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2 = 2 ω. The phase-matching condition will imply, however, that this process will only be efficient in a time frequency range Ω ≪ ω.
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0242674739
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In principle, other three-wave mixing processes may also occur inside the NL crystal, such as the sum-frequency mixing of two off-axis fundamental photons [ω](q,Ω) + [ω](q′, Ω′) → [2ω](q+q′, Ω+Ω′). However, assuming that the spontaneously emitted fields are at any point of the crystal much weaker than the coherent homogeneous waves at fundamental and SH frequency, those processes which do not involve at least one on-axis photon [ω](00) or [2ω](00) can be neglected. Mathematically, this assumption is encoded in the linearization of the propagation equations for the quantum fields.
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59
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0242422892
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note
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A description of field dynamics based on a linearization around homogeneous modes predicts correlations between transverse modes associated either with the same or with opposite wave vectors. Correlations between modes with wave vectors different in modulus would only appear if nonlinear corrections to the linearized approach would become important. This was already pointed out in Ref. [40] for the cavity case.
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60
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0242506187
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note
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In the Heisenberg picture, the evolution of the system of the coupled quantum fields during propagation is encoded in the dependence of the field operators on the propagation length, while the quantum state of the system is simply given by the initial state of the system, which is here the vacuum state. While normally ordered expectation values of any combination of input operators vanish, the same quantity for output operators in general does not.
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65
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85088492952
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i(-q), we checked that the noise level is always minimal when the intensities are equally weighted (i.e., for λ = 1).
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