Teste de 6tlca F513

2013-dezembro-20
l . A single-mode step-index fibre is designed to operate at Ao - 15 SOnm, with cut-off
wavelength Ac = 1310nm. The fibre attenuation is a = 0.20dBkm-
1
@1550nm. The
cladding is pure silica and the core is germanium doped silica:
cladding refractive index: 1.44402@1550nm; l.4468@1310nm
refractive index contrast: L1 = 0.003 at both wavelengths
(a) [21 Determine the value of core radius a.
(b) [21 Calculate the value of the power confi nement factor r@1550nm that describes t he
ratio of the power propagated in the core to the total propagat ed power .
(c) [2] The profile of the fundamental mode @1550nm can be approximated by a Gaussian
function of the fibre cross-section radius r. The corresponding power density of the
propagating mode is then given by (r) = P
0
expf-(r /a
0
)
2
J . Ca lculate the "mode radius" a
0
.
Describe the intensity profile on a CCD detector pl aced perpendicularly to t he fibre axis, at a
distanced = 3.0cm from the fibre end.
{d) [2] Determine the material dispersi on anv the waveguide dispersion aw, and the t ot al
dispersion a of the fibre @1550nm. Assuming a tolerable f ibre li nk t otal att enuati on of 20dB,
a loss of O.SdB at each {input and output) connector, and O.OSdBkm-
1
average splicing loss,
calculate the maximum link length l determi ned by the loss. Calculate the maximum data
transmission rate B achievable over the fibre link as determined by fibre dispersion.
2. Consider the following 2D model of a directional coupler, operating at the 1550nm
wavelength, using waveguides in the limit of the single-mode regi me:
two identical cores of germanium doped sil ica; wi dth: 2a
separation between the two core axes: D = 4a
silica cladding refractive index: 1.41402@1 SSOnrn
refractive index contrast: Ll = 0.003
(a) [2] Determine the value of the length L of t he coupler that performs as a 1 * 2 power 3dB
power splitter.
(b) [2] Light is launched at both coupl er i nput ports, with amplit udes A(O) = A
0
and
B(O) = (A
0
/2)expU8), so that the coupler operates as a beam combiner. Cal culate the two
coupler output ports intensities.
(c) [2] Assume again the operation as a 1 * 2 power 3dB power splitter. If the spl itting ratio
tolerance is +O.SdB, estimate the tolerance +LlD of the separation between the axes of the
two cores.
(d) [2] Consider again the operation as a 1 * 2 power 3dB power splitter. Due to a fabrication
error, one core width is l.8a. Estimate the resulting power splitting ratio at the coupler
output.
3. Consider a 2D model of a Bragg grating written in the core of a waveguide that operates in
the limit of the monomode regime at 1 SSOnm. The grating is a sinusoidal modulation of the
core refractive index along the propagation direction, with amplitude on and period 11. The
Bragg wavelength is AB = 1 SSOnm. The grating length is /, = 10.01nm and its maximum
intensity reflectance is R = 0.95.
germanium doped silica core; width: 2a
silica cladding refractive index: l.44402@1550nm
refractive index = 0.003.
(a) (2) Estimate the values of on and
11
(b) (2) Determine the freq b d . .
of the fl uency an width !Jf of the grating, defined between the first zeros
re ectance R(f) around the centre Bragg frequency [
8
.
Teste de 6tica F513
2013-novembro-15
1. A planar optical waveguide was fabricated using a silica substrat e: n
5
== 1.44402@1 SSOnm;
n
5
= 1.4467@1320nm. A core layer (thickness t , index contrast Ll == 0.006) was deposited on
top of the substrate. A cover layer was next deposited, and the resulting refractive index
profile of the planar waveguide is symmetrical.
(a) Specify the maximum thickness of the core layer that ensures mono mode (T
0
) operation
at both 1320nm and 1550nm wavelengths. If the excitation polari zation is changed t o TM, is
monomode operation to be expected? Justify.
(b) Calculate the effective index of the TE
0
mode @l550nn1.
(c) Specify the Ey(x) component of the TE
0
mode @1550nm, assuming that a power
p = 1mW is guided per l cm width along the transverse di rect ion. Estimate the minimum
acceptable thickness of a finit e superst rate layer that ensures adequate operati on of the
planar waveguide. Will this thickness ensure safe operat ion @1 320nm? Justify.
(d) A glass prism (90, 45, 45) with refract ive index n == 1.6500@1550nn1 is used to
couple to the TE
0
mode @1550nm. Calcul at e t he angle of inci dence on the input facet of t he
prism.
2. A 3d8 coupler was designed using a MM I configuration, for opera t ion@l 550n1n:
Silica substrate: l.44402@1550nm
Core layer: thickness 2d, index contrast Ll == 0.006
Cover: air
Lithographic patterning:
MM I section width W == 40.0 m
Input/Output monomode waveguides: width 2a; height 2d; sect ion nominally rectangular, but
a residual layer (thickness t) remained on the sides of the rectangul ar core due to an
incomplete lithographic step. The input channel waveguide is centered.
(a) Specify the maximum core layer thickness that guarantees mono mode operat ion, in depth,
of the MM I section. Calculate the maximum tolerable thi ckness t of t he residual layer which
exists on the sides of the input/output channel waveguides.
(b) Calculate a 2D equivalent model of the device. How many guided modes will be support ed
in the MM I section? Determine the minimum length of this section that provides 3d8 power
splitting to the output channel waveguides.
(c) Calculate the maximum value of the width 2a of the input/output waveguides compatibl e
with monomode operation. Without numerical calculation, indicate how to estimat e the
upling efficiency of the input mode to the fundamental mode of the MM I section.
stlmate the intensity profile of the radiation from one of the two output waveguides on a
ced at a distance D = 2cm from the device.
3. A surface plasmon polariton (SPP) propagates along the planar interface between a metal
(Au) and a glass, at the vacuum wavelength Ao = 800nm. The permittivity of the metal at the
operation frequency is E
711
= E;
11
+ i E ; ~ = -25 + il.4'1. The refractive index of the dielectric at
the same frequency is nd = 1.44 7.
(a) Calculate the propagation constant of the SPP, assuming negligible loss in the metal.
Considering now loss in the metal, find the attenuation length of the SP P. Estimate the
penetration depth of the magnetic field in the dielectric.
(b) Assume that a periodic surface grating (period 11, depth q) etched along the metal-
dielectric interface is used to couple to the SPP in second order. Establish the relationship
between the incidence angle 8 and 11, and the relevant SPP parameters. Does the profile of
the surface grating affect the coupling angle 8? And does it affect the coupling efficiency?
Justify qualitatively.