the two MOD methods and PLRC-FDTD method, and the IDFT

of the analytic solution. All four solutions show a good

agreement.

5. CONCLUSIONS

We have presented a general MOD formulation when using the

FDTD technique for the transient solution of wave propagation

in an arbitrary dispersive media. The time domain known and

unknown coefficients for the material parameters and fields are

approximated by a set of orthonormal associated Laguerre func-

tions. Through the use of the associated Laguerre functions, the

time variable can be eliminated analytically from the solution

procedure so that the computation methodology reduces to a

simple finite difference procedure. In addition, we have success-

fully eliminated the explicit convolutions and the temporal

derivatives analytically. We also presented a second alternate

MOD formulation based on the Helmholtz wave equation. Nu-

merical results are presented for various dispersive materials,

i.e., Debye, Drude, and Lorentz models. The agreement between

the solutions obtained using the two proposed MOD methods

and the traditional FDTD method, and the IDFT of the fre-

quency domain analytic solution is excellent as a function of

both the spatial and the temporal variables. The proposed MOD

methods can be extended to 2D and 3D formulations for disper-

sive media.

ACKNOWLEDGMENTS

This research was supported by the Academic Research Fund of

Hoseo University in 2009 (No. 20080498).

REFERENCES

1. K.S. Kunz and R.J. Ruebbers, The finite difference time domain

method for electromagnetics, CRC, Boca Raton, FL, 1993.

2. D.M. Sullivan, Electromagnetic simulation using the FDTD

method, IEEE Press, Piscataway, NJ, 2000.

3. A. Taflove and S.C. Hagness, Computational electrodynamics:

The finite-difference time-domain method, 3rd ed., Artech House,

Norwood, MA, 2005.

4. R. Luebbers, F.P. Hunsberger, K.S. Kunz, R.B. Standler, and M.

Schneider, A frequency-dependent finite-difference time-domain

formulation for dispersive materials, IEEE Trans Electromagn

Compat 32 (1990), 222–227.

5. R.J. Luebbers, F. Hunsberger, and K.S. Kunz, A frequency-de-

pendent finite-difference time-domain formulation for transient

propagation in plasma, IEEE Trans Antennas Propag 39 (1991),

29–34.

6. R.J. Luebbers and F. Hunsberger, FDTD for Nth-order dispersive

media, IEEE Trans Antennas Propag 40 (1992), 1297–1301.

7. D.F. Kelley and R.J. Luebbers, Piecewise linear recursive convolu-

tion for dispersive media using FDTD, IEEE Trans Antennas

Propag 44 (1996), 792–797.

8. Y.S. Chung, T.K. Sarkar, B.H. Jung, and M. Salazar-Palma, An

unconditionally stable scheme for the finite-difference time-domain

method, IEEE Trans Microwave Theory Tech 51 (2003), 697–704.

9. B.H. Jung and T.K. Sarkar, Analysis of transient electromagnetic

scattering with plane wave incidence using MOD-FDM, Prog Elec-

tromagn Res 77 (2007), 111–120.

10. B.H. Jung and T.K. Sarkar, Solving time domain Helmholtz wave

equation with MOD-FDM, Prog Electromagn Res 79 (2008),

339–352.

11. M. Ha, K. Srinivasan, and M. Swaminathan, A Laguerre-FDTD

formulation for frequency-dependent dispersive materials, IEEE

Microwave Wirel Compon Lett 21 (2011), 225–227.

12. B.H. Jung et al., Time and frequency domain solutions of EM

problems using integral equations and a hybrid methodology,

Wiley, Hoboken, NJ, 2010.

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its marching-on-in-degree solution for analysis of dispersive dielec-

tric objects, IEEE Trans Antennas Propag 59 (2011), 969–978.

14. Y. Shi and J.-M. Jin, Marching-on-in-degree solution of volume in-

tegral equations for analysis of transient electromagnetic scattering

by inhomogeneous dielectric bodies with conduction loss, Micro-

wave Opt Technol Lett 53 (2011), 1104–1109.

15. Y.-S. Chung, T.K. Sarkar, S. Llorento-Romano, and M. Salazar-

Palma, Finite element time domain method using Laguerre

polynomials, IEEE MTT-S Int Microwave Symp Dig 2 (2003),

981–984.

16. J. Keilson and W.R. Nunn, Laguerre transformation as a tool for

the numerical solution of integral equations of convolution type,

Appl Math Comput 5 (1979), 313–359.

17. M. Yuan, A. De, T.K. Sarkar, J. Koh, and B.H. Jung, Conditions

for generation of stable and accurate hybrid TD-FD MoM solu-

tions, IEEE Trans Microwave Theory Tech 54 (2006), 2552–2563.

VC 2012 Wiley Periodicals, Inc.

FIBER BRAGG GRATING-BASED LOADSENSOR WITHOUT TEMPERATUREDEPENDENCE

Limin Hu,1 Xinyong Dong,1 Shuqin Zhang,1 Shangzhong Jin,1

Yunpeng Wang,1 Chi Chiu Chan,2 and Ping Shum3

1 Institute of Optoelectronic Technology, China Jiliang University,Xueyuan Street, Hangzhou 310018, China; Corresponding author:xydong@cjlu.edu.cn2 School of Chemical and Biomedical Engineering, NanyangTechnological University, 639798, Singapore3Network Technology Research Centre, Nanyang TechnologicalUniversity, 637553, Singapore

Received 15 June 2011

ABSTRACT: A novel load sensor has been proposed and demonstrated

by embedding a fiber Bragg grating (FBG) into a tapered cylindrical

polymer rod. Load-induced nonuniform strain field changes the

bandwidth, and hence, the reflected optical power of the FBG.

Temperature-insensitive measurement of load has been realized by

measuring the reflected optical power with only a low-cost optical

power meter. Load measurement sensitivity of 5.0 nW/N has

Figure 6 Transient electric field versus time for a plane wave with

Gaussian pulse incident on a Lorentz slab. [Color figure can be viewed

in the online issue, which is available at wileyonlinelibrary.com]

930 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 4, April 2012 DOI 10.1002/mop

been experimentally achieved within a range up to 1800 N. VC 2012

Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:930–933, 2012;

View this article online at wileyonlinelibrary.com. DOI 10.1002/

mop.26695

Key words: fiber Bragg gratings; load sensors; optical fiber sensors

1. INTRODUCTION

In the recent decades, fiber Bragg gratings (FBGs) have

attracted lots of research interests in the area of optical sensors.

A variety of FBG sensors have been designed to monitor param-

eters such as temperature, strain, displacement [1], tilt angle [2],

acceleration [3], pressure [4], force [5], torsion [6], and so on.

Compared with conventional sensors, FBGs have many advan-

tages including immunity to radio frequency interference and

electromagnetic interference, electrically passive operation, high

sensitivity, compact size, high multiplexing, and self-referencing

capabilities. FBG-based transverse load sensors have been

reported based on various grating structures [7–10]. Transverse

load may induce birefringence into the fiber core and change the

optical spectrum of the sensing FBG. The reflection peak splits

and the wavelength separation changes linearly with the applied

load. However, these FBG load sensors are based on wavelength

(or optical spectrum) measurement. The demodulation module is

relatively complicated and expensive and thus adds to the sys-

tem cost. A different technique has been reported recently by

converting load into optical power reflected by the sensing FBG

[11]. This is a simple and relatively low cost solution for load

measurement with FBGs. In this article, a simple intensity-

modulated FBG load sensor has been proposed by embedding

the sensing FBG into a tapered polymer rod and measuring the

reflected optical power. Temperature-insensitive load measure-

ment is realized with linear response.

2. SENSOR DESIGN AND PRINCIPLE

The proposed FBG-based load sensor is illustrated in Figure 1.

The FBG was embedded in a tapered cylindrical polymer rod

along the central axis. When load is applied vertically onto top

surface of the polymer rod, different compression strain will be

generated inside the polymer rod along the FBG. The strain dis-

tribution is determined by shape (or radius profile of cross-sec-

tion) of the polymer rod.

In this work, the radius of cross-section of the polymer rod

is given by

rðzÞ ¼ r0 þ kz (1)

where r0 is the radius of the polymer rod at one end of the

FBG, k represents the slope, and z is the axial coordinate. Then,

the strain distribution is described by

eðzÞ ¼ F

SðzÞE (2)

where E and S(z) represent Young’s modulus and cross-section

area of the polymer rod, respectively. Wavelength shift of FBG,

proportional to applied local strain, is therefore, described as

KkBðzÞ ¼ kBð1� peÞFE

1

SðzÞ (3)

where kB is the Bragg wavelength of the FBG and pe is the

effective photoelastic coefficient of the fiber. Bandwidth varia-

tion is determined by wavelength shifts at both ends of the

FBG. As the grating is located from z0 to zl, bandwidth variation

is then described as

Dkchrip ¼ kBð1� peÞFEp

1

r2ðz0Þ �1

r2ðzlÞ����

����

(4)

As Eq. (4) shows the reflective bandwidth of the FBG is lin-

early changed to applied load. Provided that the high reflectivity

is maintained and broadband light source (BBS) with flat spec-

trum is available, the reflected optical power of the sensing FBG

will be linear changed to the applied load too. Furthermore, as

surrounding temperature-induced wavelength changes are the

same along the whole length of the FBG, temperature effect will

not change the bandwidth hence the reflected power of the FBG

[12]. Therefore, the proposed FBG-load sensor can be regarded

as independent of temperature.

3. EXPERIMENTAL, RESULTS, AND DISCUSSION

The FBG was fabricated on a hydrogen-loaded single-mode fiber

using a UV laser and phase mask. Its strain-free Bragg wave-

length and reflective bandwidth are 1555.7 and 0.34 nm, respec-

tively. The grating length is 15 mm. The FBG was embedded

into the polymer material before the later is solidified. The

formed tapered polymer rod has height of 20 mm. The radii are

7 and 16 mm at the two FBG ends, respectively.

The measurement system is also shown in Figure 1. A flat-

tened BBS with 1-dB bandwidth of more than 50 nm was used

to illuminate the FBG through an optical circulator. The

reflected light from the FBG was measured with an optical spec-

trum analyzer and an optical power meter simultaneously using

a 3-dB optical fiber coupler.

The applied load was changed from 0 to 1800 N. Figure 2

shows the reflection spectrum revolution of the sensing FBG

when the applied axial load was increased. It can be seen that

the reflective bandwidth of the FBG increased significantly with

load. Meanwhile, the central wavelength of the FBG moved to

shorter wavelength because the whole FBG was compressed by

the applied load. The reflectivity remained high even when the

Figure 1 Design and measurement system of the proposed FBG load

sensor. Inset: Vertical section of the polymer rod. (BBS: broadband light

source; OSA: optical spectrum analyzer; OPM: optical power meter.).

[Color figure can be viewed in the online issue, which is available at

wileyonlinelibrary.com]

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 4, April 2012 931

spectrum was broadened to 4.23 nm. It was benefited from the

high reflectivity of the used FBG (more than 99.9%).

The measured reflected optical power and bandwidth of the

FBG against applied load are shown in Figure 3. Good linear

responses were achieved. The achieved load sensitivity is 5.0

nW/N, which is limited by the relatively low power level of the

used BBS. It can be improved by changing parameters of the

tapered polymer rod. Reducing Young’s modulus of the material

and/or increasing the tapering degree can improve the sensitivity.

The accuracy of load measurement, defined by the largest dis-

crepancy of the experimental data from the linear fitting line, is

4.2% of the applied load. The response time for quasi-static load

measurement is less than 1 s. Repeatability test is performed by

measuring the sensor response with the same loading condition

for more than 10 times. The output differences are less than 5%.

Thermal dependence of the proposed load sensor was tested

by placing it inside a temperature-controlled container. The

reflected optical power was measured when temperature was var-

ied between 5 and 55 �C. Figure 4 depicts the measured results.

The maximum fluctuation of optical power is less than 60.16

lW (1.92% of the basic value), which is negligible and may be

caused by fan rotation-induced vibration in the container.

4. CONCLUSION

A novel load sensor by embedding a FBG into a tapered poly-

mer rod has been proposed and demonstrated. By measuring the

reflected optical power of the FBG, temperature-insensitive mea-

surement of load has been realized. The load measurement range

is 1800 N and the achieved sensitivity is 5.0 nW/N. Benefited

from the simple demodulation method and the inherently tem-

perature-insensitive nature, the proposed load sensor is quite

simple in structure and cost efficient. What’s more, the sensing

FBG, embedded in the polymer rod, is well protected so good

reliability is expected.

ACKNOWLEDGMENTS

This work was supported by the National Basic Research Program

of China (973 Program) under Grant No. 2010CB327804, National

Natural Science Foundation of China under Grant No. 60807021,

and Zhejiang Provincial Natural Science Foundation of China

under Grant No. R1080087.

REFERENCES

1. X. Dong, X. Yang, C.-L. Zhao, L. Ding, P. Shum, and N.Q. Ngo,

A novel temperature-insensitive fiber Bragg grating sensor for dis-

placement measurement, Smart Mater Struct 14 (2005), N7–N10.

2. H. Bao, X. Dong, L.Y. Shao, C. Zhao, C.C. Chan, and P. Shum,

Temperature-insensitive pendulum clinometer using two fiber

Bragg gratings for 2D tilt angle measurement, IEEE Photon Tech-

nol Lett 22 (2010), 863–865.

3. W. Zhou, X. Dong, K. Ni, C.C. Chan, and P. Shum, Temperature

insensitive accelerometer based on a strain-chirped FBG, Sensors

Actuators A: Phys 257 (2010), 15–18.

4. Y.S. Hsu, L. Wang, W.F. Liu, and Y.J. Chiang, Temperature com-

pensation of optical fiber Bragg grating pressure sensor, IEEE Pho-

ton Technol Lett 18 (2006), 874–876.

5. T. Guo, Q. Zhao, H. Zhang, L. Xue, G. Li, B. Dong, B. Liu, W.

Zhang, G. Kai, and X.Y. Dong, Temperature-insensitive fiber

Bragg grating force sensor via a bandwidth modulation and opti-

cal-power detection technique, Lightwave Technol 24 (2006),

3797–3802.

6. W. Zhang, G. Kai, X.Y. Dong, S.Z. Yuan, and Q.D. Zhao, Tem-

perature-independent FBG-type torsion sensor based on combinato-

rial torsion beam, IEEE Photon Technol Lett 14 (2002),

1154–1156.

7. H. Fu, X. Shu, R. Suo, L. Zhang, S. He, and I. Bennion, Transver-

sal-load sensor by using local pressure on a chirped fiber Bragg

grating, IEEE Sensors J 10 (2010), 1140–1141.

8. T. Geernaert, G. Luyckx, E. Voet, T. Nasilowski, K. Chah, M.

Becker, H. Bartelt, W. Urbanczyk, J. Wojcik, W. De Waele, J.

Degrieck, H. Terryn, F. Berghmans, and H. Thienpont, Transversal

load sensing with fiber Bragg gratings in microstructured optical

fibers, IEEE Photon Technol Lett 21 (2009), 6–8.

Figure 2 Reflection spectrum revolution of the sensing FBG when

load was applied. [Color figure can be viewed in the online issue, which

is available at wileyonlinelibrary.com]

Figure 3 Reflected optical power and 3-dB bandwidth of the pro-

posed FBG load sensor versus applied load. [Color figure can be viewed

in the online issue, which is available at wileyonlinelibrary.com]

Figure 4 Temperature dependence measurement results of the pro-

posed FBG load sensor. [Color figure can be viewed in the online issue,

which is available at wileyonlinelibrary.com]

932 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 4, April 2012 DOI 10.1002/mop

9. R.B. Wagreich, W.A. Atia, H. Singh, and J.S. Sirkis, Effects of

diametric load on fibre Bragg gratings fabricated in low birefrin-

gent fibre, Electron Lett 32 (1996), 1223–1224.

10. M. LeBlanc, S.T. Vohra, T.E. Tsai, and E.J. Friebele, Transverse

load sensing by use of pi-phase-shifted fiber Bragg gratings, Opt

Lett 24 (1999), 1091–1093.

11. T. Guo, Q. Zhao, H. Zhang, C. Zhang, G. Huang, L. Xue, and X.

Dong, Temperature-insensitive fiber Bragg grating dynamic pres-

sure sensing system, Opt Lett 15 (2006), 2269–2271.

12. X. Dong, C. Zhan, K. Hu, P. Shum, and C.C. Chan, Temperature-

insensitive tilt sensor with strain-chirped fiber Bragg gratings,

IEEE Photon Technol Lett 17 (2005), 2394–2396.

VC 2012 Wiley Periodicals, Inc.

WAVELENGTH FILTER EXPLOITINGSERIALLY COUPLED RING RESONATORSFABRICATED BY A STANDARD SILICONCMOS TECHNOLOGY

Woo-Ju Kim,1 Hak-Soon Lee,1 Gun-Duk Kim,1 Sang-Shin Lee,1

and Wan-Gyu Lee21 Department of Electronic Engineering, Kwangwoon University,Nowon-Gu, Seoul 139-701, South Korea; Corresponding author:slee@kw.ac.kr2 NIT Convergence Team, National NanoFab Center, Yuseong-gu,Daejeon 305-806, South Korea

Received 21 June 2011

ABSTRACT: A photonic compact eight-channel wavelength filter hasbeen proposed and fabricated by incorporating serially connected ringresonators based on a silicon rib waveguide. Eight different rings are

subsequently addressed by a common input bus and individually out-coupled by output buses. A vertical grating coupler is attached to the

input and output buses for efficient light coupling. Each of the launchedoptical signals is routed to the drop port of the corresponding channel,whose center wavelength is dependent on the size of the ring. The

device was designed by using a finite-difference time-domain methodand fabricated by exploiting a standard complementary metal-oxide-

semiconductor silicon-on-insulator technology. The silicon rings, seriallyplaced with a gap of 50 lm, have radii varying from 6.0 to 6.07 lm,leading to a channel wavelength ranging from 1546.3 to 1557.6 nm. As

regards, the overall performance of the fabricated device, the qualityfactor is �13,600, the channel spacing �1.6 nm, the propagation loss�3 dB, and the channel crosstalk �27 dB. Finally, a group of optical

signals modulated by a data signal at 3.2 Gbps were appropriatelyrouted to yield a decent eye diagram. VC 2012 Wiley Periodicals, Inc.

Microwave Opt Technol Lett 54:933–936, 2012; View this article online

at wileyonlinelibrary.com. DOI 10.1002/mop.26682

Key words: integrated optics devices; wavelength filtering devices;resonators; microstructure fabrication

1. INTRODUCTION

A wavelength filter is considered to be one of the most essential ele-

ments for the implementation of wavelength-division multiplexing

(WDM) communications systems [1]. Previously, various devices

such as fiber Bragg gratings, arrayed waveguide gratings, and

Mach-Zehnder interferometers were used to create such filters using

different materials. However, these devices have a bulky, compli-

cated structure [2–4]. To overcome this problem, ring resonators

have also been actively considered [5–8]. Recently, the adoption of

the silicon photonics technology to construct compact resonators

has attracted great deal of attention due to its potential benefits in

terms of its cost effective volume production, small foot print, and

flexible integration with other electronic circuits [9–11]. To fully

take advantage of these benefits, the standard complementary metal

oxide semiconductor (CMOS) compatible process, which is fully

matured and most popular in the conventional semiconductor indus-

try, is chosen as the most viable fabrication scheme.

In this article, a multichannel wavelength filter, incorporating

serially coupled ring resonators integrated with a vertical grating

coupler, was designed and fabricated in a silicon-on-insulator (SOI)

substrate by exploiting the standard CMOS compatible process. A

rib waveguide structure is introduced to achieve high quality single

mode characteristics. The prepared device was fully characterized in

terms of its quality factor, channel spacing, extinction, channel cross-

talk, and propagation loss. Finally, optical signals modulated by a

high speed digital signal were successfully routed to the correspond-

ing channel of the filter depending on the wavelength.

2. PROPOSED WAVELENGTH FILTER AND ITS DESIGN

The proposed multichannel wavelength filter is depicted in Fig-

ure 1, consisting of eight different ring resonators that are seri-

ally linked along the light propagation direction. A common

input bus, with an input port and an output through port, is used

to address the rings, which are separately out-coupled via output

buses to an output drop port. A vertical grating coupler is com-

bined with the input/output buses via a tapered structure for the

purpose of attaining efficient light coupling. The light propagat-

ing in the common bus is subsequently coupled to the rings,

whose radius progressively increases along the propagation

direction with a constant step size. For the ring resonator the

resonant wavelength is basically determined by the refractive

index and the radius. Hence, the center wavelength for the chan-

nel, composed of a specific ring, may be readily adjusted by

altering its radius. As indicated in Figure 1, each of the drop

ports serves as a band-pass drop filter whereas the through port

acts as a band-stop notch filter [12]. The spectral span for the

proposed wavelength filter is effectively equivalent to the free

spectral range of the smallest ring resonator.

The proposed multichannel filter was designed and analyzed

by using the finite-difference time-domain method. For the

Figure 1 Schematic of the proposed wavelength filter utilizing seri-

ally coupled resonators. [Color figure can be viewed in the online issue,

which is available at wileyonlinelibrary.com]

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 4, April 2012 933