J. Eur. Opt. Society-Rapid Publ. 21, 5( 2025) 43 � R V r eðrÞ dE bðr; tÞ
E~ m d 3 r instead of i x~ m
RV dt r
eðrÞ
E b ðr; tÞ E~ m d 3 r when De( r) is non-dispersive. As noted in [ 10 ], under the slowly-varying envelope approximation, dE b ðr; tÞ can often be replaced by �ixE b( r, t), where x dt is the carrier frequency of the driving pulse. This suggests that fitting a coupling constant with a driving term proportional to E b( r, t) will yield accurate predictions when x~ m x, as demonstrated in Section 5.
Nonetheless, many modern electromagnetic software tools, including general solvers like COMSOL and specialized options [ 14 – 16 ] now compute QNMs. Additionally, QNM normalization has been mastered and is implemented in specialized software [ 16 ]. As a result, the time-derivativebased analytical expression, � R V r
eðrÞ dE bðr; tÞ
E~ dt m d 3 r,
can be efficiently calculated as a spatial overlap integral. Therefore, we anticipate that CMT models without fitting parameters will be readily used to interpret both experimental and numerical results. Notably, the temporal toolbox in [ 16 ] effectively addresses the exact Maxwell evolution equation, and efforts are already underway to model the second CMT equation for port coupling [ 13, 16 – 18 ].
Funding
PL acknowledges financial supports from the WHEEL( ANR- 22CE24-0012-03) Project. Rachid Zarouf is partially supported by the pilot centre for research in education Ampiric, funded by the France 2030 Investment Program, as part of the action“ Territories of Educational Innovation” operated by the Caisse des Dépôts.
Conflicts of interest The authors declare no conflict of interest.
Data availability statement
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Author contribution statement
All authors contributed equally. TW provided the computational results of the figure.
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