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Unformatted text preview: Preliminary Exam 1 ECE 430 September 29,2004 Instructions: This is an in-class, open book exam. Attempt every problem. You may use
a calculator. Multiple Choice:
1. If the wavelength of'light is 1 pm, the frequency of'the light is a). 100 MHZ
b). 33 THz
c) 300 IHZ 2.Stimu1ated Emission
a). Requires that there be more atoms in the excited state than the ground state b) Creates a photon that is a clone of'the incident photon c). Randomly adds a photon to the photon stream 2 2 3. The wave equation is written as V2 E — 6 Eldt =0. What is the coordinate system? a) rectilinear b) spherical c) metro-temporal (1) depends on the boundary conditions 4. A narrow laserbeam is incident on an array of'parallel Wires oriented in the Z-
direction, each separated by Ax. In the far ﬁeld, the beam will look like a) A bunch of'beams spreading out at discrete angles b) A beam with shadows, each separated by Ax c) A beam with a slightly modiﬁed wavelength, given by Pt=3l.o(l+(Ax/7to)2) 5. Assume you want to sell cool-looking polaroid sunglasses to sailors. What
orientation should you orient the polar-bid? a) Horizontal b) Vertical c) 450 so that both the horizon and sky are visible 6. Which of these sources produces a spatially coherent wave?
a) ﬁlament light bulb
b) A ﬁlament light bulb observed through a 0 .5 um hole c) The radio emission from my cell phone? 7 What is the ABCD matrix fbr‘ a plane mirror? a)10 b)10 c)or
01 0—1 10 8. What is the right ABCD matrix for this system? a) 1 d1 1 0 0 d2.
0 1 1/; 1 1 0
b) 1:12 1 0 l‘dl
0 1 -1/f‘ 1 0.1
c) 1 d1 1 d1+d2 142
0 1H1/f 1 0 1 91. What is the unit cell for this ring laser? a) — b) 7: c) \/\
10.1 A ring cavity that has 30 cm perimeter has a difference equation solution rn= sin[n1t/ 100 + 0321] How long will it take for the ray to traceover itself? a) 3141.159 nsec
b) 100 nsec
c) 200 nsec l 11 Why do distant roads in the desert look wet?
a) It’s because there are oasis in the desert -
b) The hot air (1 1e. lower density air)near the surface bends light from the sky
downward due to dn/dr'
c) Total internal reﬂection occurs in the hot air just above the road surface,
reﬂecting light from the sky up away from the road. - 12‘. Which beam is described as a IBM22 mode? a) , c)_ 13.. A gaussian beam traveling in the positive 2 direction is incident on a lens of focal
length f at the beamwaist, 2 =20“ What is the radius of'curvatur'e of'the beam immediater following the lens?
a) f' b) —f‘ c) inﬁnity Page 2 L=50 cm 14“ Is this cavity stable?
a) Nope, there is no beamwaist
b) Sure, but there is no beamwaist R1=1000m R2="200°m
c) Depends on the wavelength It could be stable under some conditions 15‘ A solid state laser is made from a ceramic with index ofreﬁaction n=2‘.0.‘ What is the free spectral range ofthis cavity?
a) '75 GHz
b) 3.75 GHz
c) 1.5 GHz 16” what is the photon lifetime of'this cavity? a) 40 nsec b) 40 11: nSec
0) Cannot be determined as defined, we don’t know the wavelength Real Problems 17 Consider the laser cavity below: Assume all Inin‘oxs are high reflectors R=infinity R=inﬁnity R=100 mm
a) is the cavity stable
b) if'it is stable, Where is the beam waist? c) If it is unstable, would changing the radius of curvature ofthe curved mirror make
the cavity stable? 18‘. A laSer beam passes by you as your standing on a street corner waiting for a bus“
You’d like to determine where the laser came from. Assuming the source laser is located
at z=0, could you measure enough parameters ofthe beam at your street corner location
to determine where z=0 is? Ifthe answer is “yes”, what parameters do you need to measure? Page 3 ...
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