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Journal ArticleDOI

Design and modeling of a photonic crystal fiber gas sensor

20 Jun 2003-Applied Optics (Optical Society of America)-Vol. 42, Iss: 18, pp 3509-3515
TL;DR: The modeling results of an all-fiber gas detector that uses photonic crystal fiber (PCF) and the relative sensitivity of the PCF as a function of the fiber parameters is calculated.
Abstract: We report the modeling results of an all-fiber gas detector that uses photonic crystal fiber (PCF). The relative sensitivity of the PCF as a function of the fiber parameters is calculated. Gas-diffusion dynamics that affect the sensor response time is investigated theoretically and experimentally. A practical PCF sensor aiming for high sensitivity gas detection is proposed.

Summary (3 min read)

1. Introduction

  • Photonic crystal fiber PCF or holey fiber that incorporates air holes within the silica cladding region opens new opportunities for exploiting the interaction of light with gases through the evanescent field in the holes.
  • The sensitivity was, however, very low owing to the 0.2% mode power exposed to the sensing region.
  • Monro et al.1 examined the use of a particular PCF for gas detection and theoretically predicted that by choosing appropriately the PCF parameters, high-sensitivity gas detection can be achieved without significantly compromising the mechanical properties of the optical fiber.
  • A proof of concept demonstration of a PCF gas sensor was recently reported by the authors.

2. Relative Sensitivity of the Gas Sensor of the Photonic Crystal Fiber

  • The authors consider here the index-guided PCF Refs.
  • The effective index ne and the mode-field pattern Ex, Ey and Hx, Hy can be calculated by solving Maxwell’s equations by using a numerical technique the finiteelement method .7,8.
  • The basis for doing so is that, for both types of fiber, most of the guided power, especially for the fundamental mode the authors are interested in here, is distributed within the central silica core and the innermost ring, and the light power in the outer rings is negligible.
  • The authors also calculated the relative sensitivity of a modified fiber with the same structure as the Lucent fiber but with varying hole diameter and separation.

3. Response Time of the Sensor of the Photonic Crystal Fibers

  • One concern in using PCF as evanescent field sensors may be the limited response time due to the time required for gas to diffuse into the holes.
  • (6) It can be seen from Eq. 6 that the average gas concentration in the hole columns depends on interaction length l.
  • If the Knudsen number is larger than one, the diffusion will be dominated by the wall effect.
  • The authors may estimate the diffusion time under the worst plan by replacing DAB K in Eq. 7 with DBB K.

4. Experiments and Results

  • Experiments were conducted to investigate the relative sensitivity and the diffusion dynamics of Crystal Fiber’s PCF for acetylene measurement.
  • The other end of the PCF was spliced to a single-mode fiber connected to a photodetector.
  • The chamber was then sealed after 30 s of loading of acetylene.
  • The relativity sensitivity r was estimated by using the steady-state t 3 in Eq. 10 value of the normalized minimum transmittance as shown in Fig.

5. Sensor Design, Power Budget Analysis, and Performance Evaluation

  • From the analysis in Section 4 the authors conclude that the response time of PCF is limited by the time taken for acetylene gas to diffuse into the holes.
  • For a gassensing application that requires a response time of 1 min the length of the sensing PCF should be limited to less than 7 cm.
  • This design allows for a long sensing fiber to be used to improve the sensitivity without comprising response time.
  • Figure 9a shows an example of a sensor design based on Crystal Fiber’s 1.7- mdiameter silica core PCF where the sensing PCF with periodic openings is connected to single-mode transmission fibers at the two ends.
  • A 1.53- m distributed feedback laser is used as the source and an InGaAs photodetector as the receiver.

A. Loss Introduced from the Opening

  • The openings in the PCF modify the waveguide structure and thus change the transversal field distribution in the fiber cross section.
  • The 2 ne ne c ne ne c in Eq. 11 is the Fresnel coefficient, and the second term is the overlap integral between the fundamental modes of the respective PCF sections.
  • Results show that the difference in the effective indexes with and without an opening is very small, and the first term is approximately equal to 1.

B. Lengths of the Open Sections

  • The lengths of the opened sections l* as shown in Fig. 9b should be long enough to ensure that time required for acetylene gas diffusion into the holes is not dominated by the wall effect of the open sections.
  • Assuming that Kn 0.01, the length of the open section should be longer than 6.5 m.
  • Because the depth of the open fiber section is less than the radius of the original PCF 65 m , the time required for the acetylene to diffuse into the open air holes is estimated to be less than 0.001 s.
  • As mentioned in this subsection the variation in the mode-field distribution due to the opening is small.
  • The loss coefficient in the open section is then expected to be similar to that of the unopen fiber sections.

C. Power Budget and Performance Analysis

  • Considering as an example the sensor system shown in Fig. 9 with a required response time of 1 min, the fiber length between the two open windows can be chosen as l 7 cm.
  • Consider that the detection resolution of 3.75 parts per million for an equivalent of 1 m ppm m of acetylene has been achieved with wavelength modulation spectroscopy and digital signal processing.

6. Summary

  • The authors have proposed an all-fiber gas sensor based on periodically windowed PCF fiber.
  • Preliminary experiments and simulation show that an acetylene sensor system with a response time of 1 min and sensitivity of better than 6 ppm can be realized.
  • The PCF sensor can also be used to detect other gases such as methane with a similar expected performance.
  • The response time may be tailored with a certain range by selecting the distance between the two windowed sections.
  • These include the low-loss connection between the single-mode transmission fibers and the PCF sensing fiber, fabrication of the window openings along the PCF, and packaging of the open section with gas permeable films that allow gas to diffuse in or out but prevent dirt to enter the open sections.

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Content maybe subject to copyright    Report

Design and modeling of a photonic crystal
fiber gas sensor
Yeuk L. Hoo, Wei Jin, Chunzheng Shi, Hoi L. Ho, Dong N. Wang, and Shuang C. Ruan
We report the modeling results of an all-fiber gas detector that uses photonic crystal fiber PCF. The
relative sensitivity of the PCF as a function of the fiber parameters is calculated. Gas-diffusion dynam-
ics that affect the sensor response time is investigated theoretically and experimentally. A practical
PCF sensor aiming for high sensitivity gas detection is proposed. © 2003 Optical Society of America
OCIS codes: 060.2370, 290.1990, 330.1880.
1. Introduction
Photonic crystal fiber PCF or holey fiber that incor-
porates air holes within the silica cladding region
opens new opportunities for exploiting the interac-
tion of light with gases through the evanescent field
in the holes.
1,2
The use of the evanescent field for
gas detection was exploited previously by using
D-shaped optical fiber.
3
The sensitivity was, how-
ever, very low owing to the 0.2% mode power exposed
to the sensing region. Monro et al.
1
examined the
use of a particular PCF for gas detection and theo-
retically predicted that by choosing appropriately the
PCF parameters, high-sensitivity gas detection can
be achieved without significantly compromising the
mechanical properties of the optical fiber. A proof of
concept demonstration of a PCF gas sensor was re-
cently reported by the authors.
2
In this paper we report the results of our recent
modeling, simulation, and experiments on the design
of practical PCF gas sensors. We present first in
Section 2 our simulation results on the relative sen-
sitivities of two types of PCF, i.e., the nonlinear PCF
with a 1.7-m core from Crystal Fiber
4
and the Lu-
cent Technology PCF Ref. 5 with a 1.55-m hole
separation 共⬃1.7-m-diameter core and a 1.4-m
hole diameter. We then examine the effect of vary-
ing the hole’s size and separation on the relative sen-
sitivity of the PCF. The sensor response time
limited by gas diffusion into the holes as a function
sensing fiber length is modeled and reported in Sec-
tion 3. Experimental investigations on the relative
sensitivity and gas-diffusion dynamics into the air-
hole column of the Crystal Fiber PCF is reported in
Section 4. Based on the findings in Sections 2– 4, a
gas acetylene sensor design based on a periodically
windowed PCF is proposed in Section 5. The power
budget and performance analysis of the proposed sen-
sor system are also presented in Section 5. A brief
summary is in Section 6.
2. Relative Sensitivity of the Gas Sensor of the
Photonic Crystal Fiber
We consider here the index-guided PCF Refs. 4 and
5 where most of the guided light power is confined
within the solid-core region with a fraction evanes-
cent field of power extended into the holey region.
The evanescent field in the air holes is absorbed by
the gas species, and the gas concentration can be
obtained from the intensity attenuation through the
Beer–Lambert law
6
:
I共␭兲 I
0
共␭兲exp关⫺r
m
共␭兲lC. (1)
I and I
0
are, respectively, the output light intensities
with and without the presence of gas being detected,
m
共␭兲 is the absorption coefficient of the gas being
measured and is a function of wavelength, l is the
length of the PCF used for gas detection interaction
length, C is the gas concentration and r is a relative
sensitivity coefficient defined as
6
r n
r
n
e
f, (2)
Y. L. Hoo, W. Jin, C. Shi, H. L. Ho, and D. N. Wang are with the
Department of Electrical Engineering, The Hong Kong Polytechnic
University, Hung Hom, Kowloon, Hong Kong, China. S. C. Ruan
is with the Faculty of Engineering and Technology, Shenzhen Uni-
versity, Guang Dong, China.
Received 19 July 2002; revised manuscript received 10 Decem-
ber 2002.
0003-693503183509-07$15.000
© 2003 Optical Society of America
20 June 2003 Vol. 42, No. 18 APPLIED OPTICS 3509

where n
r
is the index of the gas species and is ap
-
proximately equal to 1, n
e
is the effective index of the
guided mode, and f is the fraction of the total power
located in the holes. For a particular ber mode f
can be calculated by integrating the optical power
inside the air holes and dividing it by the total power
carried by that mode and expressed as
f
holes
E
x
H
y
E
y
H
x
dxdy
total
E
x
H
y
E
y
H
x
dxdy, (3)
where E
x
, E
y
and H
x
, H
y
are, respectively, the trans
-
verse electric and magnetic elds of the mode. The
effective index n
e
and the mode-eld pattern E
x
, E
y
and H
x
, H
y
can be calculated by solving Maxwells
equations by using a numerical technique the nite-
element method.
7,8
Two types of PCF, i.e., the Crystal Fiber PCF and
the Lucent Technology PCF, were examined. Both
PCFs have an 1.7-m-diameter silica core sur-
rounded by an array of air holes. During numerical
calculation we considered only the two innermost
rings and a quarter of the cross section of the bers as
shown in Figs. 1 and 2. The basis for doing so is
that, for both types of ber, most of the guided power,
especially for the fundamental mode we are inter-
ested in here, is distributed within the central silica
core and the innermost ring, and the light power in
the outer rings is negligible. The eld distributions
in the other three quarters can be obtained by using
the symmetric property of the ber. The relative
sensitivity of the Crystal Fiber PCF as a function of
wavelength is shown in Fig. 3. At wavelengths of
1.53 and 1.65 m, corresponding to absorption lines
of acetylene C
2
H
2
and methane CH
4
gases, the
relative sensitivities are, respectively, 12.6% and
14.9% of that of an open path cell per equal length.
This sensitivity is more than 50 times that of the
D-shaped optical ber.
3
The relative sensitivity of
Lucents PCF with 1.4-m-diameter d air holes and
1.55-m holes of separation as a function of wave-
length is shown in Fig. 4. At 1.53 and 1.65 m the
relative sensitivities are, respectively, 3.8% and 4.7%
of that of an open path cell per equal length. We also
calculated the relative sensitivity of a modied ber
with the same structure as the Lucent ber but with
varying hole diameter and separation. Figure 4
shows the results for ⌳⫽1.33 m and d varying
from 0.69 to 0.93. The relative sensitivity for ⌳⫽
1.33 m and d 1.24 m d⌳⫽0.93 is 6.2% at a
wavelength of 1.53 m and 7.7% at 1.65 m.
Although it is difcult to establish an analytical
relationship between the relative sensitivity and -
ber parameters d, , and wavelength from the sim-
ulation results, we may conclude that the sensitivity
increases with and d but decreases with struc-
tural size d or ⌳共for the same d⌳兲. It can be seen
from Fig. 4 that, for the same value of d⌳⫽0.9 and
at a wavelength of 1.53 m, the relative sensitivity
increases from 3.8% to 5.8% as the hole separation
decreases from 1.55 m the Lucent ber to 1.33 m.
One simple method for designing the relative sensi-
tivity of the PCF is to use the scaling properties of the
Maxwell equations in combination with the simula-
Fig. 1. a, Quarter of the cross section showing the two innermost
rings of Crystal Fibers PCF. The diameter of the central silica
region is 1.7 m. ⌳⫽3.24 m and d 3 m. b, Shape of the
holes in the innermost ring: d1 1.22 m, d2 3 m, b 1.79
m.
Fig. 2. Quarter of the cross section of Lucents PCF: ⌳⫽1.55
m and d 1.4 m.
3510 APPLIED OPTICS Vol. 42, No. 18 20 June 2003

tion results in Fig. 4. For example, if we wish to
design a PCF with 3.78% relative sensitivity at a
wavelength of 1.65 m one of the methane absorp-
tion wavelengths, we need only to increase the size
d, ⌳兲 of the PCF with 3.78% relative sensitivity Fig.
4 by a factor S that equals the new working wave-
length divided by the old working wavelength, i.e.,
S 1.651.53 1.0784. The new ber parameter
should then be ⌳⫽1.67 m and d 1.5 m. With
this method the results at one length scale can be
used to deduce the design parameters at all other
length scales.
3. Response Time of the Sensor of the Photonic
Crystal Fibers
One concern in using PCF as evanescent eld sensors
may be the limited response time due to the time
required for gas to diffuse into the holes. To study
this effect, we take acetylene gas as an example and
study its diffusion into the holes of a PCF of length l
with two ends open Fig. 5. We assume that the
PCF is placed initially in air, and the air-hole col-
umns of PCF were entirely lled with air. At time
t 0 the surrounding air is suddenly replaced by
acetylene gas with concentration C
0
. This sudden
change will start a transient mass transportation
transient diffusion between the air and acetylene.
The air will diffuse out from the two ends of the PCF
column, and the acetylene will diffuse into the col-
umn. At time t the distribution of acetylene concen-
tration along the length of the air hole columns may
be written as
9
C x, t C
0
(
1 4␲兲
j1,3,5
1j
sin jxl exp关⫺ jl
2
Dt兴其
)
, (4)
where D is the binary diffusion coefcient between
the air and acetylene and can be found in the refer-
ence book
10
and x is the spatial coordinate along the
longitudinal direction of the PCF. The acetylene
concentrations at the two ends of the PCF are as-
sumed to be C
0
in the whole diffusion process t 0.
The diffusion is assumed to take place at room tem-
perature and atmospheric pressure.
The average gas concentration over the entire sens-
ing length l as a function of time
C
A
t
1
l
0
l
C x, tdx (5)
may be measured from the intensity attenuation
caused by gas absorption through the BeerLambert
law as given in Eq. 1 but with C replaced by C
A
t.
By substituting Eq. 4 into Eq. 5, we obtain
C
A
C
0
1 8
2
j1,3,5
1j
2
exp关⫺ jl
2
Dt
.
(6)
It can be seen from Eq. 6 that the average gas
concentration in the hole columns depends on inter-
action length l. For a short interaction length, i.e., l
3 0, C
A
t quickly approaches C
0
. When l is 1 m the
time for
12
C
2
H
2
gas from C
A
(t) to reach 90% C
0
is 200
min. Because the size of the holes in the PCF is
small, the wall effect between the molecules and the
wall of the hole column may also need to be taken into
account. The Knudsen number K
n
md is usu
-
ally used to represent the wall effect of a capillary
diffusion system,
11
where m is the mean free path of
the gas molecules and d is the diameter of the capil-
lary tube the hole diameter here. If the Knudsen
number is small, the diffusion has the same charac-
Fig. 3. Relative sensitivity of Crystal Fibers PCF as a function of
wavelength.
Fig. 4. Relative sensitivities of Lucents and the modied Lu-
cents PCFs as functions of wavelength: Lucents PCF, ⌳⫽1.55
m, d 1.4 m, d⌳⫽0.9; modied PCF, ⌳⫽1.33 m and the
varying hole diameter corresponding to d from 0.69 to 0.93.
Fig. 5. Gas diffusion into the holes of the PCF of length l.
20 June 2003 Vol. 42, No. 18 APPLIED OPTICS 3511

teristics as in the continuum state. If the Knudsen
number is larger than one, the diffusion will be dom-
inated by the wall effect. We now study the diffu-
sion of acetylene gas into the holes of Crystal Fibers
PCF. Because guided light power is mainly limited
to within the innermost ring of holes, we need to
consider only the gas diffusion into these holes. Be-
cause the shape of these holes is irregular, we may
use the smallest diameter d as shown in Fig. 1a to
estimate the maximum Knudsen number. The
Knudsen numbers of acetylene and air in the column
of these holes were found to be relativity small less
than 0.054, so that the diffusion process is close to
the continuum state, plus a small correction factor.
Actually the wall effect also induces the viscous ux
in the system and superimposes on the diffusive ux,
but the effect is so small and complicated that we are
concerned only with the diffusive ux in the simula-
tion. In most systems, air can be assumed to be an
independent species. The corrected binary diffusion
coefcient D
AB
C
of B acetylene in A air may be
shown as
12
D
AB
C
D
AB
D
BB
K
D
AB
D
AB
K
, (7)
where D
AB
is the diffusion coefcient of air and acet
-
ylene in the continuum state, D
AB
K
is the combined
Knudsen diffusion coefcient and can be written as
12
D
AB
K
D
AA
K
X
B
D
BB
K
X
A
, (8)
where X
A
and X
B
are the molar fractions of species A
and B and D
AA
K
and D
BB
K
are the Knudsen diffusion
coefcients of species A and B, which may be written
as
12
D
␾␾
K
13dV
, (9)
where V
is the average molecular speed of species
共␾ AorB. From Eq. 8 it can be seen that D
AB
K
and thus D
AB
C
are different at every point along the
PCF and also changes with time in the whole diffu-
sion process. This made it difcult to compute the
exact time taken for the diffusion process. However,
we may estimate the diffusion time under the worst
plan by replacing D
AB
K
in Eq. 7 with D
BB
K
. The
value of D
BB
K
acetylene, 2.069 cm
2
s
1
is larger
than D
AA
K
air, 1.966 cm
2
s
1
, and thus the esti
-
mated value of D
AB
C
from Eq. 7 will be the mini
-
mum possible value of D
AB
C
. The diffusion time
estimated with Eqs. 6 and 7 will then be the long-
est possible. The diffusion coefcient of acetylene in
air in the continuum state is 0.17774 cm
2
s
1
,
10
and
the corrected diffusion coefcient in the innermost
air-hole column Fig. 1b is 0.163 cm
2
s
1
8.3% de
-
creasing. Figure 6 shows the normalized average
concentration inside the hole column against the time
for a range of ber lengths l at room temperature
20 °C and atmospheric pressure.
If we take the time for C
A
t to reach 90% C
0
as the
response time of the ber, the response times for 3-,
5-, and 7-cm lengths of ber with both ends open for
diffusion are found to be 11.7, 32.5, and 62.7 s, re-
spectively.
4. Experiments and Results
Experiments were conducted to investigate the rela-
tive sensitivity and the diffusion dynamics of Crystal
Fibers PCF for acetylene measurement. The exper-
imental setup is shown in Fig. 7. Light from an
Er-doped amplied spontaneous emission source
passes through a tunable optic lter TOF of
0.02-nm bandwidth before coupling into the PCF.
The single-mode pigtail of the TOF was butt coupled
to the PCF with an 50-m gap between the two
ber ends to allow for gas diffusion into the holes of
the PCF. The butt-coupled joint was put inside a
gas chamber with a volume of 6 cm 6cm 6 cm.
The other end of the PCF was spliced to a single-mode
ber connected to a photodetector. The spliced end
was effectively sealed and the experimental system
can be regarded as a diffusion system with a single
open end.
Before the start of the experiments the chamber
was lled with air. Acetylene gas with a concentra-
tion approaching C
0
100% was blown into the
chamber along a direction orthogonal to the PCF with
a blow rate of 100 cm
3
s. The cross-sectional area of
the outlet valve is 2cm
2
and is 4 times bigger than
that of inlet in order to prevent additional pressure
that may affect the diffusion process when the C
2
H
2
was loaded into the chamber. The chamber was
then sealed after 30 s of loading of acetylene. Dur-
ing the experiments the TOF was repeatedly scanned
around the absorption line of acetylene
12
C
2
H
2
at
1531.53 nm with a repetition rate of 0.1 Hz. Dur-
Fig. 6. Normalized average concentration inside the holes col-
umn against the time for a range of ber lengths l. Diffusion is
assumed to be from both ends and with the wall effect considered.
Fig. 7. Experimental setup: SMF, single-mode ber; PD, photo-
detector.
3512 APPLIED OPTICS Vol. 42, No. 18 20 June 2003

ing each scan the minimum transmittance corre-
sponding to the peak absorption at 1531.53 nm was
recorded with a PC that is also used to control the
TOF. The room temperature was at 293 K. Fig-
ures 8a and 8b show the measured normalized min-
imum transmittances as functions of time for a
25- and 10-cm-long Crystal Fiber PCF, respectively.
The transmittances reach steady states at 8000 and
2000 s for the 25- and the 10-cm PCFs, respectively.
For comparison we modeled the variation of the
minimum transmittance as a function of time. By
using Eqs. 1 and 6, we may express light intensity
at the photodetector as
I I
0
exp
(
r
m
l
1 8
2
j1,3,5
1j
2
exp关⫺ j2l
2
Dt
)
. (10)
In deriving Eq. 10, we assume that the concentra-
tion of acetylene in the chamber was constant C
0
100% acetylene over the whole measurement period.
This is justied because the volume of the chamber is
1.96 10
6
times bigger than that of the air-hole
columns of the ber, and consumption of acetylene
within the chamber over the measurement period is
negligible. We also replaced l in Eq. 6 with 2l in
Eq. 10 because the experimental system uses a PCF
with a single open end and is equivalent to a system
of twice the length of the PCF of the two-end open
system. The parameters in Eq. 10 can be obtained
from various measurements. The absorption coef-
cient
m
was measured with a direct absorption cell
to be 0.2806 cm
1
. The relativity sensitivity r was
estimated by using the steady-state t 3 in Eq.
10兲兴 value of the normalized minimum transmit-
tance as shown in Fig. 9. The steady values for the
25- and 10-cm PCFs are, respectively, 0.3827 and
0.6835, giving relative sensitivities of 13.75% and
13.59%. These values are close to the simulation
results of 12.6% for the fundamental mode Fig. 3.
With r 13.7% and
m
0.2806 we tted the mea
-
surement data in Fig. 8 to Eq. 10 and found that the
diffusion coefcients for the 25- and 10-cm PCFs are,
respectively, D 0.169 cm
2
s
1
and D 0.168 cm
2
s
1
.
These values are again close to the corrected dif-
fusion coefcient 0.163 cm
2
s
1
obtained in Sec
-
tion 3. The agreements in the theoretical
calculated and the experimental measured tted
values of D and r conrmed that the modeling tech-
niques used for predicting the relativity sensitivity
and the diffusion dynamics of the PCFs are accu-
rate. The same techniques may be used to evalu-
ate the performance of sensors made from PCFs
with other geometries. The small discrepancies
between the theory and the experiments may be
Fig. 8. Measured normalized minimum transmittance as a func-
tion of time: a, 25-cm-long PCF; b, 10-cm-long PCF.
Fig. 9. a, PCF acetylene gas-sensing system: SMF, single-mode
ber; PD, photodetector; b, PCF with periodic openings; c, Quarter
of the cross section of the Crystal Fibers PCF with opening.
20 June 2003 Vol. 42, No. 18 APPLIED OPTICS 3513

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Journal ArticleDOI
TL;DR: With this method, the central hollow-core and the holes in the cladding region can be selectively infiltrated, which allows for the fabrication of novel hybrid polymer- silica and liquid-silica MOFs for various applications.
Abstract: A simple method for fabricating selective injection microstructured optical fibers (MOFs) using a conventional fusion splicer is described. The effects of fusion current, fusion duration and offset position on the hole collapse property of the MOFs are investigated. With this method, the central hollow-core and the holes in the cladding region can be selectively infiltrated, which allows for the fabrication of novel hybrid polymer-silica and liquid-silica MOFs for various applications.

234 citations

References
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Book
01 Jan 1956
TL;DR: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
Abstract: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained

20,495 citations

Book
25 May 1984
TL;DR: An overview of diffusion and separation processes brings unsurpassed, engaging clarity to this complex topic as mentioned in this paper, which is a key part of the undergraduate chemical engineering curriculum and at the core of understanding chemical purification and reaction engineering.
Abstract: This overview of diffusion and separation processes brings unsurpassed, engaging clarity to this complex topic. Diffusion is a key part of the undergraduate chemical engineering curriculum and at the core of understanding chemical purification and reaction engineering. This spontaneous mixing process is also central to our daily lives, with importance in phenomena as diverse as the dispersal of pollutants to digestion in the small intestine. For students, Diffusion goes from the basics of mass transfer and diffusion itself, with strong support through worked examples and a range of student questions. It also takes the reader right through to the cutting edge of our understanding, and the new examples in this third edition will appeal to professional scientists and engineers. Retaining the trademark enthusiastic style, the broad coverage now extends to biology and medicine.

5,195 citations

Book
01 Mar 1993
TL;DR: The Finite Element Method in Electromagnetics, Third Edition as discussed by the authors is a leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetic engineering.
Abstract: A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagneticsThe finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration.The Finite Element Method in Electromagnetics, Third Edition explains the methods processes and techniques in careful, meticulous prose and covers not only essential finite element method theory, but also its latest developments and applicationsgiving engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems.Featuring over thirty percent new material, the third edition of this essential and comprehensive text now includes:A wider range of applications, including antennas, phased arrays, electric machines, high-frequency circuits, and crystal photonicsThe finite element analysis of wave propagation, scattering, and radiation in periodic structuresThe time-domain finite element method for analysis of wideband antennas and transient electromagnetic phenomenaNovel domain decomposition techniques for parallel computation and efficient simulation of large-scale problems, such as phased-array antennas and photonic crystalsAlong with a great many examples, The Finite Element Method in Electromagnetics is an ideal book for engineering students as well as for professionals in the field.

3,705 citations

Journal ArticleDOI
TL;DR: An optical fiber that can appear single mode with propagation properties that can be achieved only in multimode waveguides is analysis of waveguide properties of microstructure optical fibers.
Abstract: We analyze the waveguide properties of microstructure optical fibers consisting of a silica core surrounded by a single ring of large air holes. Although the fibers can support numerous transverse spatial modes, coupling between these modes even in the presence of large perturbations is prevented for small core dimensions, owing to a large wave-vector mismatch between the lowest-order modes. The result is an optical fiber that can appear single mode with propagation properties that can be achieved only in multimode waveguides.

344 citations

Book
01 Nov 1980
TL;DR: In this article, the authors present a Phenomenology of Diffusive and Viscous Fluxes in Multicomponent Systems without Walls (MDSW) without walls.
Abstract: 1. Phenomenology of Diffusive and Viscous Fluxes.- 2. Elementary Prediction of Transport Coefficients.- 3. Constitutive Equations of Diffusion In Multicomponent Systems without Walls.- 4. Constitutive Equations of Diffusion and Wall Effects.- 5. Analysis of Applications.- 6. History of Diffusion.- References.

323 citations

Frequently Asked Questions (18)
Q1. What are the contributions mentioned in the paper "Design and modeling of a photonic crystal fiber gas sensor" ?

The authors report the modeling results of an all-fiber gas detector that uses photonic crystal fiber PCF. 

Because the size of the holes in the PCF is small, the wall effect between the molecules and the wall of the hole column may also need to be taken into account. 

Acetylene gas with a concentration approaching C0 100% was blown into the chamber along a direction orthogonal to the PCF with a blow rate of 100 cm3 s. 

The Knudsen number Kn m d is usually used to represent the wall effect of a capillary diffusion system,11 where m is the mean free path of the gas molecules and d is the diameter of the capillary tube the hole diameter here . 

At time t the distribution of acetylene concentration along the length of the air hole columns may be written as9C x, t C0(1 4 j 1,3,5 1 j sin j x l exp j l 2Dt ), (4)where D is the binary diffusion coefficient between the air and acetylene and can be found in the reference book10 and x is the spatial coordinate along the longitudinal direction of the PCF. 

The openings in the PCF modify the waveguide structure and thus change the transversal field distribution in the fiber cross section. 

The cross-sectional area of the outlet valve is 2 cm2 and is 4 times bigger than that of inlet in order to prevent additional pressure that may affect the diffusion process when the C2H2 was loaded into the chamber. 

For a gassensing application that requires a response time of 1 min the length of the sensing PCF should be limited to less than 7 cm. 

Preliminary experiments and simulation show that an acetylene sensor system with a response time of 1 min and sensitivity of better than 6 ppm can be realized. 

If the authors take the time for CA t to reach 90% C0 as the response time of the fiber, the response times for 3-, 5-, and 7-cm lengths of fiber with both ends open for diffusion are found to be 11.7, 32.5, and 62.7 s, respectively. 

4 and 5 where most of the guided light power is confined within the solid-core region with a fraction evanescent field of power extended into the holey region. 

Consider that the detection resolution of 3.75 parts per million for an equivalent of 1 m ppm m of acetylene has been achieved with wavelength modulation spectroscopy and digital signal processing. 

The corrected binary diffusion coefficient DABC of B acetylene in A air may be shown as12DAB C DABDBB K DAB DABK , (7)where DAB is the diffusion coefficient of air and acetylene in the continuum state, DABK is the combined Knudsen diffusion coefficient and can be written as12DAB K DAAKXB DBBKXA, (8)where XA and XB are the molar fractions of species A and B and DAA K and DBB K are the Knudsen diffusion coefficients of species A and B, which may be written as12D K 1 3 dV , (9)where V is the average molecular speed of species A or B . 

To achieve a higher sensitivity with a reasonable response time, the authors propose introducing periodic openings along the sensing fiber. 

The diffusion coefficient of acetylene in air in the continuum state is 0.17774 cm2 s 1,10 and the corrected diffusion coefficient in the innermost air-hole column Fig. 1b is 0.163 cm2 s 1 8.3% decreasing . 

From the analysis in Section 4 the authors conclude that the response time of PCF is limited by the time taken for acetylene gas to diffuse into the holes. 

Figure 9a shows an example of a sensor design based on Crystal Fiber’s 1.7- mdiameter silica core PCF where the sensing PCF with periodic openings is connected to single-mode transmission fibers at the two ends. 

The relative sensitivity of Lucent’s PCF with 1.4- m-diameter d air holes and 1.55- m holes of separation as a function of wavelength is shown in Fig.