ ❧✐t❡r❛t✉r❛✳ ❊♠❜♦r❛ ♦ ♣r✐♠❡✐r♦ ♠♦❞❡❧♦ ♣❛r❛ ❡①♣❧✐❝❛r ❛s ✢✉t✉❛çõ❡s ♥❛s s✉♣❡r✲ ❢í❝✐❡s ❞❡ ❤❡♠á❝✐❛s t❡♥❤❛ s✐❞♦ ❢❡✐t♦ ♣♦r ❇r♦❝❤❛r❞ ❡ ▲❡♥♥♦♥ ❬✶✹❪ ❡♠ ✶✾✼✺✱ ♦ ❛ss✉♥t♦ é ❛✐♥❞❛ ❜❛st❛♥t❡ ❝♦♥tr♦✈❡rs♦ ❡ ✐♥t❡r❡ss❛♥t❡ ♣❛r❛ t❡r ❛♣❛r❡❝✐❞♦ r❡❝❡♥t❡♠❡♥t❡ ❡♠ ✈ár✐♦s P❤②s✐❝❛❧ ❘❡✈✐❡✇ ▲❡tt❡rs ❡ ✈ár✐♦s P❤②s✐❝❛❧ ❘❡✈✐❡✇ ❊ ❬✽✱✶✺✕✶✾❪✳ ▼♦str❛r❡♠♦s q✉❡ ❛ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❞❡s❢♦❝❛❧✐③❛çã♦ é ♠✉✐t♦ ❡❢❡t✐✈❛ ♥❡st❛ ár❡❛ ❡✱ ❝♦♠ s❡♥s✐❜✐❧✐❞❛❞❡ s✉✜✲ ❝✐❡♥t❡ ♣❛r❛ q✉❡ ♣♦ss❛♠♦s ♠❡❞✐r ✢✉t✉❛çõ❡s ♥❛♥♦♠étr✐❝❛s ❞❛ ❛❧t✉r❛ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ❤❡♠á❝✐❛s✳ P♦❞❡♠♦s ♠❡❞✐r ❛ ❝✉r✈❛t✉r❛ ♠é❞✐❛ ❧♦❝❛❧ ❞❛s s✉♣❡r❢í❝✐❡s ❞❛s ❤❡♠á❝✐❛s✱ q✉❡ s❡rá ✐♠♣♦rt❛♥t❡ ♣❛r❛ ❝♦♠♣❛r❛çã♦ ❝♦♠ ♦ ♠♦❞❡❧♦ t❡ór✐❝♦ r❡❝❡♥t❡ ❞❡ ❆✉t❤ ❡t ❛❧✳ ❬✽❪ ❡ ❢❛③❡r ✉♠❛ r❡❝♦♥str✉çã♦ ✸✲❉ ❞❛ s✉♣❡r❢í❝✐❡ ❞❛ ❤❡♠á❝✐❛✳ ❖✉tr❛s té❝♥✐❝❛s ❞❡s❡♥✈♦❧✈✐❞❛s r❡❝❡♥t❡♠❡♥t❡ ❝♦♠♦ ❛ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❍✐❧❜❡rt ❬✶✾❪ ❞ã♦ ✐♥❢♦r♠❛çã♦ s♦❜r❡ ❛s ✢✉t✉❛çõ❡s ❞❛ ❡s♣❡ss✉r❛ ❞❛ ❤❡♠á❝✐❛ ❡ ♥ã♦ ❞❛s s✉♣❡r❢í❝✐❡s ✐♥❞✐✈✐❞✉❛✐s ❝♦♠♦ ❛ ♥♦ss❛✳ ❯♠❛ ♦✉tr❛ té❝♥✐❝❛ q✉❡ é ✉s❛❞❛ ♥♦ ❡st✉❞♦ ❞❡ ✢✉t✉❛çõ❡s ❞❡ ♠❡♠❜r❛♥❛ ❡ ❢♦✐ ✉s❛❞❛ ❡♠ ❤❡♠á❝✐❛s é ❛ té❝♥✐❝❛ ❞❡ ❘■❈▼ ✭r❡✢❡❝t✐♦♥ ✐♥t❡r❢❡r♦♠❡tr② ❝♦♥tr❛st ♠✐❝r♦s❝♦♣②✮ ❬✷✵❪✱ q✉❡ s❡ ✈❛❧❡ ❞❛ ✐♥t❡r❢❡rê♥❝✐❛ ❡♥tr❡ ❛ ❧✉③ r❡✢❡t✐❞❛ ♥❛ s✉♣❡r❢í❝✐❡ ❞❡ ❜❛✐①♦ ❞❛ ❤❡♠á❝✐❛ ❡ ❛ r❡✢❡t✐❞❛ ♥❛ ❧❛♠í♥✉❧❛✱ ♦r✐❣✐♥❛♥❞♦ ✉♠ ♣❛❞rã♦ ❞✐♥â♠✐❝♦ ❞❡ ✐♥t❡r❢❡rê♥❝✐❛✳ ❊stá té❝♥✐❝❛ t❡♠ ❛ ❞❡s✈❛♥t❛❣❡♠ q✉❡ ❛ ♠❡♠❜r❛♥❛ ♠❡❞✐❞❛ t❡♠ q✉❡ ❡st❛r ❡♠ ❝♦♥t❛t♦ ❝♦♠ ❛ ❧❛♠í♥✉❧❛ ❞♦ ♠✐❝r♦s❝ó♣✐♦ ❡ ♥ã♦ s❡ ♦❜s❡r✈❛ ❛ ♦✉tr❛ s✉♣❡r❢í❝✐❡ ❧✐✈r❡✳ ◆❡st❡ ❛s♣❡❝t♦✱ ❡st❛ t❡s❡ t❡♠ ❝♦♠♦ ✉♠ ❞♦s ♦❜❥❡t✐✈♦s ❞❡♠♦♥str❛r q✉❡ ❛ ” ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❞❡s❢♦❝❛❧✐③❛çã♦ ” é
✉♠❛ ♠✐❝r♦s❝♦♣✐❛ ó♣t✐❝❛ ❝♦♠ ✈❛♥t❛❣❡♥s ❡♠ r❡❧❛çã♦ às té❝♥✐❝❛s ❝♦♥✈❡♥❝✐♦♥❛✐s ❡ ♦✉tr❛s ♠❛✐s r❡❝❡♥t❡s q✉❡ tê♠ s✐❞♦ ✉s❛❞❛s ♥♦ ❡st✉❞♦ ❞❡ ♠♦t✐❧✐❞❛❞❡ ❞❡ ❝é❧✉❧❛s ❡ ❞❡ ✢✉t✉❛✲
çõ❡s ❞✐♥â♠✐❝❛s ❡♠ ♠❡♠❜r❛♥❛s ❡ ✐♥t❡r❢❛❝❡s✳ ❊st❛ t❡s❡ ❡stá ❞✐✈✐❞✐❞❛ ❞❛ ♠❛♥❡✐r❛ ❝♦♠♦ ♠♦str❛♠♦s ❛ s❡❣✉✐r✳
❈❛♣ít✉❧♦ ✶✿ ■♥tr♦❞✉çã♦✳
❈❛♣ít✉❧♦ ✷✿ ▼✐❝r♦s❝♦♣✐❛ ❞❡ ❉❡s❢♦❝❛❧✐③❛çã♦✳
❖ ♦❜❥❡t✐✈♦ ❞❡st❡ ❝❛♣ít✉❧♦ é ♦ ❞❡ ❛♣r❡s❡♥t❛r ❝♦♠ ❞❡t❛❧❤❡s t♦❞❛ ❛ t❡♦r✐❛ ❞❡ ♠✐❝r♦s❝♦✲ ♣✐❛ ❞❡ ❞❡s❢♦❝❛❧✐③❛çã♦✱ ♣❛r❛ q✉❡ ✜❝❛ss❡ ❝♦♠♦ ✉♠❛ r❡❢❡rê♥❝✐❛ ❝♦♠♣❧❡t❛ ♣❛r❛ ♦s ❢✉t✉r♦s ❡st✉❞❛♥t❡s ❡ ♣❛r❛ ♦ ❧❛❜♦r❛tór✐♦✳ ◆♦ ♥♦ss♦ ♠♦❞❡❧♦ ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❞❡s❢♦❝❛❧✐③❛çã♦ é ✉s❛❞❛ ❛ ❛♣r♦①✐♠❛çã♦ ♣❛r❛①✐❛❧ ♣❛r❛ ♣r♦♣❛❣❛çã♦ ❞♦ ❡s♣❡❝tr♦ ❛♥❣✉❧❛r ❞❛ ❧✉③ ❞✐❢r❛✲ t❛❞❛✱ q✉❡ é ❡q✉✐✈❛❧❡♥t❡ à t❡♦r✐❛ ❡s❝❛❧❛r ❞❡ ❞✐❢r❛çã♦ ❞❡ ❋r❡s♥❡❧✱ ♦ q✉❡ ❢❛❝✐❧✐t❛ ❜❛st❛♥t❡ ❛ ♠❛♥✐♣✉❧❛çã♦ ❛❧❣é❜r✐❝❛ ❬✷✶✱✷✷❪✳ ❉❡❝✐❞✐♠♦s ❡♥tã♦ ♣❛rt✐r ❞♦ ♠❛✐s ❢✉♥❞❛♠❡♥t❛❧✱ ♦✉ s❡❥❛✱ ❞❛s ❊q✉❛çõ❡s ❞❡ ▼❛①✇❡❧❧✱ ❡ ❞❡s❡♥✈♦❧✈❡r t♦❞❛ ❛ t❡♦r✐❛ ó♣t✐❝❛ ❞❡ ❞❡s❢♦❝❛❧✐③❛çã♦✱ ♣❛r❛ ♦❜❥❡t♦s ❞❡ ❢❛s❡ ✭♦❜❥❡t♦s tr❛♥s♣❛r❡♥t❡s✮ ❝♦♠ ✉♠❛ ❡ ❞✉❛s ✐♥t❡r❢❛❝❡s✱ ❝♦♠ ❢á❝✐❧ ❣❡♥❡r❛❧✐③❛çã♦ ♣❛r❛ ✉♠ ♥ú♠❡r♦ q✉❛❧q✉❡r ❞❡❧❛s✳ ❚♦❞❛s ❛s ♣❛ss❛❣❡♥s ♠❛t❡♠át✐❝❛s sã♦ ❛♣r❡s❡♥t❛❞❛s ❡♠ ❜❛st❛♥t❡ ❞❡t❛❧❤❡✱ ♣♦r q✉❡stõ❡s ❞✐❞át✐❝❛s✱ ❡ ♣♦❞❡♠ s❡r ♣✉❧❛❞❛s ✉♠❛ ✈❡③ q✉❡ ♦s r❡s✉❧t❛❞♦s ♣r✐♥❝✐♣❛✐s ❡stã♦ ❞❡✈✐❞❛♠❡♥t❡ ❞❡st❛❝❛❞♦s ❞❡♥tr♦ ❞❡ ❝❛✐①❛s r❡✲ t❛♥❣✉❧❛r❡s✳ ❙❡rã♦ ❛♣r❡s❡♥t❛❞❛s ❝á❧❝✉❧♦s ♥✉♠ér✐❝♦s✱ ✉s❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡s❡♥✈♦❧✈✐❞♦✱ ♣❛r❛ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛ ✢✉t✉❛çã♦ q✉❛❞rát✐❝❛ ♠é❞✐❛ ❞♦ ❝♦♥tr❛st❡ ❞❛ ✐♠❛❣❡♠ ❞❡ ❤❡♠á❝✐❛s ❡♠ ❢✉♥çã♦ ❞❛ ♣♦s✐çã♦ ❞♦ ♣❧❛♥♦ ❢♦❝❛❧ ❞❛ ♦❜❥❡t✐✈❛✱ ✉s❛♥❞♦✲s❡ ❡s♣❡❝tr♦s ❞❡ ♣♦tê♥❝✐❛ ❡s♣❛❝✐❛❧ ❞❛ ❤❡♠á❝✐❛✱ ❛ s❡r❡♠ ❞✐s❝✉t✐❞♦s ♥♦s ♦✉tr♦s ❝❛♣ít✉❧♦s✳ ❊st❡s ❝á❧❝✉✲ ❧♦s ♥✉♠ér✐❝♦s s❡rã♦ ♠♦str❛❞❛s ♥❡st❡ ❝❛♣ít✉❧♦ ❡✱ ✉♠ ❛s♣❡❝t♦ ✐♥t❡r❡ss❛♥t❡✱ é q✉❡ ❡❧❛s ❢♦r❛♠ r❡❛❧✐③❛❞❛s ❝♦♠♦ ♣r❡✈✐sã♦ t❡ór✐❝❛ ❛♥t❡s ❞♦ ❡①♣❡r✐♠❡♥t♦ s❡r r❡❛❧✐③❛❞♦✳ ❱❡r❡♠♦s ♥❛ ❛♣r❡s❡♥t❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❛ ❡①❝❡❧❡♥t❡ ❝♦♥❝♦r❞â♥❝✐❛ ❡♥tr❡ t❡♦r✐❛ ❡ ❡①♣❡r✐♠❡♥t♦✳
❈❛♣ít✉❧♦ ✸✿ ❊str✉t✉r❛ ❞❛ ▼❡♠❜r❛♥❛ ❡ ❈✐t♦❡sq✉❡❧❡t♦ ❞❡ ❍❡♠á❝✐❛s ❡ ▼♦✲ ❞❡❧♦s ❞❡ ❊❧❛st✐❝✐❞❛❞❡✳
◆❡st❡ ❝❛♣ít✉❧♦ ✐♥tr♦❞✉③✐r❡♠♦s ♦s ❡❧❡♠❡♥t♦s ❜ás✐❝♦s ❡ ❞❡✜♥✐çõ❡s ♣❛r❛ s❡ ❡♥t❡♥❞❡r ❡❧❛st✐❝✐❞❛❞❡ ❞❡ ♠❛t❡r✐❛✐s ❡♠ ❣❡r❛❧ ❬✷✸❪✱ ❞❡ ♠❡♠❜r❛♥❛s ❡ ✐♥t❡r❢❛❝❡s ❬✷✹✱✷✺❪✳ ❙❡rã♦ ❞❡✲ ✜♥✐❞♦s ♦s ♠ó❞✉❧♦s ❡❧ást✐❝♦s ❞❡ ❝✉r✈❛t✉r❛ ❡ ❝✉r✈❛t✉r❛ ●❛✉ss✐❛♥❛✱ t❡♥sã♦ s✉♣❡r✜❝✐❛❧ ❡ ♣♦t❡♥❝✐❛❧ ❞❡ ❝♦♥✜♥❛♠❡♥t♦✳ ❙❡rã♦ ❞✐s❝✉t✐❞❛s ❛s ❞❡❢♦r♠❛çõ❡s ❡♠ s✉♣❡r❢í❝✐❡s ❜✐❞✐♠❡♥✲ s✐♦♥❛✐s ❝♦♠ ♦ ❛✉①í❧✐♦ ❞❡ ❝♦♥❝❡✐t♦s ❜ás✐❝♦s ❞❡ ❣❡♦♠❡tr✐❛ ❞✐❢❡r❡♥❝✐❛❧✳ ❉❡❞✉③✐r❡♠♦s ❛
