What Does Bilinear Response Mean in Mathematical Terms?

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Bilinear response refers to a mathematical concept where a response is linear in two variables, typically denoted as δX1 and δX2. This term often appears in contexts involving expressions like xy, indicating that the response depends linearly on both inputs. Additionally, the scalar product ⟨φ|ψ⟩ is an example of a bilinear form, being linear in ψ and φ*. The discussion highlights the importance of understanding this concept in relation to specific mathematical expressions found in academic papers. Clarifying the definition of bilinear response enhances comprehension of related mathematical frameworks.
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I don't know what is "bilinear responce". I would be grateful for any help.
 
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Context?
 
DrDu said:
Context?
Yes, I saw the term "bilinear response" in a paper and I don't understand it.
 
"In a paper". Do you think this is helpful? Maybe you could give a citation and quote the relevant part?
 
It means that it is linear in both ##\delta X_1## and ##\delta X_2##. This is generally used for expressions of the form xy. Also the scalar product ##\langle \phi|\psi \rangle ## is bilinear in ##\psi## and ##\phi^*##.
 
Thread 'Unexpected irregular reflection signal from a high-finesse cavity'

Thread 'Unexpected irregular reflection signal from a high-finesse cavity'

I am observing an irregular, aperiodic noise pattern in the reflection signal of a high-finesse optical cavity (finesse ≈ 20,000). The cavity is normally operated using a standard Pound–Drever–Hall (PDH) locking configuration, where an EOM provides phase modulation. The signals shown in the attached figures were recorded with the modulation turned off. Under these conditions, when scanning the laser frequency across a cavity resonance, I expected to observe a simple reflection dip. Instead...
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