We investigate theoretically the effect of a magnetic field on intersubband polaritons in an asymmetric quantum well placed inside an optical resonator. It is demonstrated that the field-induced diamagnetic shift of electron subbands in the well increases the broadening of optical lines corresponding to intersubband electron transitions. As a consequence, the magnetic field can switch the polariton system from the regime of strong light-matter coupling to the regime of weak one. This effect paves a way to the effective control of polaritonic devices with a magnetic field.In recent decades, the significant technological progress in fabrication of optical resonators (microcavities) with high quality factor was achieved. This led to both experimental and theoretical development of the concept of strong light-matter coupling, which covers various electron-photon processes accompanying by the oscillatory energy exchange between an electromagnetic field confined in a microcavity and electrons in condensedmatter structures placed inside the microcavity 1-12 . Currently, the regime of strong light-matter coupling has been realized experimentally in a variety of condensedmatter structures, including quantum wells (QWs)13-15 , quantum dots [16][17][18] , quantum wires 19-23 , and others. Particularly, the energy exchange between electrons in QW and a confined electromagnetic field in a microcavity leads to the oscillating transitions between different electron subbands in QW. These periodical optical transitions of electrons can be described formally as a composite electron-photon quasi-particle called "intersubband polariton" [24][25][26][27][28][29][30][31] . Immediately after experimental discovery of the intersubband polaritons, they attracted great attention of research community. This was caused by their unique physical properties which meet the needs of various modern optoelectronic devices operating in a wide frequency range from infrared to terahertz domains, including quantum cascade lasers 32,33 , light emitting devices 34-36 and photodetectors 37 . In order to control the devices, the frequency tuning of intersubband polariton should be elaborated. Currently, the tuning is realized with the control of light-matter coupling constant by the electrical gating applied to QW 38,39 . In the present study, we propose the alternative method of the frequency tuning by an external magnetic field. In what follows, we will show theoretically that the magnetic field can effectively control the intersubband polaritons by switching the electron-photon system in QW from the regime of strong light-matter coupling to the weak one.Generally, the regime of strong light-matter coupling is realized when the coherent light-matter interaction overcomes the characteristic damping. In this regime, the energy is periodically exchanged between the "light part" and "matter part" of the light-matter system with the Rabi frequency, Ω R , which is given by the expressionwhere g R is the characteristic light-matter coupling constant, and Γ is...