Second harmonic generation vs interference

In summary, the mathematical expressions for interference and second harmonic generation involve the cosine of the phase difference between two waves, with interference resulting from superposition and second harmonic generation resulting from nonlinear interaction. Both expressions also include the amplitudes of the two waves.
  • #1
dziech
11
1
Hello,

I have a question about the mathematical expression of interference and second harmonic generation

If we have two waves ##E_{1,2}(\Theta ,t) = E_{1,2}e^{j(\omega t + \Theta)} = \frac{1}{2}(E_{1,2}e^{j(\omega t + \Theta)} + c.c. )##

According to the Euler's formula. Now - both interference and second harmonic generation is connected to squaring the sum of the field and c.c. Interference is connected to the phase difference (I saw somewhere ##\omega t## being omitted when calculating the interference pattern) and if I square the ##\omega t## part, we have indeed second harmonic and some interference pattern because of that phase part.

Can anyone point to, or right down the second harmonic generation sort of equation also with phase information (interference) part ? I am a bit lost in this and would like that someone clear that for me.
 
Engineering news on Phys.org
  • #2


Hello,

Thank you for your question. The mathematical expression for interference and second harmonic generation can be written as:

Interference: ##E_{int} = E_1 + E_2 + 2\sqrt{E_1E_2}\cos(\phi)##

where ##E_1## and ##E_2## are the amplitudes of the two waves, and ##\phi## is the phase difference between them.

Second harmonic generation: ##E_{SHG} = 2E_1E_2\cos^2(\phi)##

where ##E_1## and ##E_2## are the amplitudes of the two waves, and ##\phi## is the phase difference between them.

As you can see, both expressions involve the cosine of the phase difference, which represents the interference pattern. In the case of interference, this interference pattern results from the superposition of the two waves, while in the case of second harmonic generation, it results from the nonlinear interaction between the two waves.

I hope this helps to clarify the mathematical expressions for interference and second harmonic generation. If you have any further questions, please let me know.
 

What is Second Harmonic Generation (SHG)?

Second Harmonic Generation (SHG) is a nonlinear optical process in which two photons with the same frequency are converted into a single photon with twice the frequency. This process occurs in certain materials known as nonlinear crystals.

What is interference?

Interference is a phenomenon that occurs when two or more waves meet and combine with each other. This results in a new wave with a different amplitude, phase, or direction of propagation.

How does SHG differ from interference?

While both SHG and interference involve the combination of two or more waves, they differ in the mechanism by which this combination occurs. SHG involves the nonlinear response of a material, while interference is a result of the superposition of waves.

What are the applications of SHG and interference?

SHG has various applications in fields such as microscopy, spectroscopy, and telecommunications. Interference is used in many technologies, including radio, television, and fiber optics.

How do SHG and interference affect each other?

In some cases, SHG and interference can occur simultaneously, leading to complex optical phenomena. In other cases, SHG may be used to manipulate or control interference patterns, allowing for more precise measurements and applications.

Similar threads

Replies
1
Views
378
  • Electrical Engineering
Replies
17
Views
1K
  • Advanced Physics Homework Help
Replies
3
Views
888
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Linear and Abstract Algebra
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
12
Views
882
Replies
7
Views
727
  • Electromagnetism
Replies
2
Views
628
Replies
1
Views
505
  • Electrical Engineering
Replies
3
Views
4K
Back
Top