Laser beam represented with complex conjugate?

In summary, Nonlinear Optics page 5 discusses the representation of a time-dependent electric field in the form of $$\widetilde{E}(t) = Ee^{-iwt} + c.c$$. This is simply a way to represent the field, with the real part being the strength of the field. The factor of 2 in front of the amplitude is arbitrary and there are animations available online for a better understanding.
  • #1
betelgeuse91
32
0
Boyd - Nonlinear Optics page 5, there says 'Here a laser beam whose electric field strength is represented as $$\widetilde{E}(t) = Ee^{-iwt} + c.c$$But why is it written like this? Is it because the strength is the real part of the complex electric field? Then why doesn't he divide it by 2 after adding those two?
 
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  • #2
It's simply a representation of a time-dependent E-field. Your ##\tilde E(t)## is real, by the way:$$\tilde E(t)= 2E\cos(\omega t)$$and that ##2E## is some arbitrary amplitude.

You might enjoy some nice animations, like here or here
 
  • #3
BvU said:
It's simply a representation of a time-dependent E-field. Your ##\tilde E(t)## is real, by the way:$$\tilde E(t)= 2E\cos(\omega t)$$and that ##2E## is some arbitrary amplitude.

You might enjoy some nice animations, like here or here

I see. Thank you!
 

1. What is a laser beam represented with complex conjugate?

A laser beam represented with complex conjugate is a mathematical concept used to describe the properties of a laser beam. It involves using complex numbers to represent the amplitude and phase of the laser beam, which can help in understanding its propagation and interaction with different materials.

2. Why is it important to represent a laser beam with complex conjugate?

Representing a laser beam with complex conjugate allows for a more accurate and comprehensive understanding of its behavior. It can help in predicting how the laser beam will interact with different materials and how it will propagate through space.

3. How is a laser beam represented with complex conjugate different from other forms of representation?

A laser beam represented with complex conjugate is different from other forms of representation, such as using a single complex number, because it takes into account both the amplitude and phase of the laser beam. This allows for a more complete description of the beam's properties.

4. What are some applications of representing a laser beam with complex conjugate?

One major application of representing a laser beam with complex conjugate is in the design and optimization of laser systems. It can also be used in the study of laser-matter interactions, such as in laser cutting, welding, and material processing.

5. Are there any limitations to representing a laser beam with complex conjugate?

While representing a laser beam with complex conjugate can provide valuable insights, it does have limitations. It is a mathematical model and may not always accurately reflect the real-world behavior of a laser beam. Other factors, such as environmental conditions, can also affect the beam's properties.

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