- #1
Haorong Wu
- 413
- 89
Hello, there. Suppose a Gaussian beam is sent and is received at a great large distance, i.e., the propagation distance ##z \gg z_R## the Rayleigh distance.
The Gaussian beam can be described by $$E_0 \frac {1}{w(z)} \exp \left ( \frac {-r^2}{w(z)^2}\right )\exp\left ( -i\left (kz+k\frac {r^2}{2R(z)}-\psi(z)\right )\right ) $$
where ##E_0## is the amplitude of the electric field, ##w_0## is the waist radius, ##w(z)## is the radius of the beam at ##z##, ##k## is the frequency, ##R(z)## is the radius of curvature of the beam's wavefronts at ##z##, and ##\psi(z)## is the Gouy phase.
When the distance ##z## is larger than the Rayleigh distance ##z_R##, the beam will diverge noticeably. In my scenario, the propagation distance ##z## is so large that the curvature of the wavefront will approach zero. In order to simplify my analysis, I would like to treat them as parallel light when received by a finite small detection area. And since the other part that is not detected is lost, I modeled the light to be as a beam with a waist radius ##w_d##, which is the radius of the detection area, such as $$E_d \frac {1}{w_d} \exp \left ( \frac {-r^2}{w_d^2}\right )\exp\left ( -ikz \right ) $$ where ## E_d## is the received amplitude, the curvature term vanishes and the Gouy phase can be harmlessly removed.
But my professor said that he is not sure whether this approximation is correct or not and asked me to find more related papers. However, I have searched in Google scholar for days without success. Could you help me with this analysis or share possible materials? Thanks in advance.
The Gaussian beam can be described by $$E_0 \frac {1}{w(z)} \exp \left ( \frac {-r^2}{w(z)^2}\right )\exp\left ( -i\left (kz+k\frac {r^2}{2R(z)}-\psi(z)\right )\right ) $$
where ##E_0## is the amplitude of the electric field, ##w_0## is the waist radius, ##w(z)## is the radius of the beam at ##z##, ##k## is the frequency, ##R(z)## is the radius of curvature of the beam's wavefronts at ##z##, and ##\psi(z)## is the Gouy phase.
When the distance ##z## is larger than the Rayleigh distance ##z_R##, the beam will diverge noticeably. In my scenario, the propagation distance ##z## is so large that the curvature of the wavefront will approach zero. In order to simplify my analysis, I would like to treat them as parallel light when received by a finite small detection area. And since the other part that is not detected is lost, I modeled the light to be as a beam with a waist radius ##w_d##, which is the radius of the detection area, such as $$E_d \frac {1}{w_d} \exp \left ( \frac {-r^2}{w_d^2}\right )\exp\left ( -ikz \right ) $$ where ## E_d## is the received amplitude, the curvature term vanishes and the Gouy phase can be harmlessly removed.
But my professor said that he is not sure whether this approximation is correct or not and asked me to find more related papers. However, I have searched in Google scholar for days without success. Could you help me with this analysis or share possible materials? Thanks in advance.