課程名稱︰光電導論
課程性質︰選修
課程教師︰邱奕鵬
開課學院：電資學院
開課系所︰電機工程學系
考試日期（年月日）︰103.11.13
考試時限（分鐘）：180分鐘
是否需發放獎勵金：是
試題 :
1~12為填充題或圈選題, 13~18為簡答題或計算題。黃色字為參考答案。
1.(3%) One way to make white-light bulb is to excite a phosphor material with a
blue LED. In an LED bulb with color temperature of (3000K,4500K,6000K), more
blue light is absorbed and converted to yellow light as compared with the
other two.
2.(2%) Our eye is most sensitive to the color of (red,orange,yellow,green,blue,
violet).
3.(4%) In the Munsell system, "brightness" is expressed with (r,φ,z)-axis. The
saturation of "pink" is (more than,the same as,less than) that of "red".
4.(4%) Complementary colors: a.Cyan: Red b.Green: Magenta
5.(2%) Presbyopia (老花) is due to (shorter focal length, longer focal length,
decreased accommodation range, increased accommodation range) of eye lenses.
6.(2%) If the field of a guided mode is mostly confined in the core of a wave-
guide, then its normalized propagation constant is closed to (-2,-1,0,1,2).
7.(4%) The attenuation of a standard optical fiber is dominated by (absorption
from water, lattice absorption, Rayleigh scattering, Fresnel scattering) at
at the wavelength of 1700 nm. Material dispersion of glass is zero around λ
= 1.3 μm.
8.(4%) The lowest attenuation reported of silica based optical fiber is 0.15
dB/km. If the input power is 3 dBm into such a fiber, the received power will
be 0.5m W after propagating 40 km.
9.(4%) The bit rate capacity of an SMF system is 20 Gbps. If the total disper-
sion, linewidth of the source and propagation distance are all doubled, the
bit rate capacity becomes 2.5 Gbps.
10.(4%) A 100 km fiber with dispersion D = 12 ps/nm/km is spliced with a 20 km
fiber with D = -40 ps/nm/km. The effective dispersion will be D_effective =
3.33 ps/nm/km.
11.(4%) Single mode conditions (a) symmetric planar dielectric waveguides: V <
π/2 (b) step index fibers: V < 2.405
12.(2%) A beam splitter is based on frustrated total internal reflection (FTIR)
If the gap between the prisms is wider, the fraction of the transmitted light
will normally be (lower,the same,larger).
13.(a)(4%) When we look at the sky in any direction but the sun, it is blue.
Please explain it briefly based on Rayleigh scattering.
Rayleigh scattering is proportional to 1/λ^4, so scattering of the blue
light is stronger, which makes the sky look blue.
(b)(4%) The blue light is usually partially polarized. That is, one polari-
zation is stronger than the other. Please explain it briefly. (Hint: Consi-
der the radiation pattern.)
Ans: http://i.imgur.com/dsARPME.jpg
14.(4%) Larger dispersion will result in larger signal distortion, expecially
in a high-data-rate and long-distance communication system. However, zero
dispersion is avoided in a WDM system. Please point out the key issue.
Zero dispersion means all channels travel in the same speed. If there is
"crosstalk" between channels, it would be accumulated and enhanced.
15.(15%) Consider a Fabry-Perot optical cavity in air of length 200 microns
with mirrors that have a reflectance of 0.95. Calculate the cavity mode ne-
arest to the wavelength 850 nm, and corresponding wavelength. Calculate the
separation of the modes, the finesse, the spectral width of each mode and
the Q-factor.
Ans: http://i.imgur.com/VSOKs1i.jpg
16.(10%) Please derive the Fresnel equations for TM wave as the following based
on the bounary conditions at the interface between two materials of refrac-
tive indices n_1 and n_2, where n = n_2/n_1.
http://i.imgur.com/fspvORz.jpg http://i.imgur.com/Khf4JUf.jpg
Ans: http://i.imgur.com/Mf3chvv.jpg
17. The group velocity in a dispersive material is expressed as
v_g (medium) = c / [n-λ(dn/dλ)], where "d" represents differential.
(a)(5%) Show that the material dispersion coefficient can be express as
D_m ≒ -(λ/c)[(d^2)n/d(λ^2)] .
(b)(5%) If refractive index of the material is approximately by Sellmeier
equation by (n^2)-1 = G*(λ^2) / (λ^2)-[(λ_1)^2], where G = 2.0 and
(λ_1)^2 = 0.3 (μm^2). Please evaluate the material dispersion at λ =
1.0 μm. Hint: You can use finite difference to approximate the second
derivative by (d^2)f/d(x^2) ≒ [f(x+Δx)-2f(x)+f(x+Δx)] / (Δx)^2 .
Ans: http://i.imgur.com/6Gsx7t5.jpg
18.(a)(6%) As shown in the figure below, please derive the equation for the
refraction of spherical boundary
θ_2 ≒ (n_1/n_2)*θ_1 - (n_2-n_1)*y/(n_2*R) .
http://i.imgur.com/9O8fyKO.jpg
Ans: http://i.imgur.com/DH7nuVD.jpg
(b)(8%) Please use ABCD matrix method to derive the following equations for
thin lens, from ABCD matrix of free space and the ABCD matrix of spheri-
cal boundary from (a).
θ_2 = θ_1 - y/f 1/f = (n-1)[(1/R_1)-(1/R_2)]
1/z_1 + 1/z_2 = 1/f y_2 = -(z_2/z_1)*y_1
http://i.imgur.com/lRxyjGc.jpg
Ans: http://i.imgur.com/s9lM0m9.jpg