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Hi. A spherical wave ##e^{i(kr-\omega t)}## diverging from a single point ##(x=0,y=0,z=-z_0)## can be approximated as a parabolic wave in the paraxial case around the z-axis. I.e., ##k r = k \sqrt{x^2+y^2+z^2} \simeq k (z +\frac{x^2+y^2}{2z})##.

OK, then let's say a lens is placed such that its optical axis coincides with the ##z## axis and its focus points are at ##-z_0## and ##z_0##. In this case, the outgoing parabolic wave from ##-z_0## will be focused into the point ##z_0##. My question is, how is this to be modeled mathematically? Intuitively I would guess that ##k r \simeq k ( z - \frac{x^2+y^2}{2z})##, but what is ##kr## equal to in the accompanying case of a converging spherical wave? Something ala ##e^{i(kr + \omega t)} e^{i \phi}##, where ##\phi## is some phase factor?

I would appreciate it if you guys could help me in clearing this stuff up :)

Thanks

OK, then let's say a lens is placed such that its optical axis coincides with the ##z## axis and its focus points are at ##-z_0## and ##z_0##. In this case, the outgoing parabolic wave from ##-z_0## will be focused into the point ##z_0##. My question is, how is this to be modeled mathematically? Intuitively I would guess that ##k r \simeq k ( z - \frac{x^2+y^2}{2z})##, but what is ##kr## equal to in the accompanying case of a converging spherical wave? Something ala ##e^{i(kr + \omega t)} e^{i \phi}##, where ##\phi## is some phase factor?

I would appreciate it if you guys could help me in clearing this stuff up :)

Thanks

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