Spectral Characterization and Modeling of Wavelength-shifting Fibers
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Spectral Characterization and Modeling ofWavelength-shifting Fibers
R. B. Pahlka a , b , G. Elpers a , J. Huang a , c , K. Lang a , ∗ M. Proga a a University of Texas at Austin, Department of Physics C1600, 1 University Station, Austin, TX78712-0264, USA b now at Texas Children’s Hospital, Houston, TX 77030, USA c now at Universtät Zürich, Zürich, SwitzerlandE-mail: [email protected] A BSTRACT : We have constructed a detailed software model of photon transport in clear and wave-length shifting polystyrene optical fibers based on the GEANT4 framework. We validate the modelwith measurements obtained from several different lengths of fiber illuminated with several LEDs,using two independent acquisition systems. The simulated spectral and spatial light distributionsat the end of the fiber and the resultant attenuation lengths show good agreement with measure-ment. We use the model to predict the fiber behaviour for several test cases and discuss potentialapplications.K
EYWORDS : scintillation; fibers; wavelength-shifting; photomultiplier; plastic scintillator; opticalphoton transport; GEANT4; double beta decay. ∗ Corresponding author. ontents
1. Introduction 12. Materials and methods 2
3. Spectral dependence of absorption and emission 4
4. Description of the model 75. Systematics 86. Results 8
7. Additional modeling features 14
8. Discussion and conclusion 17
1. Introduction
Optical wavelength shifting fibers are now common components of liquid scintillator- and extrusion-based detector technologies in high energy physics experiments. Issues of dopant material and con-centration have been addressed [1], and light attenuation properties of plastic optical fibers havebeen discussed both in experimental [2, 3, 4] and theoretical [5, 6] frameworks. The properties ofcommon fiber materials including polystyrene [7, 8, 9], polymethylmethacrylate (PMMA) [10, 11],– 1 –nd fluorinated polymer [12] are well known. Most mechanisms and processes with respect to en-ergy transfer [13], Rayleigh scattering [14], Stokes shifting [15, 17], optical dispersion [18, 19],and molecular orientation [20] have been elucidated.Several models of photon transport and fiber simulation have been introduced in various frame-works including dynamic programming [21], Monte Carlo [22, 6, 23], finite element analysis [24],and sensitivity analysis [25, 26]. Others have considered simulations of electronic readout sys-tems [27] and photomultiplier tubes [28]. Moreover, the literature on multimode optical fiber foruse in data transmission is vast [29].We are motivated by the need to accurately predict the spectral properties of light exitingthe fiber to ensure that these spectra can be matched to the appropriate photodetector. Given theinherent large-scale nature of current and future detectors employing long WLS fibers and thenotion that many thousands of meters of fiber are used in the construction, this work serves as animportant aid to the overall design, particularly for next generation detectors.Moreover, a condition of the employment of wavelength shifting fibers in high energy physicsexperiments is the requirement of fast and efficient fluorophores in the region of high optical trans-parency. Studies of new wavelength shifters has met with some success [1] but continues to remainchallenging [30]. The flexibility of this model allows the study of the spectral distribution oflight after propagation, and as seen by the photodetector, for any supplied fluorophore emissionspectrum. This is particularly useful in studying other fluorescent compounds emitting at longwavelengths (yellow or red) as well as the green-emitting family of coumarins [41].In this work, we introduce a general model of photon transport based on the GEANT4 frame-work [31] that accounts for all of the processes mentioned above for clear and wavelength shift-ing plastic optical fiber. We perform a preliminary validation of the model using measurementsfrom Kuraray clear fibers illuminated with several LEDs to confirm spectral output and attenuationagreement with simulation. We further validate the model using measurements from Kuraray Y-11wavelength shifting fibers of various lengths then use the model to predict the spectral output be-haviour from fibers with various concentrations, diameters, and bending radii. We demonstrate thatby including the spectral properties of all components and properly accounting for absorption, ree-mission, and fluorescent quantum yield of the chromophore, this model can accurately determinethe spectral response, timing, and effective attenuation in wavelength shifting fibers.
2. Materials and methods
We used clear fibers and Y-11 Non-S type wavelength shifting fibers from Kuraray [32] of severaldiameters, lengths, and dopant concentrations in these studies. Both types of fibers are dual clad.The core is composed of polystyrene with a refractive index of 1.59 at 500 nm and a density of1.05 g/cm . The inner cladding is composed of poly-methylmethacrylate (PMMA) with a refractiveindex of 1.49 at 500 nm and a density of 1.19 g/cm . The outer cladding is composed of a PMMA-based fluorinated polymer with a refractive index of 1.42 at 500 nm and a density of 1.43 g/cm .Each cladding thickness is 3% of the diameter.The ends of each fiber were polished using a diamond-tipped cutter to obtain uniform lightcollection [33]. A small delrin collet was attached to each end for accurate positioning with respect– 2 –o the readout detectors employed and the light source. We illuminate the fiber with light orientedperpendicularly to the principal fiber axis by securing one end of a fiber in a plastic block intowhich a trench of appropriate size has been drilled. An LED was placed in an adjacent block,oriented perpendicular to the fiber axis for illumination. We used several different light emitting diodes (LEDs) from several manufacturers [REF] to illu-minate the fibers and obtain the spectral response. The LEDs were pulsed with short square wavepulses using a LeCroy 9210 pulse generator with a LeCroy 9212 300 MHz, 300 ps variable edgeoutput module. All LED emission was optimized for frequency, applied voltage, and pulse width.LEDs were illuminated and aimed at the spectrometer at a distance of approximately 12 inchesthrough air. Spectra for the LEDs used for fiber illumination are shown in Figure 1 with all curvesnormalized to peak. All LEDs exhibit spectral widths ranging from 20 to 70 nm, some with verybroad tails. We chose the 430 nm LED as a reference since it closely matches many of the pri-mary fluorescence spectra of standard plastic scintillators. The LED spectra used as inputs in thesimulation were obtained using the output spectra obtained from the spectrophotometer.
Wavelength (nm)350 400 450 500 550 600 650 700 R e l a t i v e I n t en s i t y
360 nm LED395 nm LED430 nm LED470 nm LED
Wavelength (nm)350 400 450 500 550 600 650 700 R e l a t i v e I n t en s i t y -3 -2 -1
360 nm LED395 nm LED430 nm LED470 nm LED
Figure 1.
Emission spectra for four LEDs as measured by an Ocean Optics USB-4000 spectrophotometer.The spikes at 370 nm are inherent features of both the 360 nm and 430 nm LEDs. All LEDs exhibit significantemission in the tails.
Figure 2 shows the emission spectra for the 430 nm LED measured by the spectrophotometerfor several applied voltages. The peak wavelength is the same in all cases, however higher ap-plied voltages enhance the short wavelength region of the emissions spectrum and tend to suppressemission in the long wavelength region.
We measure the spectral response from fibers using the Ocean Optics USB-4000 spectrophotome-ter. The spectral response of this detector is approximately 370–1100 nm with a resolution of0.3 nm (FWHM). Acquisition was performed using the SpectraSuite software from Ocean Optics.– 3 – avelength (nm)350 400 450 500 550 600 R e l a t i v e I n t en s i t y Figure 2.
Emission spectra for the 430 nm LED measured by an Ocean Optics USB-4000 spectrophotometerfor several applied voltages. All spectra are normalized to the peak emission.
We also measured the spatial and spectral distributions of light exiting fibers using a Spec10:100BR-N CCD camera from Princeton Instruments. Each pixel size is 20 µ m × µ m with 1340columns and 100 rows and the spectra obtained have been corrected for quantum efficiency. Wecouple the CCD camera to a Horiba Jobin-Yvon iHR550 imaging specrometer. We measure thespatial and spectral distributions from 0.7 mm 1 meter 200 ppm Y-11 WLS fibers. One end of thefiber is placed at the entrance slit to the spectrometer. Near the other end, we illuminate the fiberon the side with a 430 nm LED.
3. Spectral dependence of absorption and emission
Several different loss mechanisms contribute to the overall absorption curve in clear polystyrenefibers, which is almost entirely determined by the properties of the core material [35]. Figure 3shows a representation of these mechanisms as a function of wavelength. The shapes arise pre-dominantly from wavelength-independent scattering, Rayleigh scattering, and ultraviolet and in-frared absorption. A thorough discussion is presented in [35]. Wavelength-independent scatteringincludes absorption effects due to dust, cracks, and bubbles, and the fiber transparency generallydepends on the manufacturing process. In this case, the diameters of the inclusions issuing theeffect are on the order of one micrometer or larger. This is contrasted with Rayleigh scatteringwhich shows a pronounced wavelength dependence caused by smaller irregularities on the order ofone-tenth of a wavelength. Loss due to Rayleigh scattering is inversely proportional to the fourthpower of the wavelength [35, 9]. The effect of Rayleigh scattering (and Mie scattering) on thespatial and angular distributions of light from polymer optical fiber have been described with theo-retical models and compared with measurement [14]. Ultraviolet absorption arises from electronic– 4 –ransitions between energy levels in benzene rings [35] and the loss is typically described empiri-cally [9]. Finally, infrared absorption is due to both aliphatic and aromatic vibrational harmonicsin the polystyrene carbon-hydrogen bonds [35, 9].
While the manufacturing process is complex, wavelength-shifting fibers are realized by simplydoping the clear polystyrene with an appropriate fluorescent molecule. We consider standard fluo-rescent principles where a) the emission spectrum is independent of the excitation wavelength, b)there exist non-zero and finite energy losses between excitation and emission, and c) the absorptionand emission spectra are typically mirror-images with the absorption (and hence emission) peaksare due to the vibrational energy level spacing within the molecule. Here, transitions from thelowest vibrational level of the ground state to the higher vibrational levels of the first excited stateengender the peaks [15].For fluorescence, the energy yield is always less than unity because of Stokes’ losses and canbe quantified by the fluorescent quantum yield Q , which is simply the ratio of the radiative decayrate to the total rate: Q = k r k r + k nr where k nr is the collective non-radiative decay processes and k r is given by the Strickler-Bergequation for intrinsic radiative decay [36, 15]: k r = τ r = π cn N A R F ( ν ) d ν R ( F ( ν ) / ν ) d ν Z ε ( ν ) ν d ν F is the fluorescence spectrum corrected for instrument response, ε is the absorption spectrum, and n is the refractive index. This formalism works well modulo a few caveats [15]. While there arealso exceptions to the mirror-image rule, Figure 3 also shows idealized absorption and emissionspectra for an arbitrary fluorescent molecule.The fluorescent absorption and emission distributions of generic fluorescent molecules can becalculated from first principles using a variety of models. One in particular, has been illustratedpreviously using a model whose molecular vibrational wavefunctions are based on a displaced-distorted harmonic oscillator, convolved with a Gaussian line broadening function [42]. The groundstate vibrational wavefunction with a proportional to the displacement and R proportional to thedistortion is given by: f ( x ) = (cid:18) R π (cid:19) / e (cid:18) − ( x + a ) R (cid:19) The excited vibrational state basis functions are taken as Hermite polynomials each with a normal-ization factor N ν ′ : ψ ν ( x ) = Ne − ( x / ) (cid:20) ( − ) ν e x d ν dx ν e − x (cid:21) with the normalization factor N given by N ν ′ = p ν ′ ν ′ π / – 5 –he factors c ν ′ are the Franck-Condon factors describing the projection of the ground state ontothe excited state and are calculated as: c ν ′ = Z ∞ − ∞ f ( x ) ψ ν ′ ( x ) dx This describes the overlap between the two vibrational states which dictates the absorption ampli-tude [16]. Summing over all possible states gives the absorption (and emission) transition distribu-tions from the ground vibrational state ( ν ′′ ) to excited vibrational states ( ν ′ ) (and vice-versa) andare given by: A ( ν ′′ = → ν ′ ) = N ∞ ∑ ν ′ = c ν ′ r πω exp ( − ( ¯ ν − ¯ ν − abs ( f lr ) − ν ′ ¯ ν vib ) ω ) . where ω is the Gaussian width, ¯ ν − abs is the 0-0 absorption wavenumber, ν vib is the constant fre-quency wavenumber and ¯ ν is the spectral wavenumber. The equation above can be used to calculateeither absorption (abs) or emission (flr) spectra. Finally, the Lippert equation is introduced [15] toaccount for potential solvent effects. This is given as:¯ ν − abs ( f lr ) = ¯ ν − g − πε hc a µ g ( e ) ( µ e − µ g ) F ( n , ε ) with ¯ ν − g being the 0-0 transition in absence of solvent, a the cavity radius in which the solute isembedded, µ g and µ e the modules of the dipole moments of the molecules in the ground and excitedstates, respectively, and F ( n , ε ) for the solvent function. The above treatment shows one exampleof how fluorescence absorption and emission spectra can be calculated and, with the introduction ofthe Lippert equation, shows how the solvent engenders potential systematic shifts in the emissionspectra, which is discussed later in the context of the model. Wavelength (nm)350 400 450 500 550 600 650 700 ) - Lo ss ( d B k m infrared absorptionultraviolet absorptionRayleigh scattering-independent scattering λ infrared absorptionultravioletRayleigh scatteringwavelength-independent scatteringabsorption Wavelength (nm)300 400 500 600 R e l a t i v e I n t en s i t y absorption emissionStokes’ shift Figure 3.
Left: Absorption curves for several processes contributing to the overall absorption length for clearpolystyrene fibers. Components include wavelength-independent scattering, Rayleigh scattering, ultravioletabsorption and infrared absorption bands. This representation has been generated similar to what is presentedin [35] and only serves as an approximation to the actual absorption length of Kuraray clear fibers. Right:Idealized absorption and emission spectra for an arbitrary fluorescent molecule showing mirror symmetryand a characteristic Stokes’ shift. See for example, treatments in [16, 42]. – 6 – . Description of the model
We incorporate the spectral properties of all materials into the simulation and use the GEANT4framework as the foundation of the model. In this framework, two attenuation lengths must bespecified: one for processes where the primary photon is absorbed in polystyrene, and one forprocesses where the primary photon is absorbed by the wavelength shifting fluorescent compoundand re-emitted. The absorption/re-emission process can occur multiple times. The WLS fluorescentcompound used is K27 which has a fluorescent quantum yield of 0.7 [1]. We account for the fluores-cent quantum yield of K27 by allowing absorbed photons to be re-emitted with 70% probability [1]and at a wavelength equal to or greater than the absorbing wavelength for energy conservation.Polystyrene exhibits a small amount of fluorescence which we neglect in this model [7, 13].Figure 4 shows the absorption spectra of clear polystyrene, K27-doped polystyrene (at 200ppm), PMMA, and fluorinated polymer. The absorption spectra of the doped and un-doped polystyrenewas taken from Kuraray [32]. The absorption spectrum of PMMA was taken from [10] although ithas been measured elsewhere [24]. The absorption spectrum of the fluorinated polymer has beenestimated to be that of PMMA with the condition that the absorption bands due to the carbon-carbonbonding has been removed. Surface fluorination has been studied previously [12, 24].
Wavelength (nm)300 400 500 600 700 A b s o r p t i on Leng t h ( m ) bare polystyrenepolystyrene + k27 Wavelength (nm)300 400 500 600 700 A b s o r p t i on Leng t h ( m ) PMMAfluorinated polymer
Figure 4.
Left: Absorption lengths for K27-doped and un-doped polystyrene estimated from Kuraraydata [38]. Right: Absorption lengths for PMMA and fluorinated polymer. The absorption bands in eachcase are attributed to various carbon-hydrogen bonds in the polymers.
Figure 5 shows the emission spectrum of K27 in the absense of bulk absorption used as aninput to the simulation. The data have been estimated from [38]. Figure 5 also shows the refractiveindices of the core and each cladding. The data for the refractive index of the core and the claddingswere taken from [32] and [18], respectively.In all the simulated setups, we generate 10 million photons for propagation through the fibers.For WLS fibers, a small fraction of these are absorbed, isotropically re-emitted, and propagated inthe fiber after interaction with a WLS molecule. We assume 100% detection efficiency which isconsistent with the corrected spectra from both the Ocean Optics spectrophotometer and the CCD– 7 – avelength (nm)450 500 550 600 650 700 R e l a t i v e E m i ss i on k27 emission Wavelength (nm)200 300 400 500 600 700 R e f r a c t i v e I nde x polystyrene + k27PMMA claddingFP cladding Figure 5.
Left: The emission spectrum of the dopant molecule K27 estimated from Kuraray [32] in theabsence of bulk material absorption. Right: The refractive indices of the wavelength shifting fiber core andeach cladding. camera. The incident photons are distributed using a normal distribution across the width of thefiber with a transverse spread equal to the fiber radius including illumination of both claddings.
5. Systematics
There are several sources of systematic uncertainty in the data, largely attributed to the illumina-tion methods and LEDs. We evaluate the systematics using 1 meter fibers and considered severalsources of fluctuation. First, we varied the voltage applied to the LEDs from 2 to 3.5 V. This re-sulted in global shifts in the fiber spectra less than about 10 nm, therefore we apply a 5 nm shift asuncertainty. We varied the pulse width from 1 to 20 microseconds which led to a global shift ofabout 5 nm over this range, therefore we apply an uncertainty of 2.5 nm. We observed no effectsdue to changing the frequency.There are several sources of systematic uncertainty in the simulation model. To accountfor variation in the bulk absorption spectra, we scaled the Y-11 absorption spectrum and thepolystyrene bulk absorption spectrum individually by ± ± ±
6. Results
We considered decoupling the effects of the dopant molecule by first studying the propagation andattenuation of light in clear fibers. Figure 6 shows the data and Monte Carlo spectra obtained for il-lumination of a clear 1 m long 1.4 mm diameter polystyrene fiber using four LEDs. We illuminated– 8 –ystematic % Fluctuation Relative Difference from NominalY-11 absorption length ±
10% 0.05Polystyrene absorption length ±
10% 0.01K27 emission spectrum ± ± Table 1.
Data and Monte Carlo systematic uncertainties. Relative difference from nominal represents totaldeviation in the total collected number of photons. the face of the fiber with collimated light to allow for direct propagation. The four LEDs probemost of the region of interest between 350 nm and 600 nm. The results show good agreement forall four LEDs and indicate sufficient knowledge of the clear fiber spectral attenuation length. Thiswill be used in the subsequent simulations.
Wavelength (nm)350 400 450 500 550 600 650 700 R e l a t i v e I n t en s i t y ( no r m a li z ed ) -6 -5 -4 -3 -2 a Wavelength (nm)350 400 450 500 550 600 650 700 R e l a t i v e I n t en s i t y ( no r m a li z ed ) -6 -5 -4 -3 -2 b Wavelength (nm)350 400 450 500 550 600 650 700 R e l a t i v e I n t en s i t y ( no r m a li z ed ) -6 -5 -4 -3 -2 c Wavelength (nm)350 400 450 500 550 600 650 700 R e l a t i v e I n t en s i t y ( no r m a li z ed ) -6 -5 -4 -3 -2 -1 d Figure 6.
A comparison of data and simulation for a clear 1 m 1.4 mm diameter polystyrene fiber illuminatedwith four different LEDs. The thin line shows the data obtained from the spectrophotometer and the thickline shows the simulation. The distributions are shown for illumination with a) 360 nm LED, b) 395 nmLED, c) 430 nm LED and d) 470 nm LED.
We measured the spectral and spatial output at the end of a 1 meter long, 0.7 mm diameter, 200 ppmWLS fiber using two different acquisition systems and compared the result to simulation. Theresults of this comparison are shown in Figure 7. The top two figures show the results of the– 9 –imulation and the middle set shows the measured data for the spatial and spectral distributionsof exiting photons. The bottom set of figures shows the projection of the spatial distribution ontothe X-axis and the spectral distribution onto the wavelength axis. For the spectral distribution, weshow a comparison of the Monte Carlo results to the data obtained from both the Ocean Opticsspectrophotometer and the Horiba Jobin-Yvon spectrometer. The spatial projections in data areuniformly flat while those for Monte Carlo show a trend towards more photons arriving at theedges. We investigated this difference in several ways. First, we considered the possibility that thedifference arose from the illumination scheme. We simulted photons in a pencil beam directed atthe center of the fiber and we simulated photons in a uniform distribution across the diameter of thefiber. Both cases resulted in a similar output distribution. We also considered the possibility thatthe fiber possibly had a graded refractive index. Here, we delineated the core into ten cylindricalshells, each with an individual refractive index going radially outward from 1.55 to 1.65. This alsoresulted in a similar distribution. Finally, we increased the Rayleigh scattering attenuation lengthby a factor of two, giving similar results as well. We speculate that this difference arises from thenotion that the light propagation modes in this multi-mode fiber are ideal and that the mode mixingis minimal. The wavelength distribution, on the other hand, shows very good agreement betweenthe two sets of data and both agree well with Monte Carlo.
To investigate the evolution of spectra during propagation through the fiber, various lengths 1–24meters of 0.7 mm-diameter Kuraray Y11(200) WLS fibers were illuminated with LEDs directed onthe side of the fiber. Figure 8 show the spectra of light after propagation through several lengths offiber. All curves are normalized to collection time then normalized to unit area. The distributionswith respect to each length are very similar, which suggests that the spectral distributions at theend of each fiber is independent of illumination at different wavelengths. The dip at 525 nm arisesfrom two independent effects. At short fiber lengths (e.g 1 meter), the dip is attributed to theK27 emission spectrum. However, as shorter wavelengths are suppressed, the dip arises due to anabsorption band at this wavelength region in the polystyrene. The dips at 570, 610, and 650 nmat long fiber lengths are also attributed to absorption bands in the polystyrene. We do not observeany features consistent with absorption bands in the PMMA; this suggests that the cladding playsa minimal role in the overall absorption and resulting spectra. Suggested previously, the propertiesof the core material dictate the overall attenuation since the optical field does not penetrate very farinto the cladding [35].We further validated the model by studying the evolution of the wavelength distribution forseveral lengths of WLS fiber by holding the input data constant. Figure 9 shows a comparison ofthe wavelength spectra for data and Monte Carlo for a 0.7 mm diameter, 200 ppm WLS fiber forseveral lengths. There is good agreement for shorter fibers, especially in the 500–530 nm range.Small disagreements are seen for longer fiber lengths. The deficit in Monte Carlo near the 525 nmregion is due to an underestimation of the absorption length. Towards longer wavelengths, theenhancement is due to uncertainty in the K27 emission spectrum. This demonstrates the ability ofthe model to reproduce the data with no additional tuning.– 10 –
Position (mm)-0.4 -0.2 0 0.2 0.4 Y P o s i t i on ( mm ) -0.4-0.200.20.4 Wavelength (nm)480 500 520 540 560 580 600 620 640 P r o j e c t i on i n X -0.4-0.200.20.4 X Position (mm)-0.4 -0.2 0 0.2 0.4 Y P o s i t i on ( mm ) -0.4-0.200.20.4 × Wavelength (nm)480 500 520 540 560 580 600 620 640 P r o j e c t i on i n X -0.200.2 × Projection in X-0.4 -0.2 0 0.2 0.4 I n t en s i t y N o r m a li z ed I n t en s i t y simulationOcean OpticsHoriba Jobin-Yvon Figure 7.
Comparison of the exit position and wavelength spectra for data and Monte Carlo for a 200 ppm,0.7 mm diameter, 1 m fiber. The top left shows the simulated exit position with respect to the fiber crosssection. The top right shows the simulated exit position as a function of wavelength. The center left showsthe measured exit position with respect to the fiber cross section. The center right shows the measuredexit position as a function of wavelength, both obtained from the Horiba spectrometer/CCD. The bottomleft shows a comparison of data and simulation for the projection of the exit position onto the X-axis. Thebottom right shows a comparison of data (for both the Horiba spectrometer/CCD and the Ocean Opticsspectrophotometer) and simulation for the wavelength distribution.
Figure 10 shows a comparison of data and Monte Carlo for a 0.7 mm diameter, 200 ppm, 1 meterlength and 24 meter length fibers. The systematic error bands are generated by varying the inputparameters as discussed previously. For the 1m fiber, there is good agreement over all wavelengths,particularly the 500-550 nm region where competing effects due to the two absorption lengths arepresent. The sharp rise is due to the large attenuation below 500 nm. For the 24 m fiber, theabsorption bands are clearly evident at 530, 570, 610, and 650 nm. The systematic errors indicatea wider variation as more features become present at longer lengths. The disagreements are dueto both overcompensation of absorption band modeling combined with uncertainty in the K27emission spectrum.
The spectra obtained for the 1 to 24 m measurements and the simulation at 470 nm were integratedto find the total transmitted intensity at each fiber length. Shown in Figure 11, the attenuation– 11 – avelength (nm)480 500 520 540 560 580 600 620 640 660 680 700 R e l a t i v e I n t en s i t y ( no r m a li z ed )
360 nm LED Wavelength (nm)480 500 520 540 560 580 600 620 640 660 680 700 R e l a t i v e I n t en s i t y ( no r m a li z ed ) -6 -5 -4 -3 -2
360 nm LEDWavelength (nm)480 500 520 540 560 580 600 620 640 660 680 700 R e l a t i v e I n t en s i t y ( no r m a li z ed )
395 nm LED Wavelength (nm)480 500 520 540 560 580 600 620 640 660 680 700 R e l a t i v e I n t en s i t y ( no r m a li z ed ) -6 -5 -4 -3 -2
395 nm LEDWavelength (nm)480 500 520 540 560 580 600 620 640 660 680 700 R e l a t i v e I n t en s i t y ( no r m a li z ed )
430 nm LED Wavelength (nm)480 500 520 540 560 580 600 620 640 660 680 700 R e l a t i v e I n t en s i t y ( no r m a li z ed ) -6 -5 -4 -3 -2
430 nm LEDWavelength (nm)480 500 520 540 560 580 600 620 640 660 680 700 R e l a t i v e I n t en s i t y ( no r m a li z ed )
470 nm LED Wavelength (nm)480 500 520 540 560 580 600 620 640 660 680 700 R e l a t i v e I n t en s i t y ( no r m a li z ed ) -6 -5 -4 -3 -2
470 nm LED
Figure 8.
Spectra obtained from 1 to 24 meters for 0.7 mm-diameter WLS fiber illuminated perpendicularto the principal fiber axis using four different LEDs (See Figure 1). The linear distributions are shown onthe left and the log distributions are shown on the right. Each distribution is normalized to unit area thennormalized to the acquisition time. curves roughly follow a pattern of exponential decay. However, it appears that light is attenuatedmore rapidly at short fiber lengths than at longer fiber lengths. This may be explained by the– 12 – avelength (nm)500 550 600 650 700 R e l a t i v e I n t en s i t y ( no r m a li z ed ) Wavelength (nm)500 550 600 650 700 -6 -5 -4 -3 Wavelength (nm)500 550 600 650 700 R e l a t i v e I n t en s i t y ( no r m a li z ed ) Wavelength (nm)500 550 600 650 700 -6 -5 -4 -3 Figure 9.
Wavelength spectra comparison of data and Monte Carlo for a 200 ppm 0.7 mm diameter WLSfiber. The data is shown as dots and the Monte Carlo is represented by histograms. Left: Results for 1, 2,and 4 meter fiber lengths. Right: Results for 8, 16, and 24 meter fiber lengths.
Wavelength (nm)500 550 600 650 700 C oun t s ( no r m a li z ed ) Entries 646738Mean 538.392RMS 30.839
DataMC C oun t s ( no r m a li z ed ) Entries 10775Mean 578.217RMS 36.157
DataMC
24 m length
Figure 10.
Wavelength spectra uncertainties for a 200 ppm 0.7 mm diameter WLS fiber. Left: Results fora 1 meter length fiber. Right: Results for a 24 meter length fiber. The black points represent measured datawith uncertainty due to LED stability and LED wavelength variation, the red points represent the nominalMonte Carlo and the red histogram represents Monte Carlo estimated systematic error bands. greater interaction of the fluorophores with shorter wavelength light, which is gradually shiftedtoward longer wavelengths as light propagates farther through the fiber. The attenuation was fit toa curve of the form a ( e − λ x + e − λ x ) as suggested in [37]. The resulting attenuation lengths λ and λ for each curve are given in Table 2. The error estimates are produced by the fit. There is goodagreement between data sets. Comparison of data and Monte Carlo using the 430 nm LED alsoshows good agreement. We studied the effect of illuminating the fiber from the side and from the end. The light outputspectrum depends heavily on the orientation of the LED. Illuminating the fiber from the side resultsin transmission of long wavelengths and thus the observed spectrum is only from those photons thathave undergone at least one wavelength shifting event. Alternatively, illuminating the fiber on theface results in the propagation of all wavlengths. A clear difference can be seen in Figure 12 wherewe illuminate a 1 m 0.7 mm diameter 200 ppm fiber with a 395 nm LED as seen in Figure 1. ThisLED has a broad emission spectrum spanning most of the visible wavelength region. To confirm– 13 – iber Length (m)0 5 10 15 20 25 R e l a t i v e I n t en s i t y
360 LED data395 LED data430 LED data470 LED data430 LED simulation
Fiber Length (m)5 10 15 20 25 R e l a t i v e E m i ss i on × p0 5075.663 ± ± ± ± ± ±
430 nm LED Monte Carlo
Figure 11.
Left: Attenuation of light through several lengths of 0.7 mm-diameter, 200 ppm WLS fiber, ob-tained by wavelength-integration of collection time-normalized spectra for data, and wavelength-integrationfor the 430 nm LED Monte Carlo simulation. Right: A fit to a double exponential for simulation of the430 nm LED.
Diode λ (m) λ (m)FG360 6.80 ± ± ± ± ± ± ± ± ± ± Table 2.
Attenuation rates for several different lengths of fiber illuminated with four LEDs and for the modelprediction using a 430 nm peak input spectrum. that the long wavelength transmission contributes to the observed spectrum, we placed a filterbetween the LED and the fiber then repeated the two illumination schemes. The filter suppressedwavelengths larger than 500 nm. The results show that applying a filter to the face illuminationscheme suppresses the longer wavelengths. The results also show that the output spectra from thefiber are the same for side illumination with and without a filter, and also for face illumination witha filter applied.
7. Additional modeling features
We investigated the effect of fiber diameter on the spectral output at the end of the fiber and theattenuation rate. The fiber diameter was varied from 0.5 mm to 1.4 mm in increments of 0.1 mm.Figure 13 shows the results for the spectral output. No wavelength dependence on diameter wasobserved. – 14 – avelength (nm)500 550 600 650 700 750 800 R e l a t i v e I n t en s i t y face illumination no filterface illumination with filterside illumination no filterside illumination with filter Wavelength (nm)500 550 600 650 700 750 800 R e l a t i v e I n t en s i t y -5 -4 -3 -2 face illumination no filterface illumination with filterside illumination no filterside illumination with filter Figure 12.
The effect of LED orientation. The fiber was illuminated from the side and from the face, withand without a low-pass ( <
500 nm) filter.
Fiber Diameter (mm)0.6 0.8 1 1.2 1.4 C oun t s Figure 13.
Collection efficiency versus fiber diameter for a 1 m, 200 ppm WLS fiber.
Information on the complete spectral attenuation length as a function of concentration for the Y-11 fibers were unavailable. Here, we used the model to predict the attenuation length of Y-11 atdifferent concentrations of the K27 dopant. In the simulation, we varied the Y-11 absorption lengthby scaling the Y-11 absorption length in 5% increments to determine if this quantity alone couldreproduce measurements obtained using the Ocean Optics spectrophotometer. We assume that thespectral profile is dependent only on the WLS-doped fiber absorption length. Figure 14 shows theMonte Carlo predicted and measured distributions of photons exiting the fiber for 200, 300, 400,and 500 ppm concentrations. We found that with this scaling, approximate agreement could bereached at X% for 300 ppm, Y% for 400 ppm, and Z% for 500 ppm.
We assume a wavelength shifting time constant of 11.8 ns [1]. Figure 15 shows the time distribution– 15 – avelength (nm)500 550 600 650 700 R e l a t i v e I n t en s i t y ( no r m a li z ed )
200 ppm data200 ppm Monte Carlo
Wavelength (nm)500 550 600 650 700 R e l a t i v e I n t en s i t y ( no r m a li z ed )
300 ppm data300 ppm Monte Carlo
Wavelength (nm)500 550 600 650 700 R e l a t i v e I n t en s i t y ( no r m a li z ed )
400 ppm data400 ppm Monte Carlo
Wavelength (nm)500 550 600 650 700 R e l a t i v e I n t en s i t y ( no r m a li z ed )
500 ppm data500 ppm Monte Carlo
Figure 14.
Comparison of data and Monte Carlo for a 1 m 0.7 mm diameter WLS fiber for four concentra-tions (200, 300, 400, and 500 ppm) of the K27 fluorophore. for collected photons and the total distance versus time. We extract an effective refractive index ofapproximately 1.5 based on these results. The jitter observed between 5 and 8 ns is attributed tothe various modes of propagation within the fiber. Figure 16 shows photon propagation times forseveral lengths of 200 ppm WLS fiber. The first peak is the result of photons which propagate andinteract predominantly in the claddings while the second peak is the result of photons propagatingpredominantly in the core.
Entries 645644Mean 8.260RMS 3.880
Time (ns)0 5 10 15 20 25 3001000200030004000
Entries 645644Mean 8.260RMS 3.880
Track Length (mm)0 2000 4000 6000 8000 10000 T i m e ( n s ) Entries 645644Mean x 1751.679Mean y 8.651RMS x 1042.923RMS y 5.124Entries 645644Mean x 1751.679Mean y 8.651RMS x 1042.923RMS y 5.124
Figure 15.
Timing distribution for collected photons (left) and distance versus time (right) for a 1 m 200 ppmWLS fiber.
Figure 17 shows the distribution of the number of wavelength shifting interactions for collectedphotons. All photons have undergone at least one wavelength shift while some have undergone– 16 – iber Length (m)1 2 3 4 5 T i m e ( n s ) / ndf χ ± ± χ ± ± χ ± -0.145 p1 0.050 ± χ ± -0.145 p1 0.050 ± DataMonte Carlo
Figure 16.
The mean time for collected photons for several lengths of 200 ppm WLS fiber. Data is shownin blue and Monte Carlo is shown in red. more than five. This figure also shows the distribution of the exit angle with respect to the principalfiber axis, the number of total internal reflections, and the total track length for collected photons.Figure 18 shows the number of total internal reflections for collected photons as a function oftheir exit angle. This figure also shows the distribution of track lengths for collected photons as afunction of the exit angle, the final radial position of collected photons as a function of the finalwavelength, and the distribution of the final radial position of collected photons as a function of theexit angle.
8. Discussion and conclusion
There are several limitations to the model. We have considered an idealized fiber and have notintroduced effects such as bubbles, dust, diameter variation over the fiber length, defects, or cracks.These anomalies are macroscopically accounted for in the bulk attenuation length. The effectof Rayleigh scattering has also been absorbed in the bulk attenuation length as explained previ-ously [14]. From this, we expect idealized photon transport in the fiber which we speculate explainsthe dip in the fiber position profile that we model.We considered the possibility of the existence of a graded refractive index which can arisefrom non-uniform cooling during production, which may alter the propagation modes, potentiallygiving rise to an altered position profile. We simulated this by modeling the core of the fiber asten concentric cylindrical shells each with a different refractive index. We scaled the wavelengthdependent refractive index from 1.55 to 1.65 going radially outwards. The results were nearlyidentical to the non-graded, constant case. – 17 – umber of Wavelength Shifts0 1 2 3 4 5 6 7 8 9110 a Exit Angle (rad)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.602000400060008000 b Total Internal Reflections0 50000 100000 150000110 c Track Length (mm)0 10000 20000 30000 40000 50000110 d Figure 17.
Several additional modeling results for collected photons from a 1 meter, 0.7 mm diameter,200 ppm WLS fiber. a) The distributions of the number of wavelength shifts, b) the exit angle with respectto the principal fiber axis, c) the number of total internal reflections, and d) the total track length.
We recognize that different manufacturers employ different production methods which canresult in different optical characteristics. We also recognize that different batches of the same pro-duction may give rise to different optical properties. The simulations presented here are estimatesbased on Kuraray Y-11 data with a nominal K27 concentration of 200 ppm.We have not considered the effects of birefringence [34] nor the effects of the K27 molecularorientation within the polymer [20], both of which could potentially alter the primary emissionspectrum and subsequent propagation. It is known that the S-type fiber displays these characteris-tics [32]. We found that illuminating the fibers from the end using these LEDs produced spectrathat were somewhat different from those illuminated from the side. This is due to the notion that theLEDs typically emit light over a broad spectrum which results in attenuation at short wavelengthsand transmission at long wavelengths. Therefore, we found that simulating the LEDs correctly wasparamount. The model can be extended to any plastic based detector system employing fluorescentwavelength shifters, square fibers, and optical cuvettes provided one has the relevant input spectraincluding the doped and un-doped substrate and the corresponding bare emission spectrum (alongwith any refractive indices and reflection coefficients, if needed).In these studies, we introduce a general model of photon transport based on the GEANT4framework that accounts for all of the processes mentioned above for clear and wavelength shiftingplastic optical fiber. We validate the model using measurements from Kuraray Y-11 wavelengthshifting fibers of various lengths then use the model to predict the spectral output behavior from– 18 – otal Internal Reflections0 10000 20000 30000 40000 50000 E x i t A ng l e (r ad ) Total Track Length (mm)0 5000 10000 15000 20000 E x i t A ng l e (r ad ) Final Radial Position (mm)0 0.05 0.1 0.15 0.2 0.25 0.3 E x i t A ng l e (r ad ) Figure 18.
The distributions of the number of wavelength shifts (top left), the exit angle with respect to theprincipal fiber axis (top right), the number of total internal reflections (bottom left), and the total track length(bottom right) for collected photons from a 1 meter, 0.7 mm diameter, 200 ppm WLS fiber. fibers with various concentrations, diameters, and bending radii. We demonstrate that by includingthe spectral properties of all components and properly accounting for absorption, reemission, andfluorescent quantum yield of the chromophore, this model can accurately determine the spectralresponse, timing, and effective attenuation in wavelength shifting fibers.Acknowledgments: We thank Megan Creasey for assistance with the measurements. This– 19 –esearch was supported in part by NSF grant PHY-0902235, and DOE grant DE-FG03-93ER40757.
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