Degree of first order coherence and fluctuations

[cilestrino]

Hi! I'm new here, but I hope that someone would evenly help me!

My first question is about the problem (3.3 on page 100 from Loudon - The Quantum Theory of Light 3ed) in the attachment; the second question is about discussing (I)the physical origin of fluctuations of the electromagnetic radiation, in the classical and in the quantum model, and (II) which kind of correlation among the em radiation features brings to the limit of the coherent state (minimun uncertainty state with (deltaX)^2=(deltaY)^2) and which one else gives the squeezed states (mus with (deltaX)^2 not equal to (deltaY)^2).

Thank you very much to all of you that every night and day discuss within the forum.
Thanks for reading!
Fran

 

[TriTertButoxy]

This is a problem I'm intersted in looking at, but I'm getting a 'corrupted file' error when I try to open the zip file.

 

[cilestrino]

working attachment

thank you very much!
try this pdf. I hope you could help me also with the second question...
I'm very obliged even only for your interest!
Bye,
Fran

 

[cilestrino]

normalized correlation function

As someone could be interested in helping me to solve it, I write the equation that I need to solve to get the degree of first order coherence for a beam of light whose electric field amplitude has the following form:​

$$E(t)=E_1(t)\exp{[ik_1z-i\omega_1t+i\varphi_1(t)]}+E_2(t)\exp{[ik_2z-i\omega_2t+i\varphi_2(t)]}$$.​

The Degree of First Order Coherence, then, for it, is given by definition as its normalized correlation function as follows:

$$g^{(1)}(\tau)=\frac{\langle E^{\ast}(t)E(t+\tau)\rangle}{\langle E^{\ast}(t)E(t)\rangle}$$.​

Someone knows how to rigourously solve the means between bra and ket simbols?

I solved it as follows:

$$\frac{\langle E^{\ast}(t)E(t+\tau)\rangle}{\langle E^{\ast}(t)E(t)\rangle}=\frac{\frac{1}{T}\int_T E^{\ast}(t)E(t+\tau)}{\frac{1}{T}\int_T E^{\ast}(t)E(t)}$$​

where I put $$E^{\ast}(t)=E_1(t)\exp{[-ik_1z+i\omega_1t-i\varphi_1(t)]}+E_2(t)\exp{[-ik_2z+i\omega_2t-i\varphi_2(t)]}$$

Is this correct, where the asterisk indicates the complex conjugate of the counterpart without it? If the signs in the exp functions are correct, what does happen to the amplitudes $$E_1(t)$$ ed $$E_2(t)$$?

Please help me.

Thanks,
Fran

 

[vijay123]

wow..that problem is cool...i am only 14 and such a language intrigues me...what and were do you study celestrino?

 

[cilestrino]

wow..that problem is cool...i am only 14 and such a language intrigues me...what and were do you study celestrino?

I'm taking bachelor degree in physics in Bari, Italy.
However, I solved that problem on my own, and though it seemed to me very complex, I can assure that it is very easy (making some useful hypoteses before solving).
The subject of this problem concerns Quantum Optics, a very fascinating physics branch...

Hi