- #1
ppedro
- 22
- 0
Hi friends!
I solved the problem 8.3 of ``Problems in Lasers Physics'' book (by Cerullo, Longhi, Nisoli, Stagira and Svelto) but I think there's a mistake on the solution presented in this book in page 196. This is a problem book with problems and solutions that follows closely the laser physics theory as presented in ``Principles of Laser Physics'' book (by Svelto), referring many times to the equations derived in it.
My question has to do with the book's solution way of calculating [itex] A_{b} [/itex] which is the laser beam area inside the crystal (at its center, in the middle of the confocal resonant cavity). This laser beam is, as far as I understand, approximated to be of cylindrical form inside the crystal, and thus it has volume [itex]V=A_{b}l[/itex], where [itex]l[/itex] is the length of the crystal.
Alright, the book's solution says the area of the beam at the center of the resonator is given by
[tex] A_{b}=\frac{\pi w_{b}^{2}}{2} [/tex]
where [itex]w_{b}[/itex] is the beam spot size at the center. This value of [itex]w_{b}[/itex] is said to be given by [itex]w_{b}=\left(\frac{L\lambda}{2\pi}\right)^{1/2}[/itex] for the case of a confocal resonator, in accordance with the second equation in Eq.5.5.11 of the ``Principles of Laser Physics'' book, which I agree.
However, I don't see the reasoning in the division by 2, because, by definition, [itex]w_{b}[/itex] is the radius of the ``cross section'' (the ``spot'') of the gaussian beam, as can be seen throughout ``Principles of Laser Physics'' starting from all the definitions in section ``4.7 Gaussian beams'', and which is, for example, represented in Fig.5.9.a. To me this would just be [itex]A_{b}=\pi w_{b}^{2}[/itex]. Am I wrong? This might seem minor, but to me it's important because it makes a difference on a request to reevaluate my exam correction.
I solved the problem 8.3 of ``Problems in Lasers Physics'' book (by Cerullo, Longhi, Nisoli, Stagira and Svelto) but I think there's a mistake on the solution presented in this book in page 196. This is a problem book with problems and solutions that follows closely the laser physics theory as presented in ``Principles of Laser Physics'' book (by Svelto), referring many times to the equations derived in it.
My question has to do with the book's solution way of calculating [itex] A_{b} [/itex] which is the laser beam area inside the crystal (at its center, in the middle of the confocal resonant cavity). This laser beam is, as far as I understand, approximated to be of cylindrical form inside the crystal, and thus it has volume [itex]V=A_{b}l[/itex], where [itex]l[/itex] is the length of the crystal.
Alright, the book's solution says the area of the beam at the center of the resonator is given by
[tex] A_{b}=\frac{\pi w_{b}^{2}}{2} [/tex]
where [itex]w_{b}[/itex] is the beam spot size at the center. This value of [itex]w_{b}[/itex] is said to be given by [itex]w_{b}=\left(\frac{L\lambda}{2\pi}\right)^{1/2}[/itex] for the case of a confocal resonator, in accordance with the second equation in Eq.5.5.11 of the ``Principles of Laser Physics'' book, which I agree.
However, I don't see the reasoning in the division by 2, because, by definition, [itex]w_{b}[/itex] is the radius of the ``cross section'' (the ``spot'') of the gaussian beam, as can be seen throughout ``Principles of Laser Physics'' starting from all the definitions in section ``4.7 Gaussian beams'', and which is, for example, represented in Fig.5.9.a. To me this would just be [itex]A_{b}=\pi w_{b}^{2}[/itex]. Am I wrong? This might seem minor, but to me it's important because it makes a difference on a request to reevaluate my exam correction.