7 P (2 , 0 , 0; z ) = P (0 , 2 , 0; z ) = 2 | S$_{11}$ | $^{2}$| S$_{21}$ | 2 = 1 8 [1 − exp( − 4 σz )] 2 (42) P (1 , 0 , 1; z ) = P (0 , 1 , 1; z ) = | S$_{11}$S$_{23}$ + S$_{13}$S$_{21}$ | 2 = 1 2 exp( − 4 σz ) [1 − exp( − 4 σz )] (44) P (0 , 0 , 2; z ) = 2 | S$_{13}$ | $^{2}$| S$_{23}$ | 2 = 1 2 [1 − exp( − 4 σz )] 2 . (45) P (1 , 1 , 0; z ) = | S$_{11}$S$_{22}$ + S$_{12}$S$_{21}$ | 2 = 1 4 [1 + exp( − 4 σz )] 2 (43) such as the two-photon Hong-Ou-Mandel interference is typically revealed as a dip in intensity correlation (photon coincidence) measurements when the time delay between the two incoming wave packets is varied [18, 21]. It is therefore useful to extend the analysis of Sec.III.B to the case of polychromatic wave packets. For the sake of definiteness, let us assume that waveg- uides W$_{1}$ and W$_{2}$ are excited in their fundamental spa- tial modes by two spectrally-narrow wave packets gen- erated by spontaneous parametric down conversion in type-I nonlinear crystal. In this case, the vector state |Q〉 at the input plane of the waveguiding system is a generalization of Eq.(37) and given by a superposition of two-photon states with a spectral function C (Ω$_{1}$ , Ω$_{2}$) (see, for instance, [18, 34]) An important result is that, for propagation distances z larger than the characteristic decay length l$_{d}$ = (1 /σ ), the joint probability P (1 , 0 , 1) to find one photon in waveguide W$_{1}$ and one in the slab waveguide S vanishes, and similarly for P (0 , 1 , 1) [see Eq.(44)]. Such a result indicates that, if one of the two initially injected photons tunnels into the slab waveguide, the other photon does the same, i.e. photon pairs bunch when decaying into the continuum. This is obviously a nonclassical effect similar to the two-photon Hong-Ou-Mandel quantum interference in a 50% beam splitter [18]. In our case, the vanishing of P (1 , 0 , 1) [and similarly of P (0 , 1 , 1)] is related to a destructive interference between the probability amplitudes S$_{11}$S$_{23}$ and S$_{13}$S$_{21}$ entering in Eq.(44) which describe two possible paths for the photon pair. In the previous subsection, we have considered propa- gation of nonclassical light in the monochromatic limit, however in practice nonclassical light such as that gen- erated by spontaneous parametric down conversion in a nonlinear crystal is always polychromatic to some extent. Moreover, in experimental settings quantum interference The evolution of vector state along the propagation dis- tance z can be obtained by a straightforward extension of the analysis of Sec.III.B and reads explicitly where the operators ˆ a $_{1}$(Ω$_{1}$ ) and ˆ a $_{2}$(Ω$_{1}$ ) are defined by |Q ( z = 0) 〉 = ∫ d Ω$_{1}$ d Ω$_{2}$ C (Ω$_{1}$ , Ω$_{2}$)ˆ a † $_{1}$(Ω$_{1}$ )ˆ a † $_{2}$(Ω$_{2}$ ) | 0 〉 (46) ˆ a † 1 , $_{2}$(Ω) = ∫ dρ u$_{1}$$_{,}$$_{2}$ ( ρ ) ˆ φ $^{†}$( ρ, Ω) . (47) C. Nonclassical effects with wave packets |Q〉 = ∫ d Ω$_{1}$ d Ω$_{2}$ C (Ω$_{1}$ , Ω$_{2}$) exp [ i (Ω$_{1}$ + Ω$_{2}$) z/v$_{g}$ ] [ S$_{11}$ ( z )ˆ a † $_{1}$(Ω$_{1}$ ) + S$_{12}$ ( z )ˆ a † $_{2}$(Ω$_{1}$ ) + S$_{13}$ ( z )ˆ a † $_{3}$(Ω$_{1}$ ) ] × × [ S$_{21}$ ( z )ˆ a † $_{1}$(Ω$_{2}$ ) + S$_{22}$ ( z )ˆ a † $_{2}$(Ω$_{2}$ ) + S$_{23}$ ( z )ˆ a † $_{3}$(Ω$_{2}$ ) ] | 0 〉 (48) probability P (1 , 0 , 1; z ) = P (0 , 1 , 1; z ) for z ≫ l$_{d}$ found for monochromatic beams [Eq.(44)], let us introduce the integrated intensity correlation function at times t$_{1}$ and t$_{2}$ in waveguides W$_{1}$ and S defined as To study quantum interference effects with wave pack- ets, and in particular the vanishing of the joint photon where ˆ a † $_{3}$(Ω) = ∫ dρ θ ( ρ, z ) ˆ φ $^{†}$( ρ, Ω) . (49)