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Down-conversion and entangled photon pairs from photonic crystals

M. J. A. de Dood, William T. M. Irvine, Dirk Bouwmeester

Published May 16, 2004• 0 citations
OpenAlex

Abstract

Degenerate down-conversion in photonic crystals is investigated as a source of entangled photons. Phase matching relics on form birefringence and on a change in phase velocity near the band edge of the photonic crystal

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Nonlinear photonic crystals can be used to provide phase matching for frequency conversion in optically isotropic materials. The phase-matching mechanism proposed here is a combination of form birefringence and phase velocity dispersion in a periodic structure. Since the phase matching relies on the geometry of the photonic crystal, it becomes possible to use highly nonlinear materials. This is illustrated considering a one-dimensional periodic Al0.4Ga0.6As/air structure for the generation of 1.5 microm light. We show that phase-matching conditions used in schemes to create entangled photon pairs can be achieved in photonic crystals.
Spatial correlations of photon pairs from spontaneous parametric down-conversion (SPDC) underpin quantum imaging and entanglement certification. We present the first systematic study of spectral filter bandwidth effects on transverse spatial correlations in bulk Type-I BBO for degenerate and non-degenerate configurations. In the far field, the degenerate conditional momentum width is pump-limited and filter-invariant, while non-degenerate configurations exhibit monotonic growth in both marginal and conditional momentum widths -- with the walk-off axis ≈100\approx 100≈100 times more sensitive than the non-walk-off axis. In the near field, we identify a previously unreported flat-dip-rise profile: the conditional position width narrows by ≈10%\approx 10\%≈10% at an optimal bandwidth Δdip≈1.35 ΔλSPDCΔ_\mathrm{dip} \approx 1.35\,Δλ_\mathrm{SPDC}Δdip​≈1.35ΔλSPDC​ before rising due to geometric displacement. When the filter is placed on the idler arm, the dip shifts by the exact factor (λi/λs)2(λ_i/λ_s)^2(λi​/λs​)2. Both results are universal for any non-degenerate SPDC source, requiring only a finite crystal length, dθ/dλ≠0dθ/dλ\neq 0dθ/dλ=0, and incoherent spectral averaging. The Reid EPR uncertainty product is consistently smaller on the walk-off axis -- a structural advantage of bulk birefringent geometry absent in quasi-phase-matched sources. The optimal filter bandwidth ΔF=ΔdipΔ_F = Δ_\mathrm{dip}ΔF​=Δdip​ is determined entirely by the intrinsic phase-matching bandwidth of the crystal and is directly readable from the X-entanglement spectral width of the source.