Cavity spectrum: plan/curved mirror

Caculates the cavity spectrum and the frequency distance between TEM_00 and higher order modes m+n. Two curved mirrors possible. Programm made by T. Legero.

Parameter

Radius of curvature of mirror R1: R1= 1 m

Radius of curvature of mirror R2: R2= 1000000000 m

Cavity Length: L= 0.48 m

Reflectivity of mirrors: R= 0.99998

Speed of light: c= 299792458 m/s

Step 1: Calculate the Free-Spectral-Rang and Gouy-Phase

Free-Spectral-Rang: FSR

Gouy-Phase: Gouy

⇒

FSR = 312.284 MHz

Gouy = 76.0824 MHz

Step 2: Calculate the frequency difference between TEM_00 and TEM_mn

TEM mode number: mn

Next TEM_00: w

Frequency difference between TEM_00 and TEM_mn: Delta

Define maximum of mn and w:

mn_max = 100

w_max = 100

Define maximum of shown frequency difference to TEM_00:

abs(delta(mn,w)) < 10E6

Frequency difference von (q-w)ter höherer Mode mn zu q-ter TEM_00-Mode (Matrix):

⇒

Freq. diff. of m+n = 4 higher order mode to 00-mode is 7.95436 MHz
Freq. diff. of m+n = 37 higher order mode to 00-mode is -4.49309 MHz
Freq. diff. of m+n = 41 higher order mode to 00-mode is 3.46128 MHz
Freq. diff. of m+n = 74 higher order mode to 00-mode is -8.98616 MHz
Freq. diff. of m+n = 78 higher order mode to 00-mode is -1.03181 MHz
Freq. diff. of m+n = 82 higher order mode to 00-mode is 6.92256 MHz

Step 3: Calculate the frequency difference between TEM_00 and the nearest TEM_nm

Define the Modenumber of Higher-Order-Mode to plot (next Mode to 00):

mn = 4

Define the Vary Mirror-Curvature:

R = 0.95:0.01:1.05

Frequency difference between TEM_00 and TEM_mn:

plot(R,Delta)[Important!]:

Achtung: ROC wird hoffentlich >1m werden, damit die m+n = 4 Mode weiter weg ist!

plot(Gouy,Delta):

plot(R,Gouy):