Qutb Kerr effekti, bo'ylanma Kerr effekti va Voigt effektining sxemasi
**Voigt effekti** magnito-optik hodisa bo'lib, optik faol muhitga tushgan chiziqli qutblangan yorug'likning doiraviy yoki elliptik qutblanib qolish hodisasidir.  Magnitlanishga (yoki magnitlanmagan material uchun qo'llaniladigan magnit maydonga ) chiziqli bog'liq bo'lgan Kerr yoki Faraday effekti kabi boshqa ko'plab magnito-optik effektlardan farqli o'laroq, Voigt effekti magnitlanish (yoki magnit maydon) kvadratiga proporsionaldir va normal sharoitda eksperimental ravishda kuzatish mumkin. Adabiyotlarda bu effeektning bir nechta hollari mavjudligi aytiladi va ular quyidagilardir: *Kotton-Mouton effekti* (fransuz olimlari Aime Kotton va Anri Mouton sharafiga), *Voigt effekti* (nemis olimi Voldemar Voigt sharafiga) va *yorug'likning chiziqli ikkilanib sinishi.* Voigt effekti magnitlanish vektoriga yoki magnit maydonga parallel( {\displaystyle n\_{\parallel }} ) va perpendikulyar {\displaystyle (n\_{\perp }} ) sindirish ko'rsatkichiga ega bo'lgan muhitda yorug'likning ikkilanib sinishidir.

Chiziqli qutblangan elektromagnit to'lqin uchun {\displaystyle {\vec {E\_{i}}}=(\cos \beta ,\,\sin \beta ,\,0)e^{-i\omega (t-n\_{1}z/c)}} va yassi qutblangan to'lqin uchun {\displaystyle {\vec {m}}=(\cos \phi ,\,\sin \phi ,\,0)}, aks ettirish geometriyasida aylanish ifodasi {\displaystyle \delta \beta } bu:


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{\displaystyle \delta \beta \_{r}={\frac {2\Delta n}{n\_{0}^{2}-1}}\sin[2(\phi -\beta )]}

{\displaystyle \delta \beta _{r}={\frac {2\Delta n}{n_{0}^{2}-1}}\sin[2(\phi -\beta )]}va transmission geometriyada:


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{\displaystyle \delta \beta \_{t}={\frac {B\_{1}+n\_{0}^{2}{\Big [}{\frac {2L\omega }{c}}(1+n\_{0})Q\_{i}Q\_{r}+Q\_{r}^{2}-Q\_{i}^{2}{\Big ]}}{n\_{0}(1+n\_{0})}},}

{\displaystyle \delta \beta _{t}={\frac {B_{1}+n_{0}^{2}{\Big [}{\frac {2L\omega }{c}}(1+n_{0})Q_{i}Q_{r}+Q_{r}^{2}-Q_{i}^{2}{\Big ]}}{n_{0}(1+n_{0})}},}bu yerda {\textstyle \Delta n={\frac {n\_{\parallel }-n\_{\perp }}{2}}} Voigt parametri ({\displaystyle Q=Q\_{i}+iQ\_{r}} (Kerr effekti bilan bir xil))ga qarab sindirish ko'rsatkichlarining farqidir, {\displaystyle n\_{0}} materialning sindirish ko'rsatkichi va {\displaystyle B\_{1}} Voigt effektiga bog'liq bo'lgan parametr va paramagnit materiallarda {\displaystyle M^{2}} yoki {\displaystyle (\mu \_{0}H)^{2}} ga proporsionaldir. 

Batafsil hisob-kitob va rasm quyidagi bo'limlarda keltirilgan.

Nazariya
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 Voigt effektini olish uchun ramka va koordinatalar tizimi. {\displaystyle {\vec {E}}\_{i}}, {\displaystyle {\vec {E}}\_{r}} va {\displaystyle {\vec {E}}\_{t}} tushgan, qaytgan va muhitni kesib o'tgan elektromagnit maydonni nazarda tutadi.
Boshqa magnito-optik effektlarda bo'lgani kabi, nazariya tizimning o'ziga xos qiymatlari va xos vektorlarini hisoblaydigan samarali dielektrik tensordan foydalangan holda standart usulda ishlab chiqilgan. Odatdagidek, bu tensorda magnito-optik hodisalar asosan diagonaldan tashqari elementlar bilan tavsiflanadi.

z yo'nalishi bo'yicha tarqaladigan hodisa tushuvchi to'lqin qutblanishi ko'rib chiqaylik: {\displaystyle {\vec {E\_{i}}}=(\cos \beta ,\,\sin \beta ,\,0)e^{-i\omega (t-n\_{1}z/c)}} elektr maydoni va bir xil tekislikda magnitlangan hol uchun {\displaystyle {\vec {m}}=(\cos \phi ,\,\sin \phi ,\,0)}, bu yerda {\displaystyle \phi } [100] kristallografik yo'nalishdan hisoblanadi.{\displaystyle {\vec {E\_{r}}}=(\cos \beta +\delta \beta ,\,\sin \beta +\delta \beta ,\,0)e^{-i\omega (t+n\_{1}z/c)}}, bu yerda {\displaystyle \delta \beta } - yorug'likning magnitlanish bilan bog'lanishi tufayli qutblanishning aylanishii. {\displaystyle \delta \beta } eksperimental ravishda aniqlangan mrad (miliradian) tartibining kichik miqdoridir. {\displaystyle {\vec {m}}} bu {\displaystyle {\vec {m}}={\vec {M}}/M\_{s}} formuladan aniqlangan kamaygan magnitlanish vektoridir, bu yerda {\displaystyle M\_{s}}to'yinganlikdagi magnitlanish. Biz yorug'likning tarqalish vektori magnitlanish tekisligiga perpendikulyar bo'lganligi sababli Voigt effektini ko'rish mumkinligini ta'kidladik.

### Dielektrik tenzor

Hubertning iqtibosidan so'ng,  umumlashtirilgan dielektrik kubik tensor {\displaystyle \varepsilon \_{r}} quyidagi shaklni oldi:


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{\displaystyle (1)\qquad \varepsilon \_{r}=\epsilon {\begin{bmatrix}1&0&iQm\_{y}\\0&1&-iQm\_{x}\\-iQm\_{y}&iQm\_{x}&1\end{bmatrix}}+{\begin{bmatrix}B\_{1}m\_{x}^{2}&B\_{2}m\_{x}m\_{y}&0\\B\_{2}m\_{x}m\_{y}&B\_{1}m\_{y}^{2}&0\\0&0&B\_{1}m\_{z}^{2}\end{bmatrix}}}

{\displaystyle (1)\qquad \varepsilon _{r}=\epsilon {\begin{bmatrix}1&0&iQm_{y}\\0&1&-iQm_{x}\\-iQm_{y}&iQm_{x}&1\end{bmatrix}}+{\begin{bmatrix}B_{1}m_{x}^{2}&B_{2}m_{x}m_{y}&0\\B_{2}m_{x}m_{y}&B_{1}m_{y}^{2}&0\\0&0&B_{1}m_{z}^{2}\end{bmatrix}}}bu yerda {\displaystyle \varepsilon } materialning dielektrik singdiruvchanligi, {\displaystyle Q} Voigt parametri, {\displaystyle B\_{1}} va {\displaystyle B\_{2}}lar {\displaystyle m\_{i}^{2}} ga qarab magnito-optik effektni tavsiflovchi ikki kubik konstanta. {\displaystyle m\_{i}} esa {\displaystyle m\_{i}=M\_{i}/M\_{s}} kamayishni ifodalaydi. Hisoblash {\displaystyle B\_{1}=B\_{2}} sferik yaqinlashuvda amalga oshiriladi. Ayni paytda, bu yaqinlashuv haqiqiy emasligi haqida hech qanday dalil yo'q, chunki Voigt effektini kuzatish kamdan-kam uchraydi, chunki u Kerr effektiga nisbatan juda kichikdir.

### Xususiy qiymatlar va xos vektorlar

Xususiy qiymatlar va xos vektorlarni hisoblash uchun biz Maksvell tenglamalaridan olingan tarqalish tenglamasini konvensiya {\displaystyle {\vec {n}}={\vec {k}}c/\omega } bilan ko'rib chiqamiz.  :


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{\displaystyle (2)\qquad n^{2}{\vec {E}}-{\vec {n}}({\vec {n}}\cdot {\vec {E}})=\varepsilon {\vec {E}}}

{\displaystyle (2)\qquad n^{2}{\vec {E}}-{\vec {n}}({\vec {n}}\cdot {\vec {E}})=\varepsilon {\vec {E}}}Magnitlanish to'lqin vektori tarqalishiga perpendikulyar bo'lsa, Kerr effektidan farqli o'laroq, {\displaystyle {\vec {E}}} uning barcha uchta komponenti nolga teng bo'lishi mumkinligi hisob-kitoblarni ancha murakkablashtiradi va bunda Frennel tenglamalari amal qilmaydi. Muammoni soddalashtirishning bir usuli - elektr maydoni o'rniga elektr maydon induksiya vektori {\displaystyle {\vec {D}}=\varepsilon {\vec {E}}} dan foydalanish. {\displaystyle {\vec {\nabla }}\cdot {\vec {D}}=0} va {\displaystyle {\vec {k}}\parallel {\vec {z}}} bo'lganligidan kelib chiqadi-ki {\displaystyle {\vec {D}}=(D\_{x},D\_{y},0)}. Noqulay narsa esa teskari dielektrik tenzor bilan ishlash. Bu yerda hisoblash matematik jihatdan murakkab bo'lgan umumiy holatda amalga oshiriladi, ammo {\displaystyle \phi =0} bo'lgan holda ko'rib chiqish orqali osongina ko'zlangan natijaga erishishimiz mumkin. .

Xususiy qiymatlar va xos vektorlar {\displaystyle {\vec {D}}} noma'lum bo'lgantarqalish tenglamasini yechish orqali topiladi. Bu quyidagi tenglamalar tizimini beradi:


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{\displaystyle (3)\quad {\begin{cases}(\varepsilon \_{xx}^{-1}-{\frac {1}{n^{2}}})D\_{x}+\epsilon \_{xy}^{-1}D\_{y}=0\\\\\varepsilon \_{yx}^{-1}D\_{x}+(\varepsilon \_{yy}^{-1}-{\frac {1}{n^{2}}})D\_{y}=0\end{cases}}}

{\displaystyle (3)\quad {\begin{cases}(\varepsilon _{xx}^{-1}-{\frac {1}{n^{2}}})D_{x}+\epsilon _{xy}^{-1}D_{y}=0\\\\\varepsilon _{yx}^{-1}D_{x}+(\varepsilon _{yy}^{-1}-{\frac {1}{n^{2}}})D_{y}=0\end{cases}}}bu yerda {\displaystyle \varepsilon \_{ij}^{-1}}inversiyani ifodalaydi, {\displaystyle ij} lar {\displaystyle \varepsilon \_{r}} dielektrik tenzor elementi, va {\displaystyle n^{2}=\varepsilon }. Tizim determinantini to'g'ridan-to'g'ri hisoblab chiqqandan so'ng, {\displaystyle Q}ni 2-tartibda va {\displaystyle B\_{1}}ni birinchi tartib da ishlab chiqish kerak. Bu ikkita sindirish ko'rsatkichlariga mos keladigan ikkita xususiy qiymatga olib keladi:



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{\displaystyle n\_{\parallel }^{2}=\varepsilon +B\_{1}}

{\displaystyle n_{\parallel }^{2}=\varepsilon +B_{1}}

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{\displaystyle n\_{\perp }^{2}=\varepsilon (1-Q^{2})}

{\displaystyle n_{\perp }^{2}=\varepsilon (1-Q^{2})} {\displaystyle {\vec {D}}} va {\displaystyle {\vec {E}}} uchun tegishli xos vektorlar quyidagilar:


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{\displaystyle (4)\qquad {\vec {D}}\_{\parallel }={\begin{pmatrix}\cos(\phi )\\\sin(\phi )\\0\end{pmatrix}}\qquad {\vec {D}}\_{\perp }={\begin{pmatrix}-\sin(\phi )\\\cos(\phi )\\0\end{pmatrix}}\qquad {\vec {E}}\_{\parallel }=\varepsilon ^{-1}{\vec {D}}\_{\parallel }={\begin{pmatrix}{\frac {\cos(\phi )}{B\_{1}+\varepsilon }}\\{\frac {\sin(\phi )}{B\_{1}+\epsilon }}\\0\end{pmatrix}}\qquad {\vec {E}}\_{\perp }=\varepsilon ^{-1}{\vec {D}}\_{\perp }={\begin{pmatrix}{\frac {\sin(\phi )}{(Q^{2}-1)\epsilon }}\\{\frac {\cos(\phi )}{(1-Q^{2})\epsilon }}\\{\frac {-iQ}{(1-Q^{2})\epsilon }}\end{pmatrix}}}

{\displaystyle (4)\qquad {\vec {D}}_{\parallel }={\begin{pmatrix}\cos(\phi )\\\sin(\phi )\\0\end{pmatrix}}\qquad {\vec {D}}_{\perp }={\begin{pmatrix}-\sin(\phi )\\\cos(\phi )\\0\end{pmatrix}}\qquad {\vec {E}}_{\parallel }=\varepsilon ^{-1}{\vec {D}}_{\parallel }={\begin{pmatrix}{\frac {\cos(\phi )}{B_{1}+\varepsilon }}\\{\frac {\sin(\phi )}{B_{1}+\epsilon }}\\0\end{pmatrix}}\qquad {\vec {E}}_{\perp }=\varepsilon ^{-1}{\vec {D}}_{\perp }={\begin{pmatrix}{\frac {\sin(\phi )}{(Q^{2}-1)\epsilon }}\\{\frac {\cos(\phi )}{(1-Q^{2})\epsilon }}\\{\frac {-iQ}{(1-Q^{2})\epsilon }}\end{pmatrix}}}
### Akslantirish geometriyasi

#### Davomiylik munosabati

Material ichidagi xos vektorlar va xos qiymatlarni bilish uchun odatda tajribalarda aniqlanadigan akslantirilgan elektromagnit vektor {\displaystyle {\vec {E\_{r}}}=(E\_{rx},E\_{ry},0)} ni hisoblash kerak. Bunda {\displaystyle {\vec {E}}} va {\displaystyle {\vec {H}}}uchun uzluksizlik tenglamalaridan foydalanamiz, bu yerda {\displaystyle {\vec {H}}} - Maksvell tenglamalaridan {\textstyle {\vec {\nabla }}\times {\vec {H}}={\frac {1}{c}}{\frac {\partial {\vec {D}}}{\partial t}}} orqali aniqlangan induksiya. Muhit ichida elektromagnit maydon olingan xos vektorlarda qismlarga ajraladi:{\displaystyle {\vec {E}}\_{t}=\alpha {\vec {E}}\_{\parallel }+\beta {\vec {E}}\_{\perp }}. Yechish uchun tenglamalar tizimi:


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{\displaystyle (5)\quad {\begin{cases}\alpha {\Big (}{\frac {D\_{y\parallel }}{n\_{\parallel }}}{\Big )}+\beta {\Big (}{\frac {D\_{y\perp }}{n\_{\perp }}}{\Big )}+E\_{ry}=E\_{0y}\\\\\alpha {\Big (}{\frac {D\_{x\parallel }}{n\_{\parallel }}}{\Big )}+\beta {\Big (}{\frac {D\_{x\perp }}{n\_{\perp }}}{\Big )}+E\_{rx}=E\_{0x}\\\\\alpha E\_{x\parallel }+\beta E\_{x\perp }-E\_{rx}=E\_{0x}\\\\\alpha E\_{y\parallel }+\beta E\_{y\perp }-E\_{ry}=E\_{0y}\end{cases}}}

{\displaystyle (5)\quad {\begin{cases}\alpha {\Big (}{\frac {D_{y\parallel }}{n_{\parallel }}}{\Big )}+\beta {\Big (}{\frac {D_{y\perp }}{n_{\perp }}}{\Big )}+E_{ry}=E_{0y}\\\\\alpha {\Big (}{\frac {D_{x\parallel }}{n_{\parallel }}}{\Big )}+\beta {\Big (}{\frac {D_{x\perp }}{n_{\perp }}}{\Big )}+E_{rx}=E_{0x}\\\\\alpha E_{x\parallel }+\beta E_{x\perp }-E_{rx}=E_{0x}\\\\\alpha E_{y\parallel }+\beta E_{y\perp }-E_{ry}=E_{0y}\end{cases}}}Ushbu tenglamalar tizimining yechimi:


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{\displaystyle (6)\quad E\_{rx}=E\_{0}{\frac {(1-n\_{\perp }n\_{\parallel })\cos(\beta )+(n\_{\perp }-n\_{\parallel })\cos(\beta -2\phi )}{(1+n\_{\parallel })(1+n\_{\perp })}}}

{\displaystyle (6)\quad E_{rx}=E_{0}{\frac {(1-n_{\perp }n_{\parallel })\cos(\beta )+(n_{\perp }-n_{\parallel })\cos(\beta -2\phi )}{(1+n_{\parallel })(1+n_{\perp })}}}

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{\displaystyle (7)\quad E\_{ry}=E\_{0}{\frac {(1-n\_{\perp }n\_{\parallel })\sin(\beta )-(n\_{\perp }-n\_{\parallel })\sin(\beta -2\phi )}{(1+n\_{\parallel })(1+n\_{\perp })}}}

{\displaystyle (7)\quad E_{ry}=E_{0}{\frac {(1-n_{\perp }n_{\parallel })\sin(\beta )-(n_{\perp }-n_{\parallel })\sin(\beta -2\phi )}{(1+n_{\parallel })(1+n_{\perp })}}}
#### Burilish burchagini hisoblash

Aylanish burchagi {\displaystyle \delta \beta } va elliptiklik burchagi {\displaystyle \psi } {\displaystyle \chi =E\_{ry}/E\_{rx}} ga nisbatdan quyidagi ikkita formula bilan aniqlanadi:


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{\displaystyle (8)\quad \tan 2\delta \beta ={\frac {2\operatorname {Re} (\chi )}{1-|\chi |^{2}}}\qquad (9)\quad \sin(2\psi \_{K})={\frac {2\operatorname {Im} (\chi )}{1-|\chi |^{2}}},}

{\displaystyle (8)\quad \tan 2\delta \beta ={\frac {2\operatorname {Re} (\chi )}{1-|\chi |^{2}}}\qquad (9)\quad \sin(2\psi _{K})={\frac {2\operatorname {Im} (\chi )}{1-|\chi |^{2}}},}bu yerda {\displaystyle \operatorname {Re} (\chi )} va {\displaystyle \operatorname {Im} (\chi )} {\displaystyle \chi } ning haqiqiy va mavhum qismini ifodalaydi. Oldindan hisoblangan ikkita komponentdan foydalanib quyidagilar olinadi:


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{\displaystyle (10)\qquad \chi ={\frac {(B\_{1}+n\_{0}^{2}Q^{2})}{2n\_{0}(n\_{0}^{2}-1)}}{\frac {\sin[2(\phi -\beta )]}{\cos(\beta )^{2}}}+\tan(\beta ).}

{\displaystyle (10)\qquad \chi ={\frac {(B_{1}+n_{0}^{2}Q^{2})}{2n_{0}(n_{0}^{2}-1)}}{\frac {\sin[2(\phi -\beta )]}{\cos(\beta )^{2}}}+\tan(\beta ).}Bu Voigt aylanishining {\displaystyle B\_{1}}holatda ham qayta yozilishi mumkin bo'lgan quyidagi formulasini beradi:


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{\displaystyle (11)\qquad \delta \beta =\operatorname {Re} \left[{\frac {B\_{1}+n\_{0}^{2}Q^{2}}{2n\_{0}(n\_{0}^{2}-1)}}\right]\sin[2(\phi -\beta )],}

{\displaystyle (11)\qquad \delta \beta =\operatorname {Re} \left[{\frac {B_{1}+n_{0}^{2}Q^{2}}{2n_{0}(n_{0}^{2}-1)}}\right]\sin[2(\phi -\beta )],} {\displaystyle n\_{0}}, va {\displaystyle Q} haqiqiy:


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{\displaystyle (12)\quad \delta \beta ={\frac {2\Delta n}{n\_{0}^{2}-1}}\sin[2(\phi -\beta )],}

{\displaystyle (12)\quad \delta \beta ={\frac {2\Delta n}{n_{0}^{2}-1}}\sin[2(\phi -\beta )],}bu yerda {\displaystyle \Delta n={\frac {n\_{\parallel }-n\_{\perp }}{2}}} sindirish ko'rsatkichlarining farqidir. Binobarin, {\displaystyle \Delta n} ga proporsional narsaga erishamiz va bu hodisa chiziqli qutblanishga bog'liq. To'g'ri {\displaystyle \phi -\beta } uchun hech qanday Voigt aylanishi kuzatilmaydi. {\displaystyle \Delta n} {\displaystyle B\_{1}\propto M\_{s}^{2}} va {\displaystyle Q\propto M\_{s}} dan kelib chiqib magnitlanish kvadratiga proportsionaldir.

### Transmissiya geometriyasi

Transmissiyadagi Voigt effektining aylanishini hisoblash printsipial jihatdan Faraday effektining biriga ekvivalent. Amalda, bu konfiguratsiya umuman ferromagnit namunalar uchun qo'llanilmaydi, chunki bunday turdagi materiallarda yutilish uzunligi kichikdir. Biroq, yorug'lik material ichida osongina harakatlanishi mumkin bo'lgan paramagnit suyuqlik yoki kristall uchun transmissiya geometriyasidan foydalanish ko'proq tarqalgan.

Paramagnit materialdagi hisoblashlar ferromagnit bilan bir xil, faqat magnitlanish maydon bilan almashtiriladi. {\displaystyle \mu \_{0}{\vec {H}}=\mu \_{0}H\_{0}(\cos \phi ,\,\sin \phi )} ( {\displaystyle H\_{0}} ichida {\displaystyle \mathrm {A/m} } yoki {\displaystyle \mathrm {G} } ). Qulaylik uchun, magnito-optik parametrlarda hisoblagandan so'ng maydon qo'shiladi.

L uzunlikdagi muhit orqali o'tgan elektromagnit to'lqinlar {\displaystyle {\vec {E}}\_{t}} ni ko'rib chiqaylik. (5) tenglamadan {\displaystyle \alpha } va {\displaystyle \beta } uchun quyidagilar olinadi:


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{\displaystyle \alpha ={\frac {2E\_{0}n\_{\parallel }\cos(\theta -\phi )}{1+n\_{\parallel }}}}

{\displaystyle \alpha ={\frac {2E_{0}n_{\parallel }\cos(\theta -\phi )}{1+n_{\parallel }}}}

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{\displaystyle \beta ={\frac {2E\_{0}n\_{\perp }^{2}\sin(\theta -\phi )}{n\_{\perp }+1}}}

{\displaystyle \beta ={\frac {2E_{0}n_{\perp }^{2}\sin(\theta -\phi )}{n_{\perp }+1}}}*z* = *L* bo'lan holda {\displaystyle {\vec {E}}\_{t}} ning ifodasi:


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{\displaystyle (13)\quad {\vec {E}}\_{t}=e^{-i\omega [t+{\frac {(n\_{\parallel }+n\_{\perp })L}{2c}}]}{\Big [}\alpha {\vec {E}}\_{\parallel }e^{i{\frac {\omega \Delta nL}{c}}}+\beta {\vec {E}}\_{\perp }e^{-i{\frac {\omega \Delta nL}{c}}}{\Big ]}}

{\displaystyle (13)\quad {\vec {E}}_{t}=e^{-i\omega [t+{\frac {(n_{\parallel }+n_{\perp })L}{2c}}]}{\Big [}\alpha {\vec {E}}_{\parallel }e^{i{\frac {\omega \Delta nL}{c}}}+\beta {\vec {E}}_{\perp }e^{-i{\frac {\omega \Delta nL}{c}}}{\Big ]}}bu yerda {\displaystyle {\vec {E}}\_{\parallel }} va {\displaystyle {\vec {E}}\_{\perp }} yuqorida hisoblangan xos vektorlardir va {\displaystyle \Delta n={\frac {n\_{\parallel }-n\_{\perp }}{2}}} ikki sindirish ko'rsatkichlari farqidir. Keyin aylanish {\displaystyle \chi ={\frac {E\_{t\_{y}}}{E\_{t\_{x}}}}} nisbat orqali, ortib borish tartibida birinchi tartibli {\displaystyle B\_{1}} va ikkinchi tartibli {\displaystyle Q} ga nisbatan hisoblab chiqiladi. Bundan:


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{\displaystyle (14)\quad \chi ={\frac {c-i~\omega L(1+n\_{0})(B\_{1}+n\_{0}Q^{2})\sin[2(\beta -\phi )]}{4cn\_{0}(1+n\_{0})\cos ^{2}(\beta )}}={\frac {c-i~\omega L(1+n\_{0})\Delta n\sin[2(\beta -\phi )]}{c~(1+n\_{0})\cos ^{2}(\beta )}}}

{\displaystyle (14)\quad \chi ={\frac {c-i~\omega L(1+n_{0})(B_{1}+n_{0}Q^{2})\sin[2(\beta -\phi )]}{4cn_{0}(1+n_{0})\cos ^{2}(\beta )}}={\frac {c-i~\omega L(1+n_{0})\Delta n\sin[2(\beta -\phi )]}{c~(1+n_{0})\cos ^{2}(\beta )}}}Biz yana {\displaystyle \Delta n} va {\displaystyle L} -yorug'likning tarqalish uzunligiga proporsional narsani olamiz. {\displaystyle \Delta n} ko'rsatkich {\displaystyle (\mu \_{0}H\_{0})^{2}}ga proporsionaldir. Voigt aylanishini olish uchun biz {\displaystyle n\_{0}=\eta +i~\kappa }, {\displaystyle Q=Q\_{r}+i~Q\_{i}} va {\displaystyle B\_{1}} haqiqiy qismlarni ko'rib chiqamiz. Keyin (14) ning haqiqiy qismini hisoblashimiz kerak. Keyin olingan ifoda (8) ga olib borib qo'yiladi. Yutilish nolga yaqinlashganda, transmissiya geometriyasida Voigt aylanishi uchun quyidagilar olinadi:


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{\displaystyle (15)\quad \delta \beta =(\mu \_{0}H)^{2}{\frac {B\_{1}+n\_{0}^{2}{\Big [}{\frac {2L\omega }{c}}(1+n\_{0})Q\_{i}Q\_{r}+Q\_{r}^{2}-Q\_{i}^{2}{\Big ]}}{n\_{0}(1+n\_{0})}}}

{\displaystyle (15)\quad \delta \beta =(\mu _{0}H)^{2}{\frac {B_{1}+n_{0}^{2}{\Big [}{\frac {2L\omega }{c}}(1+n_{0})Q_{i}Q_{r}+Q_{r}^{2}-Q_{i}^{2}{\Big ]}}{n_{0}(1+n_{0})}}}

GaMnAs-da Voigt effektining tasviri
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 1-rasm : a) tekislikdagi eksperimental gisterezis sikli (Ga,Mn)As b) (a) ning simmetrik qismini ajratib olish natijasida olingan Voigt gisterezis sikli. c) (a) ning assimetrik qismini ajratib olish natijasida olingan bo'ylanma Kerr e.
 2-rasm : a) Tekislikdagi almashtirish mexanizmi (Ga,Mn)As b) a) da ko'rsatilgan mexanizmdan simulyatsiya qilingan Voigt signali
Voigt effektini qo'llash misoli sifatida magnit yarim o'tkazgichda (Ga,Mn)As katta Voigt effekti kuzatilgan.  Past haroratlarda (umuman {\displaystyle T<{\frac {T\_{c}}{2}}} ) tekislikdagi magnitlanishga ega bo'lgan material uchun (Ga,Mn)As magnitlanish <100> (yoki unga yaqin) yo'nalishlarda ikki o'qli anizotropiyani ko'rsatadi.

Voigt effektini o'z ichiga olgan odatiy gisterezis sikli 1-rasmda ko'rsatilgan. Bu sikl [110] yoʻnalishi boʻylab tushish burchagi taxminan 3° boʻlgan chiziqli qutblangan nurni yuborish (batafsilroq maʼlumotni  dan topish mumkin) va aks ettirilgan yorugʻlikning magnito-optik taʼsiri tufayli aylanishni oʻlchash yoʻli bilan olingan. Keng tarqalgan bo'ylanma / qutbli Kerr effektidan farqli o'laroq, gisterezis sikli magnitlanishga nisbatan proporsionaldir, bu Voigt effektining belgisidir. Bu sikl normalga juda yaqin yorug'lik tushishi bilan olingan va u ham kichik g'ayrioddiy qismini ko'rsatadi; Voigt effektiga mos keladigan gisterezisning simmetrik qismini va bo'ylama Kerr effektiga mos keladigan assimetrik qismini ajratib olish uchun to'g'ri harakat qilish kerak.

Bu yerda keltirilgan gisterezis holatida maydon [1-10] yo'nalishi bo'ylab qo'llanilgan. Kommutatsiya mexanizmi quyidagicha:

1. Biz yuqori manfiy maydondan boshlaymiz va magnitlanish 1-pozitsiyada [-1-10] yo'nalishiga yaqin.
2. Magnit maydonning qisqarishi 1 dan 2 gacha bo'lgan kogerent magnitlanish aylanishiga olib keladi
3. Musbat maydonda magnitlanish magnit domenlarning yadrolanishi va tarqalishi orqali 2-dan 3-ga majburiy ravishda o'tadi, bu yerda birinchi {\displaystyle H\_{1}} majburiy maydon paydo bo'ladi.
4. Magnitlanish 3-holatiga yaqin bo'lib, qo'llaniladigan maydon yo'nalishidan yaqinroq bo'lgan holda 4-holatga izchil aylanadi.
5. Yana magnitlanish magnit domenlarning yadrolanishi va tarqalishi bilan keskin ravishda 4 dan 5 ga o'tadi. Bu o'tish yakuniy muvozanat holati 5-holatdan 4-holatga nisbatan yaqinroq bo'lganligi bilan bog'liq (va shuning uchun uning magnit energiyasi pastroq). Bu boshqa majburiy maydon {\displaystyle H\_{2}} ni beradi.
6. Nihoyat, magnitlanish 5-holatdan 6-holatga izchil aylanadi.

Ushbu jarayonning simulyatsiyasi 2-rasmda keltirilgan.


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{\displaystyle \operatorname {Re} \left[{\frac {B\_{1}+n\_{0}^{2}Q^{2}}{2n\_{0}(n\_{0}^{2}-1)}}\right]P\_{\text{Voigt}}=0.5\,\mathrm {mrad} .}

{\displaystyle \operatorname {Re} \left[{\frac {B_{1}+n_{0}^{2}Q^{2}}{2n_{0}(n_{0}^{2}-1)}}\right]P_{\text{Voigt}}=0.5\,\mathrm {mrad} .}Ko'rinib turibdiki, simulyatsiya qilingan gisterezis tajribaga nisbatan sifat jihatidan bir xil. E'tibor bering, amplituda {\displaystyle H\_{1}} yoki {\displaystyle H\_{2}} {\displaystyle P\_{\text{Voigt}}}ning taxminan ikki barobariga teng

Shuningdek qarang
-----------------

* Atomic line filter (ALF)
* Kotton-Mouton effekti
* Faraday effekti

Manbalar
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1. ↑  Zvezdin, Anatoly Konstantinovich (1997), Taylor & Francis Group (muh.), *Modern magneto-optics and magneto-optical materials : Studies in Condensed Matter* (english), ISBN 978-0-7503-03620`{{citation}}`: CS1 maint: unrecognized language ().
2. ↑  Hubert, Alex (1998), Springer (muh.), *Magnetic domains* (english), ISBN 978-3-540-85054-0`{{citation}}`: CS1 maint: unrecognized language ()
3. ↑  Kimel (2005). "Observation of Giant Magnetic Linear Dichroism in (Ga,Mn)As". *Physical Review Letters* **94** (22): 227203. doi:10.1103/physrevlett.94.227203. PMID 16090433. .
4. ↑  Shihab (2015). "Systematic study of the spin stiffness dependence on Phosphorus alloying in (Ga,Mn)As ferromagnetic semiconductor". *Applied Physics Letters* **106** (14): 142408. doi:10.1063/1.4917423. .

Ko'proq ma'lumot uchun
----------------------

* Chjao, Chjung-Quan. Excited state atomic line filters Wayback Machine saytida arxivlandi (2011-07-11).. 2006 yil 26 martda olindi.