How Does Light Intensity Change When Two Laser Beams Cross?

[fogvajarash]

Homework Statement

Two laser beams, one of wavelength 633 nm and intensity I₁ = 4.00x10⁶ W/m² with a circular beam profile D₁ = 1.33 mm in diameter, and one of wavelength 442 nm and intensity I₂ = 4.00x10⁶ W/m² with the same circular beam profile are fired, crossing at an angle of θ = 45°. Determine the intensity of the light scattered out of the 633 nm beam.

Homework Equations

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The Attempt at a Solution

I'm not sure on how to begin this problem. I was thinking, that because of when light crosses with another light beam, this beam shouldn't be affected at all, so I was thinking that the intensity should be the same (I highly doubt this argument is correct though). If not, then how could we determine light scattering in this aspect? How would light interact with each other in this case?

Thanks for your patience.

 

[BvU]

Any context ? Relativity, electromagnetism, classical optics, introductory quantum mechanics, photon-photon scattering in high-energy physics?

 

[fogvajarash]

Any context ? Relativity, electromagnetism, classical optics, introductory quantum mechanics, photon-photon scattering in high-energy physics?

Context is classical optics (I'm not sure which concept to apply here though).

 

[BvU]

Can't think of anything in classical optics or electromagnetism that scatters light with light: all is linear in the Maxwell equations and superposition holds. Perhaps that's what they want you to declare.
No clue in the lecture notes or anything ?

 

[HalfLostAndSearching]

I would approach this problem by first understanding the concept of scattering of light. When two laser beams cross, they can interact with each other and cause scattering, which is the process of light being redirected in different directions. This can happen due to various factors such as the properties of the laser beams (wavelength, intensity, beam profile, etc.) and the angle at which they intersect.

In this specific scenario, we have two laser beams with different wavelengths and intensities crossing at an angle of 45°. This means that the beams will interact with each other and some amount of light will be scattered out of the 633 nm beam. To determine the intensity of the scattered light, we can use the formula for scattering cross-section, which is given by σ = (8π/3) * (r0^2) * |E1|^2 * |E2|^2 * cos^2(θ/2), where r0 is the classical electron radius, E1 and E2 are the electric field amplitudes of the two beams, and θ is the angle between the two beams.

Using this formula and plugging in the given values, we can calculate the scattering cross-section for the 633 nm beam. From there, we can determine the intensity of the scattered light by multiplying the cross-section by the intensity of the incident beam. This will give us the intensity of the light scattered out of the 633 nm beam.

In conclusion, the intensity of the scattered light can be determined by considering the properties of the incident beams and using the formula for scattering cross-section. This approach takes into account the interaction between the two beams and provides a quantitative understanding of the scattering process.