Abstract

We propose a refractive-index sensor that operates on the principle of exciting the long-range surface plasmon mode of a metal-coated waveguide with a long-period grating formed in the waveguide, where the wavelength at which the mode excitation occurs serves as a measure of the refractive index of the external medium. We analyze the sensor with a coupled-mode theory and highlight the effects of the waveguide parameters on the loss of the surface plasmon mode and the performance of the sensor. Our results show that the sensor can provide a sharp resonance for high precision measurements and a high sensitivity comparable to that of an optimized bulk prism-based surface plasmon sensor. Our sensor also offers much flexibility in the choice of waveguide parameters for different applications.

©2009 Optical Society of America

1. Introduction

A long-period fiber grating (LPFG) formed in a single-mode fiber is able to couple light from the guided core mode to selected cladding modes at specific resonance wavelengths and thus produce distinct attenuation bands in the transmission spectrum [1]. As the propagation characteristics of the cladding modes are sensitive to the surrounding medium, LPFGs have attracted much interest for sensing applications [2, 3]. To take advantage of the material and geometry flexibility offered by the optical waveguide technology, the idea of forming long-period gratings in planar waveguides, namely, long-period waveguide gratings (LPWGs), has been proposed [4]. Over the last few years, a range of LPWG devices, which include, for example, variable attenuators [5, 6], tunable optical filters [7 – 9], and add-drop multiplexers [10, 11], have emerged. The possibility of using an LPWG for refractive-index sensing has also been studied [12]. In this paper, we propose a refractive-index sensor based on LPWG-assisted coupling to the long-range surface plasmon mode of a metal-coated waveguide.

Surface plasmons (SPs) (or surface plasmon polaritons) are light waves propagating along the interface between a metal and a dielectric [13]. Excitation of SPs forms the basis of the widely known surface plasmon resonance (SPR) technique, which has found extensive applications in the area of chemical and bio-molecular sensing [14, 15]. The most common SP sensor configuration consists of a metal film sandwiched between two index-matched (or nearly index-matched) dielectrics, so that two bound modes, the anti-symmetric SP mode and the symmetric SP mode, can be excited through a high-index prism or a diffraction grating [16]. The symmetric SP mode, which is the higher order mode, has a lower loss than the antisymmetric SP mode and therefore can propagate over a longer distance. For this reason, the symmetric SP mode is referred to as the long-range SP (LRSP) mode, while the anti- symmetric SP mode the short-range SP (SRSP) mode. For sensing applications, the lower loss of the LRSP mode results in a sharper SPR and hence a higher precision [17, 18]. The use of the LRSP mode can also lead to a high sensitivity for the measurement of refractive index changes. For example, a sensitivity of 5.7 × 104 nm/RIU (refractive-index unit) has been achieved recently with an optimized prism-based LRSP sensor [19], which is higher than the sensitivity of a SRSP sensor (6 × 103 nm/RIU) by an order of magnitude [18]. Sensors based on evanescent-field coupling to the SP modes have also been proposed and realized in optical waveguides and fibers [14, 20 – 23], which offer advantages such as compactness, ruggedness, and more freedom in the fabrication and design. However, the reported waveguide/fiber SP sensors are less sensitive, compared with the prism-based SP sensors, because a high-index dielectric overlay or a complex multilayer structure is needed to achieve sufficient evanescent-field coupling [14]. As SP modes can be considered as guided modes of a multilayer waveguide structure, they can be excited by a properly designed waveguide grating. It is a matter of choosing the grating pitch to excite the SP mode and there is no need to introduce extra layers. As such, a grating-assisted waveguide SP sensor should provide a good sensitivity. In fact, a refractive-index sensor based on the detection of the resonance of the SRSP mode excited by an LPWG has been proposed recently [24]. According to a recent analysis [25], however, a large loss in the cladding mode excited by a long-period grating can significantly broaden the resonance or even make it disappear (because most of the light coupled to the cladding mode is lost within one period of the grating and the resonance function of the grating is destroyed). Therefore, the large loss of the SRSP mode excited by the LPWG is likely to weaken the SPR or even fail the sensor, but this consideration seems to be ignored in the theoretical model of the sensor [24]. The refractive-index sensor we propose in this paper is based on exciting the low-loss LRSP mode by an LPWG. Our sensor overcomes the problems arising from the large loss of the SRSP mode and, as a result, can offer a significantly higher refractive-index resolution. Our design examples give a sensitivity of -5 × 104 nm/RIU, which is comparable to that of an optimized prism-based LRSP sensor and much higher than that of waveguide/fiber SP sensors based on evanescent-field coupling. To analyze the sensor, we first find the modes of the waveguide structure of the sensor and then calculate the mode-coupling effect of the LPWG with a coupled-mode theory. We highlight the need of using a low-loss SP mode to achieve good performance. We also discuss how the performance of the sensor depends on the waveguide parameters, in particular, the metal thickness and the cladding thickness, which can be controlled effectively to modify the characteristics of the sensor for different applications. To our knowledge, our sensor is the first LPWG sensor that explores the LRSP mode.

2. Theoretical model and analysis

2.1 Waveguide modes

Figure 1(a) shows a five-layer slab waveguide structure, which consists of a substrate of refractive index n s, a guiding layer of refractive index n f and thickness d f, a cladding layer of refractive index n cl and thickness d cl, a thin metal film of refractive index n m and thickness d m, and an external medium of refractive index n ex that extends to infinity, where n f > n cl, n ex > n s. The index profile of the waveguide varies in the x direction and is invariant in both the y and z directions. A corrugated grating with period Λ and corrugation depth Δh is introduced on the surface of the guiding layer along the propagation direction z, as shown in Fig. 1(b). The metal used in our analysis is gold, which has a complex refractive index n m = 0.55 + 11.5j at the wavelength 1550 nm [26]. Gold is traditionally chosen for its good chemical resistance and stability. The values of the following waveguide parameters are fixed: n s = 1.444, n f = 1.535, n cl = 1.51, and d f = 2.0 μm, while the external index n ex, the metal thickness d m, and the cladding thickness d cl are allowed to vary. Because SP modes in a planar waveguide are transverse-magnetic (TM) waves, we consider only the TM modes of the waveguide. For the sake of simplicity, material dispersion is ignored and all the dielectric materials including the external medium are assumed to be lossless. The loss of the propagating wave is purely caused by the presence of the metal film. The slab waveguide model is chosen to illustrate the physical principle of the sensor; a practical sensor may employ a rectangular-core waveguide structure.

 figure: Fig. 1.

Fig. 1. (a) Refractive-index profile n(x) of a metal-coated planar waveguide, where (b) a corrugated long-period grating is introduced on the surface of the guiding layer (see the text for the definitions of the symbols).

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The eigenvalue equation of the composite five-layer waveguide structure is available and can be written in the form of a transfer matrix from which the mode indices and the field distributions for all the guided modes can be solved using an iterative method [27]. Figure 2(a) shows the magnetic-field distributions of all the TM modes for a waveguide with d m = 15 nm, d cl = 5.0 μm, and n ex = 1.51 at the wavelength 1550 nm, where the index profile of the waveguide is also shown as a reference. The waveguide supports only three TM modes. As shown in Fig. 2(a), the field of the first mode (green) is tightly confined around the metal film and can be identified as the SP mode derived from the anti-symmetric SP mode of a perfectly symmetric metal waveguide. Therefore, it is labeled here as the A-SP mode. This mode has a complex mode index N A-SP = 1.61915 + 1.96 × 10-2 j. As the real part of the mode index is much larger than the refractive indices of all the dielectric media, the presence of the guiding layer and the substrate has negligible effects on the field confinement. The imaginary part of the mode index gives a huge propagation loss of ~6900 dB/cm, which is obtained from the expression 8.686·(2π/λ)·Im(N) (in dB per unit length of waveguide), where λ is the operating wavelength and Im(N) is the imaginary part of the mode index N. The A-SP mode is the SRSP mode of the waveguide structure.

 figure: Fig. 2.

Fig. 2. (a) Magnetic-field (Hy) distributions of the A-SP, TM0, and TM1 modes of a metal-coated slab waveguide with n s = 1.444, n f = 1.535, n cl = 1.51, n ex = 1.51, d f = 2.0 μm, d cl = 5.0 μm, and d m = 15 nm at 1550 nm. (b) Magnetic-field distributions of the TM1 mode at different values of n ex.

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As shown in Fig. 2(a), the second mode (black) consists of no zero crossing in the field and is well confined in the guiding layer. It is identified as the TM0 mode of the waveguide. Its mode index is N 0 = 1.51862 + 6.69 × 10-7. The presence of the metal and the external medium has negligible effects on its field distribution. As expected, the TM0 mode has a very low loss (~0.2 dB/cm). The third mode (red) consists of a zero crossing in the field and is identified as the TM1 mode. Its mode index is N 1 = 1.51120 + 1.78 × 10-5 j. As the real part of the mode index is only slightly larger than the cladding index, the mode field spreads broadly into the cladding, the metal film, and the external medium. In fact, this mode exhibits a strong confinement around the metal film. The loss of the TM1 mode (~6.2 dB/cm) is much lower than that of the A-SP mode. It actually resembles the symmetric SP mode of a perfectly symmetric metal waveguide and therefore can be considered as the LRSP mode of the structure. Our result agrees with the previous finding that asymmetric waveguide structures can support LRSP modes [13, 28].

Figure 2(b) shows how the magnetic field of the TM1 mode depends on the refractive index of the external medium. When the external index n ex is sufficiently close to the cladding index n cl, the field is strong at the metal surface. On the other hand, when n ex gets lower and lower, the field at the metal surface becomes weaker and weaker and the mode approaches the TM1 mode of a conventional four-layer dielectric waveguide that does not contain the metal film [29]. Therefore, for sensor applications, the refractive index of the cladding material must be chosen to approximately match that of the external medium to be measured, so that the field of the LRSP mode can reach deeply into the external medium, which is essential for the achievement of a high sensitivity.

2.2 SPR analysis

To produce an SPR, the waveguide grating must be designed to couple light from the fundamental core mode to an SP mode. The pitch of the grating Λ is determined by the phase-matching condition

Λ=λ0Re(Nco)Re(Nsp),

where λ 0 is the SPR wavelength and N co and N sp are the mode indices of the core mode and the SP mode, respectively. The shift in the SPR is a measure of the external index, which affects mainly the mode index of the SP mode. For the SPR to be measurable with a good accuracy, the resonance dip should have a sufficiently large contrast. The transmission of a long-period grating with length L is given by [25]

T=[cos(ζL)+jσζsin(ζL)]exp[j(βcoσ)L]2,

where σ = (β co - β sp)/2 - π/Λ, ζ = (σ 2 + ∣κ2)1/2, and κ is the coupling coefficient of the grating [29]. β co and β sp are the propagation constants (complex numbers) of the core mode and the SP mode, respectively, i.e., β co = (2π/Λ)N co and β sp = (2π/λ)N sp.

To highlight the effects of the SP mode loss on the transmission spectrum, we calculate the transmission spectra from Eq. (2) at different values of the loss coefficient Im(N sp) for a grating with κL = 0.5π, L = 10 mm, Λ = 100 μm, and λ 0 = 1550 nm. The results are shown in Fig. 3(a). The contrast at λ 0 as a function of the loss coefficient Im(N sp) is shown in Fig. 3(b). The loss of the fundamental core mode is neglected in the calculation. Note that the results shown in Fig. 3 are quite general (i.e., independent of the waveguide parameters). As shown in Fig. 3, the contrast at λ 0 decreases and the bandwidth increases, as the SP mode loss increases. When the loss coefficient Im(N sp) reaches 10-3 or higher, the resonance dip becomes so weak that it can hardly be detected. Physically, when the SP mode becomes too lossy, most of the light coupled to the SP mode is lost within one period of the grating, which means that the resonance function of the grating is destroyed (in which case, the grating functions as no more than an isotropic light scattering structure and no resonance dip can be seen). For example, to excite the A-SP mode in our waveguide, the pitch required is Λ = 15.4 μm at the wavelength 1550 nm. Over a grating period, the A-SP mode experiences a loss of 6900 × 10-4 × 15.4 ≃ 10.6 dB, which practically depletes all the A-SP light. While it is possible to increase the strength of the grating by using an over-coupled grating, i.e., κL > 0.5π, our calculation shows that, with Im(N sp) ~ 10-2, practically no resonance dip can be seen even with κL as large as 3π. Therefore, our waveguide sensor will not work if the grating is designed for the A-SP mode, which has a loss coefficient of the order of 10 . On the other hand, to excite the LRSP mode (TM1), the pitch required is Λ = 209 μm. The loss of the TM1 mode over a grating period is 6.2 × 10-4 × 209 ≃ 0.13 dB, which is negligible. Therefore, for our sensor to generate a distinct SPR, we must design the grating to excite the TM1 (LRSP) mode, i.e., we must take N co = N 0 and N sp = N 1 in Eqs. (1) and (2).

 figure: Fig. 3.

Fig. 3. (a) Normalized transmission spectra at different values of the loss coefficient Im(N sp) for a 10 mm long grating with κL = 0.571 and (b) the contrast at λ 0 as a function of the loss coefficient Im(N sp), showing how the contrast decreases with an increase in the loss of the SP mode.

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2.3 Sensitivity analysis

By means of a perturbation theory [7], the sensitivity of the sensor, i.e., the change of the SPR λ 0 with the external index n ex, can be written as

dλ0dnex=(η0exη1ex)γΛ,

where η 0ex and η 1ex are the fractional powers of the TM0 and TM1 modes in the external medium, respectively, and γ = 1/{1 - Λd[Re(N 0) - Re(N 1)]/dλ} is the modal dispersion factor. The TM0 mode has a negligible power in the external medium, so η 0ex - η 1ex ~ -η 1ex. According to Eq. (3), the sensitivity of the sensor depends on the difference in the dispersion characteristics between the TM0 and TM1 modes, which is a waveguide effect and can be tuned over a wide range by changing the waveguide dimensions [7, 29]. The material dispersion produces only a secondary effect on the sensitivity, which is small and can be ignored in the analysis without causing a significant error. A high sensitivity can be achieved in principle at an arbitrary wavelength by using a proper set of waveguide parameters. On the other hand, the sensitivity of a prism-based SP sensor depends mainly on the modal dispersion of the SP mode and therefore is highly wavelength dependent [30].

Figure 4(a) shows the real and imaginary parts of the mode indices of the TM0 and TM1 modes as functions of the external index n ex. The metal thickness d m and the cladding thickness d cl are assumed to be 15 nm and 5 μm, respectively. As expected, the real part of the mode index of the TM0 mode is insensitive to n ex, as the TM0 mode is well confined in the guiding layer. Its imaginary part decreases slowly as n ex increases and maintains at a low value. On the other hand, the real part of the mode index of the TM1 mode increases with n ex quickly, especially when n ex approaches n cl, where the imaginary part drops rapidly at the same time. These are the results of dragging the field of the TM1 mode towards the external medium as n ex increases, as shown in Fig. 2(b). There is a small kink along the loss curve of the TM1 mode, which is due to the competition of the light confinements in the metal film and the external medium as n ex approaches n cl - see Fig. 2(b). Figure 4(b) shows the dependence of the sensitivity and the contrast at λ 0 on the external index n ex. According to Eq. (3), the sensitivity does not depend on the grating length L and the grating strength κL. In the calculation of the contrast, we assume L = 10 mm and κL = 0.5%. As shown in Fig. 4(a) and (b), the imaginary part of the mode index of the TM1 mode and the contrast at λ 0 depend on the external index similarly, which is consistent with the fact that a lower loss coefficient leads to a higher contrast – see Fig. 3(b). The contrast is larger than 3 dB when n ex is larger than 1.5. Figure 4 also shows that the real part of the mode index of the TM1 mode and the refractive-index sensitivity depend on the external index similarly. This is expected since both of them increase with the fractional power of the TM1 mode in the external medium. As shown in Fig. 4, to obtain a high contrast at λ 0 and a high refractive-index sensitivity, the external index must be close enough to the cladding index. In other words, the cladding index of the waveguide must be chosen to match the index of the external medium to be measured.

 figure: Fig. 4.

Fig. 4. (a) Dependence of Re(N) and Im(N) of the TM0 and TM1 modes on the external refractive index n ex for a metal-coated slab waveguide with n s = 1.444, n f = 1.535, n cl = 1.51, d f = 2.0 μm, d cl = 5.0 μm, d m = 15 nm, and λ = 1550 nm. (b) Dependence of the sensitivity and the contrast at λ 0 on the external refractive index n ex.

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3. Discussion of waveguide parameters

The performance of the sensor depends sensitively on the metal film thickness and the cladding thickness. We discuss the effects of these two design parameters in this section.

3.1 Metal film thickness

Figure 5(a) shows the variations of Re(N 0), Im(N 0), Re(N 1), and Im(N 1) with the metal film thickness d m, where the cladding thickness d cl and the external index n ex are assumed to be 5 μm and 1.51, respectively. When the metal film is thinner than 6 nm, the TM1 mode becomes cut off, i.e., Re(N 1) < 1.51. A thicker metal film results in a tighter confinement of the TM1 mode around the metal film and thus increases both Re(N 1) and Im(N 1). The loss coefficient of the TM0 mode, Im(N 0), also increases with d m, but the real part Re(N 0) is insensitive to d m. Figure 5(b) shows the variations of the refractive-index sensitivity and the grating contrast at λ 0 with d m. The sensitivity decreases initially as d m increases and then increases with d m. The grating contrast decreases with d m as a result of Im(N 1) increasing. As shown in Fig. 5, a thin enough metal film should be used to keep the losses of the modes low. For the present example, the metal film should not be thicker than 25 nm to ensure a grating contrast larger than 5 dB. The corresponding sensitivity is 5 – 6 × 104 nm/RIU.

 figure: Fig. 5.

Fig. 5. (a) Variations of Re(N) and Im(N) of the TM0 and TM1 modes with the metal film thickness d m for a waveguide with n s = 1.444, n f = 1.535, n cl = 1.51, d f = 2.0 μm, d cl = 5.0 μm, n ex = 1.51, operating at λ = 1550 nm. (b) Variations of the sensitivity and the grating contrast with the metal film thickness d m.

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3.2 Cladding thickness

The cladding serves mainly as a buffer layer to isolate the TM0 mode from the lossy metal film. Figure 6(a) shows the variations of Re(N 0), Im(N 0), Re(N 1), and Im(N 1) with the cladding thickness d cl, where the metal film thickness d m and the external index n ex are assumed to be 15 nm and 1.51, respectively. As expected, the loss of the TM0 mode increases rapidly as d cl decreases. Therefore, a thick enough cladding must be used to ensure a low loss for the TM0 mode. On the other hand, the loss of the TM1 mode depends only weakly on d cl - except near the cutoff value ~2.5 μm. The real parts of the mode indices are insensitive to d cl. Figure 6(b) shows the variations of the refractive-index sensitivity and the grating contrast with d cl. Because the fractional power of the TM1 mode in the external medium decreases with an increase in d cl, the sensitivity decreases as d cl increases. Therefore, the cladding should not be too thick. A thick cladding also leads to a weak field overlap between the TM0 mode and the TM1 mode and hence reduces the efficiency of the grating [29]. As an example, assuming a corrugation depth of Δh = 100 nm, for d cl = 10 μm, the grating length required to achieve κL = 0.5π is ~30 mm. By halving the cladding thickness to d cl = 5 μm, the grating length required is reduced by 4 times to ~7.5 mm. The grating contrast follows the loss coefficient Im(N 1) and, therefore, depends only weakly on d cl, except near the cutoff value. The grating contrast depends mainly on the metal film thickness, as shown in Fig. 5(b).

 figure: Fig. 6.

Fig. 6. (a) Variations of Re(N) and Im(N) of the TM0 and TM1 modes with the cladding thickness d cl for a waveguide with n s = 1.444, n f = 1.535, n cl = 1.51, d f = 2.0 μm, d m = 15 nm, n ex = 1.51, operating at λ = 1550 nm. (b) Variations of the sensitivity and the grating contrast with the cladding thickness d cl.

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3.3 Design examples

In a practical sensor design, the waveguide parameters should be chosen appropriately to keep the losses of the TM0 and TM1 modes as small as possible and at the same time achieve a large enough sensitivity. According to the results given in the previous sections, we choose a metal film thickness d m = 15 nm and a cladding thickness d cl = 5 μm. We then use a grating pitch of Λ = 221 μm to generate a rejection band at a wavelength of ~1550 nm for n ex ~ 1.51. The corrugation depth of the grating is assumed to be Δh = 100 nm, a typical value achieved by reactive-ion etching [7, 10]. With such a small corrugation depth (5% of the film thickness d f), the coupled-mode theory is accurate for the calculation of the grating characteristics [29]. We finally choose a grating length of L = 8 mm, so that the coupling strength of the grating is equal to κL ~ 0.5π. Figure 7(a) shows the transmission spectra of the LRSP sensor calculated at different values of n ex and Fig. 7(b) shows the dependence of the SPR wavelength on n ex. The SPR wavelength decreases as n ex increases with a sensitivity of -4.9 × 104 nm/RIU and the 3-dB bandwidths of the resonance dips are ~15 nm.

We present another example to demonstrate the possibility of performing sensing in an aqueous solution (i.e., n ex ~ 1.33). The operating wavelength is set at ~830 nm, where the refractive index of gold is n m = 0.188 + 5.39j [26]. Following similar considerations in the previous example, we come up with the following waveguide and grating parameters: n s = 1.29, n f = 1.35, n cl = 1.33, d f = 2.0 μm, d cl = 2.0 μm, d m = 15 nm, Λ = 95 μm, Δh = 100 nm, and L = 6 mm. Low-index materials like Teflon AZ amorphous fluoropolymers [19], porous silicon [31], and commercially available UV cured adhesives [32] are suitable for the realization of the waveguide. Figure 8(a) shows the transmission spectra of the sensor calculated at different values of n ex and Fig. 8(b) shows the dependence of the resonance wavelength on n ex. The sensitivity of our sensor is -4.8 × 104 nm/RIU, which is comparable to that demonstrated with an optimized prism-based sensor using the LRSP mode operated at a similar wavelength [19]. The 3-dB bandwidths of the resonance dips shown in Fig. 8(a) are ~20 nm, which are substantially narrower than those of the SPR lines of the optimized prism-based sensor (~60 nm) [19], which implies that our sensor can provide a higher precision (or resolution) for refractive-index measurement. The bandwidth of our sensor can be further reduced by increasing the grating length. The low loss of the LRSP mode together with the wavelength-selection property of the grating contributes to the sharp SPR exhibited by our sensor.

 figure: Fig. 7.

Fig. 7. (a) Transmission spectra of an LPWG-assisted waveguide LRSP sensor with n s = 1.444, n f = 1.535, n cl = 1.51, d f = 2.0 μm, d cl = 5.0 μm, d m = 15 nm, Λ = 221 μm, Δh = 100 nm, and L = 8 mm, calculated at different values of external index n ex. (b) Variation of the SPR wavelength with the external index n ex.

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 figure: Fig. 8.

Fig. 8. (a) Transmission spectra of an LPWG-assisted waveguide LRSP sensor with n s = 1.29, n f = 1.35, n cl = 1.33, d f = 2.0 μm, d cl = 2.0 μm, d m = 15 nm, Λ = 95 μm, Δh = 100 nm, and L = 6 mm, calculated at different values of external index n ex. (b) Variation of the SPR wavelength with the external index n ex.

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4. Conclusion

We propose an integrated-optic refractive-index sensor based on the excitation of the low-loss LRSP mode of a metal-coated waveguide with a long-period grating. We analyze in detail the characteristics of the sensor and discuss the effects of the key waveguide parameters on the performance of the sensor. Our analysis shows the need of using the LRSP mode for achieving good performance because of its low loss. Compared with an optimized bulk prism-based LRSP sensor, our sensor can provide almost the same high refractive-index sensitivity and yet a much sharper SPR, which is important for ultra-high precision applications. Thanks to the use of an LPWG, the waveguide structure of our sensor is much simpler than those based on evanescent-field coupling. The flexibility of the optical waveguide technology allows a wide range of materials (and hence refractive indices) to be employed to tailor for different applications.

Acknowledgment

This research was supported by a research grant from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. CityU 111907].

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24. G. Nemova and R. Kashyap, “Theoretical model of a planar integrated refractive index sensor based on surface plasmon-polariton excitation with a long period grating,” J. Opt. Soc. Am. B 24, 2696–2701 (2007). [CrossRef]  

25. M. Kulishov, V. Grubsky, J. Schwartz, X. Daxhelet, and D. V. Plant, “Tunable waveguide transmission gratings based on active gain control,” IEEE J. Quantum Electron. 40, 1715–1724 (2004). [CrossRef]  

26. E. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

27. E. Anemogiannis and E. N. Glytsis, “Multilayer waveguide: efficient numerical analysis of general structure,” J. Lightwave Technol. 10, 1344–1351 (1992). [CrossRef]  

28. N. M. Lyndin, I. F. Salakhutdinov, V.A. Sychugov, B.A. Usievich, F.A. Pudonin, and O. Parriaux, “Long-range surface plasmons in asymmetric layered metal-dielectric structures,” Sens. Actuators B 54, 37–42 (1999). [CrossRef]  

29. Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21, 3399–3405 (2003). [CrossRef]  

30. J. Homola, Surface Plasmon Resonance Based Sensors (Springer, 2006). [CrossRef]  

31. A. Loni, L. T. Canham, M. G. Berger, R. Arens-Fischer, H. Munder, H. Lüth, H. F. Arrand, and T. M. Benson, “Porous silicon multilayer optical waveguide,” Thin Solid Films 276, 143–146 (1996). [CrossRef]  

32. MY Polymers Ltd., http://www.mypolymers.com.

References

  • View by:

  1. 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]
  2. H. K. 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]
  3. S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14, R49–R61 (2003).
    [Crossref]
  4. V. Rastogi and K. S. Chiang, “Long-period gratings in planar optical waveguides,” Appl. Opt. 41, 6351–6355 (2002).
    [Crossref] [PubMed]
  5. M.-S. Kwon and S.-Y. Shin, “Tunable polymer waveguide notch filter using a thermooptic long-period grating,” IEEE Photon. Technol. Lett. 17, 145–147 (2005).
    [Crossref]
  6. K. S. Chiang, C. K. Chow, Q. Liu, H. P. Chan, and K. P. Lor, “Band-rejection filter with widely tunable center wavelength and contrast using metal long-period grating on polymer waveguide,” IEEE Photon. Technol. Lett. 18, 1109–1111 (2006).
    [Crossref]
  7. Q. Liu, K. S. Chiang, K. P. Lor, and C. K. Chow, “Temperature sensitivity of a long-period waveguide grating in a channel waveguide,” Appl. Phys. Lett. 86, 241115 (2005).
    [Crossref]
  8. Y. M. Chu, K. S. Chiang, and Q. Liu, “Widely tunable optical bandpass filter by use of polymer long-period waveguide gratings,” Appl. Opt. 45, 2755–2760, (2006).
    [Crossref] [PubMed]
  9. W. Jin, K. S. Chiang, and Q. Liu, “Electro-optic long-period waveguide gratings in lithium niobate,” Opt. Express 16, 20409–20417 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-25-20409.
    [Crossref] [PubMed]
  10. Y. Bai, Q. Liu, K. P. Lor, and K. S. Chiang, “Widely tunable long-period waveguide grating couplers,” Opt. Express 14, 12644–12654 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12644.
    [Crossref] [PubMed]
  11. C. K. Chow, K. S. Chiang, Q. Liu, K. P. Lor, and H. P. Chan, “UV-written long-period waveguide grating coupler for broadband add/drop multiplexing,” Opt. Commun. 282, 378–381 (2009).
    [Crossref]
  12. M. S. Kwon and S. Y. Shin, “Refractive index sensitivity measurement of a long-period waveguide grating,” IEEE Photon. Technol. Lett. 17, 1923–1925 (2005).
    [Crossref]
  13. J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
    [Crossref]
  14. J. Homola, S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999).
    [Crossref]
  15. J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377, 528–539 (2003).
    [Crossref] [PubMed]
  16. K. R. Welford and J. R. Sambles, “Coupled surface plasmons in a symmetric system,” J. Mod. Opt. 35, 1467–1483 (1988).
    [Crossref]
  17. K. Matsubara, S. Kawata, and S. Minami, “Multilayer system for a high-precision surface plasmon resonance sensor,” Opt. Lett. 15, 75–77 (1990).
    [Crossref] [PubMed]
  18. R. Slavík and J. Homola, “Optical multilayers for LED-based surface plasmon resonance sensors,” Appl. Opt. 45, 3752–3759 (2006).
    [Crossref] [PubMed]
  19. R. Slavík and J. Homola, “Ultrahigh resolution long range surface plasmon-based sensor,” Sens. Actuators B 123, 10–12 (2007).
    [Crossref]
  20. M. N. Weiss, R. Srivastava, and H. Groger, “Experimental investigation of surface plasmon-based integrated-optic humidity sensor,” Electron. Lett. 32, 842–843 (1996).
    [Crossref]
  21. O. Hugon, P. Benech, and H. Gagnaire, “Surface plasmon chemical/biological sensor in integrated optics,” Sens. Actuators B 51, 316–320 (1998).
    [Crossref]
  22. R. Slavík, J. Homola, J. Ctyroky, and E. Brynda, “Novel spectral fiber optic sensor based on surface plasmon resonance,” Sens. Actuators B 74, 106–111 (2001).
    [Crossref]
  23. Rajan, A. K. Sharma, and B. D. Gupta, “Fibre optic sensor based on long-range surface plasmon resonance: a theoretical analysis,” J. Opt. A: Pure Appl. Opt. 9, 682–687 (2007).
    [Crossref]
  24. G. Nemova and R. Kashyap, “Theoretical model of a planar integrated refractive index sensor based on surface plasmon-polariton excitation with a long period grating,” J. Opt. Soc. Am. B 24, 2696–2701 (2007).
    [Crossref]
  25. M. Kulishov, V. Grubsky, J. Schwartz, X. Daxhelet, and D. V. Plant, “Tunable waveguide transmission gratings based on active gain control,” IEEE J. Quantum Electron. 40, 1715–1724 (2004).
    [Crossref]
  26. E. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
  27. E. Anemogiannis and E. N. Glytsis, “Multilayer waveguide: efficient numerical analysis of general structure,” J. Lightwave Technol. 10, 1344–1351 (1992).
    [Crossref]
  28. N. M. Lyndin, I. F. Salakhutdinov, V.A. Sychugov, B.A. Usievich, F.A. Pudonin, and O. Parriaux, “Long-range surface plasmons in asymmetric layered metal-dielectric structures,” Sens. Actuators B 54, 37–42 (1999).
    [Crossref]
  29. Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21, 3399–3405 (2003).
    [Crossref]
  30. J. Homola, Surface Plasmon Resonance Based Sensors (Springer, 2006).
    [Crossref]
  31. A. Loni, L. T. Canham, M. G. Berger, R. Arens-Fischer, H. Munder, H. Lüth, H. F. Arrand, and T. M. Benson, “Porous silicon multilayer optical waveguide,” Thin Solid Films 276, 143–146 (1996).
    [Crossref]
  32. MY Polymers Ltd., http://www.mypolymers.com.

2009 (1)

C. K. Chow, K. S. Chiang, Q. Liu, K. P. Lor, and H. P. Chan, “UV-written long-period waveguide grating coupler for broadband add/drop multiplexing,” Opt. Commun. 282, 378–381 (2009).
[Crossref]

2008 (1)

2007 (3)

R. Slavík and J. Homola, “Ultrahigh resolution long range surface plasmon-based sensor,” Sens. Actuators B 123, 10–12 (2007).
[Crossref]

Rajan, A. K. Sharma, and B. D. Gupta, “Fibre optic sensor based on long-range surface plasmon resonance: a theoretical analysis,” J. Opt. A: Pure Appl. Opt. 9, 682–687 (2007).
[Crossref]

G. Nemova and R. Kashyap, “Theoretical model of a planar integrated refractive index sensor based on surface plasmon-polariton excitation with a long period grating,” J. Opt. Soc. Am. B 24, 2696–2701 (2007).
[Crossref]

2006 (4)

2005 (3)

M.-S. Kwon and S.-Y. Shin, “Tunable polymer waveguide notch filter using a thermooptic long-period grating,” IEEE Photon. Technol. Lett. 17, 145–147 (2005).
[Crossref]

Q. Liu, K. S. Chiang, K. P. Lor, and C. K. Chow, “Temperature sensitivity of a long-period waveguide grating in a channel waveguide,” Appl. Phys. Lett. 86, 241115 (2005).
[Crossref]

M. S. Kwon and S. Y. Shin, “Refractive index sensitivity measurement of a long-period waveguide grating,” IEEE Photon. Technol. Lett. 17, 1923–1925 (2005).
[Crossref]

2004 (1)

M. Kulishov, V. Grubsky, J. Schwartz, X. Daxhelet, and D. V. Plant, “Tunable waveguide transmission gratings based on active gain control,” IEEE J. Quantum Electron. 40, 1715–1724 (2004).
[Crossref]

2003 (3)

Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21, 3399–3405 (2003).
[Crossref]

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377, 528–539 (2003).
[Crossref] [PubMed]

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

2002 (1)

2001 (1)

R. Slavík, J. Homola, J. Ctyroky, and E. Brynda, “Novel spectral fiber optic sensor based on surface plasmon resonance,” Sens. Actuators B 74, 106–111 (2001).
[Crossref]

1999 (2)

N. M. Lyndin, I. F. Salakhutdinov, V.A. Sychugov, B.A. Usievich, F.A. Pudonin, and O. Parriaux, “Long-range surface plasmons in asymmetric layered metal-dielectric structures,” Sens. Actuators B 54, 37–42 (1999).
[Crossref]

J. Homola, S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999).
[Crossref]

1998 (2)

H. K. 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]

O. Hugon, P. Benech, and H. Gagnaire, “Surface plasmon chemical/biological sensor in integrated optics,” Sens. Actuators B 51, 316–320 (1998).
[Crossref]

1996 (3)

M. N. Weiss, R. Srivastava, and H. Groger, “Experimental investigation of surface plasmon-based integrated-optic humidity sensor,” Electron. Lett. 32, 842–843 (1996).
[Crossref]

A. Loni, L. T. Canham, M. G. Berger, R. Arens-Fischer, H. Munder, H. Lüth, H. F. Arrand, and T. M. Benson, “Porous silicon multilayer optical waveguide,” Thin Solid Films 276, 143–146 (1996).
[Crossref]

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]

1992 (1)

E. Anemogiannis and E. N. Glytsis, “Multilayer waveguide: efficient numerical analysis of general structure,” J. Lightwave Technol. 10, 1344–1351 (1992).
[Crossref]

1990 (1)

1988 (1)

K. R. Welford and J. R. Sambles, “Coupled surface plasmons in a symmetric system,” J. Mod. Opt. 35, 1467–1483 (1988).
[Crossref]

1986 (1)

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[Crossref]

Anemogiannis, E.

E. Anemogiannis and E. N. Glytsis, “Multilayer waveguide: efficient numerical analysis of general structure,” J. Lightwave Technol. 10, 1344–1351 (1992).
[Crossref]

Arens-Fischer, R.

A. Loni, L. T. Canham, M. G. Berger, R. Arens-Fischer, H. Munder, H. Lüth, H. F. Arrand, and T. M. Benson, “Porous silicon multilayer optical waveguide,” Thin Solid Films 276, 143–146 (1996).
[Crossref]

Arrand, H. F.

A. Loni, L. T. Canham, M. G. Berger, R. Arens-Fischer, H. Munder, H. Lüth, H. F. Arrand, and T. M. Benson, “Porous silicon multilayer optical waveguide,” Thin Solid Films 276, 143–146 (1996).
[Crossref]

Bai, Y.

Benech, P.

O. Hugon, P. Benech, and H. Gagnaire, “Surface plasmon chemical/biological sensor in integrated optics,” Sens. Actuators B 51, 316–320 (1998).
[Crossref]

Benson, T. M.

A. Loni, L. T. Canham, M. G. Berger, R. Arens-Fischer, H. Munder, H. Lüth, H. F. Arrand, and T. M. Benson, “Porous silicon multilayer optical waveguide,” Thin Solid Films 276, 143–146 (1996).
[Crossref]

Berger, M. G.

A. Loni, L. T. Canham, M. G. Berger, R. Arens-Fischer, H. Munder, H. Lüth, H. F. Arrand, and T. M. Benson, “Porous silicon multilayer optical waveguide,” Thin Solid Films 276, 143–146 (1996).
[Crossref]

Bhatia, V.

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]

Brynda, E.

R. Slavík, J. Homola, J. Ctyroky, and E. Brynda, “Novel spectral fiber optic sensor based on surface plasmon resonance,” Sens. Actuators B 74, 106–111 (2001).
[Crossref]

Bucholtz, F.

Burke, J. J.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[Crossref]

Canham, L. T.

A. Loni, L. T. Canham, M. G. Berger, R. Arens-Fischer, H. Munder, H. Lüth, H. F. Arrand, and T. M. Benson, “Porous silicon multilayer optical waveguide,” Thin Solid Films 276, 143–146 (1996).
[Crossref]

Chan, H. P.

C. K. Chow, K. S. Chiang, Q. Liu, K. P. Lor, and H. P. Chan, “UV-written long-period waveguide grating coupler for broadband add/drop multiplexing,” Opt. Commun. 282, 378–381 (2009).
[Crossref]

K. S. Chiang, C. K. Chow, Q. Liu, H. P. Chan, and K. P. Lor, “Band-rejection filter with widely tunable center wavelength and contrast using metal long-period grating on polymer waveguide,” IEEE Photon. Technol. Lett. 18, 1109–1111 (2006).
[Crossref]

Chiang, K. S.

C. K. Chow, K. S. Chiang, Q. Liu, K. P. Lor, and H. P. Chan, “UV-written long-period waveguide grating coupler for broadband add/drop multiplexing,” Opt. Commun. 282, 378–381 (2009).
[Crossref]

W. Jin, K. S. Chiang, and Q. Liu, “Electro-optic long-period waveguide gratings in lithium niobate,” Opt. Express 16, 20409–20417 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-25-20409.
[Crossref] [PubMed]

Y. Bai, Q. Liu, K. P. Lor, and K. S. Chiang, “Widely tunable long-period waveguide grating couplers,” Opt. Express 14, 12644–12654 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12644.
[Crossref] [PubMed]

Y. M. Chu, K. S. Chiang, and Q. Liu, “Widely tunable optical bandpass filter by use of polymer long-period waveguide gratings,” Appl. Opt. 45, 2755–2760, (2006).
[Crossref] [PubMed]

K. S. Chiang, C. K. Chow, Q. Liu, H. P. Chan, and K. P. Lor, “Band-rejection filter with widely tunable center wavelength and contrast using metal long-period grating on polymer waveguide,” IEEE Photon. Technol. Lett. 18, 1109–1111 (2006).
[Crossref]

Q. Liu, K. S. Chiang, K. P. Lor, and C. K. Chow, “Temperature sensitivity of a long-period waveguide grating in a channel waveguide,” Appl. Phys. Lett. 86, 241115 (2005).
[Crossref]

Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21, 3399–3405 (2003).
[Crossref]

V. Rastogi and K. S. Chiang, “Long-period gratings in planar optical waveguides,” Appl. Opt. 41, 6351–6355 (2002).
[Crossref] [PubMed]

Chow, C. K.

C. K. Chow, K. S. Chiang, Q. Liu, K. P. Lor, and H. P. Chan, “UV-written long-period waveguide grating coupler for broadband add/drop multiplexing,” Opt. Commun. 282, 378–381 (2009).
[Crossref]

K. S. Chiang, C. K. Chow, Q. Liu, H. P. Chan, and K. P. Lor, “Band-rejection filter with widely tunable center wavelength and contrast using metal long-period grating on polymer waveguide,” IEEE Photon. Technol. Lett. 18, 1109–1111 (2006).
[Crossref]

Q. Liu, K. S. Chiang, K. P. Lor, and C. K. Chow, “Temperature sensitivity of a long-period waveguide grating in a channel waveguide,” Appl. Phys. Lett. 86, 241115 (2005).
[Crossref]

Chu, Y. M.

Ctyroky, J.

R. Slavík, J. Homola, J. Ctyroky, and E. Brynda, “Novel spectral fiber optic sensor based on surface plasmon resonance,” Sens. Actuators B 74, 106–111 (2001).
[Crossref]

Daxhelet, X.

M. Kulishov, V. Grubsky, J. Schwartz, X. Daxhelet, and D. V. Plant, “Tunable waveguide transmission gratings based on active gain control,” IEEE J. Quantum Electron. 40, 1715–1724 (2004).
[Crossref]

Erdogan, T.

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]

Gagnaire, H.

O. Hugon, P. Benech, and H. Gagnaire, “Surface plasmon chemical/biological sensor in integrated optics,” Sens. Actuators B 51, 316–320 (1998).
[Crossref]

Gauglitz, G.

J. Homola, S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999).
[Crossref]

Glytsis, E. N.

E. Anemogiannis and E. N. Glytsis, “Multilayer waveguide: efficient numerical analysis of general structure,” J. Lightwave Technol. 10, 1344–1351 (1992).
[Crossref]

Groger, H.

M. N. Weiss, R. Srivastava, and H. Groger, “Experimental investigation of surface plasmon-based integrated-optic humidity sensor,” Electron. Lett. 32, 842–843 (1996).
[Crossref]

Grubsky, V.

M. Kulishov, V. Grubsky, J. Schwartz, X. Daxhelet, and D. V. Plant, “Tunable waveguide transmission gratings based on active gain control,” IEEE J. Quantum Electron. 40, 1715–1724 (2004).
[Crossref]

Gupta, B. D.

Rajan, A. K. Sharma, and B. D. Gupta, “Fibre optic sensor based on long-range surface plasmon resonance: a theoretical analysis,” J. Opt. A: Pure Appl. Opt. 9, 682–687 (2007).
[Crossref]

Homola, J.

R. Slavík and J. Homola, “Ultrahigh resolution long range surface plasmon-based sensor,” Sens. Actuators B 123, 10–12 (2007).
[Crossref]

R. Slavík and J. Homola, “Optical multilayers for LED-based surface plasmon resonance sensors,” Appl. Opt. 45, 3752–3759 (2006).
[Crossref] [PubMed]

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377, 528–539 (2003).
[Crossref] [PubMed]

R. Slavík, J. Homola, J. Ctyroky, and E. Brynda, “Novel spectral fiber optic sensor based on surface plasmon resonance,” Sens. Actuators B 74, 106–111 (2001).
[Crossref]

J. Homola, S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999).
[Crossref]

J. Homola, Surface Plasmon Resonance Based Sensors (Springer, 2006).
[Crossref]

Hugon, O.

O. Hugon, P. Benech, and H. Gagnaire, “Surface plasmon chemical/biological sensor in integrated optics,” Sens. Actuators B 51, 316–320 (1998).
[Crossref]

James, S. W.

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

Jin, W.

Judkins, J. B.

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]

Kashyap, R.

Kawata, S.

Kersey, A. D.

Kulishov, M.

M. Kulishov, V. Grubsky, J. Schwartz, X. Daxhelet, and D. V. Plant, “Tunable waveguide transmission gratings based on active gain control,” IEEE J. Quantum Electron. 40, 1715–1724 (2004).
[Crossref]

Kwon, M. S.

M. S. Kwon and S. Y. Shin, “Refractive index sensitivity measurement of a long-period waveguide grating,” IEEE Photon. Technol. Lett. 17, 1923–1925 (2005).
[Crossref]

Kwon, M.-S.

M.-S. Kwon and S.-Y. Shin, “Tunable polymer waveguide notch filter using a thermooptic long-period grating,” IEEE Photon. Technol. Lett. 17, 145–147 (2005).
[Crossref]

Lemaire, P. J.

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]

Liu, Q.

C. K. Chow, K. S. Chiang, Q. Liu, K. P. Lor, and H. P. Chan, “UV-written long-period waveguide grating coupler for broadband add/drop multiplexing,” Opt. Commun. 282, 378–381 (2009).
[Crossref]

W. Jin, K. S. Chiang, and Q. Liu, “Electro-optic long-period waveguide gratings in lithium niobate,” Opt. Express 16, 20409–20417 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-25-20409.
[Crossref] [PubMed]

Y. Bai, Q. Liu, K. P. Lor, and K. S. Chiang, “Widely tunable long-period waveguide grating couplers,” Opt. Express 14, 12644–12654 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12644.
[Crossref] [PubMed]

Y. M. Chu, K. S. Chiang, and Q. Liu, “Widely tunable optical bandpass filter by use of polymer long-period waveguide gratings,” Appl. Opt. 45, 2755–2760, (2006).
[Crossref] [PubMed]

K. S. Chiang, C. K. Chow, Q. Liu, H. P. Chan, and K. P. Lor, “Band-rejection filter with widely tunable center wavelength and contrast using metal long-period grating on polymer waveguide,” IEEE Photon. Technol. Lett. 18, 1109–1111 (2006).
[Crossref]

Q. Liu, K. S. Chiang, K. P. Lor, and C. K. Chow, “Temperature sensitivity of a long-period waveguide grating in a channel waveguide,” Appl. Phys. Lett. 86, 241115 (2005).
[Crossref]

Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21, 3399–3405 (2003).
[Crossref]

Loni, A.

A. Loni, L. T. Canham, M. G. Berger, R. Arens-Fischer, H. Munder, H. Lüth, H. F. Arrand, and T. M. Benson, “Porous silicon multilayer optical waveguide,” Thin Solid Films 276, 143–146 (1996).
[Crossref]

Lor, K. P.

C. K. Chow, K. S. Chiang, Q. Liu, K. P. Lor, and H. P. Chan, “UV-written long-period waveguide grating coupler for broadband add/drop multiplexing,” Opt. Commun. 282, 378–381 (2009).
[Crossref]

Y. Bai, Q. Liu, K. P. Lor, and K. S. Chiang, “Widely tunable long-period waveguide grating couplers,” Opt. Express 14, 12644–12654 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12644.
[Crossref] [PubMed]

K. S. Chiang, C. K. Chow, Q. Liu, H. P. Chan, and K. P. Lor, “Band-rejection filter with widely tunable center wavelength and contrast using metal long-period grating on polymer waveguide,” IEEE Photon. Technol. Lett. 18, 1109–1111 (2006).
[Crossref]

Q. Liu, K. S. Chiang, K. P. Lor, and C. K. Chow, “Temperature sensitivity of a long-period waveguide grating in a channel waveguide,” Appl. Phys. Lett. 86, 241115 (2005).
[Crossref]

Lüth, H.

A. Loni, L. T. Canham, M. G. Berger, R. Arens-Fischer, H. Munder, H. Lüth, H. F. Arrand, and T. M. Benson, “Porous silicon multilayer optical waveguide,” Thin Solid Films 276, 143–146 (1996).
[Crossref]

Lyndin, N. M.

N. M. Lyndin, I. F. Salakhutdinov, V.A. Sychugov, B.A. Usievich, F.A. Pudonin, and O. Parriaux, “Long-range surface plasmons in asymmetric layered metal-dielectric structures,” Sens. Actuators B 54, 37–42 (1999).
[Crossref]

Matsubara, K.

Minami, S.

Munder, H.

A. Loni, L. T. Canham, M. G. Berger, R. Arens-Fischer, H. Munder, H. Lüth, H. F. Arrand, and T. M. Benson, “Porous silicon multilayer optical waveguide,” Thin Solid Films 276, 143–146 (1996).
[Crossref]

Nemova, G.

Palik, E.

E. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Parriaux, O.

N. M. Lyndin, I. F. Salakhutdinov, V.A. Sychugov, B.A. Usievich, F.A. Pudonin, and O. Parriaux, “Long-range surface plasmons in asymmetric layered metal-dielectric structures,” Sens. Actuators B 54, 37–42 (1999).
[Crossref]

Patrick, H. K.

Plant, D. V.

M. Kulishov, V. Grubsky, J. Schwartz, X. Daxhelet, and D. V. Plant, “Tunable waveguide transmission gratings based on active gain control,” IEEE J. Quantum Electron. 40, 1715–1724 (2004).
[Crossref]

Pudonin, F.A.

N. M. Lyndin, I. F. Salakhutdinov, V.A. Sychugov, B.A. Usievich, F.A. Pudonin, and O. Parriaux, “Long-range surface plasmons in asymmetric layered metal-dielectric structures,” Sens. Actuators B 54, 37–42 (1999).
[Crossref]

Rajan,

Rajan, A. K. Sharma, and B. D. Gupta, “Fibre optic sensor based on long-range surface plasmon resonance: a theoretical analysis,” J. Opt. A: Pure Appl. Opt. 9, 682–687 (2007).
[Crossref]

Rastogi, V.

Salakhutdinov, I. F.

N. M. Lyndin, I. F. Salakhutdinov, V.A. Sychugov, B.A. Usievich, F.A. Pudonin, and O. Parriaux, “Long-range surface plasmons in asymmetric layered metal-dielectric structures,” Sens. Actuators B 54, 37–42 (1999).
[Crossref]

Sambles, J. R.

K. R. Welford and J. R. Sambles, “Coupled surface plasmons in a symmetric system,” J. Mod. Opt. 35, 1467–1483 (1988).
[Crossref]

Schwartz, J.

M. Kulishov, V. Grubsky, J. Schwartz, X. Daxhelet, and D. V. Plant, “Tunable waveguide transmission gratings based on active gain control,” IEEE J. Quantum Electron. 40, 1715–1724 (2004).
[Crossref]

Sharma, A. K.

Rajan, A. K. Sharma, and B. D. Gupta, “Fibre optic sensor based on long-range surface plasmon resonance: a theoretical analysis,” J. Opt. A: Pure Appl. Opt. 9, 682–687 (2007).
[Crossref]

Shin, S. Y.

M. S. Kwon and S. Y. Shin, “Refractive index sensitivity measurement of a long-period waveguide grating,” IEEE Photon. Technol. Lett. 17, 1923–1925 (2005).
[Crossref]

Shin, S.-Y.

M.-S. Kwon and S.-Y. Shin, “Tunable polymer waveguide notch filter using a thermooptic long-period grating,” IEEE Photon. Technol. Lett. 17, 145–147 (2005).
[Crossref]

Sipe, J. E.

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]

Slavík, R.

R. Slavík and J. Homola, “Ultrahigh resolution long range surface plasmon-based sensor,” Sens. Actuators B 123, 10–12 (2007).
[Crossref]

R. Slavík and J. Homola, “Optical multilayers for LED-based surface plasmon resonance sensors,” Appl. Opt. 45, 3752–3759 (2006).
[Crossref] [PubMed]

R. Slavík, J. Homola, J. Ctyroky, and E. Brynda, “Novel spectral fiber optic sensor based on surface plasmon resonance,” Sens. Actuators B 74, 106–111 (2001).
[Crossref]

Srivastava, R.

M. N. Weiss, R. Srivastava, and H. Groger, “Experimental investigation of surface plasmon-based integrated-optic humidity sensor,” Electron. Lett. 32, 842–843 (1996).
[Crossref]

Stegeman, G. I.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[Crossref]

Sychugov, V.A.

N. M. Lyndin, I. F. Salakhutdinov, V.A. Sychugov, B.A. Usievich, F.A. Pudonin, and O. Parriaux, “Long-range surface plasmons in asymmetric layered metal-dielectric structures,” Sens. Actuators B 54, 37–42 (1999).
[Crossref]

Tamir, T.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[Crossref]

Tatam, R. P.

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

Usievich, B.A.

N. M. Lyndin, I. F. Salakhutdinov, V.A. Sychugov, B.A. Usievich, F.A. Pudonin, and O. Parriaux, “Long-range surface plasmons in asymmetric layered metal-dielectric structures,” Sens. Actuators B 54, 37–42 (1999).
[Crossref]

Vengsarkar, A. M.

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]

Weiss, M. N.

M. N. Weiss, R. Srivastava, and H. Groger, “Experimental investigation of surface plasmon-based integrated-optic humidity sensor,” Electron. Lett. 32, 842–843 (1996).
[Crossref]

Welford, K. R.

K. R. Welford and J. R. Sambles, “Coupled surface plasmons in a symmetric system,” J. Mod. Opt. 35, 1467–1483 (1988).
[Crossref]

Yee, S.

J. Homola, S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999).
[Crossref]

Anal. Bioanal. Chem. (1)

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377, 528–539 (2003).
[Crossref] [PubMed]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

Q. Liu, K. S. Chiang, K. P. Lor, and C. K. Chow, “Temperature sensitivity of a long-period waveguide grating in a channel waveguide,” Appl. Phys. Lett. 86, 241115 (2005).
[Crossref]

Electron. Lett. (1)

M. N. Weiss, R. Srivastava, and H. Groger, “Experimental investigation of surface plasmon-based integrated-optic humidity sensor,” Electron. Lett. 32, 842–843 (1996).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Kulishov, V. Grubsky, J. Schwartz, X. Daxhelet, and D. V. Plant, “Tunable waveguide transmission gratings based on active gain control,” IEEE J. Quantum Electron. 40, 1715–1724 (2004).
[Crossref]

IEEE Photon. Technol. Lett. (3)

M. S. Kwon and S. Y. Shin, “Refractive index sensitivity measurement of a long-period waveguide grating,” IEEE Photon. Technol. Lett. 17, 1923–1925 (2005).
[Crossref]

M.-S. Kwon and S.-Y. Shin, “Tunable polymer waveguide notch filter using a thermooptic long-period grating,” IEEE Photon. Technol. Lett. 17, 145–147 (2005).
[Crossref]

K. S. Chiang, C. K. Chow, Q. Liu, H. P. Chan, and K. P. Lor, “Band-rejection filter with widely tunable center wavelength and contrast using metal long-period grating on polymer waveguide,” IEEE Photon. Technol. Lett. 18, 1109–1111 (2006).
[Crossref]

J. Lightwave Technol. (4)

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]

H. K. 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]

E. Anemogiannis and E. N. Glytsis, “Multilayer waveguide: efficient numerical analysis of general structure,” J. Lightwave Technol. 10, 1344–1351 (1992).
[Crossref]

Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21, 3399–3405 (2003).
[Crossref]

J. Mod. Opt. (1)

K. R. Welford and J. R. Sambles, “Coupled surface plasmons in a symmetric system,” J. Mod. Opt. 35, 1467–1483 (1988).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

Rajan, A. K. Sharma, and B. D. Gupta, “Fibre optic sensor based on long-range surface plasmon resonance: a theoretical analysis,” J. Opt. A: Pure Appl. Opt. 9, 682–687 (2007).
[Crossref]

J. Opt. Soc. Am. B (1)

Meas. Sci. Technol. (1)

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

Opt. Commun. (1)

C. K. Chow, K. S. Chiang, Q. Liu, K. P. Lor, and H. P. Chan, “UV-written long-period waveguide grating coupler for broadband add/drop multiplexing,” Opt. Commun. 282, 378–381 (2009).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[Crossref]

Sens. Actuators B (5)

J. Homola, S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999).
[Crossref]

O. Hugon, P. Benech, and H. Gagnaire, “Surface plasmon chemical/biological sensor in integrated optics,” Sens. Actuators B 51, 316–320 (1998).
[Crossref]

R. Slavík, J. Homola, J. Ctyroky, and E. Brynda, “Novel spectral fiber optic sensor based on surface plasmon resonance,” Sens. Actuators B 74, 106–111 (2001).
[Crossref]

R. Slavík and J. Homola, “Ultrahigh resolution long range surface plasmon-based sensor,” Sens. Actuators B 123, 10–12 (2007).
[Crossref]

N. M. Lyndin, I. F. Salakhutdinov, V.A. Sychugov, B.A. Usievich, F.A. Pudonin, and O. Parriaux, “Long-range surface plasmons in asymmetric layered metal-dielectric structures,” Sens. Actuators B 54, 37–42 (1999).
[Crossref]

Thin Solid Films (1)

A. Loni, L. T. Canham, M. G. Berger, R. Arens-Fischer, H. Munder, H. Lüth, H. F. Arrand, and T. M. Benson, “Porous silicon multilayer optical waveguide,” Thin Solid Films 276, 143–146 (1996).
[Crossref]

Other (3)

MY Polymers Ltd., http://www.mypolymers.com.

J. Homola, Surface Plasmon Resonance Based Sensors (Springer, 2006).
[Crossref]

E. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

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Figures (8)

Fig. 1.
Fig. 1. (a) Refractive-index profile n(x) of a metal-coated planar waveguide, where (b) a corrugated long-period grating is introduced on the surface of the guiding layer (see the text for the definitions of the symbols).
Fig. 2.
Fig. 2. (a) Magnetic-field (Hy ) distributions of the A-SP, TM0, and TM1 modes of a metal-coated slab waveguide with n s = 1.444, n f = 1.535, n cl = 1.51, n ex = 1.51, d f = 2.0 μm, d cl = 5.0 μm, and d m = 15 nm at 1550 nm. (b) Magnetic-field distributions of the TM1 mode at different values of n ex.
Fig. 3.
Fig. 3. (a) Normalized transmission spectra at different values of the loss coefficient Im(N sp) for a 10 mm long grating with κL = 0.571 and (b) the contrast at λ 0 as a function of the loss coefficient Im(N sp), showing how the contrast decreases with an increase in the loss of the SP mode.
Fig. 4.
Fig. 4. (a) Dependence of Re(N) and Im(N) of the TM0 and TM1 modes on the external refractive index n ex for a metal-coated slab waveguide with n s = 1.444, n f = 1.535, n cl = 1.51, d f = 2.0 μm, d cl = 5.0 μm, d m = 15 nm, and λ = 1550 nm. (b) Dependence of the sensitivity and the contrast at λ 0 on the external refractive index n ex.
Fig. 5.
Fig. 5. (a) Variations of Re(N) and Im(N) of the TM0 and TM1 modes with the metal film thickness d m for a waveguide with n s = 1.444, n f = 1.535, n cl = 1.51, d f = 2.0 μm, d cl = 5.0 μm, n ex = 1.51, operating at λ = 1550 nm. (b) Variations of the sensitivity and the grating contrast with the metal film thickness d m.
Fig. 6.
Fig. 6. (a) Variations of Re(N) and Im(N) of the TM0 and TM1 modes with the cladding thickness d cl for a waveguide with n s = 1.444, n f = 1.535, n cl = 1.51, d f = 2.0 μm, d m = 15 nm, n ex = 1.51, operating at λ = 1550 nm. (b) Variations of the sensitivity and the grating contrast with the cladding thickness d cl.
Fig. 7.
Fig. 7. (a) Transmission spectra of an LPWG-assisted waveguide LRSP sensor with n s = 1.444, n f = 1.535, n cl = 1.51, d f = 2.0 μm, d cl = 5.0 μm, d m = 15 nm, Λ = 221 μm, Δh = 100 nm, and L = 8 mm, calculated at different values of external index n ex. (b) Variation of the SPR wavelength with the external index n ex.
Fig. 8.
Fig. 8. (a) Transmission spectra of an LPWG-assisted waveguide LRSP sensor with n s = 1.29, n f = 1.35, n cl = 1.33, d f = 2.0 μm, d cl = 2.0 μm, d m = 15 nm, Λ = 95 μm, Δh = 100 nm, and L = 6 mm, calculated at different values of external index n ex. (b) Variation of the SPR wavelength with the external index n ex.

Equations (3)

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Λ=λ0Re(Nco)Re(Nsp) ,
T=[cos(ζL)+jσζsin(ζL)]exp[j(βcoσ)L]2 ,
dλ0dnex=(η0exη1ex)γΛ,

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