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Helium-Neon LASERS gain bandwidth

  1. Mar 22, 2012 #1
    1. The problem statement, all variables and given/known data
    A helium-neon (He-Ne) laser has a gain bandwidth (denoted here as the frequency interval
    over which the laser gain equals or exceeds the minimum threshold gain) given by ΔG= 1.0 GHz, centred on the λ = 632.8 nm emission wavelength.

    Show that in order to tune the frequency of this He-Ne laser over its entire gain
    bandwidth, the length of the resonator should be changed by ΔL = -1/2λ.
    2. Relevant equations

    3. The attempt at a solution
    The length and frequency changes are both small compared to the length and fre-
    quency, respectively so differentiation of the condition for standing waves in a
    resonator must be applied.

    The condition for standing waves is :L=mλ/2

    but dL/dλ= m/2 , how can i get ΔL = -1/2λ ?
  2. jcsd
  3. Mar 22, 2012 #2


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    You want the fundamental mode, so m=1. The calculation is pretty straightforward. Calculate the longest and shortest wavelength still within the gain bandwidth and calculate the corrsponding resonator lengths needed to get a standing wave for these two wavelengths.
  4. Mar 22, 2012 #3
    thanks for the reply but i cant understand what it means:
    longest and shortest wavelength still within the gain bandwidth ,how can you see if wavelength is within the bandwidth?
  5. Mar 22, 2012 #4


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    The problem statement says you have a bandwidth of 1 GHz around the central wavelength of 632.8 nm, so your bandwidth goes from 632.8nm-0.5 GHz to 632.8nm+0.5 GHz. The conversion between wavelength and frequency is pretty much the only math involved here. You should be able to do that yourself.
  6. Mar 22, 2012 #5
    this doesnt make sense because 0.5 Ghz corresponds to 0.6 m wavelength, so 632.8*10^-9 -0.6 gives negative wavelength which cannot be acceptable
  7. Mar 23, 2012 #6


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    Ok...let me start at the very beginning.

    Just do me the favour and calculate the wavelengths corresponding to 0nm +0.5 Ghz (as you did), 100nm+0.5 GHz, 632nm+0.5 GHz and 2000 nm+0.5 GHz by converting wavelength to frequency FIRST and then adding the 0.5 GHz.

    And while you are at it please just plot a graph of wavelength vs. corresponding frequency and have a look at whether it is linear or not. Does that help you understand why one cannot just convert 0.5 GHz into a wavelength and subtract it, but have to convert the desired wavelength into a frequency before and then add or subtract the bandwidth from that converted value?
    Last edited: Mar 23, 2012
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