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Transverse stress induced LP02-LP21 modal interference of stimulated Raman scattered light in a few-mode optical fiber
__ *._l!iiB
s5
ELSEWIER
15 February 1996
OPTICS COMMUNICATIONS Optics Communications124 ( 1996) 11l-1 17
Transverse stress induced LP,,-LP,, modal interference of stimulated Raman scattered light in a few-mode optical fiber A.Sharma, R. Posey Deparhnent of Physics, Alabama A&M University, Huntsville, AL 35762, USA Received 28 February 1995; revised version received 28 September 1995
Abstract Four-photon mixing followed by stimulated Raman scattering is observed in LPoz mode in a 7.9 p,m core diameter optical fiber. A localized transverse stress efficiency couples LPoz to the LP2r mode with a macroscopic beat length of 1.8 mm. LPor
LP1, modal interference is investigated by detecting the 550-590 nm SRS through a pinhole in the far field exit plane. Quantitative explanation of wavelength dependent intensity modulation results in a precise experimental determination of a [ &( A) - &, (A) ] /aA, for mode-propagation constants /3az(A) and &, (A) of LPoz and LP,, modes respectively, as well as A, the relative core-cladding between 50-300°C.
refractive index difference.
The LPo2-LP,,
1. Introduction
Modal interference in dual-mode or few-mode fibers has been widely investigated, largely for its application in interferometric fiber-optic sensors. This includes two-mode interference of either LPer-LPo, modes [ l] or LP,,-LP, , modes [ 2,3]. Three-mode interference using LPc,, LPe, and LP, , modes has also been used [ 41 for separating the effect of temperature from strain sensing. Generally the two or more modes are launched simultaneously in the fiber, their relative intensities depending on the light coupling conditions. We describe here the interference of LP,,--LP,, modes in a spectrally extended (550-590 nm) light produced largely in LP,, mode [5] by stimulated Raman scattering (SRS) in a few-mode fiber. Unlike the examples referenced above [ l-41, the second mode ( LP2, ) is introduced by applying a mode-coupling perturbation in the form of a localized transverse stress close to the exit end of the fiber. Effect of LP,,-LP,r 0030-4018/96/$12.00 0 1996 Elsevier Science B.V. All rights reserved SSDZOO30-4018(95)00621-4
modal interference
is used for sensing of temperature
model interference on the extended SRS spectrum is investigated by detecting the light through pinholes in a far field exit plane. Various Stokes orders of the Raman spectrum are intensity modulated with a spectral spacing that depends on the distance of the localized transverse stress from the exit end. This effect is investigated for a precise measurement of [/&(A)& (h) 1, the difference between mode propagation constants in the 550-590 nm wavelength range as well as A, the relative core-cladding refractive index difference. LPo2-LP2r model interference at the first Raman Stokes wavelength of 553 nm is also used for interferometric sensing of temperature between 50-300°C. Because of the periodic nature of the intensity detected by an interferometric sensor using a single wavelength, the value of the measurand is ambiguous. This limits the useful range of the sensor to a value rr of the intermodal phase difference change. The spectrally extended SRS light in LPo2 mode offers a convenient
A. Sharma, R. Posy
I-PO,+ LPo*
MB
LPm + LP,,
/Optics
Communications
21
Pig. 1. Schematic of the experimental set-up. 532 nm light from a Nd: YAG laser excites LPn, and LPoz modes. About 100 meter fiber in spool (S) generates four wave mixing and SRS largely in LPaa mode. Microbend (MB) couples LPc, to the LP2, mode. LPa2-LP,, interference is investigated by observing light through the pinhole (P) which is focused with a lens (L) into a monochromator (M). Heater (H ) is used to demonstrate the fiber-optic temperature sensor described in this work.
source for interferometric sensing at two or more wavelengths simultaneously, thus making it possible to sense unambiguously over an unlimited range [ 6,7].
2. Experimental
results
Fig. 1 shows the schematic of the experimental setup. SRS is produced in a 100 meter long, few-mode, circular-core, step-index optical fiber with. a core diameter of 7.9 Frn. As shown in an earlier work [5] using 5 kW pulses of 532 nm light from an Nd : YAG laser, four-photon mixing (FPM) has a major influence on SRS in such a fiber. It not only shifts the entire multiorder SRS spectrum by 220 cm-’ but also converts the mixed-mode structure (LP,, +LP,,) of the incident light into 550-600 nm spectrum of SRS light which is largely in LPO, mode. This sequential process can be described by: pump light (LP,, +LPe,) at 532 nm-tfour photon mixing (LP,,) at 538.3 nm + shifted SRS spectrum largely in LP,,, mode. The
124 (1996) I1 I-l I7
far field intensity distribution of such light exiting the fiber is shown in Fig. 2a. For 538.3 nm FPM light in LPoZ mode, the overlap integral for the first Raman Stokes line to be in LP,,, mode is 0.57 as against 0.87 for it to be also in the LP,, mode [ 81. We believe that the slight initial excess of the LPoz component in the spontaneous Raman light is sufficient to drive SRS largely in LPoZ mode. This is also supported by our earlier experiment [9] in which we put a few loops in the first half of the fiber such that the LP,, mode is attenuated more than the LP,,, mode. By doing so one can relatively increase the LP,, component over LP,, in the SRS light. A localized transverse stress is applied by keeping the fiber on a flat surface and pressing it with a stiff 0.5 mm diameter wire perpendicular to the length of the fiber. The perturbed far field light intensity distribution, which depends critically on the distance (z) of the localized strain from the exit end is shown in Fig. 2b for z = 1 cm. Not only is the mode structure in Fig. 2b different from LPo2, but the light is also spectrally redistributed over the core of the fiber. The dark and light shades in Fig. 2b have wavelengths centered around red and green light respectively. For an unperturbed fiber, Fig. 3a shows the PPM line at 538.3 nm (marked with *) , in LP,,, mode. This in turn produces the 5 SRS Stokes orders all of which are also largely in the LP,, mode. The spectra in Figs. 3b, 3c are produced in a transversely stressed fiber and correspond respectively to the light and dark shaded regions of Fig. 2b. The first and the second Stokes orders are present dominantly (Fig. 3b) in the vertical azimuthal plane corresponding to 8 = Z-l2,3 n-12 whereas the complimentary third and the fourth Stokes orders are dominant (Fig. 3c) in the
Fig. 2. Far field distribution of output light a) in an unperturbed fiber (LPm mode); due to b) perturbation induced by transverse stress at a distance, e = 1 cm from exit end. Light and dark shades correspond to green and orange light respectively. c) transverse stress at a distance, z = 100 cm from exit end.
A. Sharma, R. Posey / Optics Communications 124 (1996) 1 I l-l I7
113
spectrum of the output light for z = 100 cm is shown in Fig. 5. As in Fig. 3, the intensity variation in the horizontal and the vertical planes are again complimentary to each other, although each Raman Stokes line itself is intensity modulated. The far field intensity distribution of light for such a perturbed fiber (z = 100 cm) is shown in Fig. 2c. Due to intensity modulations within the Raman Stokes lines one does not see any azimuthal dispersion of colors. As described below, the observations in Figs. 2-5 are due to the interference of the LPoz mode of SRS light with the LP2, mode generated due to the locally stressed fiber.
3. Theory and analysis The LP,, +LP2i mode conversion is explained below on the basis of the coupled mode theory of round optical fibers [ lo]. The core-cladding interface of the perturbed fiber can be described by the function Y(X, y, z) =a+f(z)
560 WAVELENGTH
630 (nm)
Fig. 3. (a) Spectrum of light from an unperturbed fiber. (*) denotes the position of FPM line at 538.3 nm, which generates the subsequent SRS Stokes lines in, unperturbed fiber. (b) (c) The spectral distribution of light as measured through pinholes in the vertical (8= &2,3~/2) and horizontal ( B=O, r) azimuthal planes respectively in a locally stressed fiber (z= 1 cm). Unperturbed spectrum with or without the pinhole is identical to (a).
0 = 0, rr plane. The intensity of each of the Stokes lines as monitored in either the horizontal (Ii) or the vertical (Z2) azimuthal plane is an oscillatory function of the distance of the localized core perturbation from the exit end, with a period of about 2 mm. This is shown in Fig. 4 for the second SRS Stokes line at 567.5 nm. Similar curves were obtained for other Stokes lines as well. Visually, as the point of stress is moved by ifew millimeters (z = 1 cm) along the fiber, the dispersed colors in the far field mode structure of Fig. 2b oscillate between the horizontal and the vertical azimuthal planes. As distance z between the point stress and the output end is increased, the azimuthal distribution of Raman spectrum changes significantly. The Raman
cos(m@+ $1 ,
(1)
where z is the direction of fiber axis and a is the core radius. Functionf( z) describes the z dependence of the perturbation and integer m describes its azimuthal dependence. t,!tis a phase constant decided by the orientation of the applied stress. Thus the deformation due to simple bending strain is described by m = 1, whereas the elliptical deformation explained here, due to a localized, transverse, pressure induced stress can best be described by m = 2 in Eq. ( 1). Assuming the radial deformation to extend a distance L in the z direction, we can write to first approximation, f(z) = 4( Aa) z(L-z)lL2, with a maximum value f(z=L/2) =Aa in the center. If A,, and A,, represent the amplitudes for LP,, and LP2i modes respectively, we have &1(L) =&2(O)
I
K(z) [exp[i(/%-&)zl
dz,
(2)
/3e and pi represent the propagation constants for LPo2 and LP,, modes respectively. Coupling constant, K(z)=K(02,21)f(z),whereK(02,21) istheoverlap integral for LP,,, and LP2i field distributions in the (x, y) plane, weighted by the azimuthal perturbation cos( mf? f $) . For purely bending strains, m = 1 and K(n,E,, n212) = 0, unless the difference between the azimuthal mode numbers, ni - n2 = f 1 [ 111. Pure bending strains thus cannot explain the mode conversion
114
A. Sharma, R. Posey / Optics Communications 124 (1996) II I-I 17
I
I
X = 567.5 nm (SW STOKES)
I
0
I 4
I
I 8 DISTANCE
I 12
I
I
(mm)
Fig. 4. Output intensity (h = 567.5 nm) due to beating between LP,, and LP,, modes versus the distance z of the IocalIy stressed point from the exit end. I, and I2 represent intensities in the horizontal and the vertical azimuthal planes respectively. from LP,, to LP2,. This conversion with the elliptical deformation
however described
is possible here,
for
m = 2. Eq. (2) can be integrated by parts to obtain the fractional power transfer from LP,, to LP,,, as
I&,(L)/&(O)
quantitatively on the basis of a simple analysis described below. Constructive LP,,-LP2, interference to form the two horizontal (or vertical) half-lobes can be described by the condition
l*a (Au/L)’
x]~(02,21>~(P0-&>*1*~
(3)
Thus large coupling is possible only to neighbouring modes with small values of A p = & - PI. The transverse stress behaves like a point source for the coherent generation of LP,, from LP,,, and conversion as large as 50% can be easily achieved. This is manifested in the characteristic LP,,-LP,, interference as these modes propagate along the fiber. The electric field for LP,, mode has a phase difference of r between 8= 0, 7r and 0= n-/2, 3~/2 azimuthal planes [ 121. Because of this, the output light intensity distribution due to LP,,--LP,, interference periodically resembles two half-lobes which change their orientation between horizontal (8= 0, rr) and vertical (8= n-/2, 3~j2.I azimuthal planes after every half beat-length (LB/2 = n-/A/3) distance along the fiber. This is shown in Fig. 4 as the location of the point stress is moved along the fiber. A beat length LB = 1.8 mm is measured for the wavelength 567.5 nm of the second SRS Stokes line. Various features of Figs. 4 and 5 can be understood
zM02(h)
-P21(Ml=2m~9
(4)
where &*(A), P*,(h) are the wavelength dependent propagation constants for LP,, and LP2r modes respectively and m is an integer. Variation of distance z and wavelength h results in a series of maxima for successive values of m. This is described by taking the differential of Eq. (4). Thus Gz[A.P(h)]
+z[a(A/3)lahl 6h=2rr,
(5)
where A p( h) = &,*(A) - /321 (h). As the wavelength of observation is kept fixed with a monochromator, Sh=O and Eq. (5) gibes Sz[Ap(h)] =2n-. This corresponds to the condition of Fig. 4 where SZ is the beat length &,, as the position z of the transverse stress is moved along the fiber, i.e. L,=~Tu’ [A/3( h)]. As another possibility in Eq. (5), the position z of the point stress can be kept fixed and the output light intensity can be spectrally analyzed as in Fig. 5. This corresponds to 8z = 0 and Eq. (5) becomes Sh=2n-/[za(AP)/ahl
.
(6)
A. Sharma. R. Posey / Optics Communications
I24 (1996) 111-l I7
115
( 6) can however be used to make precise determination ofa(Ap>/ahaswellasof [/302(h)-&(h)] uptoan additive constant, for wavelengths between 550-580 nm. This in turn is used to measure the fiber parameter A. In Fig. 5, z = 100 cm and spacing Sh between spectral maxima can be measured accurately. Using the weakly guiding approximation [ 121, A /3 and a ( A p) / ah are calculated numerically for a step-index fiber with core-radius, LI= 3.95 p,m and core-refractive index of 1.46. The measured Sh and its calculated value, using Eq. (6) together with the numerical analysis is plotted for various values of A in Fig. 6. Clearly, for A = 0.003 18 the agreement is very good between the observed and calculated values of 6h for a range of wavelengths between 550-590 nm. The manufacturer’s quoted value for numerical aperture, NA = 0.11 as against our measured value of 0.116. The large range of wavelengths over which intensity modulations due to LPo2-LP2i interference are observed narrows down the range of possible values of A for a good fit between experimental points and the theoretical curves of Fig. 6. Further as can be seen from the dispersion curves for a-profile fibers [ 121, Ap(h) as well as a(Ap)lah are sensitive to changes in values of (Y. The technique described here can thus help to monitor any departures from the step-index refractive index profile. WAVELENGTH
(nm) 6.0 T
Fig. 5. (a) SRS in an unstressed fiber. (b) , (c) Spectral distribution of light as measured through pinholes in the vertical ( fI= ?r/2,3?r/ 2) and horizontal (6’=0, P) azimuthal planes respectively in a locally stressed fiber (2 = 100 cm). SRS spectrum through an unstressed fiber is identical to (a) with or without the pinhole aperture. Thus the spectral spacing 6h between successive maxima (or minima) in Fig. 5 varies inversely as the distance z between the point transverse stress and the exit end of the fiber. The wavelength dependence of 6h as seen in Fig. 5 is due to the factor a (A /3) /ah. In principle the two techniques, i.e. ah = 0 (Fig. 4) and Sz = 0 (Fig. 5) can be used to quantitatively determine Ap and a (A /3) /ah respectively for various wavelengths. From these measurements, the fiber parameter A can also be determined. In practice however, the data from Fig. 4 involves measurement of beat length LB = 1.8 mm by varying the position of the point transverse which itself has an extent of about 0.5 mm. Measurement of beat length LB and thus A from Fig. 4 can only be approximate. The data of Fig. 5 together with Eq.
z 5
\
3.0
c-2 Q
0.6 ! 545
I I 555
I / 565 WAVELENGTH,
I / 575 h (nm)
I 585
fig. 6. Comparison of calculated and measured values of Sh, the spectral spacing between consecutive maxima in Fig. 5 for z = 100 cm. Best agreement is observed for A =0.00318.
116
A. Sharma, R. Posey/Optics
Communications 124 (1996) III-II7
light provides a convenient source for sensing at a large number of discrete wavelengths simultaneously, thereby increasing the range of sensing to values of intermodal phase difference greater than z-.
4. Conclusion
\ i
:
:
I
50
180
TEMPERATURE
I
310
(“C)
Fig. 7. Effect of heating a 55 cm long fiber-section on the intensity of 553 nm first Stokes SRS light detected from a pinhole. The oscillations are due to the thermal dependence of the LP,,-LP2, intermodal phase difference and can be used as an interferometric temperature sensor.
As another application of the LPo2-LPzl modal interference described above, we have used it for interferometric sensing of temperature between 50-300°C. Once again a point transverse is applied on the fiber 100 cm from the exit end. A length, Z= 55 cm of this fiber is slowly heated inside an oven to a temperature of 300°C over a period of 30 minutes. The effect of heating on the intensity of Raman Stokes line at 553 nm, detected through a pinhole is shown in Fig. 7. Staring from Eq. (4)) this can be explained by the relation,
FT (~(A~)l(A~)aT+~l/l~T}=2~ll(A/3)
.
(7)
Here 6T = 75°C is the temperature difference between successive maxima of Fig. 7 and 2nV ( Ap) z 1.8 mm is the measured LPo2-LPzl beat length for this wavelength. The second term inside the brackets is the coefficient of linear expansion for silica, qu,=6~ lo-’ Y-‘. Thus the first term a(A/?)l(AP)aT= 4.3 X lo-’ “C-’ and the interferometric sensing described here is largely due to the effect of temperature on the refractive index and A/3 which are themselves wavelength dependent. The extended 550-590 nm SRS
In conclusion, the intensity modulated azimuthally dispersed stimulated Raman spectrum due to a point transverse stress is used to precisely determine the fiber parameter a&(h) -&(h)] /aA which in turn is used to measure A, the relative core-cladding refractive index difference. Further, the extended SRS spectrum in LP,, mode provides a convenient source for simultaneous interferometric sensing at a number of wavelengths as is described here for the first Stokes line at 553 nm. Although the above phenomenon was described using SRS, similar results are expected for any spectrally extended source of light in LPoz mode. The rationale for using nonlinear processes to generate light in LP,,, mode lies in the fact that one can produce very pure single transverse modes via phase matched processes like the four-wave mixing described here. Using conventional light sources to excite LPO* mode would invariably introduce a component of LPO, mode also. Additionally, SRS generated within the fiber provides a convenient strong-intensity spectrally extended source to investigate the wavelength dependence of LPOz-LP,l interference. Again, it would be difficult to introduce spectrally extended light from a conventional source at comparable spectral densities. Compared to the typical beat lengths (LB- lo-*-lo-’ mm) normally observed for most interfering neighbouring modes, our observation of LB = 2 mm for LPO-LP,, interference makes it possible to physically separate the various spectral components across the fiber core over macroscopic distances (2 mm), having implications for a new type of wavelength sensitive directional coupler. For any spectral component, as the LP,, and LP21 modes interfere constructively for @= 0, 7r ( 7~/2, 3 7r/2), the cross-sectional intensity distribution resembles the two diametrically opposite half-lobes of LPI I mode. It is well known [ 131 that the bending loss for LPI1 mode is sensitive to the orientation of the plane of bending with respect to its cross-sectional modefield pattern. This might make it possible to design a novel tunable filter for few-mode fibers in which the
A. Sharma, R. Posey /Optics
bend-induced component.
loss is maximized
for a selected spectral
Acknowledgements This study is supported by National Science Foundation grant HRD-9353548, by the AR0 grant DAAHOI-91-C-R315 and by the NASA grant NAG-1408.
References [ I 1M.R. Layton and J.A. Bucaro, Appl. Optics 18 (1979) 666.
Communications I24 (1996) 11 I-1 17
117
[2] B.Y. Kim, J.N. Balke,S.Y.HuangandH.J.Shaw,OpticsLett. 12 (1987) 729. [3] M. Spajer, Optics Lea. 13 (1988) 239. [4] M. Spajer, B. Carquille and H.J. Mailotte, Optics Comm. 60 (1986) 261. [5] A. Sharma, M. Dokhanian, Z. Wu, A. Williams and P. Venkateswarlu, Optics Lett. 19 (1994) 1122. [6] A.D. Kersey and A. Dandridge, Proc. SPJB 798 (1987) 176. [ 71 A.D. Kersey, A. Dandridge and W.K. Burns, Electron. L&t. 22 (1986) 935. [8] K.S. Chiang, Optics Lett. 17 (1992) 352. [9] A. Sharma, M. Dokhanian, Z.Q. Wu, R. Posey, A. Williams and P. Venkateswarlu, Optics Comm. 111 ( 1994) 127. [lo] D. Marcuse, Bell Syst. Tech. J. 52 (1973) 817. [ 111 W.A. Gambling, H. Matsumura and C.M. Ragdale, Optical and Quant. Electron. 11 ( 1979) 43. [ 121 T. Okoshi, Optics Fibers (Academic Press, New York, 1982) p. 64. [ 131 C.D. Poole and SC. Wang, Optics Lett. 18 (1993) 1712.
s5
ELSEWIER
15 February 1996
OPTICS COMMUNICATIONS Optics Communications124 ( 1996) 11l-1 17
Transverse stress induced LP,,-LP,, modal interference of stimulated Raman scattered light in a few-mode optical fiber A.Sharma, R. Posey Deparhnent of Physics, Alabama A&M University, Huntsville, AL 35762, USA Received 28 February 1995; revised version received 28 September 1995
Abstract Four-photon mixing followed by stimulated Raman scattering is observed in LPoz mode in a 7.9 p,m core diameter optical fiber. A localized transverse stress efficiency couples LPoz to the LP2r mode with a macroscopic beat length of 1.8 mm. LPor
LP1, modal interference is investigated by detecting the 550-590 nm SRS through a pinhole in the far field exit plane. Quantitative explanation of wavelength dependent intensity modulation results in a precise experimental determination of a [ &( A) - &, (A) ] /aA, for mode-propagation constants /3az(A) and &, (A) of LPoz and LP,, modes respectively, as well as A, the relative core-cladding between 50-300°C.
refractive index difference.
The LPo2-LP,,
1. Introduction
Modal interference in dual-mode or few-mode fibers has been widely investigated, largely for its application in interferometric fiber-optic sensors. This includes two-mode interference of either LPer-LPo, modes [ l] or LP,,-LP, , modes [ 2,3]. Three-mode interference using LPc,, LPe, and LP, , modes has also been used [ 41 for separating the effect of temperature from strain sensing. Generally the two or more modes are launched simultaneously in the fiber, their relative intensities depending on the light coupling conditions. We describe here the interference of LP,,--LP,, modes in a spectrally extended (550-590 nm) light produced largely in LP,, mode [5] by stimulated Raman scattering (SRS) in a few-mode fiber. Unlike the examples referenced above [ l-41, the second mode ( LP2, ) is introduced by applying a mode-coupling perturbation in the form of a localized transverse stress close to the exit end of the fiber. Effect of LP,,-LP,r 0030-4018/96/$12.00 0 1996 Elsevier Science B.V. All rights reserved SSDZOO30-4018(95)00621-4
modal interference
is used for sensing of temperature
model interference on the extended SRS spectrum is investigated by detecting the light through pinholes in a far field exit plane. Various Stokes orders of the Raman spectrum are intensity modulated with a spectral spacing that depends on the distance of the localized transverse stress from the exit end. This effect is investigated for a precise measurement of [/&(A)& (h) 1, the difference between mode propagation constants in the 550-590 nm wavelength range as well as A, the relative core-cladding refractive index difference. LPo2-LP2r model interference at the first Raman Stokes wavelength of 553 nm is also used for interferometric sensing of temperature between 50-300°C. Because of the periodic nature of the intensity detected by an interferometric sensor using a single wavelength, the value of the measurand is ambiguous. This limits the useful range of the sensor to a value rr of the intermodal phase difference change. The spectrally extended SRS light in LPo2 mode offers a convenient
A. Sharma, R. Posy
I-PO,+ LPo*
MB
LPm + LP,,
/Optics
Communications
21
Pig. 1. Schematic of the experimental set-up. 532 nm light from a Nd: YAG laser excites LPn, and LPoz modes. About 100 meter fiber in spool (S) generates four wave mixing and SRS largely in LPaa mode. Microbend (MB) couples LPc, to the LP2, mode. LPa2-LP,, interference is investigated by observing light through the pinhole (P) which is focused with a lens (L) into a monochromator (M). Heater (H ) is used to demonstrate the fiber-optic temperature sensor described in this work.
source for interferometric sensing at two or more wavelengths simultaneously, thus making it possible to sense unambiguously over an unlimited range [ 6,7].
2. Experimental
results
Fig. 1 shows the schematic of the experimental setup. SRS is produced in a 100 meter long, few-mode, circular-core, step-index optical fiber with. a core diameter of 7.9 Frn. As shown in an earlier work [5] using 5 kW pulses of 532 nm light from an Nd : YAG laser, four-photon mixing (FPM) has a major influence on SRS in such a fiber. It not only shifts the entire multiorder SRS spectrum by 220 cm-’ but also converts the mixed-mode structure (LP,, +LP,,) of the incident light into 550-600 nm spectrum of SRS light which is largely in LPO, mode. This sequential process can be described by: pump light (LP,, +LPe,) at 532 nm-tfour photon mixing (LP,,) at 538.3 nm + shifted SRS spectrum largely in LP,,, mode. The
124 (1996) I1 I-l I7
far field intensity distribution of such light exiting the fiber is shown in Fig. 2a. For 538.3 nm FPM light in LPoZ mode, the overlap integral for the first Raman Stokes line to be in LP,,, mode is 0.57 as against 0.87 for it to be also in the LP,, mode [ 81. We believe that the slight initial excess of the LPoz component in the spontaneous Raman light is sufficient to drive SRS largely in LPoZ mode. This is also supported by our earlier experiment [9] in which we put a few loops in the first half of the fiber such that the LP,, mode is attenuated more than the LP,,, mode. By doing so one can relatively increase the LP,, component over LP,, in the SRS light. A localized transverse stress is applied by keeping the fiber on a flat surface and pressing it with a stiff 0.5 mm diameter wire perpendicular to the length of the fiber. The perturbed far field light intensity distribution, which depends critically on the distance (z) of the localized strain from the exit end is shown in Fig. 2b for z = 1 cm. Not only is the mode structure in Fig. 2b different from LPo2, but the light is also spectrally redistributed over the core of the fiber. The dark and light shades in Fig. 2b have wavelengths centered around red and green light respectively. For an unperturbed fiber, Fig. 3a shows the PPM line at 538.3 nm (marked with *) , in LP,,, mode. This in turn produces the 5 SRS Stokes orders all of which are also largely in the LP,, mode. The spectra in Figs. 3b, 3c are produced in a transversely stressed fiber and correspond respectively to the light and dark shaded regions of Fig. 2b. The first and the second Stokes orders are present dominantly (Fig. 3b) in the vertical azimuthal plane corresponding to 8 = Z-l2,3 n-12 whereas the complimentary third and the fourth Stokes orders are dominant (Fig. 3c) in the
Fig. 2. Far field distribution of output light a) in an unperturbed fiber (LPm mode); due to b) perturbation induced by transverse stress at a distance, e = 1 cm from exit end. Light and dark shades correspond to green and orange light respectively. c) transverse stress at a distance, z = 100 cm from exit end.
A. Sharma, R. Posey / Optics Communications 124 (1996) 1 I l-l I7
113
spectrum of the output light for z = 100 cm is shown in Fig. 5. As in Fig. 3, the intensity variation in the horizontal and the vertical planes are again complimentary to each other, although each Raman Stokes line itself is intensity modulated. The far field intensity distribution of light for such a perturbed fiber (z = 100 cm) is shown in Fig. 2c. Due to intensity modulations within the Raman Stokes lines one does not see any azimuthal dispersion of colors. As described below, the observations in Figs. 2-5 are due to the interference of the LPoz mode of SRS light with the LP2, mode generated due to the locally stressed fiber.
3. Theory and analysis The LP,, +LP2i mode conversion is explained below on the basis of the coupled mode theory of round optical fibers [ lo]. The core-cladding interface of the perturbed fiber can be described by the function Y(X, y, z) =a+f(z)
560 WAVELENGTH
630 (nm)
Fig. 3. (a) Spectrum of light from an unperturbed fiber. (*) denotes the position of FPM line at 538.3 nm, which generates the subsequent SRS Stokes lines in, unperturbed fiber. (b) (c) The spectral distribution of light as measured through pinholes in the vertical (8= &2,3~/2) and horizontal ( B=O, r) azimuthal planes respectively in a locally stressed fiber (z= 1 cm). Unperturbed spectrum with or without the pinhole is identical to (a).
0 = 0, rr plane. The intensity of each of the Stokes lines as monitored in either the horizontal (Ii) or the vertical (Z2) azimuthal plane is an oscillatory function of the distance of the localized core perturbation from the exit end, with a period of about 2 mm. This is shown in Fig. 4 for the second SRS Stokes line at 567.5 nm. Similar curves were obtained for other Stokes lines as well. Visually, as the point of stress is moved by ifew millimeters (z = 1 cm) along the fiber, the dispersed colors in the far field mode structure of Fig. 2b oscillate between the horizontal and the vertical azimuthal planes. As distance z between the point stress and the output end is increased, the azimuthal distribution of Raman spectrum changes significantly. The Raman
cos(m@+ $1 ,
(1)
where z is the direction of fiber axis and a is the core radius. Functionf( z) describes the z dependence of the perturbation and integer m describes its azimuthal dependence. t,!tis a phase constant decided by the orientation of the applied stress. Thus the deformation due to simple bending strain is described by m = 1, whereas the elliptical deformation explained here, due to a localized, transverse, pressure induced stress can best be described by m = 2 in Eq. ( 1). Assuming the radial deformation to extend a distance L in the z direction, we can write to first approximation, f(z) = 4( Aa) z(L-z)lL2, with a maximum value f(z=L/2) =Aa in the center. If A,, and A,, represent the amplitudes for LP,, and LP2i modes respectively, we have &1(L) =&2(O)
I
K(z) [exp[i(/%-&)zl
dz,
(2)
/3e and pi represent the propagation constants for LPo2 and LP,, modes respectively. Coupling constant, K(z)=K(02,21)f(z),whereK(02,21) istheoverlap integral for LP,,, and LP2i field distributions in the (x, y) plane, weighted by the azimuthal perturbation cos( mf? f $) . For purely bending strains, m = 1 and K(n,E,, n212) = 0, unless the difference between the azimuthal mode numbers, ni - n2 = f 1 [ 111. Pure bending strains thus cannot explain the mode conversion
114
A. Sharma, R. Posey / Optics Communications 124 (1996) II I-I 17
I
I
X = 567.5 nm (SW STOKES)
I
0
I 4
I
I 8 DISTANCE
I 12
I
I
(mm)
Fig. 4. Output intensity (h = 567.5 nm) due to beating between LP,, and LP,, modes versus the distance z of the IocalIy stressed point from the exit end. I, and I2 represent intensities in the horizontal and the vertical azimuthal planes respectively. from LP,, to LP2,. This conversion with the elliptical deformation
however described
is possible here,
for
m = 2. Eq. (2) can be integrated by parts to obtain the fractional power transfer from LP,, to LP,,, as
I&,(L)/&(O)
quantitatively on the basis of a simple analysis described below. Constructive LP,,-LP2, interference to form the two horizontal (or vertical) half-lobes can be described by the condition
l*a (Au/L)’
x]~(02,21>~(P0-&>*1*~
(3)
Thus large coupling is possible only to neighbouring modes with small values of A p = & - PI. The transverse stress behaves like a point source for the coherent generation of LP,, from LP,,, and conversion as large as 50% can be easily achieved. This is manifested in the characteristic LP,,-LP,, interference as these modes propagate along the fiber. The electric field for LP,, mode has a phase difference of r between 8= 0, 7r and 0= n-/2, 3~/2 azimuthal planes [ 121. Because of this, the output light intensity distribution due to LP,,--LP,, interference periodically resembles two half-lobes which change their orientation between horizontal (8= 0, rr) and vertical (8= n-/2, 3~j2.I azimuthal planes after every half beat-length (LB/2 = n-/A/3) distance along the fiber. This is shown in Fig. 4 as the location of the point stress is moved along the fiber. A beat length LB = 1.8 mm is measured for the wavelength 567.5 nm of the second SRS Stokes line. Various features of Figs. 4 and 5 can be understood
zM02(h)
-P21(Ml=2m~9
(4)
where &*(A), P*,(h) are the wavelength dependent propagation constants for LP,, and LP2r modes respectively and m is an integer. Variation of distance z and wavelength h results in a series of maxima for successive values of m. This is described by taking the differential of Eq. (4). Thus Gz[A.P(h)]
+z[a(A/3)lahl 6h=2rr,
(5)
where A p( h) = &,*(A) - /321 (h). As the wavelength of observation is kept fixed with a monochromator, Sh=O and Eq. (5) gibes Sz[Ap(h)] =2n-. This corresponds to the condition of Fig. 4 where SZ is the beat length &,, as the position z of the transverse stress is moved along the fiber, i.e. L,=~Tu’ [A/3( h)]. As another possibility in Eq. (5), the position z of the point stress can be kept fixed and the output light intensity can be spectrally analyzed as in Fig. 5. This corresponds to 8z = 0 and Eq. (5) becomes Sh=2n-/[za(AP)/ahl
.
(6)
A. Sharma. R. Posey / Optics Communications
I24 (1996) 111-l I7
115
( 6) can however be used to make precise determination ofa(Ap>/ahaswellasof [/302(h)-&(h)] uptoan additive constant, for wavelengths between 550-580 nm. This in turn is used to measure the fiber parameter A. In Fig. 5, z = 100 cm and spacing Sh between spectral maxima can be measured accurately. Using the weakly guiding approximation [ 121, A /3 and a ( A p) / ah are calculated numerically for a step-index fiber with core-radius, LI= 3.95 p,m and core-refractive index of 1.46. The measured Sh and its calculated value, using Eq. (6) together with the numerical analysis is plotted for various values of A in Fig. 6. Clearly, for A = 0.003 18 the agreement is very good between the observed and calculated values of 6h for a range of wavelengths between 550-590 nm. The manufacturer’s quoted value for numerical aperture, NA = 0.11 as against our measured value of 0.116. The large range of wavelengths over which intensity modulations due to LPo2-LP2i interference are observed narrows down the range of possible values of A for a good fit between experimental points and the theoretical curves of Fig. 6. Further as can be seen from the dispersion curves for a-profile fibers [ 121, Ap(h) as well as a(Ap)lah are sensitive to changes in values of (Y. The technique described here can thus help to monitor any departures from the step-index refractive index profile. WAVELENGTH
(nm) 6.0 T
Fig. 5. (a) SRS in an unstressed fiber. (b) , (c) Spectral distribution of light as measured through pinholes in the vertical ( fI= ?r/2,3?r/ 2) and horizontal (6’=0, P) azimuthal planes respectively in a locally stressed fiber (2 = 100 cm). SRS spectrum through an unstressed fiber is identical to (a) with or without the pinhole aperture. Thus the spectral spacing 6h between successive maxima (or minima) in Fig. 5 varies inversely as the distance z between the point transverse stress and the exit end of the fiber. The wavelength dependence of 6h as seen in Fig. 5 is due to the factor a (A /3) /ah. In principle the two techniques, i.e. ah = 0 (Fig. 4) and Sz = 0 (Fig. 5) can be used to quantitatively determine Ap and a (A /3) /ah respectively for various wavelengths. From these measurements, the fiber parameter A can also be determined. In practice however, the data from Fig. 4 involves measurement of beat length LB = 1.8 mm by varying the position of the point transverse which itself has an extent of about 0.5 mm. Measurement of beat length LB and thus A from Fig. 4 can only be approximate. The data of Fig. 5 together with Eq.
z 5
\
3.0
c-2 Q
0.6 ! 545
I I 555
I / 565 WAVELENGTH,
I / 575 h (nm)
I 585
fig. 6. Comparison of calculated and measured values of Sh, the spectral spacing between consecutive maxima in Fig. 5 for z = 100 cm. Best agreement is observed for A =0.00318.
116
A. Sharma, R. Posey/Optics
Communications 124 (1996) III-II7
light provides a convenient source for sensing at a large number of discrete wavelengths simultaneously, thereby increasing the range of sensing to values of intermodal phase difference greater than z-.
4. Conclusion
\ i
:
:
I
50
180
TEMPERATURE
I
310
(“C)
Fig. 7. Effect of heating a 55 cm long fiber-section on the intensity of 553 nm first Stokes SRS light detected from a pinhole. The oscillations are due to the thermal dependence of the LP,,-LP2, intermodal phase difference and can be used as an interferometric temperature sensor.
As another application of the LPo2-LPzl modal interference described above, we have used it for interferometric sensing of temperature between 50-300°C. Once again a point transverse is applied on the fiber 100 cm from the exit end. A length, Z= 55 cm of this fiber is slowly heated inside an oven to a temperature of 300°C over a period of 30 minutes. The effect of heating on the intensity of Raman Stokes line at 553 nm, detected through a pinhole is shown in Fig. 7. Staring from Eq. (4)) this can be explained by the relation,
FT (~(A~)l(A~)aT+~l/l~T}=2~ll(A/3)
.
(7)
Here 6T = 75°C is the temperature difference between successive maxima of Fig. 7 and 2nV ( Ap) z 1.8 mm is the measured LPo2-LPzl beat length for this wavelength. The second term inside the brackets is the coefficient of linear expansion for silica, qu,=6~ lo-’ Y-‘. Thus the first term a(A/?)l(AP)aT= 4.3 X lo-’ “C-’ and the interferometric sensing described here is largely due to the effect of temperature on the refractive index and A/3 which are themselves wavelength dependent. The extended 550-590 nm SRS
In conclusion, the intensity modulated azimuthally dispersed stimulated Raman spectrum due to a point transverse stress is used to precisely determine the fiber parameter a&(h) -&(h)] /aA which in turn is used to measure A, the relative core-cladding refractive index difference. Further, the extended SRS spectrum in LP,, mode provides a convenient source for simultaneous interferometric sensing at a number of wavelengths as is described here for the first Stokes line at 553 nm. Although the above phenomenon was described using SRS, similar results are expected for any spectrally extended source of light in LPoz mode. The rationale for using nonlinear processes to generate light in LP,,, mode lies in the fact that one can produce very pure single transverse modes via phase matched processes like the four-wave mixing described here. Using conventional light sources to excite LPO* mode would invariably introduce a component of LPO, mode also. Additionally, SRS generated within the fiber provides a convenient strong-intensity spectrally extended source to investigate the wavelength dependence of LPOz-LP,l interference. Again, it would be difficult to introduce spectrally extended light from a conventional source at comparable spectral densities. Compared to the typical beat lengths (LB- lo-*-lo-’ mm) normally observed for most interfering neighbouring modes, our observation of LB = 2 mm for LPO-LP,, interference makes it possible to physically separate the various spectral components across the fiber core over macroscopic distances (2 mm), having implications for a new type of wavelength sensitive directional coupler. For any spectral component, as the LP,, and LP21 modes interfere constructively for @= 0, 7r ( 7~/2, 3 7r/2), the cross-sectional intensity distribution resembles the two diametrically opposite half-lobes of LPI I mode. It is well known [ 131 that the bending loss for LPI1 mode is sensitive to the orientation of the plane of bending with respect to its cross-sectional modefield pattern. This might make it possible to design a novel tunable filter for few-mode fibers in which the
A. Sharma, R. Posey /Optics
bend-induced component.
loss is maximized
for a selected spectral
Acknowledgements This study is supported by National Science Foundation grant HRD-9353548, by the AR0 grant DAAHOI-91-C-R315 and by the NASA grant NAG-1408.
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