A　provably　stable　summation-by-parts　simultaneous　approximation　term　(SBP-SAT)　finite-difference　time-domain　(FDTD)　subgridding　method　with　arbitrary　grid　ratios　is　proposed　to　accurately　and　flexibly　solve　2-D　electromagnetic　problems.　The　interpolation　matrix　with　the　grid　ratio　1:　$n$　　is　first　carefully　designed,　which　satisfies　the　norm-compatible　conditions　and　the　SBP　property　to　guarantee　long-term　stability.　By　introducing　a　virtual　intermediate　domain,　the　interpolation　matrix　with　an　arbitrary　grid　ratio　　$n$　:　$m$　　is　decomposed　into　two　interpolation　matrices　as　　$n$　:1　and　　$1$　:m.　By　combining　two　interpolation　matrices,　the　interpolation　matrix　with　an　arbitrary　grid　ratio　is　derived,　which　is　flexible　to　model　complex　structures.　Five　numerical　examples　were　carried　out　to　validate　the　effectiveness　of　the　proposed　SBP-SAT　FDTD　subgridding　method　with　arbitrary　grid　ratios.　Results　show　that　it　can　flexibly　model　complex　structures　and　significantly　improve　computational　accuracy　and　efficiency.　IEEE