. INTRODUCTIONhotonic crystal fibers (PCFs), also known as microstruc-ured optical fibers (MOFs) or holey fibers (HFs), haveeen thoroughly studied over the past decade due to aide spectrum of possible applications. Consisting of a
olid core of pure silica surrounded by a hexagonal arrayf air holes running along the length of the fiber, solid-ore PCFs guide light by an effective total internal reflec-ion mechanism, with the core having a refractive index of.44 at 1550 nm and the inner (air–silica) cladding havinglower index between 1.0 and 1.44, depending on the di-
meter and pitch (center-to-center distance) of the airoles. To manufacture these fibers, a preform is createdy arranging small silica capillary tubes (hollow cylin-ers) in a hexagonal pattern and a fiber is drawn. Thus,he hole diameter �dh�, the lattice pitch ���, and core di-meter �dc� can easily be changed, allowing for great flex-bility in the design of the fibers and thus in the types ofpplications. By replacing hollow cylinders with solid cyl-nders, highly birefringent and polarization-maintainingbers can also be created [1–3].Steel et al. [4], as well as Koshiba et al. [5], have shown
heoretically and numerically that perfectly sixfold sym-etric hexagonal PCFs are not birefringent. Despite this,iemi et al. [6], Peyrilloux et al. [7], and McElhenny et al.
8] have observed a characteristic polarization depen-ence in seemingly symmetric solid-core PCFs. and Pey-illoux et al. [7] have studied such fibers theoretically us-ng a finite-element method and experimentally using the
agneto-optical method. They have shown that the finite-lement method is reliable in predicting birefringence, asong as the grid applied to the cross section of the fiberespects the symmetry of the structure. Accidental bire-ringence may be caused by material stress and/or fluc-uations in the positioning and dimensions of the airoles. Hwang et al. [9] have modeled their properties nu-erically using the plane-wave expansion (PWE) method
nd found that such unintentional birefringence in PCFsan be suppressed by manufacturing fibers with widelypaced holes �� /�� or small air holes �d /��. This, however,ay not be suitable for certain applications. Both groups
ound that birefringence can be induced by nonuniformir hole size, displacement of hole positions, or residualtress. Such birefringence should affect many of the prop-rties of PCFs, particularly the stimulated Brillouin scat-ering (SBS). The effect of birefringence on the SBS inCFs, intentional or not, is particularly important sincene of their promising characteristics is, in fact, a higherBS threshold.To our knowledge, no one has yet studied the polariza-
ion dependence of SBS in PCFs, though Stolen et al. [10],pring et al. [11], and Yeniay et al. [12] as well as othersave studied the polarization dependence of SBS exten-ively in standard single-mode fibers. In this paper, we in-estigate the unexpected polarization dependence of SBSn two small-core PCFs and the polarization-dependentoss (PDL) [13–15] in the smaller-core fiber of the two. Inhe next section, we discuss the fiber structure, param-ters, and propagation properties. In Section 3, we de-cribe the details of the experimental setup used. Finally,n Sections 4 and 5, we present and analyze the experi-
ental results.
. FIBER PARAMETERS AND SIMULATIONSn the present work we study two different fibers: RB65 (6ayers of air holes) from OFS and CF (10 layers) fromrystal Fiber, with core diameters of 3.7 �m and 1.7 �m,
espectively. The parameters of these fibers can be foundn Table 1 where the core diameter, dc, is calculated fromc=2�−dh. We also studied a larger core PCF, RB61, withcore diameter of 8 �m but found no polarization depen-
ence.
008 Optical Society of America
PbhRiifi82dp
wl
3Tu
s(Eocffpteit2
fC(whtamttIwtwts(t3ss
frtpohuidtba
2108 J. Opt. Soc. Am. B/Vol. 25, No. 12 /December 2008 McElhenny et al.
Simulations using both beam propagation (Beam-ROP) and finite element (FemSIM) software showedoth fibers to be single-mode. The fundamental modesave an effective refractive index of 1.41 and 1.36 for theB65 and CF, respectively, using 1.44 for the refractive
ndex of silica at 1550 nm and 1.0 for air. As can be seenn Figs. 1(a) and 1(b), the fundamental mode of the RB65ber is confined within the core to an effective area of.07 �m2, while in the CF with a much smaller core of.22 �m2 the fundamental mode extends into the clad-ing with an effective area of 3.0 �m2. We revisit thisoint in Section 5.It should also be noted that both fibers are highly lossy,
ith the RB65 having a loss of 19.4 dB/km and the CF aoss of 70 dB/km.
. EXPERIMENTAL SETUPhe polarization dependence of the SBS was measuredsing the setup shown in Fig. 2.A 1550 nm signal from a Photonetics external cavity la-
er (ECL) was amplified by a 30 dB gain optical amplifierIPG Photonetics erbium-doped fiber amplifier, modelAD-1-C) and sent through a circulator before enteringur polarization control setup. The polarization controlomponent coupled slightly elliptically polarized light intoree space using a 10� 0.50 NA microscope objective. Inree space, a linear polarizer was used to isolate the linearolarization of the coherent beam before sending ithrough a half wave plate to control the angle of the lin-ar input polarization. Between measurements, a polar-meter (model PA530) was used after the half wave plateo accurately record the input polarization angle. Using a0� IR microscope objective, the light was coupled from
Table 1. Fiber Parameters an
FiberL
(m)dh
��m��
��m�dc
��m� d
RB65 384 2.4 3.05 3.7 0CF 353 0.72 1.2 1.7 0
(a)
Fig. 1. (Color online) Simulations of fundamenta
ree space back into the fiber under test (the RB65 or theF), which was mounted in a high-precision fiber rotator
Thorlabs HFR007) on a translation stage. The rotatoras used to align one of the axes of the hexagon with theorizontal axis and only rotated the fibers by 5° to 10° athe outset of the data collection. Once it was at a specifiedngle, the fiber was not moved for the duration of theeasurement. Because there was half a meter between
he translation stage and the spool of fiber, this small ro-ation does not contribute to the birefringence observed.n addition, the same measurements were later repeatedithout rotating the fiber rotator, and the same polariza-
ion dependence was observed. The transmitted poweras recorded using a power meter, while the backscat-
ered light traveled back through the polarization controletup and the circulator and onto the lightwave detectorAgilent 20 GHz Lightwave Detector) and electric spec-rum analyzer (ESA-L Agilent E4408B). Note that the.4 dB loss between the amplifier and the 20� IR micro-cope objective has already been accounted for in the re-ults reported below.
Three facts should be noted. First, as light is coupledrom free space to the flat tip of the fiber, there is strongeflection at the interface (up to 7 dBm reflected throughhe circulator for an input power of 27 dBm). For inputowers close to and below threshold, this strong reflectionf the input signal is of the same order of magnitude origher than the backscattered power. Therefore, the val-es of the peak powers from our ESA readings were used
nstead of obtaining the threshold measurements fromata collected with a power meter. Thus, the backscat-ered powers reported are not the absolute powers of theackscattered light but the relative powers, which give anccurate reading of the threshold. This reflection also
ulation Results at 1550 nm
� /�
�(dB/km) neff
Acore��m2�
Aeff��m2�
1.97 19.4 1.41 10.75 8.070.77 71 1.36 2.22 3.0
(b)
of the (a) RB65 and (b) CF fibers using FemSIM.
d Sim
h /�
.79
.60
l mode
en
gtcoclisrttrlltsttsbt
itF(oorwahs
4AT3i1Ttad
pc
Espi16mscct
tdestmmt
ppl
Ft
Fpcs
McElhenny et al. Vol. 25, No. 12 /December 2008 /J. Opt. Soc. Am. B 2109
liminated the need for using the self-heterodyne tech-ique, thereby simplifying the setup.Second, as mentioned above, the backscattered signal
oes back through the polarization component of the sys-em. One may be concerned that this fact itself mightause an artificial change in the polarization dependencebserved. This is not the case and was verified theoreti-ally and experimentally. It is well-known that the stimu-ated backscattered light has the same polarization as thencident light, which is controlled by the polarizationetup. If light enters a half wave plate at an angle � withespect to the wave plate’s fast axis, the polarization ofhe light will be rotated by 2�. Light propagating backhrough the wave plate, however, will be rotated by −2�,esulting in the backscattered light having the same po-arization as the input light before it passed through theinear polarizer and into the fiber under test. Experimen-ally, we verified this by placing a 92:8 polarization insen-itive beam splitter (BS) between the half wave plate andhe second microscope objective to couple the backscat-ered light into a fiber and send it to the ESA. Our resultshowed the same polarization dependence as when theackscattered light travels through the polarization con-rol section.
Finally, we imaged the fiber tip so that the input polar-zation angle could be determined relative to the orienta-ion of the fiber. The setup depicted in the dashed box inig. 2 was used to image the fiber tip. A white light source
WLS) was sent through a 92:8 beam splitter and focusednto the tip of the fiber using a 50� and 100� microscopebjective for the RB65 and the CF fibers, respectively. Theeflected light was sent back through to the CCD camerahere the image of the fiber tip was captured. The im-ges, shown later in Figs. 5(b) and 8(b), have been flippedorizontally as the images were reflected off of the beamplitter before being recorded by the CCD.
. RESULTS. RB65he Brillouin spectrum for the RB65 fiber is shown in Fig.for two different input polarization angles correspond-
ng to minimum and maximum SBS. The main peak is at0.96 GHz with a secondary peak about 100 MHz higher.he nature of these multiple peaks is not discussed fur-her here but has been studied earlier by McElhenny etl. [8]. For an input power of 23.6 dBm, there is a 40 dBifference between the SBS obtained at the two different
ig. 2. Configuration of experimental setup to study polarizatioo image the fiber tip.
olarization angles. This difference can be seen even morelearly in the threshold results below.
The backscattered power, which was recorded using anSA and not through a direct backscattered power mea-urement as discussed in Section 3, and the transmittedower are shown in Fig. 4 for four different angles. Thenput polarization angles resulting in maximum SBS are3° and 108°, and those resulting in minimum SBS are0° and −28°. With the input light polarized at angles foraximum and minimum SBS, the threshold powers mea-
ured in RB65 are 20.6 dBm and 24.1 dBm, respectively,orresponding approximately to a 3 dB difference as indi-ated in Fig. 4(a). As will be discussed in Section 5, this ishe result that would be expected for a birefringent fiber.
As shown in Fig. 4(b), the transmitted power throughhe RB65 fiber did not exhibit any polarization depen-ence for lower powers (below threshold). At higher pow-rs �Pin�Pth�, a strong polarization dependence is ob-erved with significantly more power �2–3 dBm�ransmitted for polarization angles corresponding toinimum SBS than maximum SBS. Obviously, whenore power is scattered in the backward direction, less is
ransmitted through the fiber.In Fig. 5(a), we plot the peak of the backscattered
ower vs. the input polarization angle, which reveals therecise polarization dependence of the SBS backscatteredight for two different input powers, 21.6 dBm and
ndence of SBS. The component in the dotted box was used only
10.7 10.8 10.9 11.0 11.1 11.2
-70
-60
-50
-40
-30
40 dB
13o
-28o
Sign
al(d
Bm
)
Frequency (GHz)ig. 3. (Color online) Brillouin signal in the RB65 for an inputower of 23.6 dBm and polarization angles of 13° (solid curve)orresponding to maximum SBS and −28° (dashed curve) corre-ponding to minimum SBS.
n depe
2FpFm1mSi
mgSfn
prictps
BTipBp1mppttidcp
ilmmmw
Fi
F1r hed lin
2110 J. Opt. Soc. Am. B/Vol. 25, No. 12 /December 2008 McElhenny et al.
2.6 dBm. These powers, corresponding to the data inig. 4(a), fall in the region of the threshold for the inputolarization angles corresponding to maximum SBS. Inig. 5(b), the input polarization directions are depicted foraximum and minimum SBS. These angles are shown at
4.75° and 105.5° relative to the horizontal axis for maxi-um SBS and at angles −29° and 59.5° for minimumBS. The observed birefringence is rectangular and has
ts two axes separated by 90°.As is clear from Fig. 5(b), the polarization angles foraximum SBS do not correspond to the axes of the hexa-
on, as one might have expected. In fact, according toteel et al. [4] and Koshiba et al. [5], PCFs with a per-
ectly symmetric hexagonal holey cladding should exhibito polarization dependence.Finally, when input light was polarized along a princi-
al axis, the output was found to be close to linear andelatively stable. In between the principal axes, the polar-zation of the transmitted light became more unstable,hanging in both ellipticity and orientation over time. Al-hough it could have been interesting to investigate theolarization cross talk, the unstable output preventeduch a study.
-30 0 30 60 90 120-80
-70
-60
-50
-40
-30
-30 0 30 60 90 120-80
-70
-60
-50
-40
-30
Peak
Pow
er(d
Bm
)
Angle (o)
20.6 dBm21.6 dBm(a)
ig. 5. (Color online) (a) Polarization dependence of SBS in RB65nput polarization angles resulting in maximum (solid lines) and
18 20 22 24 26-80
-70
-60
-50
-40
-30
-20
40 dB3 dB
(a)
Peak
Pow
er(d
Bm
)
Input Power (dBm)
13o
60o
108o
-28o
ig. 4. (Color online) (a) Peak and (b) transmitted powers vs. i08° (squares) corresponding to maximum SBS and 60° and −28esponds the power used in Fig. 3 above and the two shorter das
. Crystal Fiber (CF)he CF, with a much smaller core of 1.7 �m, also exhib-
ted very strong polarization dependence as well as unex-ected transmission effects. As was the case for RB65, therillouin spectrum for the CF (Fig. 6) was found to beolarization-dependent. Here, the main peak is at0.59 GHz with another peak at 10.96 GHz, approxi-ately 400 MHz from the main peak. These multiple
eaks have been studied by McElhenny et al. [8]. Theeak at 10.96 GHz had the same threshold and exhibitedhe same polarization dependence as the main peak,hough these results are not included. At 24.6 dBm, theres a difference of about 40 dB in the Stokes signal for twoifferent input polarization angles. As with the RB65, thisan be seen more clearly in a plot of the backscatteredower.The backscattered and the transmitted powers vs. the
nput power are shown in Figs. 7(a) and 7(b) for input po-arization angles of −39° and 53°, corresponding to the
aximum SBS, and of 8° and 97°, corresponding to theinimum SBS. For input polarization angles yielding theaximum SBS the threshold is approximately 21.6 dBm,hile for angles yielding the minimum SBS the threshold
MaxMin
14.75º
59.5º105.5º
151º
0º
90º
(b)
o powers, 20.6 dBm (circles) and 21.6 dBm (squares), and (b) theum (dashed lines) SBS plotted on the image of the fiber tip.
18 20 22 24 26 28
4
6
8
10 (b)
Input Power (dBm)
ower for the RB65 fiber for input polarization angles of 13° andes) corresponding to minimum SBS. The longer dashed line cor-es to the powers used in Fig. 5 below.
150150
for twminim
28
Tra
nsm
itted
Pow
er(d
Bm
)
nput p° (circl
ida3
spfp1t(ifmp
Caaam
Hl−ts
tTptsauTtTaopbsftptTib
5ATcSefeilpcP
Fpcs
F(p
McElhenny et al. Vol. 25, No. 12 /December 2008 /J. Opt. Soc. Am. B 2111
s approximately 24.6 dBm. As with the RB65 fiber, theifference in threshold power for the polarizationngles corresponding to maximum and minimum SBS isdB.The SBS polarization dependence of the CF is pre-
ented in Fig. 8. In Fig. 8(a), the backscattered power islotted against the input polarization angles for two dif-erent input powers, 22.6 dBm and 24.6 dBm. The inputolarization angles resulting in maximum SBS, 51° and41°, are 90° apart and do not correspond to the axes ofhe hexagon but rather indicate rectangular birefringenceshown in Fig. 8(b)). The input polarization angles result-ng in minimum SBS, 6° and 96°, are also 90° apart andall exactly half-way between the two angles for maxi-um SBS, which thus correspond to the direction of the
rincipal axes.From Fig. 7(b), it is clear that the transmission of the
F behaves differently than in the RB65. At high powers,bove 24.6 dBm (the saturation point for polarizationngles of maximum SBS), the transmitted light behavess expected; there is maximum transmission for mini-um SBS and minimum transmission for maximum SBS.
10.4 10.5 10.6 10.7 10.8 10.9 11.0 11.1
-70
-60
-50
-40
-30
2.5 dB
40 dB
-39o
8o
Sign
al(d
Bm
)
Frequency (GHz)ig. 6. (Color online) Brillouin signal in the CF for an inputower of 24.6 dBm and polarization angles of −39° (solid lines)orresponding to maximum SBS and 8° (dashed lines) corre-ponding to minimum SBS.
18 20 22 24 26-80
-70
-60
-50
-40
-30
-20
40 dB3 dB
(a)
Peak
Pow
er(d
Bm
)
Input Power (dBm)
-39o
8o
53o
97o
ig. 7. (Color online) (a) Peak and (b) transmitted powers vs. insquares) corresponding to maximum SBS and 8° and 97° (circleowers used in Fig. 8(a) and 9(a).
owever, below saturation, not only is the transmittedight polarization dependent but, for light polarized at39° (i.e. an angle corresponding to maximum SBS), theransmission is also maximum. When more light is back-cattered, more is also transmitted!
This is seen more clearly in Fig. 9, where the transmit-ed power is plotted against the input polarization angles.he data presented in Fig. 9(a) was taken with all of therevious data presented in this paper and is plotted forhe same input powers of 22.6 and 24.6 dBm. It can beeen that 51° corresponds to a minimum in transmission,s expected, but 141° (the other angle for maximum SBS)nexpectedly corresponds to a maximum in transmission.his is quite anomalous as one would expect minimum
ransmission for both angles resulting in maximum SBS.he angles for maximum transmission are now 180°part, while those for minimum and maximum SBS arenly 90° apart. In a later experiment, for higher inputowers (23.9 dBm and 26.2 dBm) and with a different fi-er orientation, the transmission shown in Fig. 9(b) doeshow normal behavior, a correspondence between anglesor maximum (minimum) SBS and minimum (maximum)ransmission. The earlier results at lower power suggest aolarization-dependent loss, which is confirmed by theransmission curve shown in Fig. 7(b) below threshold.hough the transmitted power behaves differently than
n the RB65 fiber, the polarization of the transmitted lightehaves the same in both fibers.
. DISCUSSION. Physical Origin of Birefringent Effects on SBShe experimental SBS results presented for two small-ore PCFs show that the intensity of the backscatteredtokes light is at maximum when the incident light is lin-arly polarized along either one of two axes separatedrom each other by 90°. The SBS measurements of anlliptical-core fiber reported below in Subsection 5.C alsondicate that the maximum SBS corresponds to linear po-arization of the incident light along either one of the tworincipal axes of the elliptical core. Therefore, the two in-ident linear polarizations that produce maximum SBS inCFs correspond to the two principal axes of these PCFs.
18 20 22 24 26 28-14
-12
-10
-8
-6
-4(b)
Input Power (dBm)
wer for the CF fiber for input polarization angles of 39° and 53°sponding to minimum SBS. The dashed lines correspond to the
28
Tra
nsm
itted
Pow
er(d
Bm
)
put pos) corre
Sftrdtpigititalmwpalsbs
oiSiomdffiopwmlptbcm
tc
F2
Fi minim
2112 J. Opt. Soc. Am. B/Vol. 25, No. 12 /December 2008 McElhenny et al.
To further understand the polarization dependence ofBS, we review four well-known facts. First, light at dif-
erent frequencies experiences different indices of refrac-ion. Second, in a birefringent medium, the difference inefractive index along the two principal axes results inifferent propagation velocities (slow and fast) alonghese axes. As such, birefringent fibers maintain linearolarization along the principal axes. Third, at each pointn an isotropic medium, the backscattered Stokes lightenerated at that point assumes the same state of polar-zation (SOP) as the incident light, irrespective of the par-icular SOP [11]. Finally, maximum SBS occurs when thencident and Stokes waves have the same SOP [10–12]. Ifhe incident light is linearly polarized along a principalxis, the polarization of both the Stokes and the incidentight will be maintained as they propagate, resulting in
aximum SBS gain. By contrast, for light polarized mid-ay between the principal axes, the polarization of theump and Stokes will not be maintained. It will evolvelong the length of the fiber becoming elliptically, circu-arly, and again linearly polarized. If both waves had theame frequency, even though their initial SOPs might note maintained, the SOP of the Stokes wave would be the
0 50 100 150-80
-70
-60
-50
-40
-30
Peak
Pow
er(d
Bm
)
Angle (o)
22.6 dBm24.6 dBm(a)
ig. 8. (Color online) (a) Polarization dependence of SBS in CFnput polarization angles resulting in maximum (solid lines) and
ame as that of the pump wave throughout the fiber. In s
ther words, the polarization of the Stokes wave, travel-ng backwards, would go through the same sequence ofOPs that the pump wave had gone through. The polar-
zation of the Stokes wave would retrace the polarizationf the pump wave. As such, the SBS gain would be maxi-um. However, the two waves have different frequencies
ue to the Doppler effect and thus experience different re-ractive indices. Thus, their polarization will evolve at dif-erent speeds (the Stokes wave will not retrace the polar-zation of the pump wave) and the two waves will phaseut. There will be negligible gain when the wave is com-letely out of phase (having opposite polarizations) buthile it is in phase (same polarization), there will beaximum gain (as in the first case mentioned where the
inear polarization of both waves is maintained along therincipal axis). Overall, there will be half as much gain ashat for maximum SBS, resulting in the threshold powereing effectively multiplied by two. This explains the 3 dBhange observed in the threshold for the conditions ofaximum and minimum SBS respectively. [11]For example, in the CF, if 24.6 dBm is launched into
he fiber at a polarization angle of 141° (i.e. along a prin-ipal axis), it remains polarized along this axis, which re-
MaxMin
0º
90º6º
51º(fast)
96º
141º(slow)
(b)
powers, 22.6 dBm (circles) and 24.6 dBm (squares), and (b) theum (dashed lines) SBS plotted on the image of the fiber tip.
ults in a maximum backscattered power of about
-50 0 50 100 150 200
-9
-8
-7
-6
-5
0 50 100 150 200-12
-11
-10
-9
-8
-7
Tra
nsm
itted
Pow
er(d
Bm
)
Angle (o)
26.2 dBm23.9 dBm
(b)(a)
Tra
nsm
itted
Pow
er(d
Bm
)
Angle (o)
24.6 dBm22.6 dBm
ig. 9. (Color online) Polarization dependence of the transmitted power in CF for (a) 22.6 dBm (circles) and 24.6 dBm (squares) and (b)3.9 dBm (circles) and 26.2 dBm (squares), taken at a different time with a different fiber orientation than previous data in the paper.
200
for two
−tr2tittltppt
BBriaaBaTt1(af15W
CTarowthtibn
rnse
fmtu2iMtvaiwattspmtpw
TtlsthsUdttstshd(
McElhenny et al. Vol. 25, No. 12 /December 2008 /J. Opt. Soc. Am. B 2113
30 dBm. However, when light polarized at 96° (45° fromhe principal axes) is launched, the pump power givingise to coherent SBS is only half the total power of4.6 dBm, resulting in 3 dB lower power in each of thewo components. Thus, each axis behaves as though thenput power were 21.6 dBm, dropping it close to thehreshold. The gain is then proportional to only half of theotal input power, resulting in a factor of 2 difference fromight polarized along a principal axis. By merely changinghe input polarization angle away from one of the princi-al axes, we are thus able to lower the effective inputower for SBS such that it falls close to or even below thehreshold, thereby reducing SBS significantly.
. Determination of Fast and Slow Axesefore analyzing the structural origin of the observed bi-efringence, determining the fast and slow principal axess essential. The principal axes are found to be at 14.75°nd 105.5° for RB65 and at 51° and 141° for the CF andre shown in Figs. 5(b) and 8(b). In the RB65 fiber, therillouin frequency, �B, is 10.955 GHz for light polarizedt 14.75° and 10.957 GHz for light polarized at 105.5°.he ordinary and extraordinary refractive indices canhus be obtained from �B=2neffvA /�. Light polarized at4.75° experiences a smaller effective refractive indexand thus a higher velocity) 14.75° corresponds to the fastxis and 105.5° to the slow axis. In the CF, the Brillouinrequency for light polarized at 51° is 10.588 GHz and0.590 GHz for light polarized at 141°. Thus, in the CF,1° corresponds to the fast axis and 141° to the slow axis.e now examine the structural origin of these axes.
. Structural Origin of Birefringencehe curves of the SBS peak powers vs. input polarizationngles for the RB65 and CF fibers, in Fig. 5(a) and 8(a)espectively, illustrate the strong birefringent characterf small-core photonic crystal fibers. Based on previousork [4,5] a perfectly symmetric PCF with sixfold symme-
ry should exhibit no birefringence. As these two fibersave a moderate to large d /� ratio (0.79 and 0.60 respec-ively) and a small � /� ratio (1.968 and 0.77 respectively),t follows from Hwang et al. [9] that in our small-core fi-ers either the air-hole structure of the inner cladding isot symmetric (size or position of the holes vary) or the
Fig. 10. SEM images of the (a) RB65 and (b) CF fibers. Th
esidual stress in the core is not symmetric. Indeed, scan-ing electron microscope (SEM) pictures of the fiber crossections (Fig. 10) reveal asymmetries in the hole pattern,specially in the core.
As the optical mode is tightly confined to the core, de-ormation of the air holes of the innermost ring are ofost significance. For RB65, it is clear from Fig. 10(a)
hat both the size and position of the air holes are non-niform. The diameter of these air holes varies between.24 �m and 2.42 �m, and the spacing between them var-es from 0.59 �m to 0.72 �m within an error of 0.02 �m.
ost relevant to the observed birefringence is the varia-ion in the core diameter from 3.56 �m to 3.81 �m. Theseariations indeed result in a slightly elliptical core withn ellipticity of 0.93. Such a break in symmetry resultingn an elliptical core causes the birefringence reported, ase confirm below. Although we have determined the slowxis to be 105.5° from one of the axes of the hexagon andhe fast axis to be 14.75° from the same axis in Fig. 5(b),here can be three such orientations in Fig. 10(a), eacheparated by 60°. Although it is difficult to relate the twoictures, it is still possible to determine the likely align-ent of the fast and slow axes. Because the slow axis has
he larger refractive index, it follows that it should be ex-ected to lie along the major axis of the elliptical core,hile the fast axis will lie along the minor axis.The CF exhibits similar deformations to the RB65 fiber.
he variation in the core diameter �1.85–1.88 �m� andhe spacing between the air holes �0.46–0.48 �m� areower, but at the same time the CF core is significantlymaller and the optical mode therefore extends beyondhe strictly silica core. In addition, not only do the airoles vary in size, but they are also more elliptical inhape with the side facing the core of the PCF flattened.nlike the RB65, the outer regions of the CF’s inner clad-ing are distinct enough so that they can actually be usedo match up the axes of the hexagon on the SEM imageso those taken with the CCD camera. Thus, the fast andlow axes shown on the SEM image (Fig. 10(b)) are ob-ained directly from the experimental results. These re-ults logically make sense. The slow axis, which shouldave the most silica and thus have a higher refractive in-ex, is aligned with the most elongated section of the coremajor axis). This supports the assumption that the ex-
d line is the fast axis and the dashed line is the slow axis.
e dotte
pfdmCam
itRfi25Ta
c[vs�itvvavutbmTc
hbcdtagt
cbpitcta
DApt5hitmsaltdsltecmh
6IdcsaiFewp
F(f
2114 J. Opt. Soc. Am. B/Vol. 25, No. 12 /December 2008 McElhenny et al.
erimentally observed birefringence is due to a deviationrom perfect hexagonal symmetry of the core produceduring the drawing process. Though the structural asym-etries in the RB65 are more severe than in the CF, theF also has a smaller core (and thus a higher intensity)nd the optical mode extends further into the cladding,aking it more sensitive to smaller asymmetries.To quantify this birefringence, we look at the difference
n the frequency shift between the light polarized alonghe fast and slow axes (f=1.6 MHz and 1.8 MHz forB65 and CF, respectively). The birefringence of the twobers is calculated (from n=�f /2cL) to be 2.1�10−4 and.4�10−4 for the RB65 and CF fiber respectively, using900 m/s for the longitudinal velocity of sound in silica.hese values are close to the value quoted by Dainese etl. [16].To further show that these small deformations can
ause such a large birefringence, we refer to Hwang et al.9]. These authors studied the birefringence induced byarying both the hole position and the hole diametereparately for a fiber with fixed d /� of 0.46 and a ratio/� of 2.1, 6.2 and 10.3. Using only the air holes of the
nnermost ring and extrapolating their results to estimatehe birefringence vs. the variation in hole position to thealue � /� of 1.97 and 0.77 of our fibers, the birefringencealues of 4�10−5 and 1.8�10−4 are obtained for the RB65nd CF fibers, respectively. Similarly, the birefringences. the variation in hole diameter for our fibers yields val-es of 2.1�10−5 and 2.7�10−4 for the RB65 and CF, respec-ively. The lower expected birefringence of the RB65 cane explained by the fact that its d /� is 0.79, which isuch higher than the value of 0.46 used by the authors.hey indeed showed that increasing the d /� value signifi-antly increases the birefringence.
Similar polarization dependence of the SBS reportedere has been observed in polarization-maintaining fi-ers. One such example is illustrated in Fig. 11 for a solidore/cladding elliptical-core fiber. In this case, the powerifference between maximum and minimum SBS was upo 45 dB, comparable to the 40 dB observed for both RB65nd CF fibers. In summary, a very significant birefrin-ence tends to be introduced accidentally in PCFs duringhe drawing process, primarily due to the weaker me-
22 24 26 28 30-80
-70
-60
-50
-40
-30
-20
Peak
Pow
er(d
Bm
)
Input Power (dBm)
0o
53o
90o
(a)
ig. 11. (Color online) (a) Peak vs. input power for an elliptical cosquares) corresponding to maximum SBS and at 53° (circles) corror two powers, 25 dBm (circles) and 30 dBm (squares).
hanical strength of the inner holey cladding. This muste taken into account as it can dramatically change theroperties of the PCF, specifically if the polarization of thenput light is not controlled. On the other hand, ratherhan being accidental, a large controlled birefringenceould also be introduced purposely in these fibers,hrough a deformation of the inner cladding, for specificpplications.
. Transmitted Power Through the Crystal Fibers discussed in Section 4.B and shown in Fig. 7(b), atowers below SBS saturation more light is transmittedhrough the CF for input light polarized at 141° than at1°, indicating a polarization-dependent loss (PDL). Thisas been numerically demonstrated by Koshiba et al. [14]
n nonuniform holey fibers. The authors have shown thathe field distribution for light polarized along the fast axisode is less confined than that of the slow-axis mode, re-
ulting in higher loss for light polarized along the fastxis. In the CF, we observe higher loss in transmission foright polarized at 51°. Based on this analysis, 51° mustherefore be the fast axis and 141° the slow axis. This in-eed is in agreement with our analysis in Section 5.B. Asuch, light polarized at 141° is more confined, has a loweross, and thus transmits more light. Because the core ofhe CF is very small and the fundamental optical modextends into the cladding (an effective area of 3.0 �m2
ompared to the core area of 2.22 �m2), changes in theode field distribution for different polarizations result inigher losses, as we have observed.
. CONCLUSIONn the present study we have reported experimental evi-ence of the polarization dependence of SBS in two small-ore PCFs. This birefringence is rectangular (twofoldymmetric) rather than hexagonal (threefold symmetric)nd results in a 3 dB increase in the overall threshold fornput light polarized midway between the principal axes.or lower powers, the transmission of the smaller-core CFxhibits a 180° polarization periodicity (unlike SBS,hich exhibits a 90° periodicity), which points toolarization-dependent losses. At higher powers, where
-150 -120 -90 -60 -30 0 30
-65
-60
-55
-50
-45
-40
-35
Angle (o)
30 dBm25 dBm
r for input polarization angles of along the major and minor axesing to minimum SBS and (b) the polarization dependence of SBS
(b)
Peak
Pow
er(d
Bm
)
re fibeespond
ttststtcmtdps
ASOCPFtSE
R
1
1
1
1
1
1
1
McElhenny et al. Vol. 25, No. 12 /December 2008 /J. Opt. Soc. Am. B 2115
he SBS gain is larger, the PDL becomes negligible andhe expected 90° periodicity is recovered for the transmis-ion. The observed strong birefringence is due to asymme-ry in the geometrical fiber structure, which even whenmall is strongly enhanced by both the small-core (andhus high intensities) and the large-index contrast ofhese PCFs. Such unintentional birefringence in small-ore PCFs must be taken into consideration as it can dra-atically alter the properties of the PCF, such as raising
he threshold by 3 dB and giving rise to polarization-ependent losses. However, it can further increase the ap-eal of PCFs for applications that are limited by SBS iningle-mode fibers.
CKNOWLEDGMENTSpecial thanks go to Ryan Bise and David Di Giovanni ofFS Inc. for supplying the RB65 fiber studied, as well asato Fagermo from Crystal Fiber Inc. for the smaller-coreCF. This work was supported by the National Scienceoundation, grant ECS-0401269and by the Center for Op-ical Technologies at Lehigh Universityfunded by thetate of Pennsylvania Department of Community andconomic Development.
EFERENCES1. A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J.
Arriaga, B. J. Mangan, T. A. Birks, and P. St. J. Russell,“Highly birefringent photonic crystal fibers,” Opt. Lett. 25,1325–1327 (2000).
2. T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A.Bjarklev, J. R. Jensen, and H. Simonsen, “Highlybirefringent index-guiding photonic crystal fibers,” IEEEPhoton. Technol. Lett. 13, 588–590 (2001).
3. S. B. Libori, J. Broeng, E. Knudsen, A. Bjarklev, and H. R.Simonsen, “High-birefringent photonic crystal fiber,” inProceedings of the Optical Fiber CommunicationConference, Vol. 54 of OSA Proceedings Series (OpticalSociety of America 2001) Paper TuM2.
4. M. J. Steel, T. P. White, C. Martinijn de Sterke, R. C.McPhedran, and L. C. Botten, “Symmetry and degeneracyin microstructured optical fibers,” Opt. Lett. 26, 488–490
(2001).
5. M. Koshiba and K. Saitoh, “Numerical verification ofdegeneracy in hexagonal photonic crystal fibers,” IEEEPhotonics Technol. Lett. 13, 1313–1315 (2001).
6. T. Niemi, H. Ludvigsen, F. Scholder, M. Legré, M.Wegmuller, N. Gisin, J. R. Jensen, A. Petersson, and P. M.W. Skovgaard, “Polarization properties of single-moded,large-mode area photonic crystal fibers,” in 28th EuropeanConference on Optical Communication (IEEE, 2002), pp.1–2.
7. A. Peyrilloux, T. Chartier, A. Hideur, L. Berthelot, G.Mélin, S. Lempereur, D. Pagnoux, and P. Roy, “Theoreticaland experimental study of the birefringence of a photoniccrystal fiber,” J. Lightwave Techol. 21, 536–539 (2003).
8. J. E. McElhenny, R. K. Pattnaik, J. Toulouse, K. Saitoh,and M. Koshiba, “Unique characteristic features ofstimulated Brillouin scattering in small-core photoniccrystal fibers,” J. Opt. Soc. Am. B 25, 582–593 (2008).
9. I. K. Hwang, Y. J. Lee, and Y. H. Lee, “Birefringenceinduced by irregular structure in photonic crystal fiber,”Opt. Express 11, 2799–2806 (2003).
0. R. H. Stolen, “Polarization effects in fiber Raman andBrillouin lasers,” IEEE J. Quantum Electron. QE-15,1157–1160 (1979).
1. J. B. Spring, T. H. Russell, T. M. Shay, R. W. Berdine, A. D.Sanchez, B. G. Ward, and W. B. Roh, “Comparison ofstimulated Brillouin scattering thresholds and spectra innon-polarization-maintaining and polarization-maintaining passive fibers,” Proc. SPIE 5708, 147–156(2005).
2. A. Yeniay, J. Delavaux, and J. Toulouse, “Spontaneous andstimulated Brillouin scattering gain spectra in opticalfibers,” J. Lightwave Techol. 20, 1425–1432 (2002).
3. W. Urbanczyk, M. Szpulak, G. Statkiewicz, T. Martynkien,J. Olszewski, J. Wojcik, P. Mergo, M. Makara, T.Nasilowski, F. Berghams, and H. Thienpont, “Polarizingproperties of photonic crystal fibers,” in InternationalConference on Transparent Optical Networks 2, 59–63(2006).
4. M. Koshiba and K. Saitoh, “Polarization-dependentconfinement losses in actual holey fibers,” IEEE PhotonicsTechnol. Lett. 15, 691–693 (2003).
5. Y. C. Liu and Y. Lai, “Optical birefringence and polarizationdependent loss of square- and rectangular-lattice holeyfibers with elliptical air holes: numerical analysis,” Opt.Express 13, 225–235 (2005).
6. P. Dainese, P. St. J. Russell, N. Joly, J. C. Knight, G. S.Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif,“Stimulated Brillouin scattering from multi-GHz-guidedacoustic phonons in nanostructured photonic crystal
