ECE 476/576 Summer 1999 In-Class Test Number 1

Answer all questions

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Q1 (a) An empty laser cavity consists of two mirrors separated by 10 cm. The mirror reflectivities are R₁=1 and R₂=0.9. Calculate the cavity photon life-time.

1(b) The cavity is filled with a material whose index of refraction is 1.1. Assuming that the material is not pumped, calculate the new cavity photon life-time.

1(c) Calculate the threshold gain in cm^-1 for this cavity, assuming that there are no other losses in the cavity. (Assume that the cavity is filled with the material described in (b))

1(d) If a tuning optical element such as a prism is introduced in the cavity, and if this element has a loss of one percent per pass, what is the new threshold gain, in cm^-1?

(Assume that the cavity is filled with the material described in (b))

Q2 (a) A diode laser emits 3 mW continuously at 1 mm. Calculate the energy of the photons emitted in the following units: cm^-1; Joules; eV.

2(b) The laser beam is focused to a spot with a diameter equal to 10l. Calculate the intensity in Watts/m²

2(c) The laser beam is passed through an optical amplifier (length 2 cm) which has been pumped so that its gain is 0.01 cm^-1. Calculate the power of the amplified beam in Watts.

2(d) In another application, this same laser beam is passed through an absorber whose absorption coefficient is 0.005 cm^-1, instead of through the amplifier. If the absorbing medium has a length of 1 m, how much energy (in Joules) is deposited in the absorber if the laser is kept on for 2.5 seconds?

Q3. Briefly, but carefully, describe:

(a) Spontaneous emission

(b) Absorption

(c) Stimulated Emission

(d) Coherence

(e) Population Inversion

3 (f) Explain why the state of population inversion is sometimes described as a negative absolute temperature.

3(g) Is a negative cavity photon lifetime possible? Explain.

3(h) Is there a connection between a negative absolute temperature and a negative cavity photon lifetime? If there is a connection, explain that connection. If here is no connection, state "None"

ECE 478/578 (Formerly 476/576) Summer 99, Test 1, Solutions