1.4.1: Polarización lineal
- Page ID
- 51098
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Un caso particular de elipse es una recta que pasa por el origen (Figura \(\PageIndex{1}\)). Esto significa que el campo está vibrando en una misma dirección del espacio. Esta situación degenerada se produce cuando
\[
\delta_{y}-\delta_{x}=\left\{\begin{array}{l} \notag
0 \\
\pi
\end{array}\right.
\]
\({ }^{6}\) Hemos descompuesto el vector amplitud compleja en módulo y argumento y expresado su fase como \(-\delta_{x}\) \(\mathrm{o}-\delta_{y}\). El haber elegido fases \(\delta_{x}\) y \(\delta_{y}\) no cambiaría nada.
o bien cuando \(\left|E_{0 x}\right|=0\) o \(\left|E_{0 y}\right|=0\). Entonces diremos que la polarización es lineal y que la luz es linealmente polarizada. Podemos usar la notación
\[
\begin{aligned}
\mathbf{E}_{0} &=\left(\begin{array}{c}
E_{0 x} \\
E_{0 y}
\end{array}\right)=\left(\begin{array}{c}
\left|E_{0 x}\right| e^{-i \delta_{x}} \\
\left|E_{0 y}\right| e^{-i \delta_{y}}
\end{array}\right) \\
&=e^{-i \delta_{y}}\left(\begin{array}{c}
\left|E_{0 x}\right| e^{-i\left(\delta_{x}-\delta_{y}\right)} \\
\left|E_{0 y}\right|
\end{array}\right)
\end{aligned}
\]
aprovechamos la condición de diferencia de fase 0 o \(\pi\) para poner
\[
\mathbf{E}_{0}=e^{-i \delta_{y}}\left(\begin{array}{c}
\pm\left|E_{0 x}\right| \\
\left|E_{0 y}\right|
\end{array}\right) \propto \text { vector real } \notag
\]
es decir, siempre que haya proporcionalidad a un vector real (aunque el coeficiente sea complejo) se dirá que la luz está linealmente polarizada.