Practice Problems

1. Show that optical intensity I and energy density u are related by the relation

I=uv

Where v is the group speed of light.

(Hint: Consider a cube of volume where A is the area perpendicular to the light flow. The optical energy crossing the left facet of the cube over a time would be present over the length . Make use of the fact that intensity is power per unit area and energy density is energy per unit volume.)

2.Show that wavelength in microns emitted by a semiconductor laser is related to the band gap energy in electron volts by the relation

3. (a)A GaAlAs laser diode has a 500 micron cavity length which has an effective absorption coefficient of 10 cm^-1 . For uncoated facets the reflectivities are0.32 at each end. What is the optical gain at the lasing threshold? (Ans. 32.78 cm^-1 )

(b) If one end of the lasers is coated with a dielectric reflector so that its reflectivity is now 90%, what is the optical gain at the lasing threshold?

(Ans: 22.44 cm^-1 . Notice that required gain to overcome the loss can be reduced by coating on one side of the cavity and take the useful output on the otherside)

4. A GaAs laser operating at 800 nm has a 400 micron cavity length with a refractive index of 3.6. If the gain exceeds the total loss in the region 750 nm << 850 nm and the loss dominates the gain for wavelengths that are out of the above range, how many modes will exist in the laser?

(Ans: 451 modes)