![]() ![]() This paper aims to demonstrate that when the number of particles increases in an optically bound cluster, the system will always pass through EPs to yield unstable conjugate pairs of complex eigenvalues, irrespective of details such as particle size, shape, composition, and the illuminating light. Thus, a stable OB (stable equilibrium) can only be achieved before reaching the EP. The force matrices for light-bound clusters are real but asymmetric (thus non-Hermitian) and they possess EPs before which all eigenvalues are real, but turn complex once these EPs are crossed. More interestingly, they are different from the usual non-Hermitian matrices studied in the exceptional point (EP) literature 32, 33, 34, 35, which typically involve symmetric matrices with complex diagonal terms 36, 37, 38, 39, 40. The force matrices governing OB stability are actually non-Hermitian because we are dealing with open systems with incoming light and radiative loss 26, 27, 28, 29, 30, 31. In nature, most systems incur losses, and hence, non-Hermitian systems are ubiquitous. However, non-Hermitian matrices have recently attracted considerable attention because they can also yield real eigenvalues (for example, in the exact phase of a parity-time symmetric system) 24, 25. ![]() Conventionally, physicists used to focus on Hermitian matrices of conservative closed systems, as they yield real eigenvalues. This inevitable instability can be explained by non-Hermitian physics 21, 22, 23. Additional forces, such as dissipative forces arising from viscosity, are indispensable in overcoming instability. The optically bound clusters found experimentally are actually not bound by light alone. Despite decades of research 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, the following question remains unanswered: can OB assemble a large number of particles to create some form of macroscopic “optical matter”? This paper aims to show that this is impossible, even for a modest number of particles ( N > ~10) in a typical situation. In addition, it has been demonstrated experimentally that quite a large number of particles can be bound by scattering, and this process is called optical binding (OB) 7, 8. Optical trapping (OT) is a process in which optical forces trap particles at the intensity extrema 1, 2, 3, 4, 5, 6. The non-Hermitian theory overturns the understanding of optical trapping and binding, and unveils the critical role played by non-Hermiticity and exceptional points, paving the way for large-scale manipulation. Our conclusion does not contradict with the observation of large optically-bound cluster in a fluid, where the ambient damping can take away the excess energy and restore the stability. As such, optical forces alone fail to bind a large cluster. Surprisingly, unstable complex eigenvalues are prevalent for clusters with ~10 or more particles, and in the many-particle limit, their presence is inevitable. Contrary to conventional systems, the operator governing time evolution is real and asymmetric (i.e., non-Hermitian), which inevitably yield complex eigenvalues when driven beyond the exceptional points, where light pumps in energy that eventually “melts” the light-bound structures. ![]() With incoming illumination and radiative losses, optical forces are inherently nonconservative, thus non-Hermitian. Intense light traps and binds small particles, offering unique control to the microscopic world. ![]()
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