Abstract:
An optical waveguide sensing method and device in which a waveguide layer receives an optical signal and propagates the optical signal in accordance with a predetermined optical waveguide propagation mode. A testing medium surface in communication with the waveguide layer is responsive to a testing medium for modifying at least one characteristic of the propagated optical signal in relation to a given parameter of the testing medium. In this manner, the modified characteristic of the propagated optical signal can be measured in view of determining the given parameter of the testing medium.

Description:
FIELD OF THE INVENTION 
     The present invention generally relates to sensors, in particular but not exclusively to plasmon-polariton refractive-index fiber bio-sensors with fiber Bragg grating. 
     BACKGROUND OF THE INVENTION 
     Bio-sensing is usually performed by measuring a parameter such as the refractive index of a liquid which is dependent on the concentration of a solute measurand. Conventional methods require an absolute measurement of the refractive index detected through a change in transmission properties, for example the Surface Plasmon Resonance angle. Such measurement can be quite difficult to implement and requires a lot of equipments generally complicated to use. An optical fiber-based interferometer may be used but the core region of the fiber(s) is difficult to access since it is completely enclosed; such an interferometer is very unstable due to the nature of the fiber. 
     A Surface Plasmon-Polariton (SPP) represents a surface electromagnetic wave that propagates between two media having respective permittivity real parts of opposite signs and made, for example, of respective dielectric and metallic materials [1]. SPP can be supported on cylindrical and planar surfaces or geometries. The SPP field components have their maxima at the interface between the media and the metal layer and decay exponentially in both media [1]. Their small penetration depth in the media makes SPPs a great tool for sensor applications. 
     Traditional planar SPP sensor systems used for bio-sensing work on the principle of prism coupling by altering the angle of the incident beam to match the propagation constant of the SPP. This relies on incorporating moving parts into the sensor. 
     Other known optical fiber sensors are based on the properties of the SPP penetrating along the surface of a thin gold or silver layer deposited on an exposed portion of the core of the optical fiber [2-10]. In the latter optical fiber sensors, the core of the fiber is used instead of the coupling prism of the traditional planar SPP sensor systems. More specifically, these fiber sensors are constructed by modifying traditional SPP planar sensor systems. Scanning the light wavelength or change in the angle of incidence of the incident light is used for SPP excitation. Generally, the resulting optical fiber sensors include moving parts which render the SPP excitation process rather difficult. 
     Therefore, there is a need for an improved optical fiber sensor using SPP, which is simple, free from instability and demonstrates a high efficiency whereby it can be used as a successful bio-sensor. 
     SUMMARY OF THE INVENTION 
     More specifically, in accordance with the present invention, there is provided an optical waveguide sensing device comprising: a waveguide layer for receiving an optical signal and propagating the optical signal in accordance with a predetermined optical waveguide propagation mode; and a testing medium surface in communication with the waveguide layer and responsive to a testing medium for modifying at least one characteristic of the propagated optical signal in relation to a given parameter of the testing medium. Therefore, the modified characteristic of the propagated optical signal can be measured in view of determining the given parameter of the testing medium. 
     The present invention also relates to an optical waveguide sensing method comprising: receiving an optical signal and propagating said optical signal through a waveguide layer in accordance with a predetermined optical waveguide propagation mode; applying a testing medium to a testing medium surface in communication with the waveguide layer; and modifying at least one characteristic of the propagated optical signal in relation to a given parameter of the testing medium. Therefore, the modified characteristic of the propagated optical signal can be measured in view of determining the given parameter of the testing medium. 
     The foregoing and other objects, advantages and features of the present invention will become more apparent upon reading of the following non-restrictive description of illustrative embodiments thereof, given by way of example only with reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the appended drawings: 
         FIG. 1  is a schematic view of a measuring device comprising an optical fiber waveguide sensor according to a first illustrative embodiment of the present invention, for measuring liquids; 
         FIG. 2  is a cross sectional view of the optical fiber waveguide sensor of  FIG. 1 ; 
         FIG. 3  is a schematic side view of an optical fiber waveguide sensor according to a second illustrative embodiment of the present invention; 
         FIG. 4  is schematic end view of the optical fiber waveguide sensor of  FIG. 3 ; 
         FIG. 5  is a schematic side view of an optical fiber sensor according to a third illustrative embodiment of the present invention; 
         FIG. 6  is a perspective view of a classical fiber having multiple layers; 
         FIG. 7  is a plot of the radial component of the electric field of the SPP times the n 2 (r) for structures with different metal layer thicknesses Δ in the vicinity of the metal layer; 
         FIG. 8  is a graph showing the dependence between a normalized propagation constant n 11   p  of the SPP and a thickness Δ of the metal layer; 
         FIG. 9  is a graph showing the dependence between the normalized propagation constant n 11   p  of the SPP and a refractive index n 1  of a testing medium; 
         FIG. 10  is a graph showing the dependence between a grating period Λ and a grating amplitude or strength σ (left axis), and the dependence between the grating period Λ and a grating reflectivity R (right axis) for a grating length L=6 cm and a thickness of the metal layer Δ=100 Å; 
         FIG. 11  is a graph showing the dependence between the grating length L and the grating reflectivity R with Δ=100 Å and (a) σ=2×10 −4 , Λ=496.8 nm, (b) σ=3×10 −4 , Λ=496.78 nm, (c) σ=5×10 −4 , Λ=496.74 nm; 
         FIGS. 12   a  and  12   b  are graphs illustrating Poynting fluxes of the Waveguided Fiber Modes (WFM) versus the optical fiber radius r Δ=50 Å, Δ=100 Å, and Δ=500 Å; 
         FIG. 13  is a graph showing the dependence between the WFM normalized propagation constant n 11   f  and the metal layer thickness Δ; 
         FIG. 14  is a graph of the wavelength corresponding to the maximum of the grating reflectivity R versus the refractive index n 1  of the surrounding medium, in which (a) L=7 cm, Λ=477 nm, σ=5×10 −4 , Δ=80 Å, (b) L=6 cm, Λ=497 nm, σ=3×10 −4 , Δ=100 Å, (c) L=5 cm, Λ=509 nm, σ=2.3×10 −4 , Δ=120 Å, and (d) L=4 cm, Λ=519 nm, σ=2×10 −4 , Δ=150 Å; 
         FIG. 15  is a graph of the reflectivity peak wavelength shift per 10 −5  change of the refractive index n 1  of the surrounding medium versus the metal layer thickness Δ for four structures: (1) Δ=80 Å, L=7 cm, Λ=477 nm, σ=5×10 −4 ; (2) Δ=100 Å, L=6 cm, Λ=497 nm, σ=3×10 −4 ; (3), Δ=120 Å, L=5 cm, Λ=509 nm, σ=2.3×10 −4 ; and (4) Δ=150 Å, L=4 cm, Λ=519 nm, σ=2×10 −4 , wherein the reflectivity R for all structures is about 70%; 
         FIGS. 16   a  and  16   b  are graphs of the plasmon-polariton propagation constant n p  versus the refractive index n s  of the surrounding medium and the metal layer thickness Δ; 
         FIG. 17  is a graph showing the grating reflectivity R versus the grating length L, for Λ=420 nm, σ=4×10 −4 , n s =1.33, and Δ=100 Å; 
         FIG. 18  is a graph of the wavelength corresponding to the maximum of the grating reflectivity R (70%) versus the refractive index n s  of the surrounding medium for (a) Δ=100 Å, L=9 cm, Λ=420 nm, σ(or GS)=4×10 −4 ; (b) Δ=130 Å, L=5 cm, Λ=469 nm, σ(or GS)=2×10 −4 ; and (c) Δ=150 Å, L=4 cm, Λ=496 nm, σ(or GS)=10 −4 ; and 
         FIG. 19  is a schematic side view of an optical fiber waveguide sensor according to a further illustrative embodiment of the present invention, comprising a metal layer modulated in thickness. 
     
    
    
     The following Table 1 shows the parameters used in  FIG. 18 : 
     
       
         
               
               
               
               
               
               
             
           
               
                 TABLE I 
               
               
                   
               
               
                 Wavelength shift per 10 −3   
                   
                   
                   
                   
                   
               
               
                 change in the refractive index, n 
                 Δ, Å 
                 L, cm 
                 GS 
                 Λ, nm 
                 R % 
               
               
                   
               
             
             
               
                 ~300 pm 
                 100 
                 9 
                 4 × 10 4   
                 420 
                 70 
               
               
                 ~190 pm 
                 130 
                 5 
                 2 × 10 4   
                 477 
                 70 
               
               
                 ~150 pm 
                 150 
                 4 
                 1 × 10 4   
                 496 
                 70 
               
               
                   
               
             
          
         
       
     
     DETAILED DESCRIPTION 
     According to a first illustrative embodiment of the present invention, a bio-sensor set-up of the interferometric type is illustrated in  FIG. 1 . The bio-sensor set-up of  FIG. 1  comprises a bio-sensor  10  having first and second optical paths of an optical interferometer  16  (Mach-Zehnder Interferometer (MZI), Michelson interferometer, etc.).  FIG. 1  illustrates, as a non-limitative example, a MZI  16  fabricated from optical waveguide sensors such as  18 . The MZI  16  comprises an optical waveguide sensor  18  for each optical path, an input  24  and an output  26 . The first optical path comprises a first optical waveguide sensor  18  defining a sensing arm  12  and the second optical path comprises a second optical waveguide sensor  18  defining a reference arm  14 . 
     The general principle of the bio-sensor set-up of  FIG. 1  is the following. The input  24  normally consists of an optical signal supplied to both the sensing arm  12  and the reference arm  14 . The introduction of a liquid  20  ( FIG. 2 ), whose parameter such as the refractive index needs to be measured, in the sensing arm  12  changes the optical propagation characteristics of the optical path corresponding to that arm  12  compared to those of the reference arm  14 . Usually, the sensing arm  12  and the reference arm  14  are, if not identical, very similar. Since the first and second paths are in very close proximity with respect to each other, a change, for example a phase or attenuation change, can be detected in the optical signal at the output  26  and this change can be converted to a change or value of the parameter of the liquid to be detected such as the refractive index. 
     As illustrated in  FIG. 2 , the optical waveguide sensors  18  (sensing arm  12  and reference arm  14 ) are formed with a number, for example two or more longitudinal trenches  22  extending through the optical waveguide layer  27 . The longitudinal trenches  22  allow the liquid  20  to be easily introduced into the first optical path (sensing arm  12 ). The liquid  20  is then in contact with the surface of the trenches and therefore with the optical waveguide layer  27 . Introduction of the liquid  20  into the trenches  22  will change the refractive index of the medium into the trenches  22  and therefore will change the optical propagation characteristics of the optical waveguide sensor  30 . As a consequence, this will also alter the phase or attenuation of the optical signal propagated through the optical waveguide sensor  18 . 
     The optical interferometer  16  is small (cms long) and is fabricated on a chip (integrated circuit). Therefore, the optical interferometer  16  is a very stable platform. Introduction of the liquid  20  into the trenches such as  22  of the sensing arm  12  can be referenced by introduction of a reference solution into the trenches  22  of the reference arm  14 . A temperature stable, highly sensitive interferometer  16  is thereby produced. Refractive index changes as low as 10 −7  can be detected in such a self-referencing interferometer system, something which is very difficult to attain any other way. 
     Optionally, two identical Bragg gratings  23  and  25  can be produced in corresponding regions of the sensing  12  and reference  14  arms, respectively. These Bragg gratings  23  and  25  cause the propagated optical signal on the output  26  to be highly sensitive to any difference between the sensing arm  12  and reference arm  14  by shifting the Bragg wavelength of the affected optical waveguide sensor  18  (sensing arm  12 ) (see “Raman Kashyap, Fiber Bragg Gratings, Academic Press, 1999, Section 6.3”). In this manner, the light reflection and transmission characteristics of the interferometer  16  change as a function of the refractive index of the liquid  20  introduced into the trenches  22  of the waveguide sensors  18 . 
     The simple set-up of  FIG. 1  enables easy introduction and removal of liquid  20  into and from the trenches  22  of the bio-sensor  10 , e.g. blood or other bodily fluids for example to conduct sugar analysis, potassium content, etc. As described hereinabove, this will also allow the bio-sensor to measure a change from an ambient reference. As the optical waveguide sensor  18  is accessible from the outside, it is very easy to clean, disinfect and otherwise maintain. 
       FIGS. 3 and 4  illustrate a second non-restrictive illustrative embodiment of an optical fiber waveguide sensor  30  that can be used, for example, as optical waveguide sensors  18  in the bio-sensor  10  of  FIG. 1 . More specifically, the optical fiber waveguide sensor  30  presents the general configuration of a modified optical fiber. 
     Before describing the optical fiber waveguide sensor  30 , characterization of a classical optical fiber  100  will be reviewed.  FIG. 6  shows the structure of such a classical fiber  100 . More specifically, a classical optical fiber  100  is generally a dielectric waveguide of a generally cylindrical shape that transmits light along its longitudinal axis  102  through total internal reflection. A classical optical fiber  100  consists of a plurality of superposed layers including a central cylindrical core layer  104  surrounded by a tubular cladding layer  106 . For total internal reflection to confine the optical signal inside the core layer  104 , the refractive index of the core layer  104  must be greater than the refractive index of the cladding layer  106 . The boundary between the core layer  104  and cladding layer  106  may either be abrupt such as in step-index optical fiber or gradual such as in graded-index optical fiber. 
     Any dielectric layer in a multi-layer optical fiber  100  will be considered as a waveguided layer (WL) if its refractive index is higher than the refractive indexes of all the other dielectric fiber layers. Therefore, the WL is generally the core layer  104 . 
     As illustrated in  FIG. 3 , the optical fiber waveguide sensor  30  can be used, for example, in the MZI  16  of  FIG. 1  as the sensing  12  and reference  14  arms. The optical fiber waveguide sensor  30  is generally of a cylindrical shape and is made of many superposed layers. At the center region of the optical fiber waveguide sensor  30  is placed a testing medium  32  which can be the liquid  20  of  FIG. 2 . The testing medium  32  has a radius r 1  and a refractive index n 1 . Surrounding the testing medium  32  is a cylindrical layer of metal  34  having a certain thickness Δ=(r m −r 1 ), where r m  is the larger radius of the cylindrical metal layer  34 . Then comes a WL  36  having a larger radius r 2  and a refractive index n 2 . Finally the last outer layer consists of a cladding layer  38  with a refractive index n 3 . 
     The electromagnetic wave oscillating in the WL  36  and exponentially decaying in all the other fiber layers is called the Waveguided Fiber Mode (WFM)  40 . The WFM  40  propagates along the longitudinal axis  42  of the optical fiber waveguide sensor  30  in a forward direction (see arrows  401 ). 
     A SPG  44  (Short-Period fiber Bragg Grating) can be imprinted in the WL  36 . Fiber Bragg gratings have shown significant potential for mode coupling in optical fibers. The SPG  44  can be viewed as a reflective mirror, in which a forward-propagation WFM  40  can be coupled to a backward-propagation SPP  46 . Therefore, the direction of propagation of the SPP  46  is opposite of the direction of propagation of the WFM  40 . Also, the SPG  44  is designed in such a way that the resonance or excitation coupling between the WFM  40  and the SPP  46  is the most efficient. For that purpose, the SPG  44  has a length L and grating parameters such as a grating period Λ, a grating amplitude or strength σ and a grating reflectivity R that can all be adjusted. 
     The SPP  46  can propagate at the interface of a dielectric and metal media. The SPP  46  has an electrical field component E and a magnetic field component H having their maxima at the interface between the metal layer  34  and the medium  32  and the interface between the metal layer  34  and the WL  36  and decay exponentially into both the medium  32  and the WL  36  as shown in  FIG. 3 . This small penetration depth in the medium  32  makes the SPP highly suitable for refractive index sensing of the testing medium  32 . 
     The principle of operation of the optical fiber waveguide sensor  30  is based on the efficient energy transfer between the WFM  40  and the SPP  46  provided by properly designing the SPG  44  imprinted into the WL  36 . More specifically, the excitation of the SPP  46  is based on the resonance coupling between the WFM  40  and the SPP  46  as provided by the SPG  44 . Furthermore, the efficiency of the SPP excitation as a function of the reflectivity R of the SPG  44  was determined on the basis of well developed coupled-mode theory for fiber Bragg gratings as described in details in a number of references [7-9, 11]. 
     Waveguided Fiber Mode (WFM) 
     Fiber modes as well as SPPs such as  46  are solutions of Maxwell&#39;s equations with standard boundary conditions at the fiber surface layers. The above described optical fiber waveguide sensor  30  comprises the cylindrical layered structure of  FIGS. 3 and 4 . Cylindrical polar coordinates (r, θ, z) are used to describe the cylindrical layered optical fiber waveguide sensor  30 . The region r&lt;r 1  is occupied by the testing medium  32  with a refractive index n 1 . The region r 1 &lt;r&lt;r m  comprises the metal layer  34  supporting a plasmon-polariton (SPP). The permittivity ∈(ω) of the metal layer  34  at a certain frequency ω is modeled by the Drude formula as follows:
 
∈(ω)=∈ ∞ [1−ω p   2 /ω(ω+ i ┌)]
 
where ∈ ∞  is a high-frequency value of ∈(ω), ω p  is a plasma frequency, ┌ is a damping rate of the plasma and i is √−1. The metal layer  34  is deposited on the inner cylindrical face of the WL  36 , as illustrated in  FIGS. 3 and 4 . The WL  36  has a refractive index n 2  and occupies the region r m &lt;r&lt;r 2 . The WL  36  is covered by the cladding layer  38  with a refractive index n 3  in the region r&gt;r 2 . The conditions n 2 &gt;n 1  and n 2 &gt;n 3  are imposed on the layered optical fiber waveguide sensor  30 . The dependence on z, θ, and time t is taken into account by means of second derivatives ∂ 2 /∂z 2 , ∂ 2 /∂θ 2 , and ∂ 2 /∂t 2 , so solutions are sought in which all field components contain a common factor exp(iβ vμ   f,p z+ivθ−iωt), where β vμ   f,p  is a propagation constant, superscripts f and p correspond to the WFM  40  and the SPP  46 , respectively, and the variable v represents an azimuth mode number. It should be noted that in the case of cylindrical geometries, except in the special case where v=0, the propagation modes do not have pure transverse electric field component Ē and/or magnetic field component  H .
 
     Each layer of the optical fiber waveguide sensor  30  is characterized by its phase parameters:
 
 u   i   2   =−w   i   2   =k   0   2   n   i   2 −(β vμ   f,p ) 2   (1)
 
where k 0  is the vacuum wave-number, n i  is the refractive index of the i th -layer of the optical fiber waveguide sensor  30 , with i=1, 2, 3 or m (the metal layer  34 ). The electric field components of the propagation modes of the cylindrical layered optical fiber waveguide sensor  30  involve Bessel functions of the real argument, which are oscillatory in character, for u i   2 &gt;0 and Bessel functions of imaginary argument, which are asymptotically exponential, for w i   2 &gt;0. Generally, non-radiative propagation modes of the cylindrical optical fiber waveguide sensor  30  are considered as well for the following regions: the cladding layer  38  (r&gt;r 2 ), the testing medium  32  (0&lt;r&lt;r 1 ), and the metal layer  34  (r 1 &lt;r&lt;r m ). The electric field components of the propagation modes of the cylindrical layered optical fiber waveguide sensor  30  are in the form of:
 
                       E   ϕ     =         -     C   1     f   ,     p   1           ⁢     w   1     ⁢       I   v   ′     ⁡     (       w   1     ⁢   r     )         -       A   1     f   ,   p       ⁢       σ   2       r   ⁢           ⁢     n   1   2         ⁢       I   v     ⁡     (       w   1     ⁢   r     )             ,     
     ⁢       E   z     =       -     A   1     f   ,   p         ⁢     w   1   2     ⁢       σ   2       v   ⁢           ⁢     β     v   ⁢           ⁢   μ     f     ⁢     n   1   2         ⁢       I   v     ⁡     (       w   1     ⁢   r     )           ,           (   2   )               
for the testing medium  32  (0&lt;r&lt;r 1 ),
 
                       E   ϕ     =       -       w   m     ⁡     (         C   m     f   ,   p       ⁢       I   v   ′     ⁡     (       w   m     ⁢   r     )         +       D   m     f   ,   p       ⁢       K   v   ′     ⁡     (       w   m     ⁢   r     )           )         -         σ   2       r   ⁢           ⁢     ɛ   ⁡     (   ω   )           ⁢     (         A   m     f   ,   p       ⁢       I   v     ⁡     (       w   m     ⁢   r     )         +       B   m     f   ,   p       ⁢       K   v     ⁡     (       w     m   ⁢           ⁢   i       ⁢   r     )           )           ,     
     ⁢       E   z     =       -         w   m   2     ⁢     σ   2           ɛ   ⁡     (   ω   )       ⁢   v   ⁢           ⁢     β     v   ⁢           ⁢   μ     f           ⁢     (         A   m     f   ,   p       ⁢       I   v     ⁡     (       w   m     ⁢   r     )         +       B   m     f   ,   p       ⁢       K   v     ⁡     (       w   m     ⁢   r     )           )         ,           (   3   )               
for the metal layer  34  (r 1 &lt;r&lt;r m ),
 
                       E   ϕ     =       -       u   2     (         C   2   f     ⁢       J   v   ′     ⁡     (       u   2     ⁢   r     )         +       D   2   f     ⁢       Y   v   ′     ⁡     (       u   2     ⁢   r     )           )       -         σ   2       r   ⁢           ⁢     n   2   2         ⁢     (         A   2   f     ⁢       J   v     ⁡     (       u   2     ⁢   r     )         +       B   2   f     ⁢       Y   v     ⁡     (       u   2     ⁢   r     )           )           ,     
     ⁢       E   z     =           u   2   2     ⁢     σ   2           n   2   2     ⁢   v   ⁢           ⁢     β     v   ⁢           ⁢   μ     f         ⁢     (         A   2   f     ⁢       J   v     ⁡     (       u   2     ⁢   r     )         +       B   2   f     ⁢       Y   v     ⁡     (       u   2     ⁢   r     )           )         ,           (   4   )               
for the WL  36  (r m &lt;r&lt;r 2 ); and
 
                       E   ϕ     =         -     D   3     f   ,   p         ⁢     w   3     ⁢       K   v   ′     ⁡     (       w   3     ⁢   r     )         -       B   3     f   ,   p       ⁢       σ   2       r   ⁢           ⁢     n   3   2         ⁢       K   v     ⁡     (       w   3     ⁢   r     )             ,     
     ⁢       E   z     =       -     B   3     f   ,   p         ⁢         w   3   2     ⁢     σ   2           n   3   2     ⁢   v   ⁢           ⁢     β     v   ⁢           ⁢   μ     f         ⁢       K   v     ⁡     (       w   3     ⁢   r     )           ,           (   5   )               
for the cladding layer  38  (r&gt;r 2 ), where σ 2 =ivn vμ Z 0 , and Z 0 =377Ω is the electromagnetic impedance in vacuum. n vμ   f =β vμ   f /k 0  is the normalized propagation constant of the WFM  40 . Subscript μ is used to distinguish the different solutions of the dispersion relation for a given azimuth mode number v.
 
     The magnetic field components of the propagation modes H z  and H φ  can be obtained on the basis of the relations presented in reference [11] for standard fiber core modes. The values A 1   f , C 1   f , A l   f , B l   f , C l   f , D l   f , (l=m, 2), and B 3   f , D 3   f  are arbitrary constants, which can be calculated from the continuity of the E z , H z , E φ  and H φ  components on the layer&#39;s boundaries and from the condition that the power carried by each propagation mode is normalized to 1 Watt. J v  and Y v  are the Bessel function of the first and second kinds of order v, respectively. I v  and K v  are the modified Bessel function of the first and second kinds of order v, respectively. The primes over these functions indicate the first derivative. The dispersion relation for cylindrical layered optical fiber waveguide sensors  30  can be obtained on the basis of the continuity conditions for the electric and magnetic components on layers&#39; boundaries. Using the above mentioned equation (1):
 
 u   i   2   =−w   i   2   =k   0   2   n   i   2 −(β vμ   f,p ) 2  
 
it is possible to find the region where n vμ   f  as a solution of the dispersion relation is given by:
 
max( n   1   ,n   3 )&lt; n   vμ   f   &lt;n   2 .  (6)
 
     Generally speaking, the case of the single mode solution is considered, since it is free from the intermodal interference; this condition is used for the interrogation unit (not shown) monitoring the transmitted WFM  40  at the output  26  of the bio-sensing set-up of  FIG. 1 . 
     Surface Plasmon-Polariton (SPP) 
     As mentioned in the foregoing description, the electric and magnetic field components of the SPP  46  have their maxima at the interface between the metal layer  34  and the medium  32  and the interface between the metal layer  34  and the WL  36  and decay exponentially into both the medium  32  and the WL  36 . In contrast to a hybrid WFM  40 , which will be discussed hereinafter, a “pure” SPP  46  of the multi-layered optical fiber waveguide sensor  30  has maxima at the above mentioned interfaces and decay exponentially in all the others layers of the optical fiber waveguide sensor  30 , including the WL  36 . 
     For a theoretical description of the electric field component of a “pure” SPP  46 , the term β vμ   f  needs to be formally replaced by β vμ   p  and the constants A 1   p , C 1   p , A m   p , B m   p , C m   p , D m   p , B 3   p , D 3   p  should be used instead of the values A 1   f , C 1   f , A m   f , B m   f , C m   f , D m   f , B 3   f , D 3   f  in the above equations (2), (3), (5). Also, the expression (4), describing the oscillating electric field components in the WL  36 , is replaced by a new expression describing the decay components of the electric field in this layer. The electric field components of the “pure” SPP  46  in the WL  36  present the form of: 
                       E   ϕ     =       -       w   2     ⁡     (         C   2   p     ⁢       I   v   ′     ⁡     (       w   2     ⁢   r     )         +       D   2   p     ⁢       K   v   ′     ⁡     (       w   2     ⁢   r     )           )         -         σ   2       r   ⁢           ⁢     n   2   2         ⁢     (         A   2   p     ⁢       I   v     ⁡     (       w   2     ⁢   r     )         +       B   2   p     ⁢       K   v     ⁡     (       w   2     ⁢   r     )           )           ,     
     ⁢       E   z     =           -     w   2   2       ⁢     σ   2           n   2   2     ⁢   v   ⁢           ⁢     β     v   ⁢           ⁢   μ     p         ⁢     (         A   2   p     ⁢       I   v     ⁡     (       w   2     ⁢   r     )         +       B   2   p     ⁢       K   v     ⁡     (       w   2     ⁢   r     )           )         ,           (   7   )               
where r m &lt;r&lt;r 2 .
 
     The values A 1   p , C 1   p , A l   p , B l   p , C l   p , D l   p , (I=m, 2), and B 3   p , D 3   p , like in the case of the WFM  40 , can be calculated from the continuity of the E z , H z , E φ , and H φ electric and magnetic field components on the layers&#39; boundaries and from the condition that the power carried by each “pure” SPP  46  is normalized to 1 Watt. 
     The dispersion relation for a “pure” SPP  46  can be obtained in the same way as the dispersion relation for the WFM  40 , that is on the basis of the continuity conditions for the electric and magnetic field components on the layers&#39; boundaries, but the expression (4) for the electric field components in the layer r m &lt;r&lt;r 2  needs to be replaced by the expression (7). In accordance with equation (1) the normalized propagation constant n 11   p  of the “pure” SPP  46  can be found as a solution of the dispersion relation in the interval:
 
n 11   p &gt;n 2 .  (8)
 
     For the sake of simplicity, in the following description, the “pure” SPP  46  will be designated as the SPP  46  of the cylindrical multi-layered optical fiber waveguide sensor  30 . 
       FIG. 7  is a plot of the radial component of the electric field of the SPP  46  times the n 2 (r) for different thicknesses Δ of the metal layer  34  in the vicinity of this metal layer  34 . The inset in  FIG. 7  shows the same dependence for the whole multi-layered optical fiber waveguide sensor  30 . When the metal layer  34  becomes thinner the SPP  46  is more confined to the vicinity of the metal layer  34 . In other words, by reducing the thickness Δ of the metal layer  34 , the sensitivity of the cylindrical multi-layered optical fiber waveguide sensor  30  is increased. 
     The dependence between the normalised propagation constant n 11   p  of the SPP  46  and the thickness Δ of the metal layer  34  is presented in  FIG. 8 . In contrast to the case of the WFM  40 , the normalised propagation constant n 11   p  of the SPP  46  is dramatically altered with a change in the thickness Δ of the metal layer  34  between approximately 20 and 150 Å. 
     The normalised propagation constant n 11   p  of the SPP  46  is also very sensitive to the refractive index n 1  of the testing medium  32  as can be seen in  FIG. 9 . The normalised propagation constant n 11   p  of the SPP  46  changes by approximately 0.1 when the refractive index n 1  of the testing medium  32  changes by 0.33. Therefore, this makes the SPP  46  an excellent tool for sensing a change in refractive index n 1 . 
     Short-period Fiber Bragg Grating (SPG) 
     The efficiency of the SPP  46  excitation as a function of the SPG  44  reflectivity R has been determined on the basis of well developed coupled-mode theory for fiber Bragg gratings described in details in a number of references [12-14]. There are two main conditions for achieving high efficiency of SPP  46  excitation. 
     The first condition is to phase-match the propagation constant of the WFM  40  with the propagation constant of the SPP  46 , by properly designing the grating period Λ the SPG  44  for a predetermined wavelength of interest. This has been done in the well known case of core-cladding fiber mode coupling as described in reference [13]. 
     The second condition is to determine the coupling constants between the WFM  40  and the SPP  46  by properly designing fiber and grating parameters of the SPG  44 . For the purpose of illustration, un-tilted fiber Bragg gratings are used in one embodiment. Of course, other types of fiber Bragg gratings can be implemented as well. Using un-tilted fiber Bragg gratings, the only non-zero coupling constants are those between the WFM  40  and the SPP  46  with the same azimuth numbers as taught by reference [13]. Following the teaching of reference [13], the coupling constants between the WFM  40  and the SPP  46  are calculated using the following relation: 
                     k     11   -   11       p   -   f       =           k   0     ⁢     n   2   2     ⁢   σ       4   ⁢     Z   0         ⁢       ∫   0     2   ⁢   π       ⁢           ⁢       ⅆ   Φ     ⁢       ∫     r   m       r   2       ⁢     r   ⁢           ⁢     ⅆ     r   (         E   r   p     ⁢     E   r     f   *         +       E   Φ   p     ⁢     E   Φ     f   *           )                         (   9   )               
where σ is the amplitude of the refractive index modulation of the SPG  44  (see reference [13]). For simplicity, σ is referred to as the grating strength. The analytical expression for k 11-11   p-f  is presented in the attached Appendix 1.
 
     For designing the optimal cylindrical multi-layered optical fiber waveguide sensor  30 , the influence of the different grating parameters (R, Λ, σ) and the layered structure on the grating reflectivity R is examined. The spectral location for the resonance connected with the WFM  40 -SPP  46  reflection on the grating is given by:
 
δ co-p   +k   f-f /2=0,  (10)
 
where δ co-p =(β 11   f +β 11   p −2π/Λ)/2, Λ is the period of the grating, and β 1   f  and β 11   p  are the fiber core propagation mode and the polariton propagation constants, respectively. k f-f  is the core-mode self-coupling constant, which is proportional to σ and is given by relation:
 
                     k     f   -   f       =           k   0     ⁢     n   2   2     ⁢   σ       2   ⁢     Z   0         ⁢       ∫   0     2   ⁢   π       ⁢           ⁢       ⅆ   Φ     ⁢       ∫     r   m       r   2       ⁢     r   ⁢           ⁢       ⅆ     r   ⁡     (              E   r   f          2     +            E         ⁢   Φ     f          2       )         .                       (   11   )               
The analytical expression for k f-f  can also be found in Appendix 1.
 
     For practical purposes, such as simplification of the production process and device miniaturization, the grating period Λ can be increased and the grating length L can be reduced. Keeping the spectral location of the WFM  40 -SPP  46  reflection resonance fixed (λ res =1.55 μm) and changing the grating strength σ, it is possible to change the period Λ of the grating. This dependence is presented in  FIG. 10  (left axis). When the grating strength σ becomes stronger, the grating period Λ decreases slightly, as a consequence of the relationships (10) and (11). Increasing the grating strength σ increases the reflectivity R dramatically, since the WFM  40 -SPP  46  coupling constant k 11-11   f-p , presented by equation (9) is proportional to σ ( FIG. 10 , right axis). 
     The second parameter of the grating, which influences the grating reflectivity R, is the length L of the grating. Again, increasing the grating length L increases the grating reflectivity R for a fixed grating period Λ, as illustrated in  FIG. 11 . 
     Results 
     In order to test the performance of the optical fiber waveguide sensor  30 , the parameters of the optical fiber waveguide sensor  30  have been set as described hereinafter and telecommunication wavelengths have been used. 
     In order to reduce losses, the layer  34  has been made of a metal having an absolute value of the real part of the permittivity sufficiently large compared to its imaginary part at telecommunication wavelengths. The best materials from this point of view are gold and silver; gold was used in the simulations reported by reference [10]. Also, the limit of zero damping, ┌→0, is a good approximation for sensing applications, as plasma resonances are far away. 
     The WFM  40  with v=1 was considered. The radius of the testing medium was r 1 =7 μm, the thickness Δ of the WL  36  was Δ=(r 2 −r m )=10 μm, the refractive index of the WL  36  was n 2 =1.442, and the refractive index of the cladding  38  was n 3 =1.4. The metal layer  34  was made of gold (Au). 
     It should be noted that in contrast to a purely dielectric fiber such as a classical fiber  100  as illustrated in  FIG. 6 , the WFM  40  of an optical fiber with a metal layer  34  has a hybrid nature. It consists of the WFM  40  of the multi-layered dielectric optical fiber coupled with the SPP  46  supported by the metal layer  34 , oscillating in the WL  36 , having maxima at the metal-dielectric boundaries r=r 1  and r=r m , and decaying exponentially in the vicinity of these boundaries. 
     The Poynting fluxes of such a hybrid WFM  40  in optical fiber waveguide sensors  30  with different thicknesses Δ of the metal layer  34  are presented in  FIGS. 12   a  and  12   b  as a function of the radius from the longitudinal axis  42 .  FIG. 12   a  shows the Poynting flux distributions throughout the layered optical fiber waveguide sensors  30 ; the SPPs  46  supported by the metal layers  34  coupled with the WFMs  40  can be seen. In the different multi-layered optical fiber waveguide sensors  30 , the metal layer  34  is thin, more specifically having a thickness given by Δ&lt;λ p /2π. This means that the SPP  46  on the boundaries r=r/ 1  and r=r m  are coupled with each other and form a single SPP  46  propagating along the metal layer  34 . 
       FIG. 12(   b ) illustrates the Poynting flux distributions in the vicinity of the metal layer  34  for metal layer thicknesses of Δ=50 Å, Δ=100 Å, and Δ=500 Å. For a metal layer thickness of Δ=500 Å, the SPP  46  is more localized at the boundary between the WL  36  and metal layer  34  than for the other thicknesses Δ of the metal layer  34 . This situation reverses as the metal layer thickness decreases (optical fiber waveguide sensors  30  with thicknesses Δ equal to 100 Å and 50 Å). The SPP  46  of the hybrid WFM  40  becomes more localized at the boundary between the metal layer and the testing medium  32 . 
     The relation between the normalized propagation constant n 11   f  of the WFM  40  and the thickness Δ of the metal layer  34  is presented in  FIG. 13 . The normalized propagation constant n 11   f  is almost insensitive to the thickness Δ of the metal layer  34 . It changes by about only 2×10 −4  when Δ changes by 20 times in the range of 20-400 Å. 
     In the process of optimizing the design of the multi-layered optical fiber waveguide sensor  30 , different parameters have been changed in order to achieve the largest grating period Λ and to reduce the grating length L as much as possible while fixing the reflectivity R approximately to 70%. As it has already been mentioned, increasing the grating strength σ for a fixed or increased grating length L increases the grating reflectivity R. At the same time, the grating period Λ will also have to be slightly reduced. 
     For example, for σ=10 −4 , the grating reflectivity R is R=16%, and the grating period is Λ=496.8 nm. For σ=5×10 −4 , the grating reflectivity R increases significantly (R=94%), and the grating period Λ remains almost unchanged (Λ=496.7 nm). In both cases the length of the gratings is L=6 cm and the thickness Δ of the metal layer  34  is Δ=100 Å. In other words, increasing the length L of the grating can increase the grating reflectivity R, but changes in the grating length L will not influence the grating period Λ at all. 
     In another example, for a multi-layered optical fiber waveguide sensor  30  with σ=3×10 −4 , Λ=496.7 nm, and Δ=100 Å, the reflectivity R is R=16% in the case the grating length L is L=2 cm, and R=94% in the case the grating length L is L=10 cm. 
     It should be mentioned that the grating period Λ does change with the thickness Δ of the metal layer  34  as a consequence of the change in the normalized propagation constant n 11   p  of the SPP  46 . 
       FIG. 14  illustrates the sensitivity of the multi-layered optical fiber waveguide sensor  30  by showing the relation between the refractive index n 1  of the testing medium  32  and the wavelength corresponding to the maximum (peak) of the grating reflectivity R. The sensitivity is presented for four different thicknesses Δ of the metal layer  34 , with a equal to 80 Å, 100 Å, 120 Å, and 150 Å. By reducing the thickness Δ of the metal layer  34 , essentially the sensitivity of the optical fiber waveguide sensor  30  is increased, but at the same time, in order to maintain high efficiency of the excitation of the SPP  46 , the grating length L and the grating strength σ have to be increased. As a consequence, the grating period Λ only slightly changes. 
     For example, for a metal thickness Δ of 80 Å, the shift of the wavelength corresponding to the peak of the grating reflectivity R is approximately 280 pm per 10 −3  change in the refractive index n 1  of the testing medium  32 . The grating reflectivity R of approximately 70% can be achieved for this thickness Δ of the metal layer  34  with a grating having the following parameters: L=7 cm, σ=5×10 −4 , and Λ≈477 nm. For a metal layer  34  with a thickness Δ=100 Å, the wavelength shift of the peak of the grating reflectivity R is approximately 230 pm per the same 10 −3  change in refractive index n 1 . 
     The grating reflectivity R of approximately 70% can also be realized with a grating characterized by the following parameters: L=6 cm, σ=3×10 −4 , and Λ≈497 nm. For a metal layer  34  with a thickness Δ=120 Å, the wavelength shift of the peak of the grating reflectivity R is approximately 190 pm per 10 −3  change in refractive index n 1 . 
     The grating reflectivity R of approximately 70% for this thickness Δ of the metal layer  34  can also be realized with a grating with L=5 cm, σ=2.3×10 −4 , and Λ≈509 nm. 
     For a multi-layered optical fiber waveguide sensor  30  with a thickness Δ=150 Å of the metal layer  34 , the wavelength shift of the peak of the grating reflectivity R is approximately 150 pm per 10 −3  change in refractive index n 1 . The grating reflectivity R of approximately 70% for this optical fiber waveguide sensor  30  can be achieved with a grating having parameters such as L=4 cm, σ=2×10 −4 , and Λ≈519 nm. 
     The relation between wavelength shifts of the peak of the grating reflectivity R for a change of 10 −5  in refractive index n 1  of the testing medium  32  in the vicinity of a nominal refractive index n 1 =1.33 (water) versus the thickness Δ of the metal layer  34  is presented in  FIG. 15 , for four different structures of optical fiber waveguide sensor  30 . The peak wavelength shift increases from 1.5 pm to 2.8 pm per 10 −5  change in refractive index n 1  when the thickness Δ of the metal layer  34  decreases from 150 to 80 Å. 
     As a non-limitative example, the transmission of the grating can be used as an input signal for the interrogation unit (not shown) used for sensor monitoring. The interrogation unit (not shown) monitoring the transmitted WFM  40  at the output  26  of the bio-sensing set-up of  FIG. 1  will then detect the shift in wavelength and by comparing the detected shift in wavelength to the shift in wavelength per 10 −3  change in the refractive index n s  for a peak reflectivity R fixed at 70% and as a function of the thickness Δ of the metal layer  34 , will determine the value of the refractive index n s . The detected value of the refractive index n s  will then be representative of detection or not of a given biological feature of the testing medium  32 . 
     Since losses in the materials of the optical fiber waveguide sensor  30  and coupling with the radiation modes were not taken into account, the transmission of the grating can be estimated as T=100%−R. The bandwidth of the reflectivity spectrum at the first zeros is inversely proportional to the grating length L as in the case of a standard optical fiber grating for counter-propagating resonance reflection as taught by reference [13]. 
     This example consists of estimating the sensitivity of the optical fiber waveguide sensor  30  for measuring a refractive index n 1  change approximately equal 10 −6  with a metal layer  32  having a thickness Δ=80 Å, a grating length L=7 cm, a grating period Λ=477 nm and a grating strength σ=5×10 −4 , assuming a measurement resolution of 0.28 pm. This resolution is possible as the slope of the transmission loss spectrum edge is about 3 dB/28 pm. Assuming that a measurement in transmission of 0.01 dB can be made results in a resolution of 1 ppm in refractive index changes. It should be reminded that temperature dependence of the refractive index is a factor that must also be taken into consideration. 
       FIG. 5  is a schematic side view of an optical fiber waveguide sensor  30 ′ according to a third illustrative embodiment of the present invention. The optical fiber waveguide sensor  30 ′ of  FIG. 5  comprises a core layer  36 ′ enclosed by a cladding layer  38 ′. Finally, a metal layer  34 ′ capable of supporting a SPP  46 ′ is deposited on the outside surface of the cladding layer  38 ′. The liquid  20  or other testing medium  32 ′ is applied to the outer surface of the metal layer  34 ′ of the optical fiber waveguide sensor  30 ′, instead of being introduced inside the sensor as in the optical fiber waveguide sensor  30 . 
     As shown in  FIG. 5 , the core layer  36 ′ has a refractive index n co  and allows for the core fiber mode FM  40 ′ to be propagated in the forward direction (see arrow  401 ′). A SPG  44  of length L is imprinted in the core layer  36 ′. The cladding layer  38 ′ has a refractive index n cl  and the surrounding testing medium  32 ′ has a refractive index n s . 
     The permittivity ∈(ω) of the metal layer  34 ′ is given by the Drude formula as provided hereinabove. The theoretical aspect for the optical fiber waveguide sensor  30 ′ is similar to the theoretical aspect for the optical fiber waveguide sensor  30 . Therefore, only the differences will be discussed hereinbelow. 
     Using the permittivity ∈(ω), the range of frequencies in which the multi-layered optical fiber waveguide sensor  30 ′ can support the SPP  46  is determined by the condition: ∈(ω)&lt;−n cl   2 . 
     As already indicated hereinabove, the field components of the SPP  46  have their maxima at the interface between the metal layer  34 ′ and the surrounding medium  32 ′ and at the interface between the metal layer  34 ′ and the cladding layer  38 ′. The SPP  46  decays exponentially into the surrounding medium  32 ′ and cladding layer  38 ′. In order to achieve a large overlap between the SPP  46  and the core fiber mode FM  40 ′, the thickness of the cladding layer has to be very small compared to a standard single mode optical fiber. 
     In order to simplify the device production process, it is beneficial to essentially increase the diameter of the fiber core  36 ′. Despite the dramatic reduction of the thickness of the cladding layer, the overall diameter of the optical fiber waveguide sensor  30 ′ due to the increase of the diameter of the core layer  36 ′ allows the overall structure to be easily handled. 
     During testing, telecommunication wavelengths were used. The diameter of the core layer was 26 μm, the refractive index n co  was 1.44072, and the outer diameter of the cladding layer was 30 μm, with a refractive index n cl  of 1.44. This resulting optical fiber was a single mode fiber. The fiber core mode was used for exciting the SPP  46 . 
     For design optimization, the relation should be understood between the SPP-FM, the parameters of the layered optical fiber waveguide sensor  30 ′ and the grating. The value of n p , corresponding to the effective refractive index of the SPP  46 , is very sensitive to changes in the refractive index n s  of the surrounding medium, as it can be seen in  FIG. 16(   a ), and to the thickness Δ of the metal layer  34 ′, as shown in  FIG. 16(   b ). 
     The sensitivity of the SPP  46  to the refractive index n s  is very suitable for sensor applications. As illustrated in  FIG. 16(   b ), increasing the thickness Δ of the metal layer  34 ′ decreases the value of the effective refractive index n p . Changes in the geometric parameters of the structure of the optical fiber waveguide sensor  30 ′, such as the diameter of the core layer  36 ′ and the diameter of the cladding layer  38 ′ do not dramatically change the parameters of the SPP  46 ′. These changes can quantitatively change the effective refractive index n p , but cannot change the relation of the index n p  with the index n s  and the thickness Δ. 
     The thickness Δ of the metal layer  34 ′ and the refractive index n s  of the surrounding medium  32 ′ are the main factors that influence the parameters of the SPP  46  such as the effective refractive index n p . However, the diameters of the core layer  36 ′ and the cladding layer  38 ′, the refractive indexes of the other layers as well as the grating length L and the amplitude of the refractive index modulation of the SPG  44  (grating strength σ) are other parameters that can be adjusted for optimizing the efficiency of the excitation of the SPP  46 . 
     The grating strength σ is a parameter that can be used for optimizing the grating period Λ, according to equation (10) given hereinbelow. At the same time, the grating length L and the grating strength σ can also be used to optimize the grating reflectivity R.
 
δ co-p   +k   co-co /2=0  (10)
 
where δ co-p =(β co +β p −2π/Λ)/2.
 
     As mentioned in the foregoing description, for device miniaturization and ease of production, the grating length L should be reduced as much as possible and the grating period Λ should be made the largest possible. By increasing the grating strength σ for a fixed grating length L, the grating reflectivity R can be increased; this also leads to a reduction in the grating period Λ. Indeed, from equation 10, β co  and β p , the fiber core mode and polariton propagation constants, respectively, are independent from the grating strength σ, while κ co-co , corresponding to the core mode self-coupling constant, is proportional to the grating strength σ. As can be seen from equation (10), the grating period Λ is proportional to the reciprocal of the grating strength σ and, as a consequence, it becomes smaller when the grating strength σ is increased. 
     As an example, for a grating strength σ=10 −4 , the grating reflectivity R is R=2.3%, and the grating period is Λ=475 nm for a metal layer thickness of 100 Å. For a grating strength σ=5×10 −4 , the grating reflectivity R increases significantly (R=55%), but the grating period Λ reduces to 404 nm. In both cases the grating length is fixed to L=8 cm. In this example, the surrounding medium  32 ′ is considered to be water with n s =1.33, which is typical in bio-sensing applications. 
     Although increasing the grating length L increases the reflectivity R, it does not affect the grating period Λ. However, changing the grating strength σ does affect the grating period Λ, since it affects the propagation constant β co  of the guided mode because the refractive index n co  of the core layer also changes as described in equation (10). The dependence of the grating reflectivity R on the grating length L is illustrated in  FIG. 17  for a refractive index n s =1.33. 
       FIG. 18  illustrates the relation between the wavelength corresponding to the maximum (peak) of grating reflectivity R of the multi-layered optical fiber waveguide sensor  30 ′ and the refractive index n s  of the surrounding medium  32 ′. The sensitivity of the fiber sensor  30 ′ is presented for three different thicknesses Δ (100 Å, 130 Å, and 150 Å) of the metal layer  34 ′. Reducing the thickness Δ of the metal layer  34 ′ essentially increases the sensitivity of the optical fiber waveguide sensor  30 ′, but at the same time in order to maintain a high excitation efficiency of the SPP  46 , the grating length L as well as the grating strength σ are increased and, as a consequence, the grating period Δ is reduced. These results are substantially the same as in the case of the optical fiber waveguide sensor  30 . 
     Table 1 summarizes the data used to build the graph of  FIG. 18 , which shows the sensitivity of the optical fiber waveguide sensor  30 ′, i.e. the shift in wavelength per 10 −3  change in the refractive index n s  for a peak reflectivity R fixed at 70% and as a function of the thickness Δ of the metal layer  34 ′. For higher sensitivity (300 pm shift in wavelength/10 −3  change in the refractive index n s ), a thin metal layer  34 ′ is required with a grating length L of 9 cm and a strong grating strength σ. 
     As a non-limitative example, the transmission of the grating can be used as an input signal for the interrogation unit (not shown) used for sensor monitoring. The interrogation unit (not shown) monitoring the transmitted FM  40 ′ at the output  26  of the bio-sensing set-up of  FIG. 1  will then detect the shift in wavelength and by comparing the detected shift in wavelength to the shift in wavelength per 10 −3  change in the refractive index n s  for a peak reflectivity R fixed at 70% and as a function of the thickness Δ of the metal layer  34 ′, will determine the value of the refractive index n s . The detected value of the refractive index n s  will then be representative of detection or not of a given biologic feature of the testing medium  32 ′. 
     However, even with a short grating length L of 4 cm, it is possible to achieve a reflectivity R of 70% for a metal layer of larger thickness Δ of 150 Å, but with half the wavelength shift sensitivity (150 pm/10 −3  change in the refractive index n s ). It should be noted that the grating length L and the grating strength σ inversely varies with the thickness Δ of the metal layer  34 ′, while maintaining the reflectivity R at 70%; this is due to the increased overlap of the SPP  46  and FM  40 ′ but this reduces the wavelength shift sensitivity to change in the refractive index n s  of the surrounding medium  32 ′. 
     According to the above presented results, it is possible to estimate the sensitivity of a optical fiber waveguide sensor  30 ′ for measuring the change in refractive index n s  with a metal layer thickness Δ=100 Å, a grating length of L=9 cm, a grating period Λ=420 nm, and a grating strength σ (or GS)=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 edge of the transmission loss spectrum is ˜3 dB/30 pm. Assuming that a change in transmission of 0.01 dB can be measured, results in a resolution of 1 ppm in refractive index change for such an optical fiber waveguide sensor  30 ′ is possible. 
     An advantage of an optical fiber waveguide sensor  30 ′ is that it can be easily exposed to the medium  32 ′ and cleaned for use in a clinical laboratory for high volume analysis. Also, several different optical fiber waveguide sensors  30 ′ of varying sensitivities or sensing capability (chemical type) can be integrated into one platform for parallel analysis. 
     Another advantage of the optical fiber waveguide sensor  30  or  30 ′ over other sensors based on prism coupling techniques is that it comprises no moving parts, it is compact and has a high sensitivity as described in the foregoing description. 
     Also, the above described SPP  46  scheme compares favorably with the attenuated-total-reflection technique since it is free from moving parts to control the incident angle of the light beam. The optical fiber waveguide sensor  30  or  30 ′ is an all fiber sensor and can be directly fusion spliced into fiber-optic systems for low insertion losses. 
     It should be noted that, although the present invention has been more extensively described for a cylindrical structure such as an optical fiber, it can be realized in a planar geometry as describe in  FIGS. 1 and 2  without loss of generality. 
     Also, a surface plasmon on an optical fiber or waveguide surface may be excited by the arrangement of  FIG. 19 . In this particular case, the metal layer  191  is modulated in thickness, material or grade in a periodic way to allow phase matching between the guided mode such as  192  and the surface plasmon  193 . The thickness, material or grade modulation can be made according to a fixed period or can be chirped. 
     The phase-matching condition is given by:
 
β guided mode +β plasmon +β grating =0
 
where β refers to the phase parameter of the subscripted item. The grating phase constant is given by:
 
β grating =2π/Λ
 
where Λ is the period of the modulation.
 
The thickness, material or grade modulation of the metal layer  191  presents the advantages that it can be easily fabricated, altered, manufactured, and has no moving parts. The liquid is placed on the top outer surface of the metal layer  191  for sensing the refractive index which is measured by detecting a shift in the wavelength of the resonance coupling given by the equation:
 
β guided mode +β plasmon +β grating =0
 
     Although the present invention has been described in the foregoing description by means of non-restrictive illustrative embodiments, these embodiments can be modified at will within the scope of the appended claims, without departing from the spirit and nature of the subject invention. 
     APPENDIX 1 
     In this appendix, the analytical expression for the coupling constant of the WFM-SPP described by equation (9) is presented. Using the expressions (4), (7) and (9) we have: 
                 k     11   -   11       f   -   p       =         πσ   ⁢           ⁢     n   2   2         4   ⁢     k   0     ⁢     Z   0         ⁢       u   ~     2     ⁢         w   ~     2     ⁡     [         -     a   f       ⁢     a   p     ⁢     I   5       +       b   f     ⁢     b   p     ⁢     I   1       +       c   f     ⁢     c   p     ⁢     I   6       -       d   f     ⁢     d   p     ⁢     I   2       +       a   f     ⁢     c   p     ⁢     I   7       -       b   f     ⁢     d   p     ⁢     I   3       -       c   f     ⁢     a   p     ⁢     I   8       +       d   f     ⁢     b   p     ⁢     I   4         ]           ;         
where
 
                 a   f     =       C   2   f     -       A   2   f       n   2   2           ;                   b   f     =       C   2   f     +       A   2   f       n   2   2           ;                       ⁢         c   f     =       D   2   f     -       B   2   f       n   2   2           ;                     d   f     =       D   2   f     +       B   2   f       n   2   2           ;                   a   p     =       C   2   p     -       A   2   p       n   2   2           ;                   b   p     =       C   2   p     +       A   2   p       n   2   2           ;                   c   p     =       D   2   p     -       B   2   p       n   2   2           ;                   d   p     =       D   2   p     +       B   2   p       n   2   2           ;           I   i   =Ĩ   i ( {tilde over (r)}   2 )− Ĩ   i ( {tilde over (r)}   m );  i= 1, 2, 3, 4, 5, 6, 7, 8.   Ĩ   1 ( {tilde over (r)} )= {tilde over (r)} ( {tilde over (w)}   2   J   0 ( ũ   2   {tilde over (r)} ) I   1 ( {tilde over (w)}   2   {tilde over (r)} )+ ũ   2   J   1 ( ũ   2   {tilde over (r)} ) I   0 ( {tilde over (w)}   2   {tilde over (r)} ))/( ũ   2   2   −{tilde over (w)}   2   2 );   Ĩ   2 ( {tilde over (r)} )= {tilde over (r)} ( {tilde over (w)}   2   Y   0 ( ũ   2   {tilde over (r)} ) K   1 ( {tilde over (w)}   2   {tilde over (r)} )+ ũ   2   Y   1 ( ũ   2   {tilde over (r)} ) K   0 ( {tilde over (w)}   2   {tilde over (r)} ))/( ũ   2   2   −{tilde over (w)}   2   2 );   Ĩ   3 ( {tilde over (r)} )= {tilde over (r)} ( {tilde over (w)}   2   J   0 ( ũ   2   {tilde over (r)} ) K   1 ( {tilde over (w)}   2   {tilde over (r)} )+ ũ   2   J   1 ( ũ   2   {tilde over (r)} ) K   0 ( {tilde over (w)}   2   {tilde over (r)} ))/( ũ   2   2   −{tilde over (w)}   2   2 );   Ĩ   4 ( {tilde over (r)} )= {tilde over (r)} ( {tilde over (w)}   2   Y   0 ( ũ   2   {tilde over (r)} ) I   1 ( {tilde over (w)}   2   {tilde over (r)} )+ ũ   2   Y   1 ( ũ   2   {tilde over (r)} ) I   0 ( {tilde over (w)}   2   {tilde over (r)} ))/( ũ   2   2   −{tilde over (w)}   2   2 );   Ĩ   5 ( {tilde over (r)} )= {tilde over (r)} ( {tilde over (w)}   2   J   2 ( ũ   2   {tilde over (r)} ) I   1 ( {tilde over (w)}   2   {tilde over (r)} )− ũ   2   J   1 ( ũ   2   {tilde over (r)} ) I   2 ( {tilde over (w)}   2   {tilde over (r)} ))/( ũ   2   2   −{tilde over (w)}   2   2 );   Ĩ   6 ( {tilde over (r)} )= {tilde over (r)} ( {tilde over (w)}   2   Y   2 ( ũ   2   {tilde over (r)} ) K   1 ( {tilde over (w)}   2   {tilde over (r)} )− ũ   2   Y   1 ( ũ   2   {tilde over (r)} ) K   2 ( {tilde over (w)}   2   {tilde over (r)} ))/( ũ   2   2   −{tilde over (w)}   2   2 );   Ĩ   7 ( {tilde over (r)} )= {tilde over (r)} ( {tilde over (w)}   2   J   2 ( ũ   2   {tilde over (r)} ) K   1 ( {tilde over (w)}   2   {tilde over (r)} )− ũ   2   J   1 ( ũ   2   {tilde over (r)} ) K   2 ( {tilde over (w)}   2   {tilde over (r)} ))/( ũ   2   2   −{tilde over (w)}   2   2 );   Ĩ   8 ( {tilde over (r)} )= {tilde over (r)} ( {tilde over (w)}   2   Y   2 ( ũ   2   {tilde over (r)} ) I   1 ( {tilde over (w)}   2   {tilde over (r)} )− ũ   2   Y   1 ( ũ   2   {tilde over (r)} ) I   2 ( {tilde over (w)}   2   {tilde over (r)} ))/( ũ   2   2   −{tilde over (w)}   2   2 );   {tilde over (r)}=r/k   0   ;ũ   2   =u   2   /k   0 , and  {tilde over (w)}   2   =w   2   /k   0 . 
A 2   f , B 2   f , C 2   f , D 2   f  correspond to the WFM, and A 2   p , B 2   p , C 2   p , D 2   p  correspond to the SPP.
 
The WFM self coupling coefficient presented by equation (10) can be found in the analytical form from the expressions (4) and (10):
 
                 k     f   -   f       =         π   ⁢           ⁢   σ   ⁢           ⁢     n   2   2         2   ⁢     k   0     ⁢     Z   0         ⁢         u   ~     2   2     ⁡     [         a     f   2       ⁢     I   1   f       +       b     f   2       ⁢     I   2   f       +       c     f   2       ⁢     I   3   f       +       d     f   2       ⁢     I   4   f       +     2   ⁢     a   f     ⁢     c   f     ⁢     I   5   f       +     2   ⁢     b   f     ⁢     d   f     ⁢     I   6   f         ]           ;         
where I i   f =Ĩ i   f ({tilde over (r)} 2 )− Ĩ   i   f ( {tilde over (r)}   m ); i=1, 2, 3, 4.
   Ĩ   1   f ( {tilde over (r)} )= {tilde over (r)}   2 ( J   2   2 ( ũ   2   {tilde over (r)} )− J   1 ( ũ   2   {tilde over (r)} ) J   3 ( ũ   2   {tilde over (r)} ))/2;   Ĩ   2   2 ( {tilde over (r)} )= {tilde over (r)}   2 ( J   0   2 ( ũ   2   {tilde over (r)} )+ J   1   2 ( ũ   2   {tilde over (r)} ))/2;   Ĩ   3   f ( {tilde over (r)} )= {tilde over (r)}   2 ( Y   2   2 ( ũ   2   {tilde over (r)} )− Y   1 ( ũ   2   {tilde over (r)} ) Y   3 ( ũ   2   {tilde over (r)} ))/2;   Ĩ   1   f ( {tilde over (r)} )= {tilde over (r)}   2 ( Y   0   2 ( ũ   2   {tilde over (r)} )+ Y   1   2 ( ũ   2   {tilde over (r)} ))/2; 
     
       
         
           
             
               
                 
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     REFERENCES 
     
         
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