Skip to main content
Physics

Return to Question

added links; Dear John Roberts, if u don't like my changes please roll back or use the parts u like.
Source Link
Qmechanic ♦
Qmechanic ♦
  • 212.7k
  • 48
  • 589
  • 2.3k

The $ABCD$ matrix$ABCD$ matrix of a glass graded-index slab with refractive index $n(y)=n_0(1-\frac{1}{2}\alpha^{2}y^{2})$ and length $d$ is $A=cos(\alpha d)$$A=\cos(\alpha d)$, $B=\frac{1}{\alpha}sin(\alpha d)$$B=\frac{1}{\alpha}\sin(\alpha d)$, $C=-\alpha sin(\alpha d)$$C=-\alpha \sin(\alpha d)$, $D=cos(\alpha d)$$D=\cos(\alpha d)$ for paraxial rays along the z axis. Usually, $\alpha$ is chosen to be sufficiently small so that $\alpha^{2}y^{2} << 1$. A Gaussian beamGaussian beam of wavelength $\lambda_0$, waist radius $W_0$ in freespacefree space, and axis in the z direction enters the slab at its waist. How can I use the $ABCD$ law$ABCD$ law to get an expression for the beam width in the $y$ direction as a function of $d$?

The $ABCD$ matrix of a glass graded-index slab with refractive index $n(y)=n_0(1-\frac{1}{2}\alpha^{2}y^{2})$ and length $d$ is $A=cos(\alpha d)$, $B=\frac{1}{\alpha}sin(\alpha d)$, $C=-\alpha sin(\alpha d)$, $D=cos(\alpha d)$ for paraxial rays along the z axis. Usually, $\alpha$ is chosen to be sufficiently small so that $\alpha^{2}y^{2} << 1$. A Gaussian beam of wavelength $\lambda_0$, waist radius $W_0$ in freespace, and axis in the z direction enters the slab at its waist. How can I use the $ABCD$ law to get an expression for the beam width in the $y$ direction as a function of $d$?

The $ABCD$ matrix of a glass graded-index slab with refractive index $n(y)=n_0(1-\frac{1}{2}\alpha^{2}y^{2})$ and length $d$ is $A=\cos(\alpha d)$, $B=\frac{1}{\alpha}\sin(\alpha d)$, $C=-\alpha \sin(\alpha d)$, $D=\cos(\alpha d)$ for paraxial rays along the z axis. Usually, $\alpha$ is chosen to be sufficiently small so that $\alpha^{2}y^{2} << 1$. A Gaussian beam of wavelength $\lambda_0$, waist radius $W_0$ in free space, and axis in the z direction enters the slab at its waist. How can I use the $ABCD$ law to get an expression for the beam width in the $y$ direction as a function of $d$?

added 85 characters in body
Source Link
John Roberts
John Roberts
  • 283
  • 2
  • 12

The $ABCD$ matrix of a glass graded-index slab with refractive index $n(y)=n_0(1-\frac{1}{2}\alpha^{2}y^{2})$ and length $d$ is $A=cos(\alpha d)$, $B=\frac{1}{\alpha}sin(\alpha d)$, $C=-\alpha sin(\alpha d)$, $D=cos(\alpha d)$ for paraxial rays along the z axis. Usually, $\alpha$ is chosen to be sufficiently small so that $\alpha^{2}y^{2} << 1$. A Gaussian beam of wavelength $\lambda_0$, waist radius $W_0$ in freespace, and axis in the z direction enters the slab at its waist. How can I use the $ABCD$ law to get an expression for the beam width in the $y$ direction as a function of $d$?

The $ABCD$ matrix of a glass graded-index slab with refractive index $n(y)=n_0(1-\frac{1}{2}\alpha^{2}y^{2})$ and length $d$ is $A=cos(\alpha d)$, $B=\frac{1}{\alpha}sin(\alpha d)$, $C=-\alpha sin(\alpha d)$, $D=cos(\alpha d)$ for paraxial rays along the z axis. A Gaussian beam of wavelength $\lambda_0$, waist radius $W_0$ in freespace, and axis in the z direction enters the slab at its waist. How can I use the $ABCD$ law to get an expression for the beam width in the $y$ direction as a function of $d$?

The $ABCD$ matrix of a glass graded-index slab with refractive index $n(y)=n_0(1-\frac{1}{2}\alpha^{2}y^{2})$ and length $d$ is $A=cos(\alpha d)$, $B=\frac{1}{\alpha}sin(\alpha d)$, $C=-\alpha sin(\alpha d)$, $D=cos(\alpha d)$ for paraxial rays along the z axis. Usually, $\alpha$ is chosen to be sufficiently small so that $\alpha^{2}y^{2} << 1$. A Gaussian beam of wavelength $\lambda_0$, waist radius $W_0$ in freespace, and axis in the z direction enters the slab at its waist. How can I use the $ABCD$ law to get an expression for the beam width in the $y$ direction as a function of $d$?

Source Link
John Roberts
John Roberts
  • 283
  • 2
  • 12

Transmission of Gaussian Beam Through Graded-Index Slab

The $ABCD$ matrix of a glass graded-index slab with refractive index $n(y)=n_0(1-\frac{1}{2}\alpha^{2}y^{2})$ and length $d$ is $A=cos(\alpha d)$, $B=\frac{1}{\alpha}sin(\alpha d)$, $C=-\alpha sin(\alpha d)$, $D=cos(\alpha d)$ for paraxial rays along the z axis. A Gaussian beam of wavelength $\lambda_0$, waist radius $W_0$ in freespace, and axis in the z direction enters the slab at its waist. How can I use the $ABCD$ law to get an expression for the beam width in the $y$ direction as a function of $d$?