Q.3 You are given the following information, Table 3.1, about a He-Ne laser Tabl
ID: 3307451 • Letter: Q
Question
Q.3 You are given the following information, Table 3.1, about a He-Ne laser Table 3.1: Helium Neon Laser parameters Laser Wavelength Laser transition probability (Au) Upper laser lifetime Stimulated emission cross section Threshold inversion density Laser gain-medium length Gas mixture Atomic weights Index of refraction of gain medium Mirror reflectances Gas temperature Mode 632.8 nm 3.4 x 10 s 3 x 10-8s 3 x 10-17 5 x 1015 m 0.5 m He:Ne at 5:1 He = 4 a.mu. Ne = 20 a.m.u. 100% and 87% 400 K TEMoo a) Calculate the linewidth of the gain curve and the threshold gain, stating any assumptions you make? [10 marks] b) Calculate the percentage extraneous losses in the laser gain medium per pass, i.e [6 marks] losses other than that at the mirrors? Mention what could cause these losses c) What is the mode number that is nearest the line centre of 632.8 nm? How many axial modes could possibly oscillate using the calculated linewidth in part (a)? [10 marks] d) What length would this cavity need to be to have a single mode laser? Show that for a temperature change which causes a change in length of the cavity oL the wavelength of a given mode would change by [4 marks]Explanation / Answer
Answer :
3 (a) The gain curve is a graph of gain as a function of frequency and it denotes the width of the fluorescence line where the loop gain is plotted along Y axis and the frequency along X axis. The line width is of the gain curve is width of the amplification curve at half the maximum height.
The linewidth of a HeNe laser is specific to the application. The linewidth of individual axial modes is usually small (~kHz) and is primarily determined by external factors and measurement timescales.
FWHM = 0 (8kTln2 mc^2)^ 1/2
= 299 792 458/632.8 x( 8 x1.38064852 × 10-23 x 300 x ln 2 x5 x 299 792 458 x 299 792 458 ) ^1/2
= 473755.46 x 0.045
=21519.53 nm
=2.15 x 10 ^ 4 nm
Since the gas mixture is 5 : 1, this is a short laser (~ 0.5 mW) . It has less number of axial modes.
The threshold gain is the lowest excitation level at which a laser's output is dominated by stimulated emission . Below the level the laser's output power rises slowly with increasing excitation. Above this, the slope of power vs. excitation is of greater magnitude.
The threshold gain is = del Nth = 1.1 x 10^ 15 m -3
The laser is dominated by doppler broadening.
(b) The loss factor M: M = exp2(-aL) = exp[-2(1.34*10-4 )*30] = 0.992
Cause of losses :
(c) The mode numbers nearest to the line center are n=2, n=4. Number of axial modes could oscillate is 5.
In this laser 5 equidistant frequencies are allowed at the output, and they are spaced at equal interval, which are equal to the distance of the space.
(d) Single Mode cavity lengths from 405 nm to 1625 nm.
Doubling the length of the cavity decreases to half the length between adjacent axial modes. Thus a single mode laser can be made by reducing the length of the cavity, such that only one longitudinal mode will remain under the fluorescence curve with GL>1.
In such single mode laser the accurate distance between the mirrors is critical, since if there will be no modes to fulfill the condition, no emission will take place. The shortcoming of this process is that the short length of the cavity shortens the power output of the system.
Therefore, lambda m = 2L/m
(del lambda m ) / lambda m = del L / L (since we count the change only)
del lambda m = (lambda m / L ) x del L
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.