Question

Problem Solving: There’s No Place Like the Laser Lab The first optical maser demonstrated was the ruby laser (Theodor Mann, 1960). The optical gain medium is a “quasi-three-state” system. The system is called “quasi” because there are actually FOUR states total… but the two uppermost states both quickly decay into the intermediate/metastable state via mechanical losses of energy (aka. vibrations).

a. Excitations into the two upper states occur for 400nm and 550nm light. The lasing wavelength is centered around 694.3nm. Use this information to explain ruby’s red color.

b. Setting the ground state as a reference of 0eV, draw an energy diagram for the ruby gain medium… draw the levels, label and calculate the energies, … and add in arrows that indicate pumping processes, transitions via vibrational losses and the lasing transition. For the upper three states, also indicate the energy spread of the state (qualitatively… by considering the lifetime of the state).

c. The first ruby lasers were pulsed, and had a coherence length of 1.27cm in air. Assuming coherence over an entire pulse… what is the time duration of the pulse (aka the “pulse width”)?

d. Calculate the bandwidth of this laser, using the simple model relating bandwidth and coherence length that we developed in class.

e. These pulsed lasers were used by the dermatological industry… including the removal of tattoos. If each pulse contains 1.5 mJ of energy, how many photons are in a pulse?

I read the comments but this is all that I know.

Answer 1

a) Given, The upper two states occur for 40ohm and 55orm. The lasing wavelength is centered around 694-3m- Laser output wavelength of Ruby sruby = 694.3m. In Electromagnetic (EM) Spectrum the wavelength truly lies in Red portion which is visible position. So, the colour of laser is Red in colour. (6) Consider the ground state as a reference of oev. Energy can be calculated as. E 124.ev. Alum) Criven wavelengths are toorm , 550nm, 694: 3 nm .. E400 = 1.24 : 3 loev Eggo = 1:24 - 0.55 €69413 = 1024 2.25ev = 1.790 0.6943 DE librational losses lor) Radiationless transmission » Metastable Boonm Stacte 550nm oer Coround state

From figure the life time of metastable state is in the order of 106 to 163s. So energy with is very small. - The chergy width of excited states that is at is higher. (C) Coherene length of pulsed Ruby laser is d. = 1.270m. Coherence time is given as, TE- l - 127X107 m 3x108 ł = 4.2x10's (1) The coherence length and bandwidth are related as e and such 1.27X102 let us calculate as to get banduliath (ou) 41-42.694.3.4189)" DX = 3,8x10mm substitute of in or OU= 3x108 AV = 729x108 HE (2) Energy of pulse = 1.5m 5 = 1.5x1035 Energy of photon = hc - 6.6x10 34 x 3x108 2.951781579 694. 3x15 9 Number of photons = 1.5x15² - 5:26*115 photons, 08517xi olan 3.8815 tong