What's the physical origin of bound states in the continuum (BICs)? 
From my point of view, BICs are modes built by destructive interference. But I'm confused about the orgin of BIC, I have two questions:

*

*The differences between BIC modes and defect modes.

It has been reported that some previous research mistaked defect modes with BICs. However, still I cannot tell the differences between BIC modes and defect modes, especially when we focus on quasi-BIC. Since we can see a DBR cavity as a structure supporting BIC, I think BIC is just a different way to view the problem instead of something new.
I know that there are some symmetry protected BICs without any defects or special designs(like BIC vortex beam generator), but I'm confused about the relationship between the topological nature and basic characteristics(symmetry protected or parametric).



*How can BICs survive in individual structures.
When it comes to individual structures without any particular design, it's so strange that they can support BICs. Are they real BICs?

Changing the parameters of the structures to reach high Q modes, I think, is very similar to normal optimization. Is there something special lies inside when we use BIC to view it?

References
1Hsu C W, et al. Nat. Rev. Mater., 2016
2Bogdanov A A, et al. Adv. Photonics, 2019
3Koshelev K, et al. Science, 2020
 A: Intro
As far as I can see from
https://en.wikipedia.org/wiki/Bound_state_in_the_continuum
https://doi.org/10.1126/science.aaz3985
and from my previous brief experience, BIC in photonics refers to having an electromagnetic excitation that looks like it 'could' propagate away but don't. What it looks like normally is that there is some structure and some specific kind of excitation that stays pinned to the spot, even though you can have other electromagnetic waves propagating in the same space.
Problem statement
Is this strange to have electromagnetic excitation being fixed to a single place? I don't think so. Imagine having an excitation sitting inside a finite-sized perfect electric conductor sphere. It will sit there it will not go anywhere etc. Clearly this is not too helpful, more generally we can ask: Under which conditions can you localize electromagnetic excitation in a space that supports propagating waves?
Dielectrics/Metals/Domains -> Currents
Before continuing it is helpful to get away from considering bits of dielectric, defects in photonic crystals etc. Instead we will focus on homogeneous space (could be free space, could be photonic crystal) and currents in that space. The time-harmonic wave equation for electric field ($\mathbf{E}$) in this case is:
$$
\begin{align}
\left(\boldsymbol{\nabla}\times\boldsymbol{\nabla}\times\mathbf{E}-\frac{\omega^2}{c^2}\epsilon\left(\mathbf{r}\right)\mathbf{E}\right)&=-i\omega \mu_0\mathbf{J} \\
\left(\boldsymbol{\nabla}\times\boldsymbol{\nabla}\times\mathbf{E}-\frac{\omega^2}{c^2}\epsilon_0\mathbf{E}\right)&=-i\omega\mu_0\left( \mathbf{J}+\frac{-\frac{\omega^2}{c^2}\cdot\left(\epsilon_0-\epsilon\left(\mathbf{r}\right)\right)\cdot\mathbf{E}}{-i\omega\mu_0}\right)
\end{align}
$$
What I have done there is to convert the spatially dependent part of the complex dielectric constant ($\epsilon\left(\mathbf{r}\right)$) into current density ($\mathbf{J}$). What this shows is that photonic BIC problems, which often rely on some non-trivially structured materials and defects, e.g. dielectric particles, can be considered as problems of electrodynamics in homogeneous space (permittivity $\epsilon_0$, permeability $\mu_0$, speed of light $c^2=1/\epsilon_0\mu_0$) with some oscillating current density.
Non-radiating configurations
Now we can restate the problem as follows:
Can you have a localized oscillating distribution of current density in homogeneous space (that supports wave propagation), which emits no radiation?
The answer is yes you can: https://doi.org/10.1103/PhysRevD.8.1044 (Devaney, Wolf, PRD 8, 1044 (1973))
In particular, a current density of the form:
$$
\mathbf{J}=\boldsymbol{\nabla}\times\boldsymbol{\nabla}\times\mathbf{f}+\alpha\mathbf{f}
$$
Where $\mathbf{f}\left(\mathbf{r}\right)$ is some localized time-harmonic vector field, and $\alpha$ is a suitable constant (depends on how you write your Maxwell's equations), will always emit no light.
Anapoles
Anapoles are point-like excitations (https://doi.org/10.1038/s42005-019-0167-z, V. Savinov et al. Comm Phys, 2:69 (2019) ) with time-harmonic current density:
$$
\mathbf{J}=\boldsymbol{\nabla}\times\boldsymbol{\nabla}\times\mathbf{N}\delta\left(\mathbf{r}\right)+\alpha\mathbf{N}\delta\left(\mathbf{r}\right)
$$
Where $\mathbf{N}$ is a vector. It should be clear that Devaney-Wolf non-radiating configurations can be assembled from anapoles.
Interestingly anapoles, and the linked toroidal dipoles occur naturally in nuclear physics https://en.wikipedia.org/wiki/Toroidal_moment
Conclusion
What is the origin of bound states? The physical origin is that electromagnetic (dyadic) Green function ($\mathbf{G}\left(\mathbf{r}-\mathbf{r'}\right)$) has non-empty null-space - such are Maxwell's equations. Hence if electric field is given by:
$$
\mathbf{E}\left(r\right)=\int_V d^3r' \mathbf{G}\left(\mathbf{r}-\mathbf{r'}\right).\mathbf{J}\left(\mathbf{r'}\right)
$$
It is possible to have vanishing electric field outside $V$ even with non-vanishing oscillating current density $\mathbf{J}$.
Light is emitted by oscillating currents and charges, but not all oscillating currents and charges have to emit light.
