Abstract:
An optical fiber polarimetric chemical sensor for capillary gas chromatography in which a sample fluid is injected into a capillary in the form of a periodic pulse train. Each individual pulse defines a moving polarization coupling zone that affects the polarization state of the light propagating in a birefringent optical waveguide that includes the capillary. The spacing between consecutive coupling zones can be made equal to the polarization beat length of the waveguide when the injection frequency of the pulses is properly selected, thus defining a resonance condition for a given analyte. The contributions of the successive coupling zones present along the length of the capillary then add up in phase, thus resulting in a detected optical signal having an enhanced amplitude peak at the injection frequency. In this manner, the sensitivity can be enhanced.

Description:
BACKGROUND 
       [0001]    Traditional capillary gas chromatography involved injecting a sample for analysis into a carrier gas. The sample is carried in the carrier gas in a capillary onto which it is partitioned which slows the migration speed of analyte vapors relative to the carrier gas. The partitioning involves a portion of the sample (which can be referred to as the partitioned portion) becoming bonded with the capillary and then released in a continuous process on the molecular scale. In the case where the capillary is coated by a fluid film, which is more common, the bonding occurs by absorption in the fluid film. Alternately, the bonding can also occur by adsorption on a solid surface. 
         [0002]    The relation between the migration rate (v) of a given chemical and the rate flow (u) of the carrier gas is given by: v=pu, where p is the retention ratio, which is the probability of an analyte to be in the carrier gas (1−p being the probability of absorption). The retention ratio is typically different for different analytes, and the analytes thus each have a characteristic migration rate in a given sample. To facilitate understanding, reference is made to  FIGS. 1A and 1B  which schematically illustrate the concentration of two analytes migrating along the length of a capillary at two different points in time. 
         [0003]    Each analyte can thus be seen to travel as a distinct packet, or zone of higher concentration, having a characteristic migration rate. Typically, the packets have a sharp zone distribution at first, and gradually broaden as they travel along the capillary, but they also separate themselves as a function of their characteristic average speed which makes them more distinct. 
         [0004]    At the exit of the capillary, a sensor (such as a thermal conductivity sensor for instance) can detect an intensity variation associated with the presence or absence of an analyte. The characteristics of the capillary and the rate flow of the carrier gas being known, a detection at a given point in time can be associated with a migration rate characteristic of a specific analyte. 
         [0005]    U.S. Pat. No. 7,403,673, the contents of which are incorporated herein by reference, taught a new approach to chemical sensors. This approach involved guiding light in a birefringent optical waveguide which has a light propagation volume (such as a core) positioned adjacent to a capillary; close enough for an analyte absorbed in the stationary phase to interact with the evanescent field of the guided light and therefore affect the polarization state of the light. Information on the fluid to analyze was obtained from the detected variations in the light polarization state by measuring the light power transmitted through a polarizer placed at the output of the waveguide. This approach involved using a birefringent optical waveguide which had two refractive indexes which defined a birefringence B and a polarization beat length L b  These two values being related, for a given wavelength λ of the light by: 
         [0000]    
       
         
           
             
               L 
               b 
             
             = 
             
               
                 λ 
                 B 
               
               . 
             
           
         
       
     
         [0006]    The beat length L b  is the distance along the birefringent waveguide which corresponds to a phase shift of 2π between the two polarization modes, and is thus the length of the waveguide for which a polarization state reproduces itself. 
         [0007]    In the case of an optical fiber polarimetric chemical sensor, where, for instance, light is injected according only to one polarization axis, the presence of locally absorbed vapor in the capillary which is adjacent the propagation volume transfers some of the light to the other polarization axis, and can thus be said to constitute a coupling point between the polarization axes. The new polarization state, which can be elliptical for instance, then evolves to the optical fiber output where it can be analyzed with a polarizer. When a single light wavelength is used, as analytes are moving at speed (migration rate) v and as polarization states reproduce themselves each distance equal to the beat length L b , the light power transmitted at an output polarizer will oscillate at an oscillation frequency, or beat frequency, f b  given by: 
         [0000]    
       
         
           
             
               v 
               
                 L 
                 b 
               
             
             . 
           
         
       
     
         [0008]    The transmittance of the optical waveguide, including the output polarizer can be given with a good approximation by: 
         [0000]    
       
         
           
             
               
                 I 
                  
                 
                   ( 
                   t 
                   ) 
                 
               
               
                 I 
                 0 
               
             
             = 
             
               
                 1 
                 2 
               
               - 
               
                 
                   ∑ 
                   
                     j 
                     = 
                     1 
                   
                   N 
                 
                  
                 
                     
                 
                  
                 
                   
                     κ 
                     j 
                   
                    
                   
                     cos 
                      
                     
                       ( 
                       
                         
                           
                             
                               2 
                                
                               π 
                             
                             
                               L 
                               b 
                             
                           
                            
                           
                             v 
                             j 
                           
                         
                         + 
                         
                           ϕ 
                           j 
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
         [0009]    where φ is a term of phase that can be discarded. The Fourier transform of the detected signal gives peaks having spectral peaks having locations corresponding to specific migration rates, and thus to corresponding analytes. 
         [0010]    κ is the strength of the polarization mode coupling. This variable is related to the concentration of analytes and to its distribution in the capillary fibre. It will be understood that for very small quantity of analytes the mode coupling is consequently very small and the oscillation amplitude at the oscillation frequency f b  can be too weak to be detected on the Fourier transform. 
         [0011]    There remained room for improvement, such as to increase the sensitivity of such chemical sensors. 
       SUMMARY 
       [0012]    The sensitivity of the former sensor was limited by the unity of the injection of a sample into the carrier gas. Indeed, at a given time, there was only one coupling zone per analyte along the length of the birefringent waveguide, so there was a limit to the polarization mode coupling caused by the partitioned molecules of the given molecule type via the evanescent field of the guided light when the analyte concentration was low. Henceforth, the strength of the signal which is to be measured, that is the amount of light which has changed polarization, can be limited, which affects the limit of detection of the sensor. 
         [0013]    This limit of detection can be enhanced by increasing the value of κ. One way is to use periodically-varying sample injection instead of punctual injection. If the variations in the injection are done at an injection frequency f i  associated to the polarizer oscillation frequency f b , successive analyte pulses can be separated in the passage (typically a capillary) by a distance equal to the beat length, or to an integer multiple thereof. In this manner, the later analyte pulses in the passage will cause a polarization coupling which will add to the amplitude of the polarization coupling caused by the earlier analyte pulses in the passage given the beat length of the birefringent optical waveguide, and the amplitude of the polarizer oscillation frequency f b  will be increased for the given analyte, facilitating detection following the Fourier transform. 
         [0014]    In accordance with one aspect, there is provided a method of analyzing a sample fluid comprising: injecting light in a propagation volume of a birefringent optical waveguide having a beat length; circulating a sample fluid along a passage located adjacent the propagation volume, with a partitioned portion of the sample fluid interacting with an evanescent wave of the injected light, thereby affecting the polarization state thereof; modulating the injection over time in a manner that a plurality of zones of higher concentration of the sample along the passage are distant from one another by integer multiples of the beat length. 
         [0015]    In accordance with another aspect, there is provided a chemical sensor including birefringent optical waveguide having a beat length, a propagation volume, and a passage defined by a partitioning material, located adjacent the propagation for sample fluid conveyed in the passage to interact with an evanescent wave of light propagating in the propagation volume and thereby affect the polarization state, a light source for injecting light into the propagation volume, an optical detector for detecting a periodical variation of the polarization state at an oscillation frequency, caused by the displacement of the sample in the passage, and a modulator for injecting the sample into the passage at a concentration varying according to an injection frequency. 
         [0016]    Because a liquid film is more typical in the case of capillary analysis, the expression absorbed will be used herein as encompassing the expression adsorb. 
         [0017]    Many further features and combinations thereof concerning the present improvements will appear to those skilled in the art following a reading of the instant disclosure. 
     
    
     
       DESCRIPTION OF THE FIGURES 
         [0018]    In the figures, 
           [0019]      FIG. 1  is a view of illustrating propagation of two analytes in a capillary; 
           [0020]      FIG. 2  is a view showing the dependence of |R| on the period, three cases are considered corresponding to three different values of the velocity; 
           [0021]      FIG. 3  is a schematic view of a sensor; 
           [0022]      FIG. 4  shows the temporal evolution of the concentration distribution of a time-varying injection (below) compared to temporal evolution of one impulse (above); 
           [0023]      FIG. 5  is a schematic view of an alternate embodiment, where the acceleration effect is compensated by temperature gradient; and 
           [0024]      FIG. 6  is a schematic view of an other alternate embodiment, where the acceleration effect is compensated by pressure control. 
       
    
    
     DETAILED DESCRIPTION 
       [0025]    When the variations in the injection are done at an injection frequency f i  associated to the oscillation frequency f b  (or f(oscillation)), successive analyte pulses, or zones of higher sample concentration, can be separated from one another in the passage by a distance Λ, or pitch, being an integer multiple of the beat length (the integer multiple being one or more), in accordance with 
         [0000]    
       
         
           
             
               1 
               
                 T 
                  
                 
                   ( 
                   injection 
                   ) 
                 
               
             
             = 
             
               
                 f 
                  
                 
                   ( 
                   injection 
                   ) 
                 
               
               = 
               
                 
                   pu 
                   Λ 
                 
                 = 
                 
                   
                     pu 
                     
                       L 
                       b 
                     
                   
                   = 
                   
                     f 
                      
                     
                       ( 
                       oscillation 
                       ) 
                     
                   
                 
               
             
           
         
       
     
         [0026]    In other words, a first injected pulse of the sample of a limited volume begins to travel within the passage. The investigated analyte being present, the absorbed molecules thereof cause polarization mode coupling of light in the first polarization to the second polarization. However, this coupling can be small since there is a limited amount of molecules of the investigated analyte in the sample. This first injected pulse travels along the passage of birefringent waveguide for a given distance, and the signal being so minute, the expected mode coupling may not even be detected. However, as the first injected pulse reaches a distance equal to the beat length, a second sample pulse is injected. This second injected pulse also causes a transfer of light to the other polarization, and since it is precisely timed, this additional signal is of the same phase than the signal caused by the first pulse and therefore strengthens the signal in the other polarization. If the birefringent optical waveguide is sufficiently long, a third, fourth, fifth, etc. pulses can all cause corresponding polarization coupling and the detected signal at the end of the birefringent optical waveguide includes the sum of each individual timed sample pulse signal contribution all being in phase. Henceforth, one can detect the collective signal sum stemming from each individual pulse where any given one of the pulses did not necessarily yield a signal of a strength sufficient to be detected. The sensitivity of the sensor is thus enhanced. More particularly: 
         [0027]    Injection and Diffusion 
         [0028]    The injection can consists of a series of pulses, each having at the entrance in the passage a concentration distribution given by f o (z). Each pulse moves at a velocity v and diffuses, taking the form f(z,t) determined by the diffusion equation (the so-called mass-balance equation). At some stage, the number of pulses simultaneously present in the passage can reach a maximum value M=L/vT, L being the fiber length, and the overall concentration distribution can read as: 
         [0000]        C ( z,t )=Σ n=0   M−1   f ( z,t−nT )  (1)
 
         [0000]    where T is the time delay between each impulse, that is the inverse of the injection frequency. 
         [0029]    For the sake of simplicity, we now consider the specific case of a Gaussian initial pulse shape: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                      
                     
                       ( 
                       
                         z 
                         , 
                         0 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       A 
                       o 
                     
                      
                     
                       
                         exp 
                          
                         
                           ( 
                           
                             - 
                             
                               
                                 z 
                                 2 
                               
                               
                                 W 
                                 0 
                                 2 
                               
                             
                           
                           ) 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0030]    This makes the model analytically tractable while having no impact on the main conclusions. The diffusion equation admits such a Gaussian solution. This means that as each of the injected pulse moves and diffuses it maintains its Gaussian shape. The distribution spreads out and its amplitude decreases according to: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       W 
                       n 
                     
                     = 
                     
                       
                         
                           W 
                           o 
                         
                          
                         
                           [ 
                           
                             1 
                             + 
                             
                               
                                 4 
                                  
                                 
                                     
                                 
                                  
                                 
                                   D 
                                   eff 
                                 
                                  
                                 
                                   t 
                                   n 
                                 
                               
                               
                                 W 
                                 o 
                                 2 
                               
                             
                           
                           ] 
                         
                       
                       
                         1 
                         / 
                         2 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   and 
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       A 
                       n 
                     
                     = 
                     
                       
                         A 
                         o 
                       
                       
                         
                           [ 
                           
                             1 
                             + 
                             
                               
                                 4 
                                  
                                 
                                     
                                 
                                  
                                 
                                   D 
                                   eff 
                                 
                                  
                                 
                                   t 
                                   n 
                                 
                               
                               
                                 W 
                                 o 
                                 2 
                               
                             
                           
                           ] 
                         
                         
                           1 
                           / 
                           2 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     t 
                     n 
                   
                   = 
                   
                     t 
                     - 
                     nT 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0000]    corresponds to the time elapsed after the injection of the n th  pulse. 
         [0031]    Sensor Response 
         [0032]    In presence of a moving coupling zone, the capillary fiber sensor can be characterized by a periodic time variation in the light intensity I(t) transmitted through an output polarizer (and thus in the second polarization axis): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       I 
                        
                       
                         ( 
                         t 
                         ) 
                       
                     
                     
                       I 
                       o 
                     
                   
                   = 
                   
                     
                       1 
                       2 
                     
                     + 
                     
                       κ 
                        
                       
                           
                       
                        
                       
                         cos 
                          
                         
                           [ 
                           
                             
                               
                                 2 
                                  
                                 π 
                                  
                                 
                                     
                                 
                                  
                                 B 
                               
                               λ 
                             
                              
                             
                               ( 
                               
                                 L 
                                 - 
                                 vt 
                               
                               ) 
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0000]    with the normalized modulation amplitude given by 
         [0000]    
       
         
           
             
               
                 
                   
                     κ 
                     = 
                     
                       K 
                        
                       
                          
                         
                           
                             ∫ 
                             0 
                             L 
                           
                            
                           
                             
                               ( 
                               
                                 
                                    
                                   C 
                                 
                                 
                                    
                                   z 
                                 
                               
                               ) 
                             
                              
                             exp 
                              
                             
                               { 
                               
                                 Δβ 
                                  
                                 
                                     
                                 
                                  
                                 z 
                               
                               } 
                             
                              
                             
                                 
                             
                              
                             
                                
                               z 
                             
                           
                         
                          
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         Δβ 
                       
                       = 
                       
                         
                           2 
                            
                           π 
                            
                           
                               
                           
                            
                           B 
                         
                         λ 
                       
                     
                     , 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0000]    B being the fiber birefringence; K depends on the fiber design and the properties of the stationary phase for the detected analyte. 
         [0033]    It can be shown that the periodic injection of Gaussian pulses will give rise to a modulation amplitude that reads as: 
         [0000]      κ≅ KΔβ|S|   (7)
 
         [0000]      where 
         [0000]        S=√{square root over (π)}e   iΔβvt   A   o   W   o Σ n=0   M   e   inΦ exp(− r   n   2 )  (8)
 
         [0000]    with the phase delay Φ≡ΔβvT=2πvT/L b  and r n ≡ΔβW n /2=πW n /L b , L b  standing for the polarization beat length. In presence of a single pulse, the amplitude κ decays exponentially in time. The periodic injection will change this instead to a small periodic (period T) variation through the time dependence of W n . For our purpose, it is sufficient to evaluate the sum S at a time t corresponding to an integer multiple of the period T. Then the sum becomes a geometric sum that can be evaluated analytically to yield: 
         [0000]    
       
         
           
             
               
                 
                   
                     S 
                     = 
                     
                       
                         π 
                       
                        
                       
                          
                         
                            
                            
                           
                               
                           
                            
                           M 
                            
                           
                               
                           
                            
                           Φ 
                         
                       
                        
                       
                         A 
                         o 
                       
                        
                       
                         W 
                         o 
                       
                        
                       
                         exp 
                          
                         
                           ( 
                           
                             - 
                             
                               r 
                               o 
                               2 
                             
                           
                           ) 
                         
                       
                        
                       R 
                     
                   
                    
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   
                     r 
                     o 
                   
                   = 
                   
                     π 
                      
                     
                       
                         W 
                         o 
                       
                       
                         L 
                         b 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     = 
                     
                       
                         1 
                         - 
                         
                           γ 
                           
                             M 
                             + 
                             1 
                           
                         
                       
                       
                         1 
                         - 
                         γ 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     γ 
                      
                     
                         
                     
                      
                     being 
                      
                     
                         
                     
                      
                     defined 
                      
                     
                         
                     
                      
                     by 
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   γ 
                   ≡ 
                   
                     exp 
                      
                     
                       [ 
                       
                         - 
                         
                           ( 
                           
                             
                               
                                 4 
                                  
                                 
                                   π 
                                   2 
                                 
                                  
                                 
                                   D 
                                   eff 
                                 
                                  
                                 T 
                               
                               
                                 L 
                                 b 
                                 2 
                               
                             
                             + 
                             Φ 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0034]    In (12), D eff  represents the effective diffusion coefficient of the analyte vapor. The velocity v and the effective diffusion D eff  of a given analyte are respectively related to the velocity u and the diffusion constant D of the carrier gas through its probability of non-absorption p: v=pu and D eff =pD. 
         [0035]    The resonance principle which increases the sensitivity can be expressed in a mathematical form (eqs (9)-(12)). For given injection conditions A o , W o  the importance of the sensor&#39;s response depends on the time period T, more particularly on the phase delay Φ≡ΔβvT=2πvT/L b  between each pulse contribution. In particular, when Φ=2π, |R| takes its maximum value. This corresponds to the case where the period T is chosen so as to make the spatial period vT equal to the beat length L b  hence putting in phase all of the mode coupling contributions of the pulses. 
         [0036]    To better illustrate the resonance principle,  FIG. 2  shows the dependence of |R| on the period T. Three cases are considered corresponding to three different values of the velocity v. The other parameters are: L=10 m, L b =4 cm and D eff =0.03 cm 2 /sec and can be considered as typical. 
         [0037]    The higher the speed, the sharper the resonance curves are and so for the maximum value of |R|. This is due mostly to the fact that as the speed increases the period for the main resonance T res =L b /v decreases; this implies that each pulse does not have the time to diffuse very much before a new one is injected so that each pulse&#39;s contribution to the mode coupling is more important. 
         [0038]    One can also notice the presence of secondary resonances. They correspond to the cases vT=q L b  (q=2, 3, 4, . . . ). In those cases, the number M of pulses is lower but the main reason for the lower values of |R| is that each pulse spreads out more before the injection of the next pulse. 
         [0039]    In practice, the fiber length and the beat length can be such that the number M of pulses is very high so that γ M+1 ≈0; moreover, for the typically small values of the diffusion coefficient, γ is well approximated by the first two terms of its Taylor expansion. The maximum and minimum values of R are then approximately given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         R 
                         max 
                       
                       ≅ 
                       
                         
                           vL 
                           b 
                         
                         
                           4 
                            
                           
                             π 
                             2 
                           
                            
                           
                             D 
                             eff 
                           
                         
                       
                     
                     = 
                     
                       
                         uL 
                         b 
                       
                       
                         4 
                          
                         
                           π 
                           2 
                         
                          
                         D 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   and 
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     min 
                   
                   ≅ 
                   
                     1 
                     2 
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
         [0040]    Eq. (13) implies that the maximum gain in sensitivity does not depend on the analyte under analysis. It is primarily determined by the velocity u of the carrier gas which can be easily modified by changing the pressure conditions. 
         [0041]    Finally, it is worth mentioning that the dependence on the initial conditions is only through eqs (9) and (10) and that R does not depend on those conditions. 
         [0042]    Turning now to  FIG. 3 , an example of a sensor  10  is illustrated. In this example, the optical waveguide  12  is an optical fiber  12   a . The optical fiber  12   a  has a passage  14  for receiving the fluid to analyze, in this embodiment, the passage  14  is a capillary  14   a  positioned adjacent a core  16  which acts as a propagation volume in which light from a light source is guided. In this case, to favor the partition effect, a wall of the capillary  14   a  is coated with a highly viscous liquid, such as polydimethylsiloxane which is more commonly known as PDMS. In the partition effect of the analytes, these are thus absorbed in the PDMS film rather than being adsorbed on the wall of the capillary  14   a  itself in this particular embodiment. Further, in this embodiment, the light can be monochromatic, though it can alternately be of a broader band as will be detailed below. The light source emanates polarized light which is injected in the core. The polarization can be according to a single one of two birefringence polarization axes of optical fiber  12   a , or alternately, the state of polarization can be measured to be known in order to later determine the change in the polarization state caused by the presence of analytes. After travelling along the optical fiber  12   a , and having interacted with the analytes via its evanescent field, light exits the other end. In the case of monochromic light injected in a linearly polarized state along a first polarization axis, the detector can be a light intensity sensor positioned after an other polarizer  18  oriented along a second, orthogonal polarization axis. Detection of intensity in the second polarization axis is thus an indication of a coupling effect caused by the interaction. In cases where the light source will have a broader band, the detector can be a spectrophotometer. The power of the source can be continuously measured in a manner to compensate for power fluctuations. In an alternate embodiment, the polarizer can be replaced by a polarization beam splitter to measure the power of two orthogonal polarizations, this can also serve in compensating for power fluctuations of the light source or for losses in the system. 
         [0043]    In this embodiment, the second path in the optical fiber is that used to channel the sample to analyze. The gas can be collected with a pump  20  with which it can be pressurized to the desired value and then be transferred to a modulator  22  which injects the gas in the passage according to a periodic concentration modulation. The modulator  22  can, for example, use the effect of cold trapping in a capillary containing a stationary phase, or function by periodical insertion of a sample vector gas in the carrier gas flux. Known devices can be used at this stage, such as devices used in the GC×GC technique for instance. Other means of providing a varying rate of injection can alternately be used. 
         [0044]    In order to better control the speed of the carrier gas, the capillary fiber can be placed in an oven  24 , especially if it is desired to increase the migration rate of the analytes. The modulator can be positioned inside or outside the oven  24 . 
         [0045]    The sensor can be controlled by a data acquisition system which can also be used to control the modulator  22 , the pump  20  (rate and pressure), and the detector, for instance. 
         [0046]    Since satisfactorily timed distinct pulses of sample injection can be a challenge to achieve in practice, the variation of the injection can be done in a sinusoidal-like manner, for instance. 
         [0047]      FIGS. 4A to 4D  illustrate such an example. In each successive image, the solid curve (lower graph) shows the temporal evolution of the concentration distribution of a varying injection in comparison with the dashed curve (upper graph) which corresponds to a single pulse injection. In this example, provide for the sole purpose of illustration, the period is 2 seconds, the velocity is 2 cm/s and the effective diffusion coefficient (Deff) is 2 cm 2 /s.  FIGS. 4A to 4D  progress successively from t=9 s; t=9.67 s; t=10.3 s; and t=11 s; and depict the spatial distribution of concentration at different times over one period of modulation. 
         [0048]    Typically, the injection frequency can be established as a function of a predetermined analyte for which the sensor is adapted to detect. This can be done by first establishing the beating frequency for a specific analyte and test conditions, such as by testing the sensor with a sample of known analyte concentration, and then operating the sensor with a sample injection frequency corresponding to the established frequency before testing the presence of the analyte in actual samples. 
         [0049]    Alternately or additionally to establishing the injection frequency beforehand, one can scan several frequencies, or scan a frequency range for detecting the presence of peaks associated with a given variety of molecule types. If a signal is obtained at a given frequency, one can slightly vary the frequency in an iterative manner to attempt to strengthen the signal and more clearly establish the frequency. However, in practice, some embodiments may render frequency scanning unpractical given time considerations. An other way to look for unpredicted resonances would be to establish an injection frequency and then vary the speed (u) of the carrier gas such as by varying the pressure differential. 
         [0050]    An other way of obtaining data is to measure the spectrum of transmission of the fiber after the polarizer for white light injection. This can allow to detect more than one analyte at a time. In fact, it can be noted that for multiple analytes (j) injected at a same frequency, as the beat length depends on the wavelength of light, there will be resonance in all cases where the pitch A of an analyte equals the beat length L b . A resonance peak can thus be expected in the transmitted light spectrum for each analyte present. A numerical simulation has demonstrated, for instance, that for p=0.50 and 0.52, u=85 cm/s, and Δβ=0.0256 cm −1 , resonance peaks can be expected at 1.297 um and 1.349 um. The numerical simulation also showed that the resolution was greater when the column was longer. Accordingly, the injection can be modulated for more than one frequency at a time. 
         [0051]    The above description places the groundwork of the theory, but it will be noted that it has up to now assumed that the speed of the carrier gas, or the migration speed of given analytes, will be strictly constant along the entire length of the column. In practice, it is likely that the speed will accelerate nearing the exit of the capillary due to the effect of decompression of the carrier gas. 
         [0052]    In fact, it can be said that the progression of the gas in the capillary follows the following equation: 
         [0000]    
       
         
           
             
               
                 
                   
                     u 
                      
                     
                       ( 
                       z 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         r 
                         2 
                       
                       
                         16 
                          
                         
                             
                         
                          
                         L 
                          
                         
                             
                         
                          
                         η 
                       
                     
                      
                     
                       
                         
                           
                             p 
                             in 
                           
                            
                           
                             ( 
                             
                               1 
                               - 
                               
                                 
                                   p 
                                   out 
                                   2 
                                 
                                 
                                   p 
                                   in 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                          
                         
                           [ 
                           
                             1 
                             - 
                             
                               
                                 z 
                                 L 
                               
                                
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     
                                       p 
                                       out 
                                       2 
                                     
                                     
                                       p 
                                       in 
                                       2 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           ] 
                         
                       
                       
                         
                           - 
                           1 
                         
                         / 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where p in  and p out  are the inlet and outlet pressures, respectively, η is the viscosity, L is the length of the fiber and r is the radius of the capillary. 
         [0053]    Recalling that: 
         [0000]    
       
         
           
             
               
                 
                   
                     1 
                     
                       T 
                        
                       
                         ( 
                         injection 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       f 
                        
                       
                         ( 
                         injection 
                         ) 
                       
                     
                     = 
                     
                       
                         pu 
                         Λ 
                       
                       = 
                       
                         
                           pu 
                           
                             L 
                             b 
                           
                         
                         = 
                         
                           f 
                            
                           
                             ( 
                             oscillation 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
         [0054]    It will be understood that an increase in the carrier gas speed u has the effect of increasing Λ as a function of z for a given frequency. A variation of Λ as a function of z will theoretically limit the sensitivity of the sensor since it would broaden the frequency peak associate with a given analyte. 
         [0055]    These limits can be at least partially overcome in several ways, three of which are now provided: 
         [0056]    Compensation of Acceleration by Temperature Variation 
         [0057]    A first way to compensate for carrier gas acceleration is to lower the temperature (F) along the capillary to increase absorption and therefore decrease p. That which is sought would be a complete compensation for u(z): 
         [0000]    
       
         
           
             
               
                 
                   
                     p 
                      
                     
                       ( 
                       
                         F 
                          
                         
                           ( 
                           z 
                           ) 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     1 
                     
                       u 
                        
                       
                         ( 
                         z 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
         [0058]    In this embodiment, the decompression leading to the acceleration of the carrier speed will remain present, but the analyte will be more highly absorbed and its migration rate can remain stable by decreasing relative to the increasing carrier speed. To achieve even further precision, variations of the carrier speed as a function of temperature change can also be taken into consideration. 
         [0059]    Since p will diminish with F, we can expect the attenuation to be less and less important as the temperature cools compared with an embodiment where the temperature would be homogeneous. 
         [0060]    It will be noted here that this type of compensation is of the first order, and its optimization can be limited to the case of a specific analyte. The variation of p with F will likely vary depending on the anayte in accordance with Arrhenius law. Nonetheless, it can be practical for monochromatic sensors adapted to the detection or quantification of a single analyte. 
         [0061]      FIG. 5  is an embodiment showing compensation by temperature variation. In this embodiment, a coil  30  or another temperature control device imposes a temperature gradient along the length of the optical waveguide. It can be used to reduce the temperature of the optical waveguide toward its exit or increase the temperature of the optical waveguide toward its entry, for instance. 
         [0062]    Compensation of Acceleration by Pressure Control 
         [0063]    Another way is to reduce, or minimize, the carrier gas speed gradient u(z) along the capillary. This can be done by diminishing the pressure differential between the entry and the exit of the capillary and by increasing its length. In this latter case, one could add a post column after the capillary. 
         [0064]      FIG. 6  schematizes an example where the capillary optical fiber has 5 meters in length, and to which a 16 meter post-column is added. 
         [0065]    Compensation of Acceleration by Lowering Birefringence 
         [0066]    A still other way to compensate for acceleration is to reduce the birefringence along the capillary fiber, in a manner for the beat length L b  to follow the increasing pitch A of the analyte. The variation can follow: 
         [0000]        L   b ( z )∝ u ( z )  (19)
 
         [0067]    Such a birefringence variation can be achieved in several ways. One way is to coil the birefringent optical fiber in a spiral, such as around a wheel having a varying radius for instance. Alternatives include designing the optical fiber in a manner for a variation in pressure or in temperature to have a satisfactory effect on the birefringence characteristics along its length. 
         [0068]    Of course, two or more ways to compensate for the acceleration effect can be combined in some embodiments for better results. 
         [0069]    It will be understood that the examples of  FIGS. 3 ,  5  and  6  provided above are exemplary only, and many alternate embodiments can be realized. For instance, U.S. Pat. No. 7,403,673 illustrates different forms of birefringent waveguides which can be used to channel the sample, and several optical assemblies which allow to inject both light and the fluid in the waveguide. As can be seen from the above, the examples described above and illustrated are intended to be exemplary only. The scope is indicated by the appended claims.