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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 1 — Jan. 9, 2006
  • pp: 19–34
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Mode transition in high refractive index coated long period gratings

A. Cusano, A. Iadicicco, P. Pilla, L. Contessa, S. Campopiano, A. Cutolo, and M. Giordano  »View Author Affiliations


Optics Express, Vol. 14, Issue 1, pp. 19-34 (2006)
http://dx.doi.org/10.1364/OPEX.14.000019


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Abstract

In this work, the numerical and experimental investigation of the cladding modes re-organization in high refractive index (HRI) coated Long Period Gratings (LPGs) is reported. Moreover, the effects of the cladding modes re-organization on the sensitivity to the surrounding medium refractive index (SRI) have been outlined. When azimuthally symmetric nano-scale HRI coatings are deposited along LPGs devices, a significant modification of the cladding modes distribution occurs, depending on the layer features (refractive index and thickness) and on the SRI. In particular, if layer parameters are properly chosen, the transition of the lowest order cladding mode into an overlay mode occurs. As a consequence, a cladding modes re-organization can be observed leading to relevant improvements in the SRI sensitivity in terms of wavelength shift and amplitude variations of the LPGs attenuation bands.

© 2006 Optical Society of America

1. Introduction

In the last years, in fiber Long Period Gratings (LPGs) have been widely investigated for both sensing and communications applications [1

1. S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and applications,” Meas. Sci. Technol. 14,R49–R61 (2003). [CrossRef]

]. They consist of a refractive index periodic modulation of a single mode fiber core. The index modulation induces light coupling between guided core mode and co-propagating cladding modes. In optical communications many LPGs based devices have been developed, such as band rejection filters [2

2. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band rejection filters,” J. Lightwave Technol. 14, 58–65 (1996). [CrossRef]

], gain equalizers [3

3. J. R. Qiang and H. E. Chen, “Gain flattening fibre filters using phase shifted long period fibre grating,” Electron. Lett. 34, 1132–1133 (1998). [CrossRef]

], tunable filters [4

4. K. W. Chung and S. Yin, “Analysis of widely tunable long-period grating by use of an ultrathin cladding layer and higher-order cladding mode coupling,” Opt. Lett. 29, 812–814 (2004). [CrossRef] [PubMed]

, 5

5. X. Shu, T. Allsop, B. Gwandu, L. Zhang, and I. Bennion, “Room-temperature operation of widely tunable loss filter,” Electron. Lett. 37, 216–218 (2001). [CrossRef]

] and optical switches [6

6. B. J. Eggleton, R. E. Slusher, J. B. Judkins, J. B. Stark, and A. M. Vengsarkar, “All-optical switching in long period fiber gratings,” Opt. Lett. 22, 883–885 (1997). [CrossRef] [PubMed]

]. With regard to sensing applications, many studies including strain, bending, torsion, temperature measurements have been widely reported [7

7. V. Bhatia, “Applications of long-period gratings to single and multi-parameter sensing,” Opt. Express 4, 457–466 (1999), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-11-457. [CrossRef] [PubMed]

, 8

8. C. Y. Lin, L. A. Wang, and G. W. Chern, “Corrugated long period fiber gratings as Strain, Torsion, and Bending Sensors,” J. Lightwave Technol. 19, 1159–1168 (2001). [CrossRef]

]. In addition, due to the sensitivity of the cladding modes to the surrounding refractive index, interesting works have been proposed for in fiber refractometers [9

9. H. J. Patrick, A. D. Kersey, and F. Bucholtz, “Analysis of the response of long period fiber gratings to external index of refraction,” J. Lightwave Technol. 16, 1606–1612 (1998). [CrossRef]

, 10

10. R. Hou, Z. Ghassemlooy, A. Hassan, C. Lu, and K. P. Dowker, “Modelling of long-period fibre grating response to refractive index higher than that of cladding,” Meas. Sci. Technol. 12, 1709–1713 (2001). [CrossRef]

] and for the detection of chemical substances in the ambient [11

11. S. T. Lee, R. D. Kumar, P. S. Kumar, P. Radhakrishnan, C. P. G. Vallabhan, and V. P. N. Nampoori, “Long period gratings in multimode optical fibers: application in chemical sensing,” Opt. Comm. 224, 237–241 (2003). [CrossRef]

].

Up to now, the majority of studies have been concentrated upon the analyses of the sensitivity to the surrounding medium refractive index (SRI) of the bare LPG [9

9. H. J. Patrick, A. D. Kersey, and F. Bucholtz, “Analysis of the response of long period fiber gratings to external index of refraction,” J. Lightwave Technol. 16, 1606–1612 (1998). [CrossRef]

, 12

12. T. Allsop, D. J. Webb, and I. Bennion, “A comparison of the sensing characteristics of long period gratings written in three different types of fiber,” Optical Fiber Technol. 9, 210–223 (2003). [CrossRef]

]. The idea of coated LPGs with thin high refractive index (HRI) layers was first proposed by James et al. [13

13. S. W. James, N. D. Rees, G. J. Ashwell, and R. P. Tatam, “Optical fibre long period gratings with Langmuir Blodgett thin film overlays,” Opt. Lett. 9, 686–688 (2002).

]. Recently, a comprehensive theoretical and numerical investigation was proposed by Del Villar at al. [14

14. I. Del Villar, M. Achaerandio, I. R. Matias, and F. J. Arregui, “Deposition of overlays by electrostatic self-assembly in long-period fiber gratings,” Opt. Lett. 30, 720–722 (2005). [CrossRef] [PubMed]

, 15

15. I. Del Villar, I. R. Matias, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in long period fiber gratings with overlay deposition,” Opt. Exp. 13, 56–69 (2005),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-56. [CrossRef]

] which demonstrated that thin HRI coatings are able to favor the transition from cladding guided modes to overlay guided modes, causing a strong re-organization of the cladding modes. More recently, Wang et al. [16

16. Z. Wang, J. R. Heflin, R. H. Stolen, and S. Ramachandran, “Analysis of optical response of long period fiber gratings to nm-thick thin-film coatings,” Opt. Exp. 13, 2808–2813 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-2808. [CrossRef]

] presented a detailed study of LPGs sensitivity when they are coated with nm-thick films of refractive index higher than silica. In particular, they considered the influence of cladding mode order and showed that resonant wavelength shifts due to similar film coating thickness and refractive index values can be vastly different, depending on the coupled cladding mode.

The presence of HRI coatings has been also investigated by the authors to develop a species-specific opto-chemical sensor based on nano-scale HRI polymeric sensitive overlay [17

17. P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, “Optical Chemo-Sensor based on long period gratings coated with δ form Syndiotactic Polystyrene,” IEEE Photon. Technol. Lett. 17, 1713–1715 (2005). [CrossRef]

]. The sensing mechanism relies on the sensitivity of the LPGs attenuation bands to the optical properties of the coating itself. In that case, the coating was able to change its refractive index as direct consequence of the analyte absorption. The same authors demonstrated that a strong improvement in the SRI sensitivity can be obtained in HRI coated LPGs with a proper choice of the SRI itself and the coating 'eatures [18

18. A. Cusano, A. Iadicicco, P. Pilla, L. Contessa, S. Campopiano, A. Cutolo, and M. Giordano, “Cladding modes re-organization in high refractive index coated long period gratings: Effects on the refractive index sensitivity,“ Opt. Lett. 30, (2005). [CrossRef] [PubMed]

].

As a matter of fact, the presence of thin HRI overlays induces strong changes in the cladding modes distribution, leading to a lowering of the modes bounding factor and a consequent enhancing of the evanescent wave interaction with the surrounding medium.

Due to the refractive-reflective regime at the cladding-overlay interface, the cladding modes in a HRI coated LPG are bounded within the structure comprising the core, the cladding and the overlay. This means that a relevant part of the optical power carried by the cladding modes is radiated within the overlay. The field enhancement in the overlay depends strongly on the overlay features (thickness and refractive index) and the SRI. For a fixed overlay thickness and refractive index, by increasing the SRI, the transition from cladding to overlay modes occurs: the lowest order cladding mode (cladding mode with highest effective refractive index) becomes guided into the overlay. At the same time, the higher order modes move to recover the original field configuration leading to strong improvements in the SRI sensitivity. In this paper, a numerical and experimental treatment of the modes transition in HRI coated LPGs is reported. The numerical analysis has been carried out by using an approximate model based on the LP modes, while the experiments were conducted by using Syndiotatic Polystyrene (sPS), which refractive index is 1.578 [17

17. P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, “Optical Chemo-Sensor based on long period gratings coated with δ form Syndiotactic Polystyrene,” IEEE Photon. Technol. Lett. 17, 1713–1715 (2005). [CrossRef]

], as nano-scale overlay. Particular regard was given to the effects on the resonance wavelengths and loss peaks when the SRI is changed within the transition region.

2. Theoretical analysis

An LPG is an ultraviolet (UV)-induced modulation of the fiber core refractive index, with typical modulation depth of 10-4, period between 100μm - 500μm and length of 2-4 cm. The LPG acts to couple light from the propagating core mode to co-propagating cladding modes. Because the cladding modes suffer from high attenuation, the transmission spectrum consists of a series of attenuation bands centred at resonant wavelengths depending on the effective index of the coupled modes and the grating pitch. In a standard LPG, the phase matching between the core mode and the ith forward-propagating cladding mode is achieved at resonant wavelengths given by [15

15. I. Del Villar, I. R. Matias, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in long period fiber gratings with overlay deposition,” Opt. Exp. 13, 56–69 (2005),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-56. [CrossRef]

]:

2πλ(neff,01neff,0i)+s0(ζ01,01(λ)ζ0i,0i(λ))=2πΛ
(1)

where neff,01 is the effective refractive index of the core mode, neff,0i is the effective refractive index of the ith radial cladding mode, s0 is the coefficient of the first Fourier component of the grating, ζ01,01 and ζ0i,0i are the self-coupling coefficients of the core and the ith cladding modes, respectively, and Λ is the grating pitch.

The effective refractive indices of the cladding modes are strongly dependent on the refractive index of the surrounding environment. This means that the ith cladding mode resonant wavelength will change as the refractive index of the surrounding environment changes.

The normalized transmitted power by the fundamental guided mode through the grating at the resonant wavelength regarding the ith cladding mode can be approximately expressed as [19

19. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997). [CrossRef]

]:

T=cos2(kiL)
(2)

where L is the length of the LPG and ki is the coupling coefficient of the ith cladding mode, which is determined by the overlap integral of the core and cladding mode and on the photo-induced refractive index modulation.

According to the coupled mode theory [19–22

19. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997). [CrossRef]

], the interaction between optical modes is proportional to their coupling coefficient. In cylindrical coordinates the coupling coefficient between each two modes can be expressed as [15

15. I. Del Villar, I. R. Matias, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in long period fiber gratings with overlay deposition,” Opt. Exp. 13, 56–69 (2005),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-56. [CrossRef]

]:

Kvj,μi=ω4P0×ϕ=02πr=0Δε(r,ϕ,z)ψvj(r,ϕ)ψμi(r,ϕ)rdrdϕ
(3)

where Ψ(r,φ) is the transverse field for an LP mode, Δε(r,φ,z) is the permittivity variation, and P0 is the power of each mode supposed to be the same. Under the assumptions of no azimutal and radial variation of the perturbed index profile the coupling would affect only the LP0i modes, and approximating the longitudinal refractive index perturbation factor by a Fourier series of two terms, the coupling coefficients can be expressed as:

K0j,0i=[s0+s1cos((2πΛ)z)]ζ0j,0i
(4)

with:

ζ0j,0i=2πω2P0n1r=0r1R0j(r)R0i(r)rdr
(5)

The way in which light is coupled out of the core mode depends on the refractive index of the material, supposed infinitely thick that surrounds the LPG [19

19. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997). [CrossRef]

]. If the refractive index of the surrounding material is lower than that of the cladding, the fiber supports bounded cladding modes that are maintained by total internal reflection (TIR) at the cladding-surrounding interface. In this case, the SRI sensitivity arises from the evanescent wave interaction between the cladding modes and the external medium leading to a strong modification of the central wavelength of the attenuation bands according to Eq. (1). As the external refractive index increases, the main effect is a blue wavelength shift, which is particularly pronounced in the largest wavelength resonance and when the SRI approaches the cladding one [1

1. S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and applications,” Meas. Sci. Technol. 14,R49–R61 (2003). [CrossRef]

, 23

23. X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long period fiber gratings,” J. Lightwave Technol. 20, 255–266 (2002). [CrossRef]

].

When the SRI is equal to the cladding one, the cladding layer acts as an infinitely extended medium and thus supports no discrete cladding modes. In this case, a broadband radiation-mode coupling occurs with no distinct attenuation bands [26

26. Y. Koyamada, “Numerical analysis of core-mode to radiation-mode coupling in long-period fiber gratings,” IEEE Photon. Technol. Lett. 13, 308–310 (2001). [CrossRef]

].

If the refractive index in the surrounding medium is higher than the cladding one, the fiber does not support any bounded cladding mode and the core mode couples with the radiation modes [24

24. D. B. Stegall and T. Erdogan, “Leaky cladding mode propagation in long-period fiber grating devices,” IEEE Photon. Technol. Lett. 11, 343–345 (1999). [CrossRef]

, 25

25. O. Duhem, J.-F. Henninot, M. Warenghem, and M. Douay “Demonstration of long-period grating efficient couplings with an external medium of a refractive index higher than that of silica,” Appl. Opt. 37, 7223–7228 (1998). [CrossRef]

]. The presence of the attenuation bands in this situation is because the fiber confines the radiated field at the resonant wavelengths by the Fresnel reflection, rather than by total internal reflection, at the boundary between the cladding and the surrounding medium, forming the leaky modes [26

26. Y. Koyamada, “Numerical analysis of core-mode to radiation-mode coupling in long-period fiber gratings,” IEEE Photon. Technol. Lett. 13, 308–310 (2001). [CrossRef]

]. As the SRI increases, the leaky modes are better confined, increasing the resonant losses. In contrast, in this case the resonant wavelengths are not influenced by the external index [26

26. Y. Koyamada, “Numerical analysis of core-mode to radiation-mode coupling in long-period fiber gratings,” IEEE Photon. Technol. Lett. 13, 308–310 (2001). [CrossRef]

].

When azimuthally symmetric nano-scale HRI coatings are deposited along LPGs and the SRI is lower than the cladding one, refraction-reflection regime at the cladding-overlay interface occurs. In this case, the immediate consequence is the change in the distribution of cladding modes, depending on the layer features (refractive index and thickness) and on the SRI. Within the transverse section of the coated optical fiber, a lowering of the cladding mode power bounded within the core and cladding layers occurs, favoring a relevant enhancement of the evanescent wave interaction with the surrounding medium [18

18. A. Cusano, A. Iadicicco, P. Pilla, L. Contessa, S. Campopiano, A. Cutolo, and M. Giordano, “Cladding modes re-organization in high refractive index coated long period gratings: Effects on the refractive index sensitivity,“ Opt. Lett. 30, (2005). [CrossRef] [PubMed]

].

Fig. 1. Transversal section of the investiated structure (not in scale).

Here, a detailed investigation of the effects of the HRI overlay on the cladding mode distribution is reported with particular attention to its influence on the SRI sensitivity. The case investigated here is focused on SRI lower than the cladding one. Since the calculation of the modes in a cylindrical four-layer waveguide (see Fig. 1) becomes a difficult and computational expensive task, a scalar approximation analysis based on the LP modes of a cylindrical dielectric waveguide is used [15

15. I. Del Villar, I. R. Matias, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in long period fiber gratings with overlay deposition,” Opt. Exp. 13, 56–69 (2005),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-56. [CrossRef]

, 21

21. E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Transmission characteristics of long- period fiber gratings having arbitrary azimutal/radial refractive index variation,” J. Lightwave Technol. 21, 218–227 (2003). [CrossRef]

]. Although the LP modes are adequate to describe a cylindrical waveguide under assumption of weak guidance, in Ref. [21

21. E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Transmission characteristics of long- period fiber gratings having arbitrary azimutal/radial refractive index variation,” J. Lightwave Technol. 21, 218–227 (2003). [CrossRef]

] is proved that the high contrast between surrounding medium and cladding refractive indices plays no important role in the results. In the same way, the presence of a higher refractive index overlay, which shows not important contrast with cladding will not affect the results in a great manner. As the overlay shows a higher contrast a greater error will be induced, but results will remain qualitatively correct [15

15. I. Del Villar, I. R. Matias, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in long period fiber gratings with overlay deposition,” Opt. Exp. 13, 56–69 (2005),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-56. [CrossRef]

].

Moreover, in the following analysis, the dispersion of the polymeric coating as well as that of the surrounding medium and of the optical fiber materials has not been taken into account. Furthermore, the overlay considered here is assumed to be optically transparent in the investigated wavelength range. Last, the presented analysis holds until the cladding modes are supported, i.e. for SRI lower than the cladding index. For higher SRI, a more complex model is required taking into account the core mode to radiation cladding modes in a four-layer waveguide [26

26. Y. Koyamada, “Numerical analysis of core-mode to radiation-mode coupling in long-period fiber gratings,” IEEE Photon. Technol. Lett. 13, 308–310 (2001). [CrossRef]

, 27

27. Y. Koyamada, “Analysis of core-mode to radiation-mode coupling in Fiber Bragg Gratings with Finite Cladding Radius,” Journal of Lightwave Technol. 18, 1220–1225, (2000). [CrossRef]

].

Since the investigated four-layer structure is supposed azimuthally symmetric, efficient coupling is achieved only between the core mode and azimuthally symmetric cladding modes [20

20. T. Erdogan, “Cladding mode resonances in short and long period fibre grating filters,” J. Opt. Soc. Am. 14, 1760–1773 (1997). [CrossRef]

], consequently only LP0i cladding modes have been taken into account. The analysis used the standard Corning SMF-28 optical fiber parameters: numerical aperture 0.14, refractive index difference 0.36%, cladding and core diameter 125μm and 8.3μm, respectively and has been carried out for HRI polymeric overlays (index 1.578, as in the experimental testing) with different thicknesses ranging between 50-300nm.

The LP mode fields in a doubly cladding fiber were proposed by Monerie [28

28. M. Monerie, “Propagation in doubly clad single-mode fibers,” IEEE J. of Quantun Electron. 18, (1982).

]. Based on this result, an extended model, adequate to four-layer waveguide, can be achieved with simple mathematical steps. The Fig. 1 shows the transversal section (not in scale) of the investigated structure. The transverse electrical field component, with azimuthal order ν, propagating along the z axis, is given by:

Rv(r)={A0Zv,1(u1rr1)forrr1A1Zv,2(u2rr2)+A2Tv,2(u2rr2)forr1<rr2A3Zv,3(u3rr3)+A4Tv,3(u3rr3)forr2<rr3A5Kv(vrr3)forr>r3
(6)

where:

Zv,i(x)={Jv(x)ifneff<niIv(x)ifneff>ni
Tv,i(x)={Yv(x)ifneff<niKv(x)ifneff>ni
ui=rik0ni2neff2fori=1,2,3
v=r3k0neff2nout2

In Fig. 2(a), the effective indices of the first 7 cladding modes (LP02-LP08) are represented as function of the SRI for a 150nm HRI overlay. As it can be observed, the effective refractive indices increase as the SRI goes up, until a critical point is reached. At this point, a significant shift in the effective index of cladding modes occurs. For a fixed overlay thickness, there is a value of the SRI which leads the lowest order cladding mode (higher effective index) to be guided within the overlay. The transition from cladding mode to overlay mode is characterized by an effective index of the involved mode higher than the cladding one. As the lowest order cladding mode moves to be guided within the overlay, a re-organization of the other cladding modes occurs. The immediate consequence is a simultaneous shift in the effective index of all the cladding modes to recover the original distribution. As a matter of fact, the effective index of the ith mode shifts to match the index of the (i-1)th mode, and so on. The same mechanism occurs for a fixed SRI by increasing the HRI overlay thickness as shown by Del Villar et al. [14

14. I. Del Villar, M. Achaerandio, I. R. Matias, and F. J. Arregui, “Deposition of overlays by electrostatic self-assembly in long-period fiber gratings,” Opt. Lett. 30, 720–722 (2005). [CrossRef] [PubMed]

, 15

15. I. Del Villar, I. R. Matias, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in long period fiber gratings with overlay deposition,” Opt. Exp. 13, 56–69 (2005),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-56. [CrossRef]

]. Moreover, since the effective refractive index difference between consecutive cladding modes increases with the mode order, higher is the mode order greater the effective index shift.

Fig. 2. Effective refractive index of the LP02-LP08 cladding modes versus the surrounding refractive index in HRI coated fiber with: (a) 150nm thin film; (b) 200nm; (c) 250nm and (d) 300nm thin film.

Based on these argumentations and taking into account the direct relationship between effective index and resonant wavelength (eq. 1), a displacement of all the attenuation bands is expected. The attenuation band corresponding to the ith cladding mode would move to recover the loss peak regarding the (i-1)th cladding mode. In addition, as the mode order increases, greater shift is required for the ith mode to cover the position of the (i-1)th mode.

This means that improved SRI sensitivity is expected in HRI coated LPGs near the transition point compared with uncoated devices. Figures 2(b), 2(c) and 2(d) show the modes transition for a HRI overlay of 200nm, 250nm and 300nm, respectively, with the same coating index of 1.578. As observable in the figures, the transition region moves to lower SRI as the overlay thickness increases, approaching the ambient index of 1.33, where typically classical LPGs demonstrate a significantly lower sensitivity.

As secondary effect the SRI sensitivity results smaller as the overlay thickness increases. A fundamental feature of this mechanism is the possibility to tune the transition region in the desired SRI range by acting on the overlay thickness. This means that by using thick enough HRI coating, strong sensitivity can be obtained also for SRI approaching the air index, leading to the possibility to develop volatile organic compounds and gas sensors.

In Fig. 3(a) the coupling coefficients of the first 7 cladding modes (LP02-LP08) are represented as function of the SRI for a 150nm HRI overlay. It is apparent from the figure that the coupling coefficients are a decreasing function of the SRI. This behavior can be attributed to the increasing of the SRI that favors the transverse field profile of the cladding modes to be stretched towards the HRI coating causing a reduction of the overlap intergral between cladding and core mode. When the first cladding mode becomes guided into the overlay, in correspondence of the transition point, its coupling coefficient vanishes to zero rapidly. At the same point, the coupling coefficients of the higher order cladding modes shift to quasi recover the original configuration of the coupling coefficients. As already noticed for the effective refractive indices, the maximum sensitivity of the coupling coefficients to the SRI is shown in the transition region where the slope of the curves increases dramatically. On the other hand an opposite behavior is observed concerning the mode order, in fact for the coupling coefficients lower is the mode order greater the shift. This is clearly expected since the lowest order cladding modes are the first to experience the transition between cladding modes to overlay modes.

Fig. 3. Coupling coefficients of the LP02-LP08 cladding modes versus the surrounding refractive index in HRI coated fiber with: (a) 150nm thin film; (b) 200nm; (c) 250nm and (d) 300nm thin film.

In Figs. 3(b), 3(c) and 3(d) the coupling coefficients versus the SRI are reported for overlay thicknesses of 150 nm, 200 nm and 250 nm respectively, with the same coating index of 1.578. From these figures can be clearly inferred that increasing the overlay thickness the coupling coefficients curves shift toward lower SRI as it happens for the effective refractive indices curves.

Finally, the Fig. 4 summarizes the surrounding refractive indices corresponding to the maximum sensitivity versus the overlay thickness for the first seven cladding modes. As observable, the transition can be considered to occur simultaneously for each cladding mode. This means that as the lowest order mode becomes guided into the overlay a simultaneous re-organization of all the cladding modes occurs. Small differences can be seen only for thicker overlays.

A better understanding of the cladding modes re-organization as direct consequence of the SRI changes is provided in Fig. 5, in the case of 200nm coated LPG. In particular, the Figs. 5(a), 5(b) and 5(c) show the transverse field profile of the LP02, LP03 and LP04 cladding modes, respectively, before the transition (SRI=1), during the transition (SRI=1.40) and after the transition (SRI=1.45). All the fields were normalized to the maximum amplitude of the LP01 core mode. As observable, during the transition, the field content in the overlay, and so the interaction between the evanescent wave and the surrounding medium, reaches its maximum value. In addition, it can be clearly observed that the LP04 mode after the transition [dotted line in Fig. 5(c)] is qualitatively similar to LP03 mode before the transition [solid line in Fig. 5(b)]. In the same way, the LP03 mode after the transition [dotted line in Fig. 5(b)] is similar to LP02 mode before the transition [solid line in Fig. 5(a)], while the LP02 mode after the transition [dotted line in Fig. 5(a)] is clearly guided within the overlay.

Fig. 4. SRI corresponding to the maximum sensitivity versus the overlay thickness for first 7 cladding modes.

3. Sensitive overlay

Thin films of sPS in the Δ form were recently proposed by the authors as sensitive layers for Fabry Perot based and LPG based opto-chemical sensors [17

17. P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, “Optical Chemo-Sensor based on long period gratings coated with δ form Syndiotactic Polystyrene,” IEEE Photon. Technol. Lett. 17, 1713–1715 (2005). [CrossRef]

, 33

33. M. Giordano, M. Russo, A. Cusano, G. Mensitieri, and G. Guerra “Syndiotactic Polystyrene Thin Film as sensitive layer for an optoelectronic chemical sensing device”, Sensors and Actuators B 109, 177–184 (2005). [CrossRef]

, 34

34. M. Giordano, M. Russo, A. Cusano, A. Cutolo, G. Mensitieri, and L. Nicolais, “Optical sensor based on ultrathin films of δ-form syndiotactic polystyrene for fast and high resolution detection of chloroform”, Applied Physics Lett. 85, 5349–5351 (2004). [CrossRef]

]. The main effect of the analyte sorption is a strong increase in the density and thus in the refractive index according to the Lorentz-Lorenz law [34

34. M. Giordano, M. Russo, A. Cusano, A. Cutolo, G. Mensitieri, and L. Nicolais, “Optical sensor based on ultrathin films of δ-form syndiotactic polystyrene for fast and high resolution detection of chloroform”, Applied Physics Lett. 85, 5349–5351 (2004). [CrossRef]

]:

n21n2+1=N3ρβ
(7)

where ρ is the density, β the polarizability, N the Avogadro number, M molecular weight of the repetitive polymer unit and ε the vacuum permittivity.

Fig. 5. Cladding mode field in a 200nm coated LPG, before transition (SRI=1), in transition (SRI=1.40) and after transition (SRI=1.45): (a) LP02; (b) LP03; and (c) LP04.

Since sorption occurs mainly in the crystalline nanocavities it can be assumed that, at low concentration of analyte, no volume change of polymer layer occurs, while the average refractive index increases. Moreover, low absorption is expected from this material in the NIR range.

4. Experimental

In order to experimentally prove the transition effects on LPG sensitivity, dip coating technique and Syndiotactic Polystyrene as HRI overlay were used.

Fig. 6. SEM Photogram reveals an overlay thickness of about 150nm.

The use of dip coating technique allows to obtain different overlay thicknesses by acting on the solution density and extraction velocity as stated by the Landau-Levich equation [35

35. L. D. Landau and B. G. Levich, Acta Physiochim, U.R.S.S. , 17, 42–54 (1942).

]:

t=k(U)23(ρ)12
(8)

where t is the overlay thickness, U is the extraction velocity and ρ is the solution density.

Here, the polymeric overlay is not used as species-specific sensitive overlay, since no reactivity is expected towards the investigated liquids. First, nano-scale films of sPS were cast by dip-coating on a 30mm long LPG with period of 340μm, written in standard borongermania co-doped Corning single mode fiber. Since the LPGs are strongly sensitive to strain and bending, a proper holder was designed and realized in order to fix the fiber ensuring strain and bending free operations. The optoelectronic set-up, involved for transition characterization, comprises a white light source in 400-1800nm wavelength range and an optical spectrum analyzer to record the spectral response of the device. Investigation was focused on the attenuation bands in the spectral range 1200-1680nm. In addition, thickness measurements were performed by SEM and AFM analysis. In particular a standard optical fiber without the sensing element was hosted together with the LPG in the holder for the overlay deposition. In this way, thickness measurements by SEM analysis were possible on standard fibers with the same overlay thickness of the coated LPG. The SEM photogram, shown in Fig. 6, revealed an overlay thickness of about 150nm.

Figure 7 shows the transmission spectrum, regarding the LP06 mode, of the bare and 150nm sPS coated LPG. As observable, a slight wavelength blue shift of about 1.4 nm is achieved due to the increase of the cladding modes effective refractive indices. The spectral shift is obviously greater for higher order cladding modes. As predicted by the numerical analysis, the measured wavelength shift is small since for this overlay thickness and refractive index the cladding modes are very far from the transition region when air is the surrounding medium. Consequently, low sensitivity of the effective refractive indices to the overlay thickness is expected as shown by Del Villar et al. [15

15. I. Del Villar, I. R. Matias, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in long period fiber gratings with overlay deposition,” Opt. Exp. 13, 56–69 (2005),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-56. [CrossRef]

].

Fig. 7. Bare and 150nm sPS coated LPG transmission spectra for the LP06 cladding mode.

With regards to the attenuation bands amplitude, the loss peaks are characterized by a remarkable reduction until the SRI reaches the value of 1.439 very close to the cladding one. After this value, an increasing of the attenuation bands amplitude is observed as the SRI is slightly increased. This means that good agreement was found between numerical and experimental results for SRI lower than the cladding one demonstrating the validity of the LP approximation to model the mode transition especially when the contrast between fiber indexes and overlay one is not so pronounced. Differently from the numerical analysis, the experimental results demonstrate a strong decrease in the attenuation bands amplitude especially for the higher order modes. This behavior can be attributed to two main effects: the first one is due to the limit of the LP approximation to provide exact results form the quantitative point of view. The second relies on the approximations to neglect the materials dispersion and the absorbance in the external medium as well as in the HRI overlay especially in the NIR range.

For SRI approaching the cladding one, as previously aforementioned, the nature of the core to cladding modes coupling changes, since core mode to radiation modes coupling occur leading to a strong modification of the radiation losses and thus of the attenuation bands amplitudes.

Fig. 8. Transmission spectra of a 150nm sPS coated LPG for different values of SRI in the range 1.33-1.472
Fig. 9. Transmission spectra of a 150nm sPS coated LPG zoomed on LP07 and LP08 cladding modes

Fig. 10. Wavelength shift of different cladding modes for the LPG coated with a 150nm sPS overlay versus SRI.
Fig. 11. Peak Loss of different cladding modes versus SRI for the LPG coated with a 150nm sPS overlay.

In order to demonstrate that the sensitivity gain region can be tuned over the desired SRI range by acting on the overlay thickness, two more sPS overlays were deposited along a different LPG. The second LPG had a grating period of 360μm, and the sPS overlays were measured and found to be about 140 and 180 nm, respectively. A blue wavelength shift of 1 nm and 2.8 nm, respectively, were recorded after the deposition of the two films. Also in these cases the SRI sensitivity has been investigated.

Figure 12 shows the wavelength shift of different cladding modes for the LPG coated with a 140nm sPS overlay versus the surrounding refractive index. Since the thickness of this overlay is slightly different from the one previously analysed, small differences in the placement of the transition region are expected. In fact, a large wavelength shift for all the attenuation bands was observed as the SRI becomes greater than 1.42. On the other side, a transmission spectrum very close the original one is achieved as the SRI reaches 1.45. Far from the transition region the SRI sensitivity increases, compared with the bare LPG, of a factor ranging from 2 to over 4 as the mode order decreases. Within the transition region, the SRI sensitivity enhancement around 1.43 was estimated to be 5 to 40 times, as the mode order decreases, the sensitivity of the uncoated LPG. In addition, the sensitivity gain respect to the maximum sensitivity of the uncoated LPG (around 1.45) was estimated to be a factor ranging from 2 to over 8.

Fig. 12. Wavelength shift of different cladding modes for the LPG coated with a 140nm sPS overlay versus SRI.
Fig. 13. Wavelength shift of a higher cladding mode for the LPG coated with a 180nm sPS overlay versus SRI.

In Fig. 13 is reported the wavelength shift for the LP08 mode (centred around 1650nm) of a 180nm SPS coated LPG. As the SRI approaches the value of 1.35, large shift in the central wavelength was observed. In correspondence of the transition, a wavelength shift of over 200nm was observed for a refractive index change of approx. 0.1. It is worth to note that in good agreement with the numerical analysis, the transition results slower and less marked as the overlay thickness increases. This means that low cost and commercially available spectrometer with a wavelength resolution of 0.1nm would ensure a SRI resolution of approximately 5∙10-5. In addition this value can be obtained in correspondence of air (n=1), water (n=1.33) or other solutions as surrounding media, by using the proper overlay thickness. This feature enable the use of low cost equipment based on HRI coated LPGs in advanced chemical sensing for volatile organic compounds, gases and liquid monitoring in light of the easy multiplexing capability and lower complexity compared with plasmon resonance or waveguide sensors.

The presented experimental results prove that HRI coating along a standard LPG is able to enhance the SRI sensitivity. In particular, by a proper choice of the overlay features a high sensitivity gain is possible around 1.33, where standard LPGs demonstrate a significantly lower sensitivity. Future works would experimentally investigate how the relationship between the transition region and the overlay thickness can be tuned by changing the overlay refractive index.

5. Conclusion

In this work, the cladding mode re-organization in HRI coated LPGs has been numerically and experimentally investigated. Our attention was focused on the enhancement of the SRI sensitivity as the transition of the first cladding mode into an overlay mode is reached. When azimuthally symmetric nano-scale HRI coatings are deposited along LPGs, a significant modification of the cladding modes distribution occurs, depending on the layer features and on the SRI. During the transition, the field content is in the overlay, and so the interaction between the evanescent wave and the surrounding medium, reaches its maximum value. Both numerical and experimental results demonstrate how by a proper choice of the HRI thickness is possible to tailor and significantly enhance the SRI sensitivity of HRI coated LPGs based refractometers. In addition, the transition mechanism could lead to new tuning concepts for advanced active filter design.

Acknowledgments

The authors wish to thank: Antonio Maggio and Stefano Marrazzo (Officina Meccanica, Dipartimento di Scienze Fisiche di Ingegneria, Università Fedeico II Napoli) for the realization of the sensor packaging. Manlio Colella (Laboratorio di Microscopia Ottica di Ingegneria, Università Federico II Napoli) for the SEM analysis.

References and links

1.

S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and applications,” Meas. Sci. Technol. 14,R49–R61 (2003). [CrossRef]

2.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band rejection filters,” J. Lightwave Technol. 14, 58–65 (1996). [CrossRef]

3.

J. R. Qiang and H. E. Chen, “Gain flattening fibre filters using phase shifted long period fibre grating,” Electron. Lett. 34, 1132–1133 (1998). [CrossRef]

4.

K. W. Chung and S. Yin, “Analysis of widely tunable long-period grating by use of an ultrathin cladding layer and higher-order cladding mode coupling,” Opt. Lett. 29, 812–814 (2004). [CrossRef] [PubMed]

5.

X. Shu, T. Allsop, B. Gwandu, L. Zhang, and I. Bennion, “Room-temperature operation of widely tunable loss filter,” Electron. Lett. 37, 216–218 (2001). [CrossRef]

6.

B. J. Eggleton, R. E. Slusher, J. B. Judkins, J. B. Stark, and A. M. Vengsarkar, “All-optical switching in long period fiber gratings,” Opt. Lett. 22, 883–885 (1997). [CrossRef] [PubMed]

7.

V. Bhatia, “Applications of long-period gratings to single and multi-parameter sensing,” Opt. Express 4, 457–466 (1999), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-11-457. [CrossRef] [PubMed]

8.

C. Y. Lin, L. A. Wang, and G. W. Chern, “Corrugated long period fiber gratings as Strain, Torsion, and Bending Sensors,” J. Lightwave Technol. 19, 1159–1168 (2001). [CrossRef]

9.

H. J. Patrick, A. D. Kersey, and F. Bucholtz, “Analysis of the response of long period fiber gratings to external index of refraction,” J. Lightwave Technol. 16, 1606–1612 (1998). [CrossRef]

10.

R. Hou, Z. Ghassemlooy, A. Hassan, C. Lu, and K. P. Dowker, “Modelling of long-period fibre grating response to refractive index higher than that of cladding,” Meas. Sci. Technol. 12, 1709–1713 (2001). [CrossRef]

11.

S. T. Lee, R. D. Kumar, P. S. Kumar, P. Radhakrishnan, C. P. G. Vallabhan, and V. P. N. Nampoori, “Long period gratings in multimode optical fibers: application in chemical sensing,” Opt. Comm. 224, 237–241 (2003). [CrossRef]

12.

T. Allsop, D. J. Webb, and I. Bennion, “A comparison of the sensing characteristics of long period gratings written in three different types of fiber,” Optical Fiber Technol. 9, 210–223 (2003). [CrossRef]

13.

S. W. James, N. D. Rees, G. J. Ashwell, and R. P. Tatam, “Optical fibre long period gratings with Langmuir Blodgett thin film overlays,” Opt. Lett. 9, 686–688 (2002).

14.

I. Del Villar, M. Achaerandio, I. R. Matias, and F. J. Arregui, “Deposition of overlays by electrostatic self-assembly in long-period fiber gratings,” Opt. Lett. 30, 720–722 (2005). [CrossRef] [PubMed]

15.

I. Del Villar, I. R. Matias, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in long period fiber gratings with overlay deposition,” Opt. Exp. 13, 56–69 (2005),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-56. [CrossRef]

16.

Z. Wang, J. R. Heflin, R. H. Stolen, and S. Ramachandran, “Analysis of optical response of long period fiber gratings to nm-thick thin-film coatings,” Opt. Exp. 13, 2808–2813 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-2808. [CrossRef]

17.

P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, “Optical Chemo-Sensor based on long period gratings coated with δ form Syndiotactic Polystyrene,” IEEE Photon. Technol. Lett. 17, 1713–1715 (2005). [CrossRef]

18.

A. Cusano, A. Iadicicco, P. Pilla, L. Contessa, S. Campopiano, A. Cutolo, and M. Giordano, “Cladding modes re-organization in high refractive index coated long period gratings: Effects on the refractive index sensitivity,“ Opt. Lett. 30, (2005). [CrossRef] [PubMed]

19.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997). [CrossRef]

20.

T. Erdogan, “Cladding mode resonances in short and long period fibre grating filters,” J. Opt. Soc. Am. 14, 1760–1773 (1997). [CrossRef]

21.

E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Transmission characteristics of long- period fiber gratings having arbitrary azimutal/radial refractive index variation,” J. Lightwave Technol. 21, 218–227 (2003). [CrossRef]

22.

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

23.

X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long period fiber gratings,” J. Lightwave Technol. 20, 255–266 (2002). [CrossRef]

24.

D. B. Stegall and T. Erdogan, “Leaky cladding mode propagation in long-period fiber grating devices,” IEEE Photon. Technol. Lett. 11, 343–345 (1999). [CrossRef]

25.

O. Duhem, J.-F. Henninot, M. Warenghem, and M. Douay “Demonstration of long-period grating efficient couplings with an external medium of a refractive index higher than that of silica,” Appl. Opt. 37, 7223–7228 (1998). [CrossRef]

26.

Y. Koyamada, “Numerical analysis of core-mode to radiation-mode coupling in long-period fiber gratings,” IEEE Photon. Technol. Lett. 13, 308–310 (2001). [CrossRef]

27.

Y. Koyamada, “Analysis of core-mode to radiation-mode coupling in Fiber Bragg Gratings with Finite Cladding Radius,” Journal of Lightwave Technol. 18, 1220–1225, (2000). [CrossRef]

28.

M. Monerie, “Propagation in doubly clad single-mode fibers,” IEEE J. of Quantun Electron. 18, (1982).

29.

G. Guerra, V. M. Vitagliano, C. De Rosa, V. Petraccone, and P. Corradini, “Polymorphism in melt crystallized syndiotactic polystyrene samples,” Macromolecules , 23(5), 1539-44 (1990). [CrossRef]

30.

V. Petraccone, F. Auriemma, F. Dal Poggetto, C. De Rosa, G. Guerra, and P. Corradini, “On the structure of the mesomorphic form of syndiotactic polystyrene,” Makromolekulare Chemie 194, 1335–1345, (1993). [CrossRef]

31.

G. Guerra, C. Manfredi, P. Musto, and S. Tavone, “Guest conformation and diffusion into Amorphous and emptied Clathrate phases of Syndiotactic Polystyrene,” Macromolecules , 31(4), (1998), 1329–1334. [CrossRef]

32.

G. Mensitieri, V. Venditto, and G. Guerra, “Polymeric sensing films absorbing organic guests into a nanoporous host crystalline phase,” Sensors and Actuators, B: Chemical B92(3), (2003), 255–261. [CrossRef]

33.

M. Giordano, M. Russo, A. Cusano, G. Mensitieri, and G. Guerra “Syndiotactic Polystyrene Thin Film as sensitive layer for an optoelectronic chemical sensing device”, Sensors and Actuators B 109, 177–184 (2005). [CrossRef]

34.

M. Giordano, M. Russo, A. Cusano, A. Cutolo, G. Mensitieri, and L. Nicolais, “Optical sensor based on ultrathin films of δ-form syndiotactic polystyrene for fast and high resolution detection of chloroform”, Applied Physics Lett. 85, 5349–5351 (2004). [CrossRef]

35.

L. D. Landau and B. G. Levich, Acta Physiochim, U.R.S.S. , 17, 42–54 (1942).

OCIS Codes
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(120.0280) Instrumentation, measurement, and metrology : Remote sensing and sensors
(260.2110) Physical optics : Electromagnetic optics
(350.2770) Other areas of optics : Gratings

ToC Category:
Fiber Optics and Optical Communications

Citation
A. Cusano, A. Iadicicco, P. Pilla, L. Contessa, S. Campopiano, A. Cutolo, and M. Giordano, "Mode transition in high refractive index coated long period gratings," Opt. Express 14, 19-34 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-1-19


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References

  1. S. W. James and R. P. Tatam, "Optical fibre long-period grating sensors: characteristics and applications," Meas. Sci. Technol. 14, R49-R61 (2003). [CrossRef]
  2. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band rejection filters," J. Lightwave Technol. 14, 58-65 (1996). [CrossRef]
  3. J. R. Qiang and H. E. Chen, "Gain flattening fibre filters using phase shifted long period fibre grating," Electron. Lett. 34, 1132-1133 (1998). [CrossRef]
  4. K. W. Chung, and S. Yin, "Analysis of widely tunable long-period grating by use of an ultrathin cladding layer and higher-order cladding mode coupling," Opt. Lett. 29, 812-814 (2004). [CrossRef] [PubMed]
  5. X. Shu, T. Allsop, B. Gwandu, L. Zhang and I. Bennion, "Room-temperature operation of widely tunable loss filter," Electron. Lett. 37, 216-218 (2001). [CrossRef]
  6. B. J. Eggleton, R. E. Slusher, J. B. Judkins, J. B. Stark, and A. M. Vengsarkar, "All-optical switching in long period fiber gratings," Opt. Lett. 22, 883-885 (1997). [CrossRef] [PubMed]
  7. V. Bhatia, "Applications of long-period gratings to single and multi-parameter sensing," Opt. Express 4, 457- 466 (1999), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-11-457">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-11-457</a>. [CrossRef] [PubMed]
  8. C. Y. Lin, L. A. Wang, and G. W. Chern, "Corrugated long period fiber gratings as Strain, Torsion, and Bending Sensors," J. Lightwave Technol. 19, 1159-1168 (2001). [CrossRef]
  9. H. J. Patrick, A. D. Kersey and F. Bucholtz, "Analysis of the response of long period fiber gratings to external index of refraction," J. Lightwave Technol. 16, 1606-1612 (1998). [CrossRef]
  10. R. Hou, Z. Ghassemlooy, A. Hassan, C. Lu, K. P. Dowker, "Modelling of long-period fibre grating response to refractive index higher than that of cladding," Meas. Sci. Technol. 12, 1709-1713 (2001). [CrossRef]
  11. S. T. Lee, R. D. Kumar, P. S. Kumar, P. Radhakrishnan, C. P. G. Vallabhan, and V. P. N. Nampoori, "Long period gratings in multimode optical fibers: application in chemical sensing," Opt. Commun. 224, 237-241 (2003). [CrossRef]
  12. T. Allsop, D. J. Webb and I. Bennion, "A comparison of the sensing characteristics of long period gratings written in three different types of fiber," Optical Fiber Technol. 9, 210-223 (2003). [CrossRef]
  13. S. W. James, N. D. Rees, G. J. Ashwell, R. P. Tatam, "Optical fibre long period gratings with Langmuir Blodgett thin film overlays," Opt. Lett. 9, 686-688 (2002).
  14. I. Del Villar, M. Achaerandio, I. R. Matias, and F. J. Arregui, "Deposition of overlays by electrostatic self-assembly in long-period fiber gratings," Opt. Lett. 30, 720-722 (2005). [CrossRef] [PubMed]
  15. I. Del Villar, I. R. Matias, F. J. Arregui and P. Lalanne, "Optimization of sensitivity in long period fiber gratings with overlay deposition," Opt. Express 13, 56-69 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-56">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-56</a>. [CrossRef]
  16. Z. Wang, J. R. Heflin, R. H. Stolen and S. Ramachandran, "Analysis of optical response of long period fiber gratings to nm-thick thin-film coatings," Opt. Express 13, 2808-2813 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-2808">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-2808</a>. [CrossRef]
  17. P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano and A. Cusano, "Optical Chemo- Sensor based on long period gratings coated with ä form Syndiotactic Polystyrene," IEEE Photon. Technol. Lett. 17, 1713-1715 (2005). [CrossRef]
  18. A. Cusano, A. Iadicicco, P. Pilla, L. Contessa, S. Campopiano, A. Cutolo and M. Giordano, " Cladding modes re-organization in high refractive index coated long period gratings: Effects on the refractive index sensitivity," Opt. Lett. 30, (2005). [CrossRef] [PubMed]
  19. T. Erdogan, "Fiber grating spectra," J. Lightwave Technol. 15, 1277-1294 (1997). [CrossRef]
  20. T. Erdogan, "Cladding mode resonances in short and long period fibre grating filters," J. Opt. Soc. Am. 14, 1760-1773 (1997). [CrossRef]
  21. E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, "Transmission characteristics of long- period fiber gratings having arbitrary azimutal/radial refractive index variation," J. Lightwave Technol. 21, 218-227 (2003). [CrossRef]
  22. A. W. Snyder, and J. D. Love, "Optical waveguide theory," (Chapman and Hall, New York, 1983).
  23. X. Shu, L. Zhang, and I. Bennion, "Sensitivity characteristics of long period fiber gratings," J. Lightwave Technol. 20, 255-266 (2002). [CrossRef]
  24. D. B. Stegall and T. Erdogan, "Leaky cladding mode propagation in long-period fiber grating devices," IEEE Photon. Technol. Lett. 11, 343-345 (1999). [CrossRef]
  25. O. Duhem, J.-F. Henninot, M. Warenghem and M. Douay "Demonstration of long-period grating efficient couplings with an external medium of a refractive index higher than that of silica," Appl. Opt. 37, 7223-7228 (1998). [CrossRef]
  26. Y. Koyamada, "Numerical analysis of core-mode to radiation-mode coupling in long-period fiber gratings," IEEE Photon. Technol. Lett. 13, 308-310 (2001). [CrossRef]
  27. Y. Koyamada, "Analysis of core-mode to radiation-mode coupling in Fiber Bragg Gratings with Finite Cladding Radius," J. Lightwave Technol. 18, 1220-1225, (2000). [CrossRef]
  28. M. Monerie, "Propagation in doubly clad single-mode fibers," IEEE J. Quantum Electron. 18, (1982).
  29. G. Guerra, V. M. Vitagliano, C. De Rosa, V.Petraccone, and P. Corradini, "Polymorphism in melt crystallized syndiotactic polystyrene samples," Macromolecules 23, 1539-44 (1990). [CrossRef]
  30. V. Petraccone, F. Auriemma, F. Dal Poggetto, C. De Rosa, G. Guerra, and P. Corradini, "On the structure of the mesomorphic form of syndiotactic polystyrene," Makromolekulare Chemie 194, 1335-1345, (1993). [CrossRef]
  31. G.Guerra, C. Manfredi, P. Musto, and S. Tavone, "Guest conformation and diffusion into Amorphous and emptied Clathrate phases of Syndiotactic Polystyrene," Macromolecules 31, 1329-1334 (1998). [CrossRef]
  32. G. Mensitieri, V. Venditto, and G. Guerra, "Polymeric sensing films absorbing organic guests into a nanoporous host crystalline phase," Sensors and Actuators, B: Chemical B 92, 255-261 (2003). [CrossRef]
  33. M. Giordano, M. Russo, A. Cusano, G. Mensitieri, and G.Guerra "Syndiotactic Polystyrene Thin Film as sensitive layer for an optoelectronic chemical sensing device", Sensors and Actuators B 109, 177-184 (2005). [CrossRef]
  34. M. Giordano, M. Russo, A. Cusano, A. Cutolo, G. Mensitieri, and L. Nicolais, "Optical sensor based on ultrathin films of δ-form syndiotactic polystyrene for fast and high resolution detection of chloroform", Appl. Phys. Lett. 85, 5349-5351 (2004). [CrossRef]
  35. L. D. Landau, and B. G. Levich, Acta Physiochim, U.R.S.S., 17, 42-54 (1942).

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