Guidewave surface plasmon-polariton sensors

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Guidewave surface plasmon-polariton sensors Raman Kashyap *,a,b and Galina Nemova a a Department of Engineering Physics and b Department of Electrical Engineering, École Polytechnique de Montréal, C.P. 6079, succ.Centre-ville, Montréal, Canada ABSRACT Theoretical models of surface plasmon-polariton (SPP) refractive index sensors with Bragg grating and long period grating (LPG) are presented and comprehensively investigated for fiber and planar structures. The main principle of operation of these devices is based on high efficiency energy transfer between a guided mode propagating in a waveguide layer of the structure and counter- or co-propagating SPP supported by a metal layer separated from the waveguide layer by a buffer. The high efficiency energy transfer is realized by means of a properly designed Bragg grating or LPG imprinted in the waveguide layers of the structures or engraved on the top of the metal layer. These devices are compact, free from any moving parts and can be easily integrated into any fiber or planar schemes. Our simulations are made for telecom wavelengths in the 1500nm window. Keywords: Surface plasmon-polariton, fiber sensor, SPP sensor, refractive index sensor 1. INTRODUCTION A surface plasmon-polariton (SPP) is an electromagnetic excitation at a metal-dielectric interface, which consists of a surface-charge-density oscillation coupled to the electromagnetic fields 1,2 . The SPP field components are concentrated at the interfaces and decay exponentially in both media with a small penetration depth. For a planar structure the SPP exists as a p-polarized (TM) wave when the permittivities of the two adjacent media have opposite signs, and as a s-polarized (TE) wave when the permeabilities of the two adjacent media have opposite signs 3 . Since the permabilities of the two adjacent media are unity, only the p polarization is an option. The SPP is a promising tool for sensor applications for investigating the refractive index medium near the interface. 4-9 The standard techniques for the SPP excitation is by matching the parallel wave-vector components of the incident free space radiation field to that of the SPP are the prism by the (Kretschmann scheme) or grating coupling technique 10-12 . The method of enhancing the sensitivity of the sensor using periodic metallic structures in the Kretschmann scheme was suggested and investigated in Ref. 12 for operation in the visible part of the spectrum. These schemes are not very compact normally, as they incorporate moving parts and require precise angular control. An evanescent-field fiber Bragg grating sensor with a metal layer was recently presented as a compact alternative 13 . In this scheme counter-directional coupling between the guided mode and a surface plasmon wave (SPW) is promoted by means of a properly designed Bragg reflection grating imprinted in the waveguide layer. A SPW used as a sensor tool in this sensor is an electromagnetic wave combining the guided mode of the dielectric part of the structure associated with the SPP localised at the metal layer. Since most of SPW’s energy is localised in the waveguide layer, its sensitivity is limited, but may be replaced by a “pure” SPP as suggested in Ref. 14 to enhance sensitivity. In this a “pure” SPP is used in which most of energy is concentrated at the metal – dielectric boundaries and decays exponentially in all other layers including the waveguide layer. This paper reviews our recent work on simple integrated schemes for surface plasmon-polariton refractive index sensors which are free from any moving parts and are assisted with Bragg or long period gratings (LPG). The central idea of these sensors is a novel method for the excitation of the SPP. The SPP excitation is invoked on the basis of resonance coupling of the waveguide mode propagating in the waveguide layer of the structure with the counter- or co-propagating SPP by means of the properly designed Bragg grating or LPG, respectively. The Bragg grating or LPG can be imprinted into the waveguide layer of the structure or engraved on the top of the surface of the metal layer in contact with the sensed medium. The guided mode transmitted through the Bragg grating or LPG serves as an input signal for interrogating the sensor. *[email protected]; phone (514) 340 4711 (4742); fax (514) 340 3218 Invited Paper Integrated Optics: Devices, Materials, and Technologies XIII, edited by Jean-Emmanuel Broquin, Christoph M. Greiner, Proc. of SPIE Vol. 7218, 72180W · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.812072 Proc. of SPIE Vol. 7218 72180W-1

Transcript of Guidewave surface plasmon-polariton sensors

Guidewave surface plasmon-polariton sensors

Raman Kashyap*,a,b and Galina Nemovaa

aDepartment of Engineering Physics and bDepartment of Electrical Engineering, École Polytechnique de Montréal, C.P. 6079, succ.Centre-ville, Montréal, Canada

ABSRACT

Theoretical models of surface plasmon-polariton (SPP) refractive index sensors with Bragg grating and long period grating (LPG) are presented and comprehensively investigated for fiber and planar structures. The main principle of operation of these devices is based on high efficiency energy transfer between a guided mode propagating in a waveguide layer of the structure and counter- or co-propagating SPP supported by a metal layer separated from the waveguide layer by a buffer. The high efficiency energy transfer is realized by means of a properly designed Bragg grating or LPG imprinted in the waveguide layers of the structures or engraved on the top of the metal layer. These devices are compact, free from any moving parts and can be easily integrated into any fiber or planar schemes. Our simulations are made for telecom wavelengths in the 1500nm window. Keywords: Surface plasmon-polariton, fiber sensor, SPP sensor, refractive index sensor

1. INTRODUCTION A surface plasmon-polariton (SPP) is an electromagnetic excitation at a metal-dielectric interface, which consists of a surface-charge-density oscillation coupled to the electromagnetic fields1,2. The SPP field components are concentrated at the interfaces and decay exponentially in both media with a small penetration depth. For a planar structure the SPP exists as a p-polarized (TM) wave when the permittivities of the two adjacent media have opposite signs, and as a s-polarized (TE) wave when the permeabilities of the two adjacent media have opposite signs3. Since the permabilities of the two adjacent media are unity, only the p polarization is an option. The SPP is a promising tool for sensor applications for investigating the refractive index medium near the interface.4-9 The standard techniques for the SPP excitation is by matching the parallel wave-vector components of the incident free space radiation field to that of the SPP are the prism by the (Kretschmann scheme) or grating coupling technique10-12. The method of enhancing the sensitivity of the sensor using periodic metallic structures in the Kretschmann scheme was suggested and investigated in Ref. 12 for operation in the visible part of the spectrum. These schemes are not very compact normally, as they incorporate moving parts and require precise angular control. An evanescent-field fiber Bragg grating sensor with a metal layer was recently presented as a compact alternative13. In this scheme counter-directional coupling between the guided mode and a surface plasmon wave (SPW) is promoted by means of a properly designed Bragg reflection grating imprinted in the waveguide layer. A SPW used as a sensor tool in this sensor is an electromagnetic wave combining the guided mode of the dielectric part of the structure associated with the SPP localised at the metal layer. Since most of SPW’s energy is localised in the waveguide layer, its sensitivity is limited, but may be replaced by a “pure” SPP as suggested in Ref. 14 to enhance sensitivity. In this a “pure” SPP is used in which most of energy is concentrated at the metal – dielectric boundaries and decays exponentially in all other layers including the waveguide layer. This paper reviews our recent work on simple integrated schemes for surface plasmon-polariton refractive index sensors which are free from any moving parts and are assisted with Bragg or long period gratings (LPG). The central idea of these sensors is a novel method for the excitation of the SPP. The SPP excitation is invoked on the basis of resonance coupling of the waveguide mode propagating in the waveguide layer of the structure with the counter- or co-propagating SPP by means of the properly designed Bragg grating or LPG, respectively. The Bragg grating or LPG can be imprinted into the waveguide layer of the structure or engraved on the top of the surface of the metal layer in contact with the sensed medium. The guided mode transmitted through the Bragg grating or LPG serves as an input signal for interrogating the sensor. *[email protected]; phone (514) 340 4711 (4742); fax (514) 340 3218

Invited Paper

Integrated Optics: Devices, Materials, and Technologies XIII, edited by Jean-Emmanuel Broquin, Christoph M. Greiner,Proc. of SPIE Vol. 7218, 72180W · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.812072

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2. SPP REFRACTIVE-INDEX FIBER SENSOR the first sensor is constructed as a device with the Bragg grating imprinted into the core of the fiber. This refractive index fiber sensor couples the fundamental fiber core mode and the SPP counter-propagating with the fiber guided mode (Fig.1) resonantly, by the Bragg grating imprinted in the fiber core. To model the sensor, the length of the Bragg grating imprinted into the fiber core is assumed to be L and the refractive index of the fiber core is nco. The thin metal layer supporting SPP is deposited on the fiber cladding with the refractive index ncl. The permittivity of the metal layer is based on the Drude formula ε(ω) = ε∞[1- ωp

2/ω(ω+iГ)], where ε∞ is the high-frequency value of ε(ω), ωp is the plasma frequency, Г is its damping factor. This scheme compares favourably against the attenuated-total-reflection technique, since it is free from any precision angle control of the incident radiation. As it is all fiber, it can be directly fusion spliced into fiber-optic systems with low insertion loss. The electromagnetic fields of SPP are solutions of Maxwell’s equations, as the electromagnetic fields of the fundamental fiber core mode, but standard boundary conditions for the multilayered cylindrical structure has a negative permittivity of the metal layer. The calculations of the electromagnetic fields for the cylindrical geometry are described by many authors15-18.

Fig.1. Structure under consideration. Bragg grating is imprinted into the fiber core. FM is the fiber mode.

Using cylindrical polar coordinates (r, θ, z) for the fiber geometry, all fields components contain a common factor exp[i(βνμz+mθ –ωt)], where βνμ is the propagation constant and m is the azimuth number. The modes do not have pure transverse E or H character, except in the special case of m = 0. The most important characteristic of each layer of the structure is its phase parameters ui

2 = - wi2 = k0

2ni2- βvμ

2, where k0 is the vacuum wave-number, ni is the refractive index of the i-layer (core, cladding, metal, surrounding media). The solutions for the mode fields involve Bessel functions of real argument, which are oscillatory in character for ui

2 > 0, and Bessel functions of imaginary argument, which are asymptotically exponential for ui

2 < 0. The range of frequencies, in which the structure can support the SPP is determined by the condition ε(ω) < - ncl

2. The SPP propagation constant (np) is in the range np > ncl. The efficiency of excitation of the SPP as a function of the reflectivity of the Bragg grating is simulated using coupled-mode theory for fiber Bragg gratings described in details in a number of papers.19-21 There are two main conditions for high efficiency SPP excitation. The first condition is phase-matching between the propagation constant of the fiber core mode and the SPP propagation constant provided by the properly designed period of the fiber Bragg grating for the predetermined wavelength of interest, as it has been done in the case of core-cladding fiber mode coupling.19 The second condition is the large coupling constant of the fiber core mode to the SPP (kco-p), provided by a properly designed fiber and grating parameters. Since an un-tilted fiber Bragg grating is used in this device, the only nonzero coupling constants are those between the fiber core mode and the SPP with the same azimuth numbers.19 As was already mentioned before, the SPP field components are concentrated at the interfaces and decay exponentially into the surrounding media. In order to achieve a large overlap between the SPP and fiber core mode the cladding thickness must be made small in compare with the cladding thickness of the standard fiber. In order to accommodate device production, it is beneficial to increase the fiber core diameter; thus, in spite of the dramatic reduction of the fiber cladding diameter, the structure will be "handle able". The fiber core diameter used in the simulations is 26 µm, the refractive index is 1.44072, and the fiber cladding diameter is 30 µm, and the refractive index is 1.44. This is a single mode fiber, and the fiber core mode is used for exciting the SPP. For design the best structure, optimisation is important to understand the dependence between the SPP propagation constant on the parameters of the structure and the grating. The value of np is very sensitive to the changes in the refractive index of the surrounding medium (ns) [Fig. 2(a)] and metal layer thickness (∆) [Fig. 2(b)].

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205

1.95

1.85

(b) 1.33

1.65

1.55

1.45

55 105 155 205 255A (A

1.553

1.55250

1.552

1.5515-c

1.551ci)

1.5505

1.55

1.33 1.332 1.334 1.336 1.338n

Fig.2. Plasmon polariton propagation constant np versus the refractive index of surrounding media ns (a), and the metal

layer thickness ∆ (b).

Fig. 2(b) shows that increasing the metal layer thickness decreases the value of the SPP propagation constant. Changes in the geometric parameters of the structure such as core and cladding diameters do not dramatically change the SPP parameters. These changes can quantitatively alter the SPP propagation constant, but can not qualitatively change its dependence on ns and ∆. In order to reduce system losses, metal layer materials are used for which the absolute value of the real part of the permittivity is sufficiently larger than its imaginary part at telecom wavelengths. The best materials from this point of view in the telecom region are gold and silver. Chemically passive gold is therefore used in all the simulations.22 The metal thickness and the refractive index of the surrounding media are the main parameters which influence the SPP propagation constant. The core and cladding diameters, the refractive indexes as well as the grating length and the amplitude of Bragg grating refractive index modulation (σ) significantly impact the efficiency of excitation of the SPP. σ is the main parameter for optimising the grating period. Indeed, the approximate spectral location for the resonance connected with the fiber mode – SPP reflection on the grating is given by δco-p+ kco-co/2 = 0, where δcop=(βco+ βp - 2π/Λ)/2, βco and βp are the fiber core mode and the polariton propagation constants, respectively. kco-co is the core mode self coupling constant, which is proportional to σ.19 For device miniaturization and simplification of the production process the grating length should be short and the grating period large. For the fixed grating length ,the grating reflectivity may be increased by increasing the grating strength. At the same time the grating period will be reduced.

Fig.4. Wavelength corresponding to the maximum of grating reflectivity versus the refractive index of surrounding media ns. (a) L = 9 cm, Λ = 420 nm, σ = 4 × 10-4, ∆ = 100 Å, (b) L = 5 cm, Λ = 469 nm, σ = 2 × 10-4, ∆ = 130 Å, (c) L = 4 cm, Λ = 496 nm, σ = 10-4, ∆ = 150 Å. For example, for σ = 10-4 the grating reflectivity is R = 2.3%, and the grating period is Λ = 475 nm. For σ = 5 ×10-4, the grating reflectivity increases significantly (R = 55%), and the grating period reduces to Λ = 404 nm. In both cases the grating length is L = 8 cm. For typical sensing applications, the surrounding media is assumed to be water with ns = 1.33. Fig. 4 illustrates the sensitivity of this structure as the dependence of the wavelength corresponding to the maximum (peak) of grating reflectivity on the refractive index of the surrounding media. The device sensitivity is presented for three different metal layer thicknesses 100Å, 130Å, and 150Å. Reducing the thickness of the metal layer the device sensitivity can be increased, however, to maintain the high efficiency SPP excitation the grating length and the strength of the grating must be increased and, as a consequence, the grating period will be reduced. For example, for a metal layer

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thickness Δ = 100 Å, the shift in the peak of the grating reflectivity is ~ 300 pm per 10-3 change in the surrounding media refractive index (ns). We estimate the sensitivity for measuring refractive index change for the device with a metal layer ∆ = 100 Å, L = 9 cm, Λ = 420 nm , and σ = 4 ×10-4 to be approximately 10-6, assuming a measurement resolution of 0.3 pm. This resolution is possible as the slope of the transmission loss spectrum edge is ~3dB/30pm. Assuming that a change in transmission of 0.01dB can be made, results in a resolution of 1ppm in refractive index change.

3. SPP REFRACTIVE-INDEX PLANAR SENSORS In this part of the paper will focus attention on planar structures assisted by the Bragg grating or LPG imprinted into the waveguide layer or engraved on the top of the metal layer. These should be simpler to fabricate and use compared to the fiber based SPP refractive index sensors. 3.1 Planar Bragg grating and LPG assisted refractive index sensors

A comprehensive study of the properties of the guided mode and “pure” SPP propagating in a 5-layer structure as well as the properties of the Bragg grating or LPG imprinted into the waveguide layer which provides high efficiency energy transfer between the guided mode and the “pure” SPP may be found in Ref. 14,23 Optimisation of the design of an optical sensor with the Bragg grating imprinted into the waveguide layer [Fig. 5(a)] is of prime importance, and will be discussed here.

(a) (b)

Fig.5. Structures under consideration. GM is the guided mode. (a): Bragg grating is imprinted into the waveguide layer. (b): LPG is imprinted into the waveguide layer and buffer.

In this sensor, the power in the guided mode transmitted through the grating serves as an input signal for interrogating the sensor. An ~ 30% transmission is used as a reference, as it provides a dip sufficient for discriminating changes. As found in Ref. 14, decreasing the metal layer thickness increases the sensor’s sensitivity, since the change in the SPP propagation constant (np) per fixed change in the refractive index of the sensed medium also increases as the metal layer thickness is reduced. However, decreasing the metal layer thickness increases the value of np for any fixed refractive index of the sensed medium (Fig. 6) and increases the grating period to maintain the same wavelength of operation. To allow sensing with high sensitivity, the metal layer thickness is reduced to the minimum practically possible and the resonance wavelength is fixed at a nominal λres = 1.55 µm for a sensed medium with nsen = 1.33. The grating period will decreases slightly if strength of the grating (σ) remains fixed. However, this decrease in the grating period is not significant; at the same time decreasing the metal layer thickness will decrease the guided mode - SPP coupling constant (κco-p), and as a consequence, will demand a stronger or longer grating in order to maintain ~30% transmission. However, reducing the thickness of the buffer or removing the buffer from the structure altogether increases not only the guided mode – SPP coupling constant, but unfortunately also the losses in the guided mode. Indeed, the imaginary part of the effective refractive index of the guided mode is approximately 9 × 10-6 and κco-p /σ = 0.036 for the structure without a buffer, and approximately 6 × 10-7 and κco-p /σ = 0.027 for the structure with a buffer thickness b = 2 µm. The imaginary part of the effective refractive index of the SPP does not depend significantly on the buffer’s thickness, since almost all the SPP energy is concentrated at the metal layer boundaries. However, compromise thin (~1 µm) buffer in the structure reduces the guided mode losses whilst maintaining a relatively high coupling efficiency between the guided mode and

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the SPP. The transmission of ~30% at λres = 1.55 µm for the sensed medium with nsen = 1.33 can be realised by different combinations of grating strength and grating length. If the refractive index of the sensed medium is altered in the vicinity of 1.33 (water), the dip in transmission centered at λres = 1.55 µm for nsen = 1.33 (water) will shift but will maintain its value of ~ 30%. The bandwidth of this transmission spectrum remains approximately constant at ~500 pm. The sensitivity of the structure can be characterized by the shift in the wavelength of the grating transmission dip versus the refractive index of sensed medium. For structures with ∆ = 10 nm, the resonance wavelength shifts by ~ 250 pm per 10-3 change in the refractive index of the sensed medium. With ∆ = 13.0 nm, the resonance wavelength shift is ~ 180 pm for the same change in nsen. Increasing the buffer thickness, leads to a reduced SPP interaction with the grating in the waveguide layer of the structure, requiring a longer and stronger grating in order to maintain ~30% transmission. This is undesirable for fabricating compact sensors. The simplest case of a structure with the grating imprinted in the waveguide layer has been considered. However, imprinting a grating in the buffer will slightly complicate sensor production but on the other hand it increases the guided mode – SPP coupling constant κco-p. A Bragg grating imprinted simultaneously in the waveguide layer and in the buffer of the structure will reduce the length of the grating by a factor of almost 2 whilst maintaining ~30% transmission with the same sensor sensitivity.

Fig. 6. Dependence between the SPP effective refractive index (np) and the refractive index of the sensed medium (nsen), for the structures with the different metal layer thicknesses (∆), the buffer thickness is 1 µm. A structure with ∆ = 10 nm, σ = 8 × 10-4, L = 7 cm, Λ ≈ 492.5 nm, and a buffer thickness of 1 µm has a sensitivity of ~250nm/RIU (refractive index units). Using a “pure” SPP as a sensor tool instead of a SPW, which is really an electromagnetic configuration combining the guided mode coupled with a SPP, increase the sensor sensitivity by a factor of 5 approximately. In this part of the paper, a refractive index sensor assisted with a LPG imprinted into the waveguide layer of the planar structure is discussed. As before we the power in the guided mode transmitted through the LPG is used as an input signal for interrogating the sensor, and a ~ 30% transmission will be used as a reference. For this structure with a LPG as well as in the case of the Bragg grating assisted sensor considered in Ref. 14, a decrease in the metal layer thickness will cause an increase in the sensitivity of the sensor. For the LPG sensor structure, a metal layer thickness of Δ = 10 nm is used. The period of the LPG for a predetermined resonance wavelength (λres = 1.55 µm) and nsen = 1.33 (water) can be calculated with the formula obtained in Ref. 23. Changes in the grating strength have only a small influence on the period of the grating, changing by only 0.43% per Δσ = 10 change in the grating’s strength. Change in the length of the grating, does not influence the grating period at all. Thus, only the thickness of the buffer needs to be chosen. Indeed, if the buffer is very thick (b > 2 µm) the loss of the guided mode is low, however, in order to keep the grating’s transmission dip at ~ 30% a very long (L > 10 cm) and very strong (σ > 1×10-3) grating has to be used. This can complicate the LPG production process. If the buffer is very thin or absent from the structure, the guided mode loss is significant and the sensor monitoring process becomes very difficult. The optimal thickness of the buffer is in the range 1 – 1.5 µm. The sensitivity of the sensor as before can be characterized as a shift in the wavelength of grating’s transmission dip versus the refractive index of sensed medium. For the refractive index of the sensed medium the range in the vicinity of nsen = 1.33 (water) with the orientation on the biological sensor applications is chosen. Fig. 7 illustrates the shift of the LPG grating’s transmission dip with a change in the refractive index of the sensed medium. The bandwidth of the transmission dip is approximately 2.4 nm, remaining unchanged with the change in the refractive

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Fig.7. LPG transmission spectra for different nsen with b = 1 μm, L = 2.5 cm, Δ = 10 nm, Λ ≈ 6.95 μm, the minima shifts ~ 1.1 nm per 10-3 change in nsen. index of the sensed medium. The value of the LPG’s transmission minimum changes slightly with a change in the refractive index of the sensed medium. For the structure with b = 1 μm, L = 2.5 cm, Δ = 10 nm, and Λ ≈ 6.95 μm, the sensor resolution is approximately 1100 pm per 10-3 change in the refractive index of the sensed medium or 1100 nm/RIU (refractive index unit). Thus the sensitivity of a LPG assisted sensor is significantly higher than the sensitivity of a sensor based on the Bragg grating, which is only ~250 nm/RIU. The higher sensitivity of the LPG comapred to the Bragg grating assisted sensor is easy to explain: the larger grating period of the LPG results from the difference between the propagation constants of the guided and SPP modes. On the other hand the shorter period for the Bragg grating assisted sensor is a result of the sum of the propagation constants of the guided and SPP modes. Any small change in the refractive index of the surrounding medium (nsens) has a larger fractional effect on the LPG based sensor as it changes the SPP propagation constant, i.e. if δn is the change in the SPP effective refractive index with a change in nsens, then the fractional change in the mismatch is:

)( gp nn

n−δ

(1)

In the counter-propagating scheme with the Bragg grating, the small change in the propagation constant of the SPP has a smaller fractional influence on the sum of the propagation constants of the SPP and the guided mode as:

)( gp nn

n+δ

(2)

The ratio of the sensitivities of the LPG and the Bragg grating sensors is therefore:

gp

gp

nnnnr

−+

≈ (3)

Equation (3) shows that the ratio r for typical parameters used in this paper is ~5, indicating an enhanced sensitivity for the LPG (co-propagating) compared to the Bragg grating (counter-propagating) based sensor. 3.2 Planar corrugated Bragg grating and LPG assisted refractive index sensors

In the part of the paper structures, in which the SPP is exited by the corrugated Bragg grating or LPG engraved on the top of the metal layer (Fig. 8) will be considered. A corrugated Bragg grating or LPG engraved on the surface of the metal layer separated from the waveguide layer by a buffer of constant thickness can be used as a device for energy transfer between a forward-propagating guided mode to a counter or co-propagating SPP (Fig. 8). To model the sensor, the amplitude of the grating is assumed to be H, its period, Λ and L is the length of the grating. To calculate the grating transmission the transfer matrix method is used with the mode-matching technique, also known as the exact coupled-mode theory.24-26 Details of this analysis may be found in Refs. 27 & 28.

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(a) (b)

Fig.8. Structures under consideration. GM is the guided mode. (a): Bragg grating is corrugated in the metal layer. (b): LPG is corrugated in the metal layer.

Again, the optimisation of these structures with the Bragg grating engraved on the top of the metal layer is necessary for best performance. As in the case of the grating imprinted into the waveguide layer, device miniaturization and simplification of the production process is possible if a short grating length is used with a large grating period. Since as before, the transmitted guided mode serves as an input signal for interrogating the sensor, ~ 30% or 40% transmission will be used as a reference signal. As in the case of the gratings imprinted into the waveguide layer, the sensor sensitivity in the structures with the corrugated gratings is linked with the metal layer thickness, the details this dependence can be found in Ref. 27. Reducing the thickness of the metal layer increases the sensor sensitivity. As before, in the sensor structures with the corrugated grating the minimum value in the spectrum of the transmitted guided mode dip localized at the position λres = 1.55 μm for nsen = 1.33 is equal to ~ 40% for all sensor structures. Increasing the buffer thickness requires an increase in the length of the grating if the minimum in the transmitted spectrum is to be maintained at a fixed value for constant grating amplitude. Increasing the grating amplitude, for a constant buffer thickness, reduces the length of the grating to achieve the same result. When the device is operated as a sensor, the minimum value of the guided mode transmitted spectrum shifts along the wavelength axis as a function of the refractive index of sensed

Fig.9. Guided mode transmitted spectrum sensitivity is 247 nm/RIU, for nsen = 1.330 and nsen = 1.331, b = 4.5 μm, L = 5.3 cm, H = 1 nm, Δ = 10 nm and Λ ≈ 485 nm.

medium, but remains almost constant in value in the vicinity of the nsen range of around 1.33 (Fig. 9). As an example, a structure for the design of the sensor with the b = 4.5 μm, L = 5.3 cm, H = 1 nm, Δ = 10 nm, and Λ ≈ 485 nm with the sensitivity ~ 247 nm/RIU (refractive index unit) can be recommended. The value of the minimum in the guided mode transmitted spectrum for this structure is ~ 40%. The sensor assisted with LPG engraved on the top of the metal layer separated by a buffer from the waveguide layer is shown in Fig.8 (b). The sensitivity of this sensor is dependent on several parameter and details may be seen in Ref. 28. The metal layer thickness influences the shape of the LPG transmission spectrum. Obviously, an increase in the metal layer thickness, again increases the losses in the structure. The guided mode transmission spectra for two different metal layer thicknesses are presented in Fig. 10. For the solid line in this Figure, Δ = 10 nm, Λ ≈ 6.1 μm and L = 4 cm, and for the dashed line, Δ = 15 nm, Λ ≈ 16.08 μm and L = 11 cm. On the one hand, increasing the metal layer thickness

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broadens the transmission spectrum complicating discrimination in the monitoring process; however, the length of the grating has to be increased in order to maintain the value of the transmission minimum localised at λres= 1.55μm.

Fig.10. LPG transmission spectra for different metal layer thicknesses with b = 4.5 μm, H = 1 nm, nsen = 1.33, Λ ≈ 6.1 μm (solid line), Λ ≈ 16.08 μm (dashed line).

Following the results presented in Ref. 28 for the sensor structure with the parameters b = 4 μm, Δ = 10 nm, H = 1 nm, and L = 4 cm, which were obtained as a result of the optimization process, the sensor sensitivity is approximately ~ 1.1 nm shift per 10-3 change in the refractive index of the sensed medium (Fig. 11), that is, the sensor sensitivity is again ~1100 nm/RIU (refractive index unit).

Fig.11. LPG transmission spectra for different nsen with b = 4 μm, L = 3 cm, H = 1 nm, Δ = 10 nm, Λ ≈ 6.1 μm, the minima shifts ~ 1.1 nm per 10-3 change in nsen. In both cases of the Bragg grating and LPG imprinted into waveguide layer, or in the case of the Bragg grating and LPG engraved on the top of the metal layer, the sensitivity of a sensors based on the LPG is significantly higher than the sensitivity of a sensor based on the Bragg grating. This is explained by the Equations (1) - (3) as consequence of the counter-propagation and co-propagation between the guided mode and SPP provided by the Bragg grating and LPG, respectively.

4. CONCLUSIONS

In this paper theoretical models of a fiber and planar Bragg grating and LPG assistant integrated surface plasmon-polariton sensors for refractive index sensing with a “pure” SPP as a promising sensor tools have been presented. These sensors are compact, free from any moving parts and have high sensitivity. The main principle of their operation is based on the high efficiency energy transfer between the fiber or guided mode propagating in the core or waveguide layer of the structure separated by a buffer from a metal layer, and a “pure” SPP propagating in the metal layer. The energy transfer between the guided mode and the “pure” SPP can be achieved by a properly designed Bragg grating imprinted into the guided layer or engraved on the top of the metal layer. This coupling may also be promoted by a LPG imprinted in the guided layer or engraved on the top of the metal layer. In the case of a thin metal layer, the “pure” SPP exists in a

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single mode regime; all its energy is concentrated in the vicinity of the metal boundaries. These properties have a significant benefit, and distinguish the “pure” SPP as a sensor tool, from the SPW which combines the guided mode with a rather “weak” SPP in a multimode regime. The ~30% transmission dip in the spectrum of the guided mode is used as an input signal for the interrogation unit in all the sensor structures presented. The LPG in comparison to the Bragg grating dramatically increases the sensor sensitivity (approximately by a factor of 4.5). The sensor can be used for sensing of any medium with the refractive index smaller than the refractive index of the waveguide layer. As an example a scheme generally considered interesting for biological sensing, which has a refractive index of the sensed medium in the vicinity of 1.33 (water) has been studied. These sensors are based on simple and well developed technology and have a distinct advantage of other sensors based on moving components.

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