and that of �28 dB for horizontal polarization are achieved. The

proposed element is of numerous advantages such as simple

structure, easy fabrication, low production cost, wide bandwidth,

and good isolation and cross-polarization performances, which is

attractive for the applications in the DBDP shared-aperture SAR

array antennas.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Founda-

tion of China under Grant No.60871030 and the National High-

Technology Research and Development (863) Project of China

under Grant No.2007AA12Z125.

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band microstrip antenna, Electron Lett 18 (1992), 1785–1787.

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Microwave Opt Technol Lett 42 (2004), 448–551.

VC 2011 Wiley Periodicals, Inc.

EFFECT OF BENDING AND ORIENTATIONON THE FIBER MODAL MACH–ZEHNDERINTERFEROMETER

Yan Liu,1 Bo Liu,1 Yinping Miao,2 Hao Zhang,1 and Jian Liu11 Key Laboratory of Optical Information Science and Technology,Ministry of Education, Institute of Modern Optics, NankaiUniversity, Tianjin 300071, China2 School of Electronics Information Engineering, Tianjin KeyLaboratory of Film Electronic and Communication Device, TianjinUniversity of Technology, Tianjin 300384, China; Correspondingauthor: liubo@mail.nankai.edu.cn

Received 29 March 2011

ABSTRACT: By introducing two notches along the fiber axis in anormal single-mode fiber through CO2 laser exposure, a vectorcurvature sensor based on a modal Mach–Zehnder interferometer has

been proposed and experimentally demonstrated. Transmission spectralresponse regarding the spectrum shift and transmission loss variation of

the proposed sensor has been characterized and the experimental resultsshow that due to the nonperfect circular geometry of the fiber cladding,the peak wavelength and the transmission loss of its spectrum are

sensitive to applied bending orientation. Our proposed sensor has manyadvantages such as low cost, easy fabrication and good stability under

harsh environment. VC 2011 Wiley Periodicals, Inc. Microwave Opt

Technol Lett 54:136–139, 2012; View this article online at

wileyonlinelibrary.com. DOI 10.1002/mop.26471

Key words: optical fiber sensor; bending and orientation; vector

curvature sensing; modal Mach–Zehnder interferometer

1. INTRODUCTION

With the increasing demand for health monitoring in engineer-

ing structures, direction-sensitive optical fiber bending sensors

have attracted a lot of considerable research interests. By far, a

good variety of curvature sensors have been proposed by using

the long period gratings (LPGs) as core sensing components

[1–3]. Various types of sensing fibers have been also investi-

gated for simultaneous measurement of bending and direction,

such as multicore fibers [4], D-shaped cladding fibers [5],

eccentric core fibers [6], and asymmetric fiber gratings [7].

Although these devices are able to determine the bending

orientation, there are still several issues to be resolved for

practical applications, such as high cost of special fibers, their

compatibility with standard optical fibers, and complex fabrica-

tion procedure.

In recent years, owing to their high sensitivities to various

physical parameters, interferometric sensors have been inten-

sively studied in the field of optical fiber sensing technology.

Particularly, the modal interferometers whose interferometric

optical path difference is determined by the effective refrac-

tive indices difference between different order modes have

been widely investigated [8, 9]. Their most common configu-

ration is based on the fiber modal field interferometer utiliz-

ing the interference between the core mode and a selected

specific cladding mode, which could be constructed by

imprinting a twin LPG along the fiber; misaligned splicing;

introducing a compressed or expanded region of a fiber taper;

inserting a short segment of multimode fiber upstream of an

LPG or TFBG; using an LPG/TFBG hybrid structure consist-

ing of an LPG and a TFBG; etc. [10–15]. Some of these

studies are focused on bending characteristics of the proposed

structures sensors, however, their orientation direction sensi-

tivity was seldom addressed. Hence, to develop a low-cost

vector bending sensor with simple configuration would be of

great significance.

We have provided a preliminary experimental report on the

bending characteristics of a fiber modal Mach–Zehnder inter-

ferometer (MMZI), exploiting the modal interference built in a

segment of common single mode fiber under CO2 laser expo-

sure [16]. To further develop it into a vector bending sensor,

in this article, the bending and orientation responses of its

transmission spectrum have been characterized and experimen-

tal results indicate that the transmission characteristics of our

proposed MMZI are strongly dependent not only upon the

degree of curvature but also on the orientation along which

bending is applied. More detailed theoretical analysis has been

added, which is basically in agreement with our experimental

observation.

2. EXPERIMENTAL SETUP AND OPERATION PRINCIPLE

First, the MMZI is fabricated in a segment of conventional sin-

gle-mode fibers with a core diameter of 8.2 lm and a cladding

diameter of 125 lm. The fiber is placed around the focus of a

CO2 laser to acquire effective laser illumination and two cou-

pling regions are fabricated in a same fabrication process to

ensure the same physical conditions for the two micronotches.

Figure 1 illustrates schematic diagram of the modal interferome-

ters, in which two micronotches serve as mode splitter and

mode combiner, respectively. Its fundamental operation principle

136 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 1 January 2012 DOI 10.1002/mop

has been introduced in Ref. 16. The interference length Lbetween the two micronotches can be accurately adjusted by

computer control. A supercontinuum light source and an optical

spectrum analyzer with a resolution of 0.1 nm are used to moni-

tor the transmission spectrum in real time.

Bending and orientation characteristics of the MMZI with

the interference length of 2.5 cm are experimentally investi-

gated when the MMZI is bent along different orientations, and

the transmission spectrum with no bending applied is illus-

trated in Figure 2. The experimental setup for MMZI-based ori-

entation and bend sensing is similar to that described in Ref.

17, as shown in Figure 3. The interferometer is placed inside a

capillary (~320 lm inner diameter; �500 lm outer diameter),

which could protect the fiber from uneven bending. Both the

fiber and the capillary are clamped between two holders with

one of the clamps mounted on a translation stage. As it moves

inward, the bending curvature (C) along the interferometer can

be induced, which could be described as [17]:

C ¼ 1

R¼ 2d

d2 þ S2(1)

where d is the bending displacement at the center point of the

interference region and S is the half of the distance between

two rotational fiber holders. The 0� angle corresponds to the

case that when the outer normal vector of the fiber arc points

oppositely to the CO2 laser illumination side, as is named plane

x–y in Figure 1. The bending experiment starts from 0� orienta-

tion and then the fiber is rotated by 90� and later by 180�. Thisbending test has been repeated for three orthogonal orienta-

tions. For each bending orientation, the curvature ranges from

0 to 18 cm�1. To keep the MMZI from flipping to another ori-

entation during the bending process, some smaller curvatures

are chosen, especially in 0�-orientation and 90�-orientationtests.

3. EXPERIMENTAL RESULT AND DISCUSSION

As shown in Figure 4, the MMZI for 0�, 90�, and 180� rotation

angle cases, the transmission loss of the MMZI increases with

curvature. On the contrary, when bending is applied, transmis-

sion peak slightly shifts toward longer wavelength for 0� case

while shifts oppositely for 180� case but has no distinguishable

fringe variation for 90� case.

The above phenomena can be explained as follows. For the

above three orientation cases, when bending occurs, some modes

will no longer comply with the total reflection condition, and

hence leak off the fiber. Moreover, a lower effective index

mismatch between the fundamental and cladding modes could

lead to a larger bending loss. At the coupling point, the excited

cladding modes number and the coupling energy decrease,

resulting in lager transmission loss. Therefore, as shown in Fig-

ure 5(a), the transmission loss would considerably become

higher as curvature increases for all of the three cases, although

there still exists a slight difference amongst the curve slopes,

which may be attributed to the experimental environment

fluctuations.

According to the two-mode interferometer condition

described in Ref. 16, the interference peak wavelength is deter-

mined by optical path difference between fundamental core

mode and certain cladding mode, which could be described as:

D1 ¼ nco � ncl;m� �

L (2)

where nco and ncl,m represent the effective refractive indices of

core mode and mth order cladding mode, respectively, and L is

the interference length. The optical path difference induced by

two coupling points is not given in Eq. (2) because it is a bend-

ing-independent constant term. Besides the interference between

core mode and first order cladding mode, there may also exist

some weaker interferences between the core mode and higher

order cladding modes and even between different order cladding

modes. However, these interferences are not the main factor that

affects the transmission characteristics of the MMZI due to their

rather low fringe contrast as most of the light energy is distrib-

uted in core mode and first cladding mode. Eq. (4) expresses a

universal interference condition for the interferences between

core mode and cladding modes. As bending is applied, both the

mode effective index and physical length of the MMZI will

vary at the same time. It should be noted that only the cladding

mode path can be elongated or compressed because the core

mode is located in the neutral layer, which is immune to applied

bending. Therefore, after bending, the optical path difference

could be expressed as:

Figure 1 Schematic diagram of the fiber modal MMZIs. [Color figure

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

wileyonlinelibrary.com]

Figure 2 Transmission spectrum of the MMZI with an interference

length of 2.5 cm

Figure 3 Experimental setup for bending and orientation sensing tests

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 1 January 2012 137

D2 ¼ nco þ Dncoð ÞL� ncl;m þ Dncl;m� �

Lþ DLð Þ (3)

where Dnco and Dncl,m are the effective refractive index varia-

tions of core mode and mth order cladding mode, respectively,

and DL is the elongation of the cladding mode physical path. By

substituting Eq. (3) with Eq. (2), we will obtain

D2 ¼ D1 þ Dnco � Dncl;m� �

L� ncl;m þ Dncl;m� �

DL (4)

When bending occurs, the two interference modes approxi-

mately experience the same amount of effective index varia-

tion [16], i.e., the second term in Eq. (4) could be

neglected. Thus, DL is the major factor that affects the vari-

ation of optical path difference. For 0� case, the coupling

points are located around the inner cladding area, leading to

a decrease of the physical path of cladding modes. As opti-

cal path difference enlarges, the transmission spectrum turns

out a red wavelength shift accordingly. While for 180� case,

the coupling points are located around the outer cladding

area so that the optical path difference reduces as the curva-

ture increases. Therefore, the peak wavelength sharply shifts

towards the shorter wavelength direction. According to mate-

rial mechanics, bending brings strain localization around the

two micronotches of MMZI, and the side where strain local-

ization takes place experiences a larger physical deformation

than the opposite side. Consequently, for the same curvature,

much more obvious wavelength shift can be obtained for

180� case than 0� case, as illustrated in Figure 5(b). In

addition, for 90� case, both of the physical paths of core

mode and cladding mode are located in the neutral layer,

leading to the interference peak wavelength insensitive to

applied bending. On the whole, nonperfect circular geometry

of the fiber cladding causes strong directional dependence

during bending test. Bending degree and orientation could be

determined through transmission loss and wavelength shift

measurement, fulfilling the vector curvature sensing within a

semisphere space.

Figure 4 Interference peak evolution of the MMZI transmission spec-

trum corresponding to different curvatures for orientation angles of (a)

0� (b) 90�, and (c) 180�. [Color figure can be viewed in the online issue,

which is available at wileyonlinelibrary.com]

Figure 5 Spectral response of a MMZI as a function of curvature:

(a) transmission loss and (b) interference peak shift. [Color figure

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

wileyonlinelibrary.com]

138 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 1 January 2012 DOI 10.1002/mop

4. CONCLUSION

We have proposed an SMF-based MMZI exploiting the modal

interference built in a segment of common single mode fiber

under CO2 laser exposure. The bending and orientation

responses of its transmission spectrum have been characterized

and experimental results indicate that the transmission character-

istics of our proposed MMZI are strongly dependent not only on

the degree of curvature but also on the orientation along which

bending is applied. The simple fabrication process and low cost

of this novel sensor ensure its advantages over other orientation-

sensitive fiber sensors. It provides an opportunity to develop sin-

gle curvature sensing component with orientation recognition

ability. Furthermore, the potentiality of being embedded into

structural materials makes it promising for various multiple-pa-

rameter sensing applications.

ACKNOWLEDGMENTS

This work was jointly supported by the National Key Natural Sci-

ence Foundation of China (Grant No. 60736039), the National Nat-

ural Science Foundation of China (Grant Nos. 10904075,

11004110, and 50802044), the Fundamental Research Funds for the

Central Universities, and the National Key Basic Research and De-

velopment Program of China (No. 2010CB327605) and the Open

Project Foundation of Key Laboratory of Optical Information Sci-

ence and Technology, Ministry of Education in Nankai University.

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Ferreira, and F. Farahi, All-fiber Mach–Zehnder curvature sensor

based on multimode interference combined with a long-period gra-

ting, Opt Lett 32 (2007), 3074–3076.

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VC 2011 Wiley Periodicals, Inc.

NEW COUPLED-LINE DUAL-BAND DC-BLOCK TRANSFORMER FOR ARBITRARYCOMPLEX FREQUENCY-DEPENDENTLOAD IMPEDANCE

Yongle Wu, Yuanan Liu, Shulan Li, and Cuiping YuSchool of Electronic Engineering, P.O. Box. 171, Beijing Universityof Posts and Telecommunications, 100876, Beijing, China;Corresponding author: wuyongle138@gmail.com

Received 4 April 2011

ABSTRACT: A novel impedance transformer is constructed byinterpolating coupled line in this article. This proposed coupled-line

transformer not only has arbitrary dual-band operation for arbitrarycomplex frequency-dependent load impedance but also features inherent

DC-block function. The design of its electrical parameters can beobtained by using simple closed-form design equations. Furthermore,the practical scope of load impedance for this transformer is analyzed,

and the corresponding analytical design approach is verified by sevennumerical examples. Finally, experimental results for a microstrip

coupled-line dual-band impedance transformer with center frequenciesat 1.45 and 2.61 GHz are in excellent agreement with the circuit-basedsimulated results. VC 2011 Wiley Periodicals, Inc. Microwave Opt

Technol Lett 54:139–142, 2012; View this article online at

wileyonlinelibrary.com. DOI 10.1002/mop.26480

Key words: coupled line; dual band; dual frequency; transformers;

complex frequency-dependent impedance

1. INTRODUCTION

Impedance transformers, as fundamental components, are widely

used in several microwave circuits. Recently, dual-band opera-

tions are often required in modern wireless communication sys-

tems. Therefore, dual-band impedance transformers have been

developed in Refs. 1–5. On the other hand, the equivalent load

impedances of many active components such as power ampli-

fiers and oscillators are complex and their values vary with the

operating frequency. The impedance transformers given in Refs.

3–5 can effectively match such complex frequency-dependent

load impedances to a desired port impedance at two arbitrary

frequencies or dual band. However, the design equations in

Refs. 3 and 4 are relatively complicated, in particular, the

recently developed transformer in Ref. 5 needs solving nonlinear

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 1 January 2012 139