Manuscript En01-C@1 · En01-C.tex · section · 00a2161c

A physical two-mode diagnostic

Finite packet and finite-window corrections › A physical two-mode diagnostic · lines 1172–1189

Choose fixed normalized packet modes $u_{+}, u_{-}$ with disjoint supports within distance $ℓ$ of centres $d /2, - d /2$ . Their real envelopes are nonnegative after one declared common phase compensation. For an unnormalized block $τ$ , define

P_{\pm} = ⟨ u_{\pm}, τ u_{\pm} ⟩, B = ⟨ u_{+}, τ u_{-} ⟩, V_{mode} = \frac{∣ B ∣}{P _{+} P _{-}} .

Positivity gives $0 \leq V_{mode} \leq 1$ . This is a projected two-mode coherence, still not automatically the final fringe visibility.

Displayed formulas in this passage

unlabeled · line 1179
$P_{\pm} = ⟨ u_{\pm}, τ u_{\pm} ⟩, B = ⟨ u_{+}, τ u_{-} ⟩, V_{mode} = \frac{∣ B ∣}{P _{+} P _{-}} .$

Nearby in this section

proposition: Proposition: Finite-width Gaussian bound
section: A physical two-mode diagnostic