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the counter - propagating wave approach is commonly used to study the electromagnetic response of spatially nondispersive , homogeneous and isotropic plane - parallel - faces linear media ( fabry - perot framework ) .
it consider forward and backward monochromatic plane waves to derive the optical properties as the transmittance and reflectance @xcite .
this method uses the conventional variables of electromagnetic fields : moduli and phases of these waves which should be found from the helmholtz equation with the corresponding boundary conditions .
it is well - known that for a single harmonic plane wave propagating through an unbounded linear medium , the time - averaged poynting vector modulus is equivalent to the squared - field amplitude modulus @xcite .
this statement is generally accepted even if the wave propagation takes place in bounded linear media .
the counter - propagating approach does not point out the possible nonequivalence between the above magnitudes since utilizes the amplitudes and phases as field variables .
however , the phase of the wave can be replaced by the time - averaged poynting vector modulus as field variable . then the time - averaged poynting vector and the squared - field amplitude modulus can be monitored simultaneously within the medium so that the conditions that leads to the nonequivalence among them will manifest naturally in this equivalent frame .
the so - called s - formalism use the time - averaged pointing vectos as a field variable .
it was recently introduced @xcite and applied to study the optical response of nonlinear slabs .
the nonequivalence between the time - averaged poynting vector and the squared - field amplitude modulus was the key to define a nonlinear medium whose nonlinearity is proportional to the time - averaged poynting vector modulus .
its transmittance was calculated and found to differ with that obtained for the kerr medium , whose nonlinearity is proportional to the squared - field amplitude modulus .
however , the method was not yet used to analyze the linear case .
therefore , the aim of this paper is to apply the s - formalism to study the optical properties of homogeneous , isotropic and spatially non - dispersive dielectric as well as ohmic conductor media , inside the fabry - perot frame complementing to the well - known results of this problem within the counter - propagating wave approach .
the s - formalism shows , in direct form , how this non - equivalence is related to the superposition dynamic of opposite traveling waves which is only possible in bounded media . also , the exact transmittance is compared with that given by the approximated beer s law , commonly used in experiments , and appreciable differences were found for certain material parameters values . moreover ,
the reflectance of positive and negative permittivity media are considered and interesting results appears for small absorption when negative permittivity accounts .
it must be stressed that the s - formalism does not substitute the counter - propagating wave approach because the idea of forward and backward waves within the medium has a deep physical content .
however , the alternative method adds conceptual and practical implications that remains hidden when the conventional scheme is utilized .
we believe that both methods should be complementary , helping for a complete physical understanding on wave propagation in bounded linear media .    below , this paper reviews the principal features of the s - formalism introduced in ref . as function of the new set of field variables .
then , it is applied to derive the spatial evolution of both variables for absorbent and nonabsorbent linear media showing the cases in which the equivalence does not hold true , and their causes and consequences .
finally , practical implications of this features are explored : the comparison between the exact transmittance and the beer s law , and the analysis of positive and negative permittivity media .
, wave vector @xmath0 and frequency @xmath1 strikes a linear , non - magnetic , homogeneous , isotropic , and spatially non - dispersive plane - parallel - faces , to be reflected and transmitted .
the field in region ii can be represented by a general complex field of real amplitude @xmath2 and phase @xmath3 .
the regions i and iii constitute , for simplicity , the same linear dielectric medium ( e.g. , air ) . @xmath4 and @xmath5 are the reflection and transmission complex coefficients , respectively ; @xmath6 is the dimensionless propagation coordinate.,width=283 ]    when a linear , non - magnetic , homogeneous , isotropic , and spatially non - dispersive plane - parallel - faces medium of dimensionless thickness @xmath7 is excited perpendicularly by a plane wave ( see fig .
[ fig = problema ] ) , the s - formalism @xcite states that the transmittance and reflectance are respectively      where @xmath9 is the field variable , representing the dimensionless time - averaged poynting vector modulus , given by @xmath10 where @xmath11 is the incident intensity with @xmath12 , the vacuum permittivity , @xmath13 the unit vector in the @xmath14 direction , and @xmath2 and @xmath3 are the electric field amplitude modulus and phase , respectively . @xmath15 and @xmath16 evolve according to the coupled system @xcite          @xmath18_{\tilde{z}=0}=4,\label{eq = condecont1}\\[3pt ] & & \left[s-\mathcal{e}^{2}\right]_{\tilde{z}=\tilde{d}}=0,\\[3pt ] & & \left[\frac{d\mathcal{e}}{d \tilde{z}}\right]_{\tilde{z}=\tilde{d}}=0.\end{aligned}\ ] ]      being @xmath19 , the relative permittivity , and @xmath20 , the relative conductivity . from eq .
( [ sye ] ) it is clear that @xmath9 and @xmath2 are equivalents only when @xmath3 is a linear function on @xmath14 .
this point is not , in general , emphasized in the literature .
thereby , it is mandatory to ask : is the equivalence of both magnitudes generalized to cases where it could be not longer true ? .
an example : in ref .
@xcite , the energy flux of a tem@xmath21 gaussian beam propagating in free - space is calculated from the squared - field amplitude modulus instead of the time - averaged poynting vector which could lead to non - physical results .
for details see appendix [ appendix ] .
equation ( [ eq = poyntinhtheo ] ) represents the time - averaged poynting theorem being @xmath22 the responsible for the energy loss in the medium .
here we used it _ explicitly _ to analyze and solve wave propagation problems in bounded media . on the other hand , note that , eqs .
( [ eq = condecont ] ) are independent of the medium properties .
also , the second interface produces different values of @xmath23 and @xmath9 at the first interface through the spatial dependence of @xmath2 , as can be seen in eq .
( [ eq = condecont1 ] ) .
however at the second interface @xmath23 and @xmath9 are always equals with the advertisement that this should not lead to false view that they are equivalents .
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this paper uses an alternative approach to study the monochromatic plane wave propagation within dielectric and conductor linear media of plane - parallel - faces . 
 this approach introduces the time - averaged poynting vector modulus as field variable . 
 the conceptual implications of this formalism are that the nonequivalence between the time - averaged poynting vector and the squared - field amplitude modulus is naturally manifested as a consequence of interface effects . 
 also , two practical implications are considered : first , the exact transmittance is compared with that given by the beer s law , employed commonly in experiments . 
 the departure among them can be significative for certain material parameter values . 
 second , when the exact reflectance is studied for negative permittivity slabs , it is show that the high reflectance can be diminished if a small amount of absorption is present .