- #1

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- Homework Statement
- Try plotting....

- Relevant Equations
- $$U(\vec{r}) \approx \frac{A_0}{z} exp(-jkz) \exp(-jk\frac{x^2 + y^2}{2z})$$

We can either plot the real part of the complex amplitude, or the wavefront.

However, how is wavefront meaningful for varying amplitude? In order to plot the paraboloid, we must vary ##z##, which varies the amplitude ##\frac{A_0}{z}##. Unless the amplitude is varies little, i.e. ##1/z## approximately constant within ##\Delta z = \lambda##?

In the book Fundamentals of Photonics, Saleh & Teich, the author mentions that the phase of the second exponential function serves to bend the planar wavefronts into paraboloidal surfaces i.e. ##frac{x^2 + y^2}{2z} = \text{const}##, however, shouldn't it be ##z + frac{x^2 + y^2}{2z} = \text{const}## when plotting surfaces of constant phase i.e. wavefronts?

The result should look like this.

Thanks in advance!

However, how is wavefront meaningful for varying amplitude? In order to plot the paraboloid, we must vary ##z##, which varies the amplitude ##\frac{A_0}{z}##. Unless the amplitude is varies little, i.e. ##1/z## approximately constant within ##\Delta z = \lambda##?

In the book Fundamentals of Photonics, Saleh & Teich, the author mentions that the phase of the second exponential function serves to bend the planar wavefronts into paraboloidal surfaces i.e. ##frac{x^2 + y^2}{2z} = \text{const}##, however, shouldn't it be ##z + frac{x^2 + y^2}{2z} = \text{const}## when plotting surfaces of constant phase i.e. wavefronts?

The result should look like this.

Thanks in advance!