Mode transition in high refractive index coated long ... - OSA Publishing

Mode transition in high refractive index coated long period gratings A. Cusano, A. Iadicicco, P. Pilla, L. Contessa, S. Campopiano, and A. Cutolo Optoelectronic Division, Engineering Department, University of Sannio, Benevento, Italy [email protected]

M. Giordano Institute of Composite Biomedical Materials, National Research Council, Napoli, Italy

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 OCIS codes: (060.2370) Fiber optics sensors; (350.2770) Gratings; (260.2110) Electromagnetic theory; (120.0280) Polymers.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

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Received 21 July 2005; revised 1 October 2005; accepted 19 December 2005

9 January 2006 / Vol. 14, No. 1 / OPTICS EXPRESS 19

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35.

I. Del Villar, M. Achaerandio, I. R. Matias, and F. J. Arregui, “Deposition of overlays by electrostatic selfassembly in long-period fiber gratings,” Opt. Lett. 30, 720-722 (2005). 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. 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. P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano and A. Cusano, “Optical ChemoSensor based on long period gratings coated with δ form Syndiotactic Polystyrene,” IEEE Photon. Technol. Lett. 17, 1713-1715 (2005). 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). T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997). T. Erdogan, "Cladding mode resonances in short and long period fibre grating filters," J. Opt. Soc. Am. 14, 1760–1773 (1997). 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). A. W. Snyder, and J. D. Love, “Optical waveguide theory,” (Chapman and Hall, New York, 1983). X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long period fiber gratings,” J. Lightwave Technol. 20, 255–266 (2002). D. B. Stegall and T. Erdogan, “Leaky cladding mode propagation in long-period fiber grating devices,” IEEE Photon. Technol. Lett. 11, 343-345 (1999). 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). Y. Koyamada, “Numerical analysis of core-mode to radiation-mode coupling in long-period fiber gratings,” IEEE Photon. Technol. Lett. 13, 308-310 (2001). 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). M. Monerie, “Propagation in doubly clad single-mode fibers,” IEEE J. of Quantun Electron. 18, (1982). 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). 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). 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. 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. 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). 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). L. D. Landau, and B. G. Levich, Acta Physiochim, U.R.S.S., 17, 42-54 (1942).

1. Introduction In the last years, in fiber Long Period Gratings (LPGs) have been widely investigated for both sensing and communications applications [1]. 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], gain equalizers [3], tunable filters [4, 5] and optical switches [6]. With regard to sensing applications, many studies including strain, bending, torsion, temperature measurements have been widely reported [7, 8]. 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, 10] and for the detection of chemical substances in the ambient [11]. 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, 12]. The idea

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of coated LPGs with thin high refractive index (HRI) layers was first proposed by James et al. [13]. Recently, a comprehensive theoretical and numerical investigation was proposed by Del Villar at al. [14, 15] 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] 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]. 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 features [18]. 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], 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]:

2π

λ

(n

eff ,01

− neff,0i ) + s0 (ζ 01,01(λ) −ζ 0i,0i (λ)) =

2π Λ

(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

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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]: (2) T = cos 2 (k i L) 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 photoinduced refractive index modulation. According to the coupled mode theory [19-22], 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]:

K vj , μi =

ω 4 P0

×

2π

∞

∫ ∫ Δε

(r ,φ , z )Ψvj (r ,φ )Ψμi (r ,φ )rdrd φ

(3)

φ =0 r = 0

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 : ⎡ ⎛ ⎛ 2π ⎞ ⎞⎤ (4) K 0 j ,0i = ⎢s0 + s1 cos⎜⎜ ⎜ ⎟ z ⎟⎟⎥ζ 0 j ,0i ⎝ ⎝ Λ ⎠ ⎠⎦ ⎣ with: 1 2πω (5) n1 ∫ R0 j (r )R0i (r )rdr 2 P0 r =0 Where n1 is the refractive index of the fiber core, r1 is the radius of the fiber core, s0 and s1 are the Fourier coefficients of the longitudinal refractive index modulation, and R(r) is the radial variation of the modal field. 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]. 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 claddingsurrounding 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, 23]. 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 radiationmode coupling occurs with no distinct attenuation bands [26]. 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, 25]. 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]. 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]. 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

r

ζ 0 j , 0i =

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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].

Fig. 1. Transversal section of the investigated 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, 21]. Although the LP modes are adequate to describe a cylindrical waveguide under assumption of weak guidance, in Ref. [21] 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]. 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, 27]. 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], 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. #8237 - $15.00 USD

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

⎧ ⎛ r⎞ ⎪ A0 Zν ,1 ⎜⎜ u1 ⎟⎟ ⎝ r1 ⎠ ⎪ ⎪ ⎛ r⎞ ⎛ r⎞ ⎪ A1 Zν ,2 ⎜⎜ u2 ⎟⎟ + A2Tν , 2 ⎜⎜ u2 ⎟⎟ ⎪ ⎝ r2 ⎠ ⎝ r2 ⎠ Rν (r ) = ⎨ ⎪ A Z ⎛⎜ u r ⎞⎟ + A T ⎛⎜ u r ⎞⎟ 4 ν ,3 ⎜ 3 ⎟ ⎪ 3 ν ,3 ⎜⎝ 3 r3 ⎟⎠ ⎝ r3 ⎠ ⎪ ⎪ A K ⎛⎜ v r ⎞⎟ ⎪ 5 ν ⎜⎝ r3 ⎟⎠ ⎩ where:

⎧ Jν ( x ) Zν ,i ( x ) = ⎨ ⎩Iν ( x ) ⎧Yν ( x ) Tν ,i ( x ) = ⎨ ⎩ Kν ( x ) 2 ui = ri k0 ni2 − neff

for

r ≤ r1

for

r1 < r ≤ r2

for

r2 < r ≤ r3

for

r > r3

(6)

if neff < ni if neff > ni if neff < ni if neff > ni for i = 1,2,3

2 2 v = r3k0 neff − nout

where r is the radius, Jν and Iν are the ordinary Bessel functions of first and second kind of order ν and Yν and Kν are the modified Bessel functions of first and second kind of order ν, respectively. n1, n2 and n3 are the core, cladding and overlay refractive indices, respectively, while nout is the surrounding refractive index and neff is the effective refractive index. r1 and r2 are the core and cladding radius and r3-r2 is the overlay thickness. In addition, A1, A2, A3, A4 and A5 can be obtained, as function of A0, by imposing the continuity of the fields at the interface between core and cladding, cladding and overlay and overlay and surrounding medium while A0 is related to the optical power of the mode. Here, the effective refractive index of every cladding mode is achieved by numerical solution of the dispersion equation obtained by the continuity condition of the transverse fields. 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, 15]. 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. #8237 - $15.00 USD

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1.4565

(a) LP0

1.456

LP0

LP0

LP0

1.454 1

LP0

1.456

1.2

1.3

LP0 LP0

1.454 1

1.4

1.1

1.457

(c) LP0

1.456

LP0 LP0

1.4555

1.4545

LP0

1.454 1

LP0

1.456

1.455

1.4545

1.1

(d)

1.2

1.3

1.4

Surrounding Refractive Index

1.4

1.454 1

LP0

LP0

LP0 LP0

1.4555

LP0

1.455

1.3

1.457

1.4565

LP0 LP0

1.2

Surrounding Refractive Index Effective Refractive Index

Effective Refractive Index


1.4565

LP0 LP0

LP0 LP0

1.455

1.4545

1.1

(b)

1.4555

LP0

1.455

1.457

1.4565

LP0

1.4555

1.4545

LP0



1.457

LP0 LP0 1.1

1.2

1.3

1.4


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 #8237 - $15.00 USD

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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. 5

x 10

LP0

4

LP0

LP0

LP0 3

LP0 LP0

2

LP0

1

(a) 0 1

1.1

1.2

1.3

Coupling Coefficients [m-1]


5

5

1.4

5

x 10

LP0

4

LP0 LP0

2

LP0

1

(b) 0 1

1.1


1.3

1.4


LP0

4

LP0

LP0

LP0 3

LP0 LP0

2

LP0

1

(c) 1.1

1.2

1.3

1.4


5



1.2

5

x 10

0 1

LP0

LP0 3

5

5

LP0

x 10

LP0

4

LP0

LP0

LP0 3

LP0 LP0

2

LP0

1

(d) 0 1

1.1

1.2

1.3

1.4


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

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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.

1.45 1.4 1.35 1.3 1.25 50

100

150

200

250

300

Overlay Thickness [nm] Fig. 4. SRI corresponding to the maximum sensitivity versus the overlay thickness for first 7 cladding modes.

Experimental confirmation of the reported numerical analysis has been achieved by using sPS overlays and dip coating technique as described in detail in the next sections. 3. Sensitive overlay

Syndiotactic Polystyrene is a polymorph semi-crystalline polymer exhibiting four different crystalline forms: α and β characterized by a transplanar conformation of the chains and two others δ and γ consisting of s(2/1)2 TTGG helical chains [29]. Among these crystalline structures the δ form raises particular interest, as it is nanoporous [30]. In this form sPS can adsorb reversibly certain analytes, whose size and shape well fit the nanocavities establishing specific host guest interactions, when exposed to vapor or liquid environment where these compounds are present even in traces. The nanoporous structure of the δ sPS is responsible of its higher sorption capability respect with other semi-crystalline polymers as it allows the penetration not only in the amorphous phase but also within the crystalline domains that usually are more compact and then impervious to penetrants. However a previous study [31, 32] showed that, for low concentration of analyte, δ form sPS exhibits sorption levels in the amorphous phase much lower than that of the crystalline phase; thus, when exposed to very low concentration of analyte it can be safely assumed that the sorption occurs almost completely in the sole crystalline phase where only those molecules of proper dimensions and which are able to establish host guest interaction with the nanocavities, like low molecular chlorinated or aromatic compounds, are admitted to pass. 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, 33, 34]. 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] :

n2 −1 N = ρβ 2 n + 1 3Mε

(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.

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0.25 LP for SRI=1 02 LP for SRI=1.40 02 LP for SRI=1.45

Transversal Fields (a.u.)

0.2

02

0.15 0.1

(a)

0.05 0 -0.05 -0.1 0

10

20 30 40 50 Optical Fiber Radius [μm]

60

70


0.15 0.1

(b)

0.05 0 -0.05 LP for SRI=1 03 LP for SRI=1.40 03 LP for SRI=1.45

-0.1

03

0

10


60

70

0.15


0.1

(c)

0.05 0 -0.05 LP for SRI=1 04 LP for SRI=1.40 04 LP for SRI=1.45

-0.1

04

0

10


60

70

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.

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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]:

(U ) 3 t=k 1 (ρ ) 2 2

(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].

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0

Transmission [dB]

-2 -4

Bare Coated

-6 -8 -10 1270

1290

1310

1330

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

Figure 8 reports the transmission spectra of the 150nm coated LPG for different values of SRI in the range 1.33-1.472, while a zoom on the LP07 and LP08 modes in the wavelength range 1350-1680 nm is shown in Fig. 9. In both figures the LP0i mode has been marked with i, i’, and so on for the different SRI cases. In agreement with the numerical formulation, as the SRI reaches approximatively 1.42, corresponding to the transition value, a larger wavelength shift in all the attenuation bands is observed. In particular, it is worth to note how, at the end of the transition for a SRI value approaching 1.45, all the attenuation bands, related to the novel modes distribution, demonstrate a blue shift able to quasi completely recover the spectral configuration before the transition. 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.

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0

Transmission [dB]

III

IV 5I 6IV66II I 7 7III 6 -5 5 7II

7

6

-10

8IV

8III

I

8II

-15

1.33 1.364 1.399 1.42 1.472

7

-20 1200

1300

1400

1500

8I

8

1600

Wavelength [nm] Fig. 8. Transmission spectra of a 150nm sPS coated LPG for different values of SRI in the range 1.33-1.472

0

Transmission [dB]

-5 7III

8V

7II

-10 -15 -20

VII

8

7I

7

8IV 8III

8VI

1.33 1.364 1.399 1.42 1.431 1.439 1.449 1.472

8II 8I

8

-25 1350 1400 1450 1500 1550 1600 1650 Wavelength [nm] Fig. 9. Transmission spectra of a 150nm sPS coated LPG zoomed on LP07 and LP08 cladding modes

A more clear understanding of attenuation bands behavior is provided in Fig. 10, where the wavelength shifts are reported. Far from the transition region, the presence of the HRI coating leads to a slight increase in the SRI sensitivity of a factor ranging from 2 to over 10 as the mode order decreases. In addition, within the transition region, a relevant enhancement in the SRI sensitivity is observed. As the mode order decreases, the sensitivity enhancement around 1.43 was estimated to be 8 to 70 times the sensitivity of the uncoated LPG at the same SRI, while the sensitivity gain respect to the maximum sensitivity of the uncoated LPG (around 1.45) was estimated to be a factor ranging from 4 to over 10. In Fig. 11 is reported the behavior of the loss peak for different cladding modes. In particular, the attenuation band related to the LP05 cladding mode, during the transition, moves to shorter wavelengths and disappears from the spectral window under investigation. With regard to the attenuation bands amplitudes, as previously explained, for SRI approaching the cladding one, a significative disagreement was found between the numerical analysis and the experimental one. In this

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case, a more complex investigation is required taking into account the nature of the core mode coupling with radiation cladding modes. This aspect is actually under investigation and will be the subject of further work based on the extension of the theoretical model proposed by Koyamada et al. [26, 27] in the case of bare LPGs. 1700

LP08

Wavelength [nm]

1600 1500 1400

LP07

1300

LP06

1200

LP05

1100 1

1.1

1.2

1.3

1.4

1.5

Surrounding Refractive Index Fig. 10. Wavelength shift of different cladding modes for the LPG coated with a 150nm sPS overlay versus SRI.

-5 Loss Peak [dB]

LP05 LP06

-10

-15

LP07 -20 1

1.1

1.2

1.3

1.4

1.5

Surrounding Refractive Index 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 #8237 - $15.00 USD

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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. 1700

LP08

Wavelength [nm]

1600 1500

LP07

1400 1300 1200 1100 1

LP06 LP05

1.1

1.2

1.3

1.4

1.5

Surrounding Refractive Index Fig. 12. Wavelength shift of different cladding modes for the LPG coated with a 140nm sPS overlay versus SRI.

1700

Wavelength [nm]

1650

LP08 1600 1550 1500 1450 1400 1

1.1

1.2

1.3

1.4

1.5

Surrounding Refractive Index 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 #8237 - $15.00 USD

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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.

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