Intermodal interference in photonic crystal fibres

Intermodal interference in photonic crystal fibres I. Tureka∗, D. Káčika, J. Canningb, I. Martinčeka, N. Issab a

Department of Physics, Faculty of Electrical Engineering, University of Zilina Univerzitna 8215/1, 010 26 Zilina, Slovakia b Optical Fibre Technology Centre, University of Sydney 206 National Innovation Centre, Australian Technology Park, Eveleigh Sydney NSW 1430 Australia ABSTRACT The equipment for intermodal interference investigation is described. The results of an investigation of intermodal interference within a photonic crystal fibre (from Centaurus Technologies, Sydney) in terms of length and frequency region are presented. From the measured values the difference of the phase constant of the fundamental and the first higher order (antisymmetric) modes, as well as the decay constant of the mode in the wavelength region exceeding the two modes region, are determined. Photonic crystal fibre, intermodal interference, difference of phase constants of modes

1. INTRODUCTION The term intermodal interference is most often used in connection with sensors 1-,3 or when the determination of optical fiber parameters is studied 4,5. The origin of this effect lies in the fact that the phase constants of particular modes and their derivation with respect to wavelength, βj(λ), are different. Therefore the phase difference of the optical fields belonging to the modes at the end of the fiber of length L, is (1) ∆ϕ jk (λ, L ) = ∆β jk (λ ) L . It is seen from equation (1) that the intermodal interference can be studied as a function of length or frequency because the value of the resulting field periodically depends on the phase difference ∆ϕ(λ,L). However, the phase difference itself does not necessarily mean a change of a signal measured with a (quadratic) detector. It is so because the modes are orthogonal. Their orthogonality means that there are regions where the interference of the modes are constructive and in the same time regions with destructive interference. So the average value of changes is zero. To avoid averaging at u

SMF 28

PCF A

Optical source

B

OSA

T1 T2

Fig. 1. Experimental setup. PCF- photonic crystal fibre, SMF 28 – detection fibre, OSA Optical spectral analyzer, T1 – 1D microstage, T2 – 3D microstage. ∗

Further author information: [email protected] 15th Czech-Polish-Slovak Conference on Wave and Quantum Aspects of Contemporary Optics, edited by Miroslav Miler, Dagmar Senderáková, Miroslav Hrabovský, Proc. of SPIE Vol. 6609, 66090I, (2007) 0277-786X/07/$18 · doi: 10.1117/12.739496 Proc. of SPIE Vol. 6609 66090I-1

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detection of the interference term, detection of a fraction of the optical field can be used. Naturally, such part of the field where the sign of interfering fields does not change6 should be selected. In the equipment we used for intermodal interference investigation the restriction of detected area is realized using another (conventional) fiber (the detecting fiber) which serves as a pigtail transporting the registered field to the detector. This detecting fiber is mounted on a 3D stage which allows the fibre to be positioned at the end of the fiber to the best position where the condition is fulfilled. The scheme of the equipment is drawn in Fig.1. In the equipment a halogen lamp is used as the optical source. The filament of the lamp is projected onto the input face of the fiber under investigation using an objective. The front of the fiber under investigation is glued by a hard wax on a rotating stage A. This stage allows the input face to be rotated by an angle at which the input optical field phase in the places of maxima of the mode under study is opposite to the phase in the place of its minima (when the interference of a symmetric and an antisymmetric mode is investigated). It allows the optimal generation of the antisymmetric mode. The second end of the fiber is glued to the moving table T1. The direction of its possible shift is the same as the direction of the fiber, which allows stretching of the fiber. The detecting fiber input end is carried by the 3D table T2 in order to place its core in the place in which the interference fringe contrast is highest. The signal is detected by an optical signal analyser (Optical Signal Analyser – model: ANRITSU MS9710B).

λeq

Fig. 2. Intermodal interference in 72 cm long sample of standard telecommunication fiber.

The final setup permits us to measure the spectral dependencies either keeping the fiber length constant or changing it. Consequently, this allows investigation of intermodal interference as a function of both length and frequency (spectral) region. The characteristic spectral dependence of the interference term in a standard telecommunication fiber is presented in Fig. 2. The shape of the dependence can be used as a source of information about the refractive index distribution of the fiber. It was shown, for example that a small changes of the refractive index profile of conventional fibers leads to remarkable changes of the wavelength where the period of this dependence is maximal (to changes of equalization wavelength λeq) 5.

2. INTERMODAL INTERFERENCE OF PHOTONIC CRYSTAL FIBER AS A FUNCTION OF WAVELENGTH Photonic Crystal Fibers (PCFs)7, also known as “microstructured fibers”, represent a new group of optical fibers with potentially significant applications in telecommunications, fiber lasers and amplifiers, nonlinear elements or application in sensor techniques8, 9 . The nature of guiding in PCF is not based on the total reflection on the boundary between the fiber core and its cladding with smaller refractive index. It is based on coherent (Bragg) scattering on regularly (periodically) distributed inhomogeneities (most often in form of a cylinder). The contribution of diffractive propagation and an associated effective step index remain the subject of much research. None the less, as a result of scattering from inhomogeneities in

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the cross section, the fiber properties differ from the properties of conventional fibers. Hence, it is expected that the results of measuring intermodal interference will differ from those of conventional fibers. To confirm this we investigated the intermodal interference in PCF from Centaurus Technologies, Sydney. The fiber contains 4 layers of cylindrical air holes around the fiber “core”. The diameter of the holes is 2.6 µm and the pitch is 7.1 µm. The structure of the fiber is shown in the Fig. 3. The fiber is designed to be single mode at wavelengths longer than about 1000 nm.

Fig.3. Photo of the investigated fiber.

The spectral dependence of the interference term for the fundamental mode and the first higher order mode measured in this fiber is presented in the Fig. 4. It is seen from this figure that the spectral dependence of the interference term in the PCF significantly differs from that in standard telecommunication fiber (Fig.2.). The main differences between them are that if a PCF is investigated, the function of the period is monotone and that the period (the difference of wavelength for which the interference term is again maximal) is significantly smaller than in the conventional fiber of the same length10.

Fig. 4. Spectral dependencies of the signal interference measured in PCF from Centaurus Technologies for two positions of the detecting fiber. The length of the fiber was 7.3 cm. The curves are not rectified for sensitivity of the detector nor for emissivity of the source.


signal [a.u.]

Figure 4 shows the observed spectral interference arising from two positions of the detection. One is measured for the position for which the amplitude of the interference term is maximal and the second is symmetrically conjugated. The fact that these curves have opposite phase indicates that an interference of the symmetric and antisymmetric modes have been measured. The curves in Fig.4 also reveal that the amplitude of the antisymmetric (higher order) mode is not zero, including within the single mode regime where it should not be present. However, this mode should be deeply lossy in this wavelength region and the measurement on fibers with different lengths confirms this (Fig.5).

0.216m 0.180m 0.162m 0.145m 0.110m

1100

1200

1300

1400

wavelength [nm]

Fig.5. The interference terms measured at fibers with different length.

The measurement of the spectral dependence of interference term amplitude allows an estimate the loss coefficient11. The values obtained by this way are given in the figure 6.

loss coefficient [Np]

0.2

0.15

0.1

0.05 1100

1200

1300 wavelength [nm]

1400

Fig.6. Spectral dependence of the loss coefficient.


O.O14 - - - HE 11with TE 01-like mode WItfl ht-IIKe moae I

flI VVILII I VI —IIre IIIUU

I —v—-- PynirimpnfiI Iifi U.UI)1

a

:- -

-

• -O.O12 - - II 0 UI) I I 1

n n-in--I--

u.0

I.u

I.

I.'-F

1.0

1.0

(i m\

• vt-'•

Fig. 7. Spectral dependence of the interference term period. X – measured values, line – calculated for the designed structure. The obtained spectral dependence of the interference term in the PCF exhibit no extreme of its period in all investigated region (700 - 1500 nm). So, the dependence of the interference term period can be used as indicator of structural parameters. The wavelength dependence of measured interference term period is given in Fig. 7. There are drawn also the dependence calculated for the designed fibre structure. It is seen that the main feature – the positive derivative according the wavelength – agrees with the calculated dependence. However there is a difference of their values. Just the difference signalises some deviation from the designed structure.

3.

INTERMODAL INTERFERENCE IN PCF IN LENGTH REGION

The changes of the fibre length needed for intermodal interference investigation as a function of length can be realized by several means, including grinding off the fiber, changing its temperature or stretching the fibre. In this work we use the last approach. After stretching of the fiber in discrete amounts, the spectral dependence of the signal was recorded in the wavelength region 950 to 1200nm, i.e. in the region where the interference in the “singlemode region” of the fiber could be detected. The changes of the fiber length were controlled using an indicator of position (EDK’93 from Imeco Brno). The obtained dependencies are plotted in the Fig. 8. An initial examination reveals that the changes in fiber length affect the measured signal. According to Eq. 1, the length dependence of the interference term should be described by a harmonic function with the spatial period LBj,k. (i.e. the “beat length”) which can be expressed as L B, jk (λ) =

2π , ∆β jk (λ)

(2)

since the phase difference during a change of its length equal to the beat length is 2π . The changes of the phase determined for the particular wavelengths from the curves given in Fig. 8. are plotted in the Fig. 9. A harmonic function which fits the values determined from previous figure at wavelength 1060 nm is also plotted.


signal [a.u.]

1050

1075

1100

wavelength [nm]

Fig. 8. Some spectral dependencies of intermodal interference LP01 LP11 modes for different change of length of fibre 0.022, 0,102, 0,204, 0,303, 0,453, 0,553, 0,602mm). The curves are vertical shifted.

Knowledge of the beat lengths gives information about the difference in phase constants of the interfering modes. In our case it is the difference of phase constants of the fundamental and the first antisymmetric mode. These values for selected wavelengths are given in the Fig. 10 or in Tab.1. .

.

relative amplitude

1

0

-1

0

0.1

0.2

0.3

0.4

0.5

0.6 elongation [mm]

Fig.9. Amplitude dependence on fibre elongation for wavelength 1060 nm (the curves were normalised).

The solid line is a harmonic function with period fitted to measured values (x).


12500 ∆β 12000

11500

11000

10500

950

1000

1050

1100

1200 1150 wavelength [nm]

Fig.10. Dependence of phase constants difference of interfering modes on wavelength.

Tab.1. wavelength [nm] beat length [µm]

990 574±5

1061 546±5

1175 519±5

4. CONCLUSION The realized intermodal interference investigation in a special type of optical fibre confirmed that the investigation of intermodal interference enables the determination of the spectral dependence of the loss coefficient for the first higher order mode (supposing that the loss coefficient of the fundamental mode is negligibly small) as well as to determine the difference between their phase constants. Knowledge of these parameters and their spectral dependence can provide useful information permitting a comparison between the fabricated optical fibre and the initial design upon which it was based. This includes potential information on the inhomogeneity of a fabricated fiber since this can also affect the interference obtained so that it differs from the results predicted from the initial fibre design.

ACKNOWLEDGEMENT Jospeh Zagari and Katja Lyytikainen (now Digweed) for stacking and drawing of the PCF preform respectively. The fibre fabrication was funded by an Australian Research Council (ARC) Discovery Project Grant. This work was partly supported by Slovak National Grant Agency No. 1/2048/05 and by Science and Technology Assistance Agency contract No. APVT 20-013504.

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5.

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