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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 4 — Feb. 13, 2012
  • pp: 4630–4644
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Side-illumination fluorescence critical angle: theory and application to F8BT-doped polymer optical fibers

Iñaki Bikandi, María Asunción Illarramendi, Joseba Zubia, Jon Arrue, and Felipe Jiménez  »View Author Affiliations


Optics Express, Vol. 20, Issue 4, pp. 4630-4644 (2012)
http://dx.doi.org/10.1364/OE.20.004630


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Abstract

In this work we have analyzed theoretically and experimentally the critical angle for the emission generated in doped polymer optical fibers as a function of different launching conditions by using the side-illumination fluorescence technique. A theoretical model has been developed in order to explain the experimental measurements. It is shown that both the theoretical and experimental critical angles are appreciably higher than the meridional critical angle corresponding to the maximum acceptance angle for a single source placed at the fiber axis. This increase changes the value of several important parameters in the performance of active fibers. The analysis has been performed in polymer optical fibers doped with a conjugated polymer.

© 2012 OSA

1. Introduction

In this work we perform a detailed study of the internal critical angle (maximum acceptance angle for the generated emission) in doped POFs. The fibers analyzed are POF samples of a few centimeters doped with a conjugated polymer. In particular, we analyze theoretically and experimentally the variation of the critical angle under different launching conditions when the fiber is pumped transversally to its axis. This type of excitation of the fiber, known as the side-illumination technique, was first proposed by Kruhlak and Kuzyk in 1999 and it is usually employed to characterize the emission and the optical losses in doped POFs [24

24. R. J. Kruhlak and M. G. Kuzyk, “Side-illumination fluorescence spectroscopy. I. Principles,” J. Opt. Soc. Am. B 16(10), 1749–1755 (1999). [CrossRef]

, 25

25. R. J. Kruhlak and M. G. Kuzyk, “Side-illumination fluorescence spectroscopy. II. applications to squaraine-dye-doped polymer optical fibers,” J. Opt. Soc. Am. B 16(10), 1756–1767 (1999). [CrossRef]

].The side-illumination method has recently been proposed for fluorescence sensing [9

9. C. Pulido and O. Esteban, “Multiple fluorescence sensing with side-pumped tapered polymer fiber,” Sens. Actuators B Chem. 157(2), 560–564 (2011). [CrossRef]

] because it has some advantages, such as higher signal-to-noise ratios than those offered by the usual sensor configurations based either on evanescent wave or guided light.

The paper is organized as follows. The experimental techniques are described in section 2. The theoretical model that describes the variation of the maximum acceptance angle as a function of launching conditions is explained in detail through section 3. The comparison between experimental and theoretical behaviors is shown and discussed in section 4. Finally, the summary of the work is presented in section 5.

2. Experimental set-up

Measurements have been performed in polymer optical fibers doped with the fluorene F8BT (poly(9,9-dioctylfluorene-co-benzothiadiazole)) at a concentration of 0.003%wt in the fiber core. The cladding material is not doped. The diameter of the fiber core is 980 μm and the thickness of the cladding is 20 μm. These doped fibers were produced using an adapted perform-drawing technique by the plastic fiber manufacturer Luceat S.p.A (Italy) and their fabrication details are described in [26

26. L. Bazzana, G. Lanzani, R. Xia, J. Morgado, S. Schrader, and D. G. Lidzey, “Plastic optical fibers with embedded organic semiconductors for signal amplification,” in Proceedings of the 16th international plastic optical fibers conference, (Torino, Italy, 2007), 327–332.

]. Fiber samples were cut into 40 cm lengths, and the fiber ends were carefully polished by hand with polishing papers.

The far-field-pattern (FFP) intensity at the output of the fiber sample was measured as a function of the incident angle and of the launching lateral height when the fiber is illuminated transversally. Figure 1
Fig. 1 Measurement of the angular distribution of the emission at the output of the fiber as a function of the launching conditions. (a) Angular scan: ai is the angle made by the incident beam with the normal to the fiber surface at yP = 0 μm. The incident beam always lies in the xz-plane. (b) Lateral scan: yP refers to the y-coordinate of the point of incidence relative to yP = 0 μm. The incident beam lies in the xy-plane.
shows the two geometrical configurations that have been analyzed. In the first one, the light is focused on the fiber axis with the incident plane containing the fiber axis, and the angle of incidence is varied (angular scan) (see Fig. 1(a)). In the second one, the direction of the incident light is fixed within an incident plane perpendicular to the fiber axis and, in this case, it is the position of the incident spot what actually varies (lateral scan) (see Fig. 1(b)).

3. Theoretical modeling

In the side-illumination-fluorescence technique, the light source inside the fiber is the fluorescence generated when the fiber is illuminated from its lateral side. The emitted light intensity that reaches one of the fiber ends is detected and analyzed. The light detected is calculated as the emitted light within the maximum axial angle allowed for guided and tunneling rays. Although tunneling rays have larger losses than guided ones, they may not attenuate sufficiently in short distances to be neglected. Since the propagation distance through the analyzed fibers is extremely short (17 cm), we will assume that the propagation losses of both ray types (guided and leaky) are equal and negligible. Due to the geometry of excitation, it is assumed that the emission is generated by point sources placed along the refracted beam in the fiber core. A point source Q in our model has to be understood as an infinitesimal volume element (of length dxQ) containing several atoms or molecules. Taking into account that the molecules of F8BT are distributed inhomogeneously in the polymer matrix [28

28. G. E. Khalil, A. M. Adawi, A. M. Fox, A. Iraqi, and D. G. Lidzey, “Single molecule spectroscopy of red- and green-emitting fluorene-based copolymers,” J. Chem. Phys. 130(4), 044903 (2009). [CrossRef] [PubMed]

], we can suppose that this infinitesimal volume emits isotropically, independently of the polarization of the refracted beam. The attenuation of the refracting beam due to the absorption will not be considered, because the absorption length at the incident wavelength is larger than the diameter of the fiber. The effects of the cladding thickness in our fibers have also been neglected and, consequently, we have taken the same value for the total fiber radius and the core radius (ρcore). The doped fibers have been assumed to be step-index.

Let us start by analyzing the dependence of the FFP of the emitted light from the output fiber as a function of the angle of incidence (see Fig. 1(a) and Fig. 3(a)
Fig. 3 Geometrical arrangement of the POF with respect to the incident beam. (a) angular scan: αi is the angle made by the incident beam with the normal to the fiber surface at yP = 0 μm. The incident beam i always lies in the xz-plane. e represents the emitted beam, while r is the refracted beam. (b) lateral scan: yP refers to the y-coordinate of the point of incidence relative to yP = 0 μm. The incident beam i lies in the xy-plane. e represents the emitted beam, while r is the refracted beam.
). In this case, the incident beam at the wavelength λ = λexc is refracted at point P(ρcore,0,z) of the fiber output surface and then it propagates across the core until it finally exits the fiber. Along its path through the core, the incident light is absorbed by a set of molecules at each point Q, which, in turn, emit light isotropically in all directions at wavelengths λ = λemi. Some of the emitted light will refract out of the fiber, and the remaining light lying within the internal critical angle (θz)c will propagate through the fiber and it will be detected at one of the ends. Since the emission is generated from sources placed along the refracted beam, an analysis of the variation of (θz)c inside the fiber is needed. By performing calculations similar to those exposed in [29

29. C.-A. Bunge, R. Kruglov, and H. Poisel, “Rayleigh and Mie scattering in polymer optical fibers,” J. Lightwave Technol. 24(8), 3137–3146 (2006). [CrossRef]

, 30

30. M. A. Illarramendi, “Side-illumination scattering theory in step-index polymer optical fibers,” J. Opt. Soc. Am. B (to be published).

] the following expression for sin(θz)c corresponding to the beam emitting from the point source Q(xQ,0,z) is obtained:
sin((θz)c)(xQ,ϕx)=1nratio2(λemi)1(xQρcoresinϕx)2,
(2)
where ϕx represents the angle of the emitted beam relative to the x-axis in the xy-plane and xQ is the x-position of the source along the refracting beam (see Fig. 3(a)). The angle θz is measured with respect to the fiber axis (z-axis). nratio(λemi) represents the quotient nclad/ncore at λ = λemi. We see that the maximum acceptance angle of the fiber (θz)c depends on xQ and ϕx, and also on the refractive indices at λ = λemi, whereas it does not depend on the incident angle αi. It can be seen that sin(θz)c expressed in Eq. (2) is higher than that corresponding to bound rays (meridional angle), which is a simplified expression of Eq. (2) for the case in which the fluorescence were produced from one source placed just at the center of the fiber (xQ = 0), i.e.

sin((θz)c)=1(ncladncore)2=1nratio2(λemi).
(3)

A model assuming that all the fluorescence is produced at one point in the center of the fiber, together with Eq. (3), has been used to analyze the emission intensity of a doped fiber as a function of propagation distance [24

24. R. J. Kruhlak and M. G. Kuzyk, “Side-illumination fluorescence spectroscopy. I. Principles,” J. Opt. Soc. Am. B 16(10), 1749–1755 (1999). [CrossRef]

, 31

31. M. G. Kuzyk, Polymer Fiber Optics: Materials, Physics, and Applications (Taylor and Francis, 2007).

]. The fact that the critical angle calculated for any emitted beam (Eq. (2) is higher than that obtained from Eq. (3) indicates that both guided and leaky (tunneling) rays are excited inside the fiber as the refracted ray propagates along the fiber [23

23. M. J. Adams, An introduction to optical waveguides (John Wiley & Sons, 1981).

].

Since (θz)c cannot exceed π/2 (sin(θz)c ≤ 1), it is required that xQ and ϕx satisfy the following constraint:

1>nratio2(λemi)(xQρcoresinϕx)2.
(4)

This condition defines a valid region in terms of the source position (xQ) and the emitted direction (ϕx) where guided and tunneling rays are generated within the fiber. As an example, Fig. 4
Fig. 4 2D image of the sin(θz)c as a function of parameters xQ and ϕx for angular incidence. Black painted areas indicate the forbidden regions for xQ and ϕx giving no real sin(θz)c . White solid lines correspond to xQ = ±ρcore nratio(λemi). Calculations performed with NAmeridional = 0.5, ncore(λemi) = 1.495, and ρcore = 490 μm.
shows the representation of sin(θz)c as a function of both xQ and ϕx corresponding to the doped plastic optical fiber analyzed. This representation has been obtained with the characteristic fiber parameters supplied by the manufacturer (ncore(λemi) = 1.495, rcore = 490 μm and NAmeriodional = (ncore2-nclad2)1/2 = 0.5). It can be seen that the curves are symmetrical respect to xQ = 0 and ϕx = π and that there are some source points (near to the fiber interfaces) emitting light in certain specific directions whose maximum acceptance angle is not defined. Those emitted beams generated very close to the core-cladding interface that yield imaginary values for sin(θz)c can be interpreted as evanescent modes along the fiber axis. These modes describe the energy stored in the immediate vicinity of fiber discontinuities [17

17. A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman and Hall, 1983).

]. As the quotient nratio(λemi) approaches the value 1, the forbidden regions, where (θz)c is not defined, become smaller and, consequently, the effects of the truncation of the sine function on the emitted intensity are insignificant. The imposition that (θz)c cannot exceed π/2 and its effects on the near-field patterns and on the scattered light curves of step-index fibers have been reported in [23

23. M. J. Adams, An introduction to optical waveguides (John Wiley & Sons, 1981).

].

By considering the restrictions for sin(θz)c (Eq. (4)), we can now calculate an average of the sine of (θz)c for the doped fiber as follows:

sin((θz)c)=[0arcsin(nratio)dϕxρcore+ρcoresin(θz)c(xQ,ϕx)dxQ+πarcsin(nratio)πdϕxρcore+ρcoresin(θz)c(xQ,ϕx)dxQ++arcsin(nratio)πarcsin(nratio)dϕx0ρcorenratiosinϕxsin(θz)c(xQ,ϕx)dxQ]/[0arcsin(nratio)dϕxρcore+ρcoredxQ++πarcsin(nratio)πdϕxρcore+ρcoredxQ+arcsin(nratio)πarcsin(nratio)dϕx0ρcorenratiosinϕxdxQ].
(5)

This expression has been worked out and the result obtained is the following:

sin(θz)c==i1nratio2(λemi)2(arcsin(nratio(λemi))+nratio(λemi)log(cot(arcsin(nratio(λemi))2)))k=1((inratio(λemi)1nratio2(λemi))kk2(inratio(λemi)1nratio2(λemi))kk2+(inratio(λemi)+1nratio2(λemi))kk2(inratio(λemi)+1nratio2(λemi))kk2).
(6)

An approximated average of the sine of (θz)c can be calculated by taking all the point sources placed in a reduced region, −ρcore nratio(λemi) ≤xQρcore nratio(λemi) and 0 ≤ ϕx ≤ 2π, i.e.

sin(θz)c=nρcore+nρcoredxQ02πsin(θz)c(x,ϕx)dϕxnρcore+nρcoredxQ02πdϕx.
(7)

This selected integration region can be seen in Fig. 4. The analytical expression corresponding to Eq. (7) can be written as:
sin(θz)c=1nratio2(λemi)F32[{12,12,12},{1,32},nratio2(λemi)],
(8)
where 3F2[{1/2,1/2,1/2},{1,3/2},nratio2(λemi)] represents the generalized hypergeometric function [32

32. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover Publications, 1965).

]. The average of sin(θz)c obtained under this assumption (Eq. (8)) does not differ very much from the one calculated exactly (Eq. (6)) [30

30. M. A. Illarramendi, “Side-illumination scattering theory in step-index polymer optical fibers,” J. Opt. Soc. Am. B (to be published).

], since it represents the average of the sine of the critical angle when the contribution of some tunneling rays is neglected, particularly those with a high (θz)c. Notice that Eq. (6) and Eq. (8) depend only on nratio(λemi). By averaging Eq. (2) in the reduced region and by taking into account that the emission is isotropic, we have obtained the dependence of the sine of (θz)c with the position of the emission source. The average of the sine is calculated as follows:

sin(θz)c(xQ)=02πsin(θz)c(xQ,ϕx)dϕx02πdϕx.
(9)

The analytical expression obtained for this calculation (Eq. (9)) can be expressed as:
sin(θz)c(xQ)=1nratio2(λemi)π(K(xQρcore)2+K((xQ/ρcore)2(xQ/ρcore)21)1(xQ/ρcore)2),
(10)
where K is the complete elliptic integral of the first kind [32

32. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover Publications, 1965).

]. The dependence of sin(θz)c on the position of the emission point source xQ along the path of the refracting beam in the fiber core has been plotted in Fig. 5
Fig. 5 Average value of the sine of the critical angle as a function of the position of the emission point source in the fiber core, or <sin(θz)c>(xQ), calculated from Eq. (10) (solid line); meridional sin(θz)c = 0.335, from Eq. (3) (dotted line); <sin(θz)c> = 0.375 obtained from Eq. (8) (dash-dotted line); <sin(θz)c> = 0.381 obtained from Eq. (6) (dashed line). Calculations performed with NAmeridional = 0.5, ncore(λemi) = 1.495, and rcore = 490 μm.
. In the same figure we have included the averages of the sine of (θz)c obtained from Eq. (6) and approximately estimated from Eq. (8) as well as the value of sin(θz)c for bound rays (see Eq. (3)). The symmetrical curve obtained indicates that the closer to the core-cladding interface the point source is placed, the larger its maximum acceptance angle is. It can be observed that sin(θz)c increases from the value corresponding to bound rays (i.e. sin(θz)c for one point source placed at the center of the fiber) to <sin(θz)c> obtained from Eq. (6). The relative difference between sin(θz)c obtained from Eq. (3) and from Eq. (6) is around 12%, whereas the relative difference between the values obtained from Eqs. (6) and (8) is only 1.5% (much smaller, as expected).

In Fig. 6
Fig. 6 Sine of the critical angle as a function of nratio(λemi). Meridional sin(θz)c obtained from Eq. (3) (dotted line); <sin(θz)c> from Eq. (8) (dotted line); <sin(θz)c> from Eq. (6) (dash-dotted line).
we have compared the variation with nratio(λemi) of the values for sin(θz)c obtained from Eq. (6), Eq. (8) and Eq. (3). The values obtained from Eq. (6) and those calculated in the reduced region (Eq. (8)) differ in less than 2% at any value of nratio(λemi). On the other hand, the difference between the sine of the maximum acceptance angle obtained from Eq. (3) and that from Eq. (6) increases with nratio(λemi), particularly from 3% to 17%. It can be verified that, if nratio(λemi) tends to 1, the values of the average sin(θz)c obtained from Eqs. (6) and (8) are equal, and that the quotient between this average value and that obtained from Eq. (3) can be expressed as:
sin(θz)c1nratio2(λemi)=4Catalanπ,
(11)
where Catalan constant has a numerical value ≅ 0.915966. This expression gives the maximum difference between the average value and the meridional one (17%).

Now let us analyze the variation of sin(θz)c with the lateral height of the incident beam. The geometrical situation corresponding to this excitation was plotted in Figs. 1(b) and 3(b). The calculation of the sine of (θz)c for any point source located at the refracting beam (at point Q) in the xy-plane gives the following expression [29

29. C.-A. Bunge, R. Kruglov, and H. Poisel, “Rayleigh and Mie scattering in polymer optical fibers,” J. Lightwave Technol. 24(8), 3137–3146 (2006). [CrossRef]

, 30

30. M. A. Illarramendi, “Side-illumination scattering theory in step-index polymer optical fibers,” J. Opt. Soc. Am. B (to be published).

]:
sin(θz)c(xQ',ϕx,yP)=1nratio2(λemi)sinΔ,
(12)
with

sinΔ=[1(x'Q)2+(yPncore(λext))2ρcore2sin2(ϕx+arctan(yPncore(λext)x'Q)+arctan(yPρcore2yP2)arcsin(yPρcorencore(λext)))]12.

This expression depends now on three variables: x'Q, or position of the source along the refracting beam (the x'-axis is directed along the path covered by the refracted beam); ϕx, or angle of the emitted beam relative to the x-axis in the xy-plane; and yP, or height of the incident point on the fiber. In contrast to the expression of sin(θz)c obtained for the angular dependence, sin(θz)c depends now on the refractive index of the fiber core at the excitation wavelength, in addition to the refractive indices of the core and the cladding at the emission wavelength.

As commented before, a constraint for the allowed values of the source position (x'Q), the direction of the emitted beam (ϕx) and the lateral height (yP) is found in order to obtain real-valued arguments for the sine function in Eq. (12). This restriction defines a valid region where bound and tunneling rays are created within the fiber. It can be expressed as:

1>nratio2(λemi)(x'Q)2+(yPncore(λext))2ρcore2sin2(ϕx+arctan(yPncore(λext)x'Q)+arctan(yPρcore2yP2)arcsin(yPρcorencore(λext))).
(13)

The modes associated to the regions that yield imaginary values for sin(θz)c can be interpreted as non-propagating modes whose energy is stored close to fiber discontinuities. As an example, Fig. 7
Fig. 7 2D image of sin(θz)c as a function of parameters x'Q and ϕx for lateral incidence. The lateral height yP has been fixed to yP = ρcore/2. Black areas indicate the forbidden regions for x'Q and ϕx giving no real sin(θz)c. The white solid vertical lines correspond to x'Q(min) and x'Q(max). Calculations performed with NAmeridional = 0.5, ncore(λemi) = ncore(λexc) = 1.495, and ρcore = 490 μm.
shows the representation of sin(θz)c (ϕx,x'Q) as a function of ϕx and x'Q for a lateral height yP = ρcore/2, in which there are some forbidden regions corresponding to specific values of ϕx and x'Q whose maximum acceptance angle is not defined. The results correspond to a doped POF fiber with NAmeriodional = 0.5, ncore(λemi) = 1.495, and ρcore = 490 μm. The refractive index of the fiber core at λexc has been taken to be the same as that at λemi. In contrast to Fig. 4, the curves are not symmetrical with respect to x'Q = 0 and to ϕx = π. Notice that if variable yP were 0, Eqs. (12) and (13) would be simplified to Eqs. (2) and (4), respectively.

sin(θz)c(yP)=RRsin(θz)c(x'Q,ϕx,yP)dx'QdϕxRRdx'Qdϕx.
(14)

If we choose the limited region, 0 ≤ fx ≤ 2π, and x'Q(min) ≤ x'Qx'Q(max), where x’Q(min) and x’Q(max) are defined as
xQ(min)=ρcorenratio2(λemi)yP2ncore2(λext)xQ(max)=+ρcorenratio2(λemi)yP2ncore2(λext),
(15)
the average of the sine of the critical angle at an incidence yP can be calculated as follows:

sin(θz)c(yP)=xQ(min)xQ(max)dxQ02πsin(θz)c(xQ,ϕx,yP)dϕxxQ(min)xQ(max)dxQ02πdϕx.
(16)

This approach represents the average sin(θz)c for the emitted light in the fiber by neglecting the contribution of some tunneling rays. As we have shown before, the differences between the <sin(θz)c> from the exact Eq. (14) and the approximated Eq. (16) are expected to be small [30

30. M. A. Illarramendi, “Side-illumination scattering theory in step-index polymer optical fibers,” J. Opt. Soc. Am. B (to be published).

].

4. Results and discussion

In this section we compare the results obtained from the theoretical model with the experimental ones. In Fig. 9
Fig. 9 Normalized FFP of the emission (λemi = 535 nm) at the output of the fiber for different angles of incidence: αi = −45°, αi = 0°, and αi = +45°.
we can observe 2D images of the angular distribution of the emission at the output end of the fiber for three different incident angles of the launching beam, namely, αi = −45°, αi = 0° and αi = +45°.

Concerning the results for the lateral scan, in Fig. 11
Fig. 11 Normalized FFP of the emission (λemi = 535 nm) at the output of the fiber for different positions of the lateral exciting beam: yP = −450 μm, yP = 0 μm, and yP = +450 μm.
we show 2D images of the measured FFP of the emission at 535 nm for three different positions of the exciting beam, namely, yP = −450 μm, yP = 0 μm and yP = +450 μm.

The experimental NA of the emission at the output of the fiber as a function of yP is shown in Fig. 12
Fig. 12 Evolution of the NA at the output end of the F8BT-doped POF as a function of yP: Experimental values (■); fitting to NA = <sin(θz)c>(yP) ncore(λemi) (solid line); NAmeridional = 0.489 obtained from Eq. (3) (dotted line); theoretical average NA = <sin(θz)c> ncore(λemi) = 0.572 (dash-dotted line); measured NA exciting the fiber with a cylindrical lens NA = 0.575 (dashed line).
. As expected from theoretical predictions, we detect a noticeable increase in the NA as the incidence beam moves up and down towards the upper and lower edges of the fiber, with a minimum value when the fiber is excited at yP = 0 (NA = 0.557). The fitting of the experimental values to the equation NA = <sin(θz)c>(yP) ncore(λemi), where <sin(θz)c>(yP) is given by Eq. (14), has also been included in Fig. 12. The fiber parameters obtained from this fitting are the same as those obtained in the fitting of Fig. 10 (NAmeridional = 0.49 and ncore(λemi) = ncore(λexc) = 1.495). As can be observed, both curves are in fairly good agreement again. Finally, the experimental value for NA obtained by exciting all the lateral surface of the fiber with a cylindrical lens has been included in the figure as a dashed line and it has been compared with the theoretical calculation of the average sin(θz)c for all the possible lateral incidences yP, from −ρcore to + ρcore (dash-dotted line). It can be observed that the measured value is very close to the theoretically predicted average <sin(θz)c> (0.575 and 0.572, respectively). On the other hand, we can also notice that the meridional NA (0.49) is 15% lower than the averaged NA.

Finally, in Fig. 13
Fig. 13 Evolution of the measured NA of the emission (λemi = 535 nm) for the F8BT-doped POF as a function of the propagation distance.
we illustrate the evolution with the propagation distance through the doped fiber of the NA measured at the end of the fiber. We can observe that there is a low decrease in the angular distribution of the emission along the doped POF sample. Specifically, the measured NA decreases from 0.571 to 0.558 (2%) in 17 centimeters, which is the propagation distance used in our measurements. This very slight reduction in the value of NA with propagation distance validates the assumption made in the theoretical model, in which propagation losses in the calculation of the critical angle are neglected.

5. Conclusions

Acknowledgments

This work was supported by the institutions Ministerio de Ciencia e Innovación, Gobierno Vasco/Eusko Jaurlaritza, and Diputación Foral de Bizkaia/Bizkaiko Foru Aldundia, under projects TEC2009-14718-C03-01, GIC07/156-IT-343-07, UFI11/16 (UPV-EHU), AISHA + , AIRHEM-II, S-PR10UN04, S-PE09CA03 and DENSHIA, and 06-12-TK-2010-0022, respectively.

References and links

1.

J. Zubia and J. Arrue, “Plastic optical fibers: an introduction to their technological processes and applications,” Opt. Fiber Technol. 7(2), 101–140 (2001). [CrossRef]

2.

T. Kaino, “Polymer optical fibers,” in Polymers for Lightwave and Integrated Optics (Marcel Dekker, Inc., 1992), chap. 1.

3.

O. Ziemann, J. Krauser, P. E. Zamzow, and W. Daum, POF Handbook: Optical Short Range Transmission Systems, 2nd ed. (Springer, 2008).

4.

D. Kalymnios, P. Scully, J. Zubia, and H. Poisel, “POF sensors overview,” in Proceedings of the 13th international plastic optical fibers conference, (Nürnberg, 2004), pp. 237–244.

5.

H. Liang, Z. Zheng, Z. Li, J. Xu, B. Chen, H. Zhao, Q. Zhang, and H. Ming, “Fabrication and amplification of rhodamine B-doped step-index polymer optical fiber,” J. Appl. Polym. Sci. 93(2), 681–685 (2004). [CrossRef]

6.

A. Tagaya, S. Teramoto, E. Nihei, K. Sasaki, and Y. Koike, “High-power and high-gain organic dye-doped polymer optical fiber amplifiers: novel techniques for preparation and spectral investigation,” Appl. Opt. 36(3), 572–578 (1997). [CrossRef] [PubMed]

7.

J. Clark and G. Lanzani, “Organic photonics for communications,” Nat. Photonics 4(7), 438–446 (2010). [CrossRef]

8.

C. Pulido and O. Esteban, “Improved fluorescence signal with tapered polymer optical fibers under side-illumination,” Sens. Actuators B Chem. 146(1), 190–194 (2010). [CrossRef]

9.

C. Pulido and O. Esteban, “Multiple fluorescence sensing with side-pumped tapered polymer fiber,” Sens. Actuators B Chem. 157(2), 560–564 (2011). [CrossRef]

10.

H. Y. Tam, C.-F. Jeff-Pun, G. Zhou, X. Cheng, and M. L. V. Tse, “Special structured polymer fibers for sensing applications,” Opt. Fiber Technol. 16(6), 357–366 (2010).

11.

M. Sheeba, K. J. Thomas, M. Rajesh, V. P. N. Nampoori, C. P. G. Vallabhan, and P. Radhakrishnan, “Multimode laser emission from dye doped polymer optical fiber,” Appl. Opt. 46(33), 8089–8094 (2007). [CrossRef] [PubMed]

12.

G. V. Maier, T. N. Kopylova, V. A. Svetlichnyi, V. M. Podgaetskii, S. M. Dolotov, O. V. Ponomareva, A. E. Monich, and E. A. Monich, “Active polymer fibers doped with organic dyes: generation and amplification of coherent radiation,” Quantum Electron. 37(1), 53–59 (2007). [CrossRef]

13.

J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton. 2(1), 023504 (2008). [CrossRef]

14.

M. A. Illarramendi, J. Zubia, L. Bazzana, G. Durana, G. Aldabaldetreku, and J. R. Sarasua, “Spectroscopic characterization of plastic optical fibers doped with fluorene oligomers,” J. Lightwave Technol. 27(15), 3220–3226 (2009). [CrossRef]

15.

R. J. Potter, “Transmission properties of optical fibers,” J. Opt. Soc. Am. 51(10), 1079–1089 (1961). [CrossRef]

16.

Y. Xu, A. Cotteden, and N. B. Jones, “A theoretical evaluation of fibre-optic evanescent wave absorption in spectroscopy and sensors,” Opt. Lasers Eng. 44(2), 93–101 (2006). [CrossRef]

17.

A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman and Hall, 1983).

18.

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, “Er3+ -Yb3+ and Er3+ doped fiber lasers,” J. Lightwave Technol. 7(10), 1461–1465 (1989). [CrossRef]

19.

C. P. Achenbach and J. H. Cobb, “Computational studies of light acceptance and propagation in straight and curved multimodal active fibres,” J. Opt. A, Pure Appl. Opt. 5(3), 239–249 (2003). [CrossRef]

20.

I. Ayesta, J. Arrue, F. Jimenez, M. A. Illarramendi, and J. Zubia, “Computational analysis of the amplification features of active plastic optical fibers,” Phys. Status Solidi A 208(8), 1845–1848 (2011). [CrossRef]

21.

J. Arrue, F. Jimenez, I. Ayesta, M. A. Illarramendi, and J. Zubia, “Polymer-optical-fiber lasers and amplifiers doped with organic dyes,” Polymers 3(3), 1162–1180 (2011). [CrossRef]

22.

Y. Zhao and S. Fleming, “Analysis of the effect of numerical aperture on Pr:ZBLAN upconversion fiber lasers,” Opt. Lett. 23(5), 373–375 (1998). [CrossRef] [PubMed]

23.

M. J. Adams, An introduction to optical waveguides (John Wiley & Sons, 1981).

24.

R. J. Kruhlak and M. G. Kuzyk, “Side-illumination fluorescence spectroscopy. I. Principles,” J. Opt. Soc. Am. B 16(10), 1749–1755 (1999). [CrossRef]

25.

R. J. Kruhlak and M. G. Kuzyk, “Side-illumination fluorescence spectroscopy. II. applications to squaraine-dye-doped polymer optical fibers,” J. Opt. Soc. Am. B 16(10), 1756–1767 (1999). [CrossRef]

26.

L. Bazzana, G. Lanzani, R. Xia, J. Morgado, S. Schrader, and D. G. Lidzey, “Plastic optical fibers with embedded organic semiconductors for signal amplification,” in Proceedings of the 16th international plastic optical fibers conference, (Torino, Italy, 2007), 327–332.

27.

M. Aslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikainen-Digweed, “The influence of skew rays on angular losses in air-cladd fibres,” Opt. Commun. 262(1), 77–81 (2006). [CrossRef]

28.

G. E. Khalil, A. M. Adawi, A. M. Fox, A. Iraqi, and D. G. Lidzey, “Single molecule spectroscopy of red- and green-emitting fluorene-based copolymers,” J. Chem. Phys. 130(4), 044903 (2009). [CrossRef] [PubMed]

29.

C.-A. Bunge, R. Kruglov, and H. Poisel, “Rayleigh and Mie scattering in polymer optical fibers,” J. Lightwave Technol. 24(8), 3137–3146 (2006). [CrossRef]

30.

M. A. Illarramendi, “Side-illumination scattering theory in step-index polymer optical fibers,” J. Opt. Soc. Am. B (to be published).

31.

M. G. Kuzyk, Polymer Fiber Optics: Materials, Physics, and Applications (Taylor and Francis, 2007).

32.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover Publications, 1965).

OCIS Codes
(060.2300) Fiber optics and optical communications : Fiber measurements
(060.2310) Fiber optics and optical communications : Fiber optics
(060.2400) Fiber optics and optical communications : Fiber properties
(300.2140) Spectroscopy : Emission

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: December 5, 2011
Revised Manuscript: January 23, 2012
Manuscript Accepted: January 23, 2012
Published: February 9, 2012

Virtual Issues
Vol. 7, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Iñaki Bikandi, María Asunción Illarramendi, Joseba Zubia, Jon Arrue, and Felipe Jiménez, "Side-illumination fluorescence critical angle: theory and application to F8BT-doped polymer optical fibers," Opt. Express 20, 4630-4644 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-4630


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References

  1. J. Zubia and J. Arrue, “Plastic optical fibers: an introduction to their technological processes and applications,” Opt. Fiber Technol.7(2), 101–140 (2001). [CrossRef]
  2. T. Kaino, “Polymer optical fibers,” in Polymers for Lightwave and Integrated Optics (Marcel Dekker, Inc., 1992), chap. 1.
  3. O. Ziemann, J. Krauser, P. E. Zamzow, and W. Daum, POF Handbook: Optical Short Range Transmission Systems, 2nd ed. (Springer, 2008).
  4. D. Kalymnios, P. Scully, J. Zubia, and H. Poisel, “POF sensors overview,” in Proceedings of the 13th international plastic optical fibers conference, (Nürnberg, 2004), pp. 237–244.
  5. H. Liang, Z. Zheng, Z. Li, J. Xu, B. Chen, H. Zhao, Q. Zhang, and H. Ming, “Fabrication and amplification of rhodamine B-doped step-index polymer optical fiber,” J. Appl. Polym. Sci.93(2), 681–685 (2004). [CrossRef]
  6. A. Tagaya, S. Teramoto, E. Nihei, K. Sasaki, and Y. Koike, “High-power and high-gain organic dye-doped polymer optical fiber amplifiers: novel techniques for preparation and spectral investigation,” Appl. Opt.36(3), 572–578 (1997). [CrossRef] [PubMed]
  7. J. Clark and G. Lanzani, “Organic photonics for communications,” Nat. Photonics4(7), 438–446 (2010). [CrossRef]
  8. C. Pulido and O. Esteban, “Improved fluorescence signal with tapered polymer optical fibers under side-illumination,” Sens. Actuators B Chem.146(1), 190–194 (2010). [CrossRef]
  9. C. Pulido and O. Esteban, “Multiple fluorescence sensing with side-pumped tapered polymer fiber,” Sens. Actuators B Chem.157(2), 560–564 (2011). [CrossRef]
  10. H. Y. Tam, C.-F. Jeff-Pun, G. Zhou, X. Cheng, and M. L. V. Tse, “Special structured polymer fibers for sensing applications,” Opt. Fiber Technol.16(6), 357–366 (2010).
  11. M. Sheeba, K. J. Thomas, M. Rajesh, V. P. N. Nampoori, C. P. G. Vallabhan, and P. Radhakrishnan, “Multimode laser emission from dye doped polymer optical fiber,” Appl. Opt.46(33), 8089–8094 (2007). [CrossRef] [PubMed]
  12. G. V. Maier, T. N. Kopylova, V. A. Svetlichnyi, V. M. Podgaetskii, S. M. Dolotov, O. V. Ponomareva, A. E. Monich, and E. A. Monich, “Active polymer fibers doped with organic dyes: generation and amplification of coherent radiation,” Quantum Electron.37(1), 53–59 (2007). [CrossRef]
  13. J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton.2(1), 023504 (2008). [CrossRef]
  14. M. A. Illarramendi, J. Zubia, L. Bazzana, G. Durana, G. Aldabaldetreku, and J. R. Sarasua, “Spectroscopic characterization of plastic optical fibers doped with fluorene oligomers,” J. Lightwave Technol.27(15), 3220–3226 (2009). [CrossRef]
  15. R. J. Potter, “Transmission properties of optical fibers,” J. Opt. Soc. Am.51(10), 1079–1089 (1961). [CrossRef]
  16. Y. Xu, A. Cotteden, and N. B. Jones, “A theoretical evaluation of fibre-optic evanescent wave absorption in spectroscopy and sensors,” Opt. Lasers Eng.44(2), 93–101 (2006). [CrossRef]
  17. A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman and Hall, 1983).
  18. W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, “Er3+ -Yb3+ and Er3+ doped fiber lasers,” J. Lightwave Technol.7(10), 1461–1465 (1989). [CrossRef]
  19. C. P. Achenbach and J. H. Cobb, “Computational studies of light acceptance and propagation in straight and curved multimodal active fibres,” J. Opt. A, Pure Appl. Opt.5(3), 239–249 (2003). [CrossRef]
  20. I. Ayesta, J. Arrue, F. Jimenez, M. A. Illarramendi, and J. Zubia, “Computational analysis of the amplification features of active plastic optical fibers,” Phys. Status Solidi A208(8), 1845–1848 (2011). [CrossRef]
  21. J. Arrue, F. Jimenez, I. Ayesta, M. A. Illarramendi, and J. Zubia, “Polymer-optical-fiber lasers and amplifiers doped with organic dyes,” Polymers3(3), 1162–1180 (2011). [CrossRef]
  22. Y. Zhao and S. Fleming, “Analysis of the effect of numerical aperture on Pr:ZBLAN upconversion fiber lasers,” Opt. Lett.23(5), 373–375 (1998). [CrossRef] [PubMed]
  23. M. J. Adams, An introduction to optical waveguides (John Wiley & Sons, 1981).
  24. R. J. Kruhlak and M. G. Kuzyk, “Side-illumination fluorescence spectroscopy. I. Principles,” J. Opt. Soc. Am. B16(10), 1749–1755 (1999). [CrossRef]
  25. R. J. Kruhlak and M. G. Kuzyk, “Side-illumination fluorescence spectroscopy. II. applications to squaraine-dye-doped polymer optical fibers,” J. Opt. Soc. Am. B16(10), 1756–1767 (1999). [CrossRef]
  26. L. Bazzana, G. Lanzani, R. Xia, J. Morgado, S. Schrader, and D. G. Lidzey, “Plastic optical fibers with embedded organic semiconductors for signal amplification,” in Proceedings of the 16th international plastic optical fibers conference, (Torino, Italy, 2007), 327–332.
  27. M. Aslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikainen-Digweed, “The influence of skew rays on angular losses in air-cladd fibres,” Opt. Commun.262(1), 77–81 (2006). [CrossRef]
  28. G. E. Khalil, A. M. Adawi, A. M. Fox, A. Iraqi, and D. G. Lidzey, “Single molecule spectroscopy of red- and green-emitting fluorene-based copolymers,” J. Chem. Phys.130(4), 044903 (2009). [CrossRef] [PubMed]
  29. C.-A. Bunge, R. Kruglov, and H. Poisel, “Rayleigh and Mie scattering in polymer optical fibers,” J. Lightwave Technol.24(8), 3137–3146 (2006). [CrossRef]
  30. M. A. Illarramendi, “Side-illumination scattering theory in step-index polymer optical fibers,” J. Opt. Soc. Am. B (to be published).
  31. M. G. Kuzyk, Polymer Fiber Optics: Materials, Physics, and Applications (Taylor and Francis, 2007).
  32. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover Publications, 1965).

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