What is the Group Velocity of Infrared Radiation in a Dispersive Medium?

I need to find another wayIn summary, the conversation discusses the calculation of the speed at which infrared radiation, with a wavelength of 1um in air, carries information through a dispersive medium with a refractive index of 1.4505 and a change in refractive index of -0.01 per um at this wavelength. The group velocity dw/dk is the speed at which the radiation carries information and can be calculated using the formula c/(n + w(dw/dn)). The link provided contains alternative expressions for this formula, which can be used to convert dn/d(lambda) into dw/dn.
  • #1
nathangrand
40
0
Infrared radiation, of wavelength λair = 1um in air, travels through a
dispersive medium with refractive index n = 1.4505 and with
dn/dλair = -0.01 per um at this wavelength. Calculate the speed at which the
radiation carries information.

So know that

c/n = λf

radiation carries information at group velocity dw/dk

can also show that dw/dk = c/(n + w(dw/dn))

but don't know where to go from here

feel http://en.wikipedia.org/wiki/Group_velocity has some useful expression in alternative expressions but need to be able to show, and can't
 
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  • #2
w is angular frequency. In the other expression are formula needed to calculate w. The convert dn/d(lambda) into dw/dn.
 
  • #3
how?
 
  • #4
Take at look at the link you posted in the other expressions sections. It all there.
 
  • #5
I know the expressions are there, I just can't fiddle around with the differetiation
 

1. What is group velocity information?

Group velocity information refers to the speed at which a group of particles or waves travel through a medium. It is calculated by taking the derivative of the group's dispersion relation, which relates the frequency and wavelength of the group.

2. How is group velocity information used in scientific research?

Group velocity information is used in various areas of research, including optics, acoustics, and quantum mechanics. It helps scientists understand the behavior of waves and particles in different mediums, and can be used to design and optimize systems such as communication networks and lasers.

3. How is group velocity different from phase velocity?

Group velocity and phase velocity are both measures of the speed at which a wave travels, but they are calculated differently. Group velocity takes into account the speed at which the overall shape of the wave packet moves, while phase velocity refers to the speed at which individual wave cycles travel. In some cases, group velocity can be faster or slower than phase velocity.

4. Can group velocity information be negative?

Yes, group velocity information can be negative in certain situations. This occurs when the group's dispersion relation has a negative slope, which can happen in materials with a high refractive index or in systems with negative refraction. Negative group velocities have been observed in experiments and have important implications for applications such as superluminal communication.

5. How does the concept of group velocity relate to the speed of light?

The speed of light in a vacuum is a fundamental constant and is not affected by group velocity. However, in materials with a refractive index greater than 1, the group velocity of light can be slower than the speed of light in a vacuum. This is due to the interaction between light and the atoms in the material, which causes a delay in the propagation of the wave packet.

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