Applications of highly oscillatory integrals

Question

I was reading a series of articles on numerical integration of highly oscillatory functions, e.g.,

1. S. Olver, Numerical approximation of highly oscillatory integrals

2. S. Xiang, H. Wang, Fast integration of highly oscillatory integrals with exotic oscillators

3. A. Iserles, S.P. Nørsett, Efficient quadrature of highly oscillatory integrals using derivatives

etc

All these papers immediately start with the problem. They may want to integrate

\begin{equation} I_1 = \int_{0}^{1} dx\,f(x)e^{i\omega g(x)}, \end{equation}

or exotic oscillator

\begin{equation} I_2 = \int_{0}^{11} dx\,f(x)\text{Ai}\left(-\omega g(x)\right), \end{equation}

or some other highly oscillatory function challenging for standard integration methods.

The papers are well-written, and I have no question how to evaluate these integrals. In place of that, I have a question why compute them? All papers I found are diligently trying to avoid discussing applications. Even the dissertation of S. Olver (Numerical Approximation of Highly Oscillatory Integrals, Sheehan Olver, Trinity Hall, University of Cambridge, 14 June 2008) allot meager 5 pages (out of 153) to applications that are still described in very high-level details.

Given that background, I have the following questions:

1. What are the concrete applications of highly oscillatory integrals?

2. Where can I find articles/books describing these applications in details?

3. Is there an example of software that uses those integration methods?