HW4 solutions

HW4 solutions - 4.3 The Ar ion laser The argon-ion laser...

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Unformatted text preview: 4.3 The Ar ion laser The argon-ion laser can provide powerful CW visible coherent radiation of several watts. The laser operation is achieved as follows: The Ar atoms are ionized by electron collisions in a high current electrical discharge. Further multiple collisions with electrons excite the argon ion, Ar + , to a group of 4 p energy levels ∼ 35 eV above the atomic ground state as shown in Figure 4Q3. Thus a population inversion forms between the 4 p levels and the 4 s level which is about 33.5 eV above the Ar atom ground level. Consequently, the stimulated radiation from the 4 p levels down to the 4 s level contains a series of wavelengths ranging from 351.1 nm to 528.7 nm. Most of the power however is concentrated, approximately equally, in the 488 and 514.5 nm emissions. The Ar + ion at the lower laser level (4 s ) returns to its neutral atomic ground state via a radiative decay to the Ar + ion ground state, followed by recombination with an electron to form the neutral atom. The Ar atom is then ready for "pumping" again. a Calculate the energy drop involved in the excited Ar + ion when it is stimulated to emit the radiation at 514.5 nm. b The Doppler broadened linewidth of the 514.5 nm radiation is about 3500 MHz ( Δ υ ) and is between the half-intensity points. (i) Calculate the Doppler broadened width in the wavelength; Δ λ (ii) Estimate the operation temperature of the argon ion gas; give the temperature in ° C c In a particular argon-ion laser the discharge tube, made of Beryllia (Beryllium Oxide), is 30 cm long and has a bore of 3 mm in diameter. When the laser is operated with a current of 40 A at 200 V dc, the total output power in the emitted radiation is 3 W. What is the efficiency of the laser? Figure 4Q3 a Given wavelength λ o = 514.5 nm or 514.5 × 10-9 m, the change in the energy is Δ E = hc / λ o = (6.626 × 10-34 J s)(3.0 × 10 8 m s-1 )/(514.5 × 10-9 m) Ar atom ground state Ar + ion ground state 4 p levels 4 s 15.75 eV 488 nm 514.5 nm 72 nm The Ar-ion laser energy diagram Energy Pumping i.e. Δ E = 3.86 × × × × 10-19 J or 2.41 eV b The center frequency of the lasing emission is υ o = c λ o = (3.0 × 10 8 m s- 1 ) (514.5 × 10- 9 m) = 5.831 × 10 14 s-1 The relationship between wavelength and frequency linewidths...
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HW4 solutions - 4.3 The Ar ion laser The argon-ion laser...

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