Measurement and analysis of light transmission through amodified cladding optical fiber with applications tosensors
Ady Arie, Reuven Karoubi, Yigal S. Gur, and Moshe Tur
The effect of a modified cladding on the transmission of light through a step-index optical fiber is investigatedusing 3-D geometrical optics. Measurements of the light transmission of the optical fiber as a function of themodified cladding refractive index and length are presented for the case of focused illumination andcompared with 3-D ray theory. The effect of defocus on the transmission of the modified fiber is also studied.Applications to intensity sensors are discussed.
1. Introduction
In recent years, several fiber sensors have been sug-gested, where a section of the fiber cladding is replacedby an environmentally sensitive materials 2 (see Fig. 1).For example, by using a material with temperaturesensitive index of refraction, a fairly sensitive set tem-perature sensor is constructed3 whose transition pointcan be controlled by varying the wavelength of thelight source.4
Analysis of the effect of the modified cladding wascarried out in Refs. 3 and 4 using 2-D slab geometryand assuming that the optical power is equally distrib-uted among the propagating modes. However, closeagreement between this theory and the experimentalresults could be obtained only after the Fresnel reflec-tion formulation was empirically augmented by anexcess loss factor. In this work, we overcome thisproblem by using a model based on a 3-D initial powerdistribution formed by a focused beam. This distribu-tion, together with Fresnel's reflection formula andproper choice of the effective number of the ray core-cladding encounters, was then used to calculate theeffect of the modified cladding's refractive index andlength on the transmitted intensity. These theoreti-cal predictions were found to be in close agreement
Yigal Gur is with Soreq Nuclear Research Center, Yavne, Israel;the other authors are with Tel Aviv University, Ramat Aviv 69978,Israel.
with our experimental results without further adjust-ment.
The theoretical analysis of the dependence of thefiber transmission on the parameters of the modifiedcladding is given in Sec. II. Experiments in which partof the fiber's original cladding is replaced by an indexmatching oil acting as a modified cladding are de-scribed in Sec. III followed by a summary and sugges-tions for future work (Sec. IV).
11. Transmission Variations due to the Modified Cladding
A. Mathematical Formulation
Consider Fig. 1 again: part of the cladding of alarge-core (several hundreds microns) step-index fiberis replaced by another material-the modified clad-ding. Since the size of the core is large compared withthe optical wavelength, this problem can be accuratelyhandled using geometrical optics. The total guidedpower, carried by the bound rays in the fiber, Pbr(O) iS5
Pbr(0) = dO f rdr o 4 Jd o I I(r,Oo,r,04,) sinOod0o. (1)
Omax is the largest angle in air between a bound rayand the fiber's axis, as determined either by the fiber'snumerical aperture or by the input distribution of rays.4,rpO,,Oo are shown in Fig. 2.5 I(rOf ,O4 ,) is the inten-sity distribution in air.
When a ray enters the modified cladding section,either 0, < 0 c, and the ray remains guided, or 0 > O0,and the ray is only partially reflected from the core-cladding boundary. 0, is the angle between the rayand fiber axis inside the fiber, and Oc is the criticalangle for which a ray is still bound.
Fig. 1. Optical fiber with a modified cladding section.
N
nO
Fig. 2. Reflection and refraction of a source ray at Q at the fiberendface. Polar coordinates (r,o) define the position of Q, and theprojection of the ray path onto the endface makes an angle 0, with
the azimuthal direction at Q (adapted from Ref. 5).
As long as the illuminating cone of light is cylindri-cally symmetrical around the core axis, all propagatingrays are meridional, no tunneling rays are excited, andthe reflection coefficient at the core-cladding bound-ary is given by6
01; 0, < 0, (bound ray)
ncore cosa -nm.c. cosat\2
tncore COSat + nmo.cl. cosat)
0, > 0, (refracting ray, Fresnel formula), (3)
a is the angle between the incident ray (in the fiber)and the normal to the core-cladding interface. at isthe angle between the transmitted ray and the normalto the core-cladding interface.
Each ray has a characteristic length it passes be-tween two successive reflections, denoted by zp. In astep-index fiber zp is given by
(4)ZP=2pB/_(p
ncore 2
where f and are the ray invariants:
= ncore COSO,;
=cre sinO, cos0O;
g(p) axncore2
- - 12. (5c)
B. Effective Number of Core-Cladding Encounters
The number of reflections (i.e., core-cladding en-counters) in a modified cladding region of length Lo isdetermined by the relation N = Lo/zp and by the initialconditions in which a ray enters the modified claddingsection. While the initial conditions are not known apriori, the number of reflections must be an integer.We have chosen to treat the fractional part of N in
statistical terms: if N = 3.2 we shall say that the rayhas an 80% probability of undergoing three reflectionsand a 20% probability of undergoing four reflections.More generally, if a ray suffers N reflections, an effec-tive reflection coefficient can be defined in terms of NandR:
[N] denotes the integer part of N.These considerations are important since the ray
undergoes very few reflections in the modified clad-ding region. For a typical meridional ray with 0, = 0.1rad, entering a 1-cm modified cladding section with acore diameter of 300 Atm, the number of reflections isthree or four. Our particular choice of the number ofreflections is experimentally justified in Sec. III.
If only meridional rays are considered, Eqs. (3) and(4) can be considerably simplified to obtain
zp 2p cotg(O,), (7)
ncore sino - nmo.cl sinO,)2 (8)kncore sino + nmo.cl. sinOt)
and the power remaining in the fiber after the modifiedcladding section of length Lo is
Pbr(LO) A do rdr J dOo Im I(r,O0,oO,)(R) sinOodO0 . (9)
While (R) can be calculated from Eqs. (6)-(8),I(r,00,,00,) is determined by the input illuminationconditions.
C. Intensity Distribution of the Incident Beam
One of the most common ways to couple light intothe fiber is by focusing a collimated laser beam ontothe fiber axis. Only meridional rays are excited. Letus suppose that the collimated beam carries uniformpower Pi per unit cross-sectional area. The intensitydistribution that is excited is given by5
e3(r)f2 P
ax27cr cos3O0 for 0 S °o <O°max(0
0 for Om. < 00 • ` '2
f is the lens focal length, and 5(r) is the Dirac delta(5a) function. From Eqs. (1) and (9) the ratio of the output
power in the fiber at z = Lo to the power at z = 0 (which(5b) equals the input launched power) is
Omax
Pbr(Lo) 2 J (R) [sinao/(cos3 0,)]do
Pbr(0 ) tan2 (0m".)
and N, Eq. (6), is given by
N=
(11)
(12)2p- cot~sin-'[sin(o)/ncoreII
We have also examined the effect of defocus, i.e., thesituation in which the optical axes of the lens and fiber'coincide, but the fiber endface is not in the focal plane
of the (same) lens. As long as the defocusing distancea [see Fig. 4(b)] is smaller than p cot[sin'l(N.A.)](N.A. is the lens numerical aperture), the light trans-mission through the fiber, Eq. (11), remains un-changed, since this slight defocusing is equivalent to asmall axial translation of the modified cladding sec-tion, and Eq. (11) is independent of the absolute axiallocation of the modified section.
Considerable defocusing [see inset in Fig. 4(b)]means that not all the light is coupled into the core.However, this situation is equivalent to a slightly defo-cused illumination from a lens with a smaller numeri-cal aperture [see inset in Fig. 4(b)]. This effectivenumerical aperture is
N.A.eff = sinjarctan[p/a]j,
and the relative change in power is
(13)
Controller/Computer
Fig. 3. Experimental setup.
(R) [sin@O(cos300)]d00
tan 2(0ma)(14)
We used the setup shown in Fig. 3 with a #2-m long,0300-Atm plastic cladding silica step-index fiber havinga numerical aperture of 0.4. The spatially filteredHe-Ne expanded beam was coupled into the fiberusing a X10 lens with N.A. of 0.25. Being smaller thanthe fiber's N.A., it is the lens which determines Omax ofEq. (1). The beam splitter and TV camera were usedto form an image of the fiber's entrance face therebyenabling proper focusing and centering of the inputbeam. An ideally centered illuminating spot will ex-cite only meridional rays.
The light travels in the fiber for a length of -1 mbefore it reaches the modified cladding. The fiber isheld straight so that there would be no perturbationsthat might change the initial intensity distribution.
A short section of the original cladding was removed.The material we used as a modified cladding was anindex matching liquid.7 This liquid has n = 1.468 at250C, 0.6328,um, and a temperature coefficient dn/dT= -0.00037° C-1. The modified cladding was held ona metallic mount with a diameter of 5 mm. The mountdiameter determines the length of the modified clad-ding region. Experiments were also made with othermount diameters. The mounts were heated with ablower that changed the oil's temperature and, subse-quently, the modified cladding's refractive index ac-cording to
nmo.C.(T) = nm. ci (250C) + dT [T - 250C]
= 1.468-0.00037OC-l[T-25oC], (15)
where T is the temperature in degrees celsius. The oilwas initially heated to a point where the oil refractiveindex is lower than ncore, and all measurements weretaken on the free slow-cooling cycle of the mount. Thetemperature of the mount, and hence of the oil, was
measured by a digital thermometer placed on themount. Simultaneously with the temperature mea-surement, the light coming out of the fiber end was alsomonitored by a power meter. Both meters were con-trolled by a GPIB computer/controller.
The dependence of the fiber transmission on therefractive index of the modified cladding is shown inFig. 4(a) and compared with Eq. (11) of the previoussection [solid line in Fig. 4(a)]. The index of the core istaken as the index that gives minimum transmission;ncore = 1.46 + 0.001. Both the experimental and theo-retical curves are referenced to their values at thelowest measured refractive index.
There is good agreement between the theoreticaland experimental results except near n = core- Webelieve that this discrepancy is due to small inhomo-geneities in the oil's temperature that tend to averagethe true steeper behavior of the measured curve.
The broken curves in Fig. 4(a) show two alternateways to treat the fractional part of the number ofreflections Lo/zp [see Eq. (6)]. In curve 1, Eq. (11) wasevaluated based on Kopera's expression for (R),34
(R) =RL ZP, (16a)
while in curve 2, (R) follows Eq. (7-3) in Snyder andLove 5 :
(R) = exp[-(1 - R)Lo/z,]. (16b)
As can be seen, our formulation, Eq. (6), gives a muchbetter fit.
Transmission of a defocused incident beam wasmeasured by moving the fiber in an axial direction,thereby increasing a, see inset in Fig. 4(b), from 0 to 1.5mm. The effective numerical aperture was experi-mentally determined from the far-field pattern at thefiber output end.5 Two sets of measurement havebeen made, results of which are given in Fig. 4(b) forN.A.eff = 0.15 and N.A.eff = 0.085. These results werecompared with Eq. (14) with the appropriate max asdetermined by N.Aeff.
Depending on the amount of defocusing, Fig. 4(b)shows that the transmitted power becomes saturatedbelow a certain value of nmo.cl. for which the fiber N.A.is equal to the input N.A. Evidently, smaller values of
Fig. 4. Fiber transmission vs oil index of refraction and temperature: (a) Lo = 5 mm. Dotted curve-experimental results; solicurve-theoretical results based on Eq. (6); broken curves 1 an2-theoretical calculations based on Eqs. (16a) and (16b), respectively. (b) Defocusing effects for N.A-ef = 0.15 and N.A-eff = 0.08(
nmo.cl. will increase the fiber N.A., and all the raysbecome completely guided with no attenuation. Thissaturation region does not appear in Fig. 4(a) becauselarger input angles were involved, and the presentedrange of nmo.cl. does not extend far enough to the left toshow this region.
Experimental and theoretical results for the depen-dence of the fiber transmission on the length of themodified cladding region at a constant oil temperature(250 C) is shown in Fig. 5(a). The length of the oil wasvaried by replacing the mount on which the oil isplaced. (The Lo = 0 point is the transmission withoutoil.) When nmo.cl. < nore, curve 1 in Fig. 5(a), theintroduction of the oil just reduces the fiber's N.A., andafter a short transition period the transmission satu-rates at a level determined by the new N.A. and theinput illumination. The power remaining in the coreis actually the power carried by the bound rays alone.On the other hand, if nmo.cl. > ncore, curve 2 in Fig. 5(a),light is no longer guided, and all of it can be extractedout of the fiber provided the modified cladding region
48 Fig. 5. Relative transmitted intensity vs the length of the modifiedcladding region. ncore = 1.46. (a) Curve 1 -nmo.cl. = 1.452; curve2-nmc1. = 1.468. The solid and broken curves are the appropriatetheoretical calculations, and the squares and circles are the experi-
a- mental results. (b) More general theoretical results: (1) nmo.cl. a=
is long enough. Figure 5(b) depicts more theoreticalresults for various values of nmo.c. and ncore,
IV. Conclusions
We have analyzed and measured the effect of a mod-ified cladding region on the optical fiber transmission.While previous work3'4 did require an additional core-cladding attenuation factor to fit the theory with theexperiment, it was shown here that a 3-D ray theory,which takes into account the input intensity distribu-tion, as well as a proper choice of the effective numberof core-cladding encounters [Eq. (6)], is indeed suffi-cient for a fairly accurate prediction of the experimen-tal results.
Now that transmission of the modified cladding fi-ber is understood with respect to its dependence on therefractive index and length of the modified claddingand also with respect to errors in the launch conditions(e.g., defocus); better designs can be achieved for fibersensors incorporating modified cladding segments.The results of this study can also be applied to thedesign of linear mode strippers.8
l . . . . . . . . . . . . . . . . . . . . ..l l l l l l l l l, I ,
References1. A. M. Scheggi, M. Brenchy, G. Conforty, and R. Falciai, "Optical
Fiber Thermometer for Medical Use," IEE Proc. 131, Part H, No.4, 270 (1984).
2. M. Gottlieb and G. Brandt, "Temperature Sensing in OpticalFibers Using Cladding and Jacket Loss Effect," Appl. Opt. 20,3867 (1981).
3. P. M. Kopera and V. J. Tekippe, "Transmission of Optical Fiberswith a Short Section of Modified Cladding," Opt. News 7, 44(1981).
4. P. M. Kopera, J. Melinger, and V. J. Tekippe, "Modified Clad-ding Wavelength Dependent Fiber Optic Temperature Sensor,"Proc. Soc. Photo-Opt. Instrum. Eng. 412, 82 (1983).
5. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chap-man & Hall, London, 1983).
6. See, for example, M. Born and E. Wolf, Principles of Optics(Pergamon, London, 1965) p. 40.
7. Series A 1809X index matching liquid manufactured by R. P.Cargille Laboratories, Inc., 55 Commerce Rd., Cedar Grove, NJ07009.
8. See, for example, J. N. Fields and J. Cole, "Fiber MicrobendAcoustic Fiber," Appl. Opt. 19, 3265 (1980).
Patents continued from page 1721
4,558,925 17 Dec. 1985 (Cl. 350-358)Multi-function acousto-optic signal processor.M. W. CASSEDAY, N. J. BERG, and A. N. FILIPOV. Assigned toU.S.A. as represented by Secretary of the Army. Filed 2 Aug. 1984.
This processor combines two well-known acoustooptic architectures, thecoherent time-integrating correlator and the rf spectrum analyzer in a mannerretaining all the disadvantages of a discrete two-armed interferometer withrespect to operation in a harsh environment. I.J.A..
TCEI01EORATIRA DETEC 0ARRAY _
READOUT I
DETECTOR _
4,560,243
4,560,254 24 Dec. 1985 (Cl. 350-427)Zoom lens system.Y. DOI and K. SADO Assigned to Fuji Photo Optical Co., Ltd.Filed 14 May 1984 (in Japan 18 May 1983).
A complex twenty-element zoom lens is described having a 12:1 zoom rangeat an aperture of f/1.59. The semifield ranges from 2.7 to 29.5° during a zoom.The front and rear components are fixed, and four internal airspaces arevaried during a zoom. The fixed front component has four elements; thenegative variator has four elements; the positive compensator is a cementeddoublet; and a second positive compensator has three elements. Followingthe stop is a fixed rear component with seven elements. A single example isgiven. R.K.
4,561,730 31 Dec. 1985 (Cl. 350-432)Synthetic resin lens system for imaging apparatus.J. A. LAWSON, M. R. KUEHNLE, and J. D. KNOX. Assigned toCoulter Systems Corp. Filed 30 Sept. 1982.
A four-element molded plastic 1:1 f/5.6 copying lens covering a 64° field ofview is described. It is a compact symmetric arrangement of aspherizedmeniscus lenses about a central stop. There are twenty specific design exam-ples given some embodying PMMA and polystyrene elements and othersembodying PMMA and polycarbonate elements. There are twenty-oneclaims. D.C.G.
66\
S2 S 3
SI
R4 R5
R R2 [J R7 Re8
4,561,736 31 Dec. 1985 (Cl. 351-159)Eyeglass lenses for persons suffering from severe ametropia.G. FURTER and H. LAHRES. Assigned to Carl-Zeiss-Stiftung.Filed 29 July 1983. (in Fed. Rep. Germany 7 Aug. 1982).
An eyeglass lens for persons requiring a very strong correction is described.The shape claimed is said to give good vision, reduced lens weight, and bettercosmetic appearance. The aspheric curves required may make the lens quitecostly. J.J.J.S.
n la to
I I L
24 Dec. 1985 (Cl. 350-469)Projection lens.H. TERASAWA. Assigned to Nippon Kogaku K.K. Filed 26 June1984 (in Japan 30 June 1983).
Four fully symmetrical copying lenses of the Plasmat type are described.The aperture is f/11, the semifield is 23°, and the aberration corrections areexcellent. The design is controlled by seven conditions. R.K.
A remarkably simple two-component zoom lens is described covering arange of focal lengths from 36 to 68mm atf/4. The front negative componentcontains two or three elements and a single aspheric surface. The rearpositive component has four elements (+ + - +). Two embodiments aregiven controlled by two conditions. The published aberration graphs indicatethat, as would be expected, the corrections are not as good as in some othermore complex two-component zooms. R.K.
4,563,060 7 Jan. 1986 (Cl. 350-414)Microscope objective.M. YAMAGISHI. Assigned to Olympus Optical Co., Ltd. Filed 2July 1984 (in Japan 6 July 1983).
Three embodiments are given of a ten-element flat-field microscope objec-tive having a magnification of 20X and a numerical aperture of 0.4. Theworking distance is long, being 1.4 times the focal length. The front elementis a positive meniscus concave to the front; this is followed by another positiveelement and a series of cemented doublets, two of which are negative. Thedesign is controlled by seven conditions. R.K.
