ICMM-CSIC researcher discovers the existence of a Physics law that creates a novel scenery of the force exerted by light on matter

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To efficiently measure the force that light exerts on certain molecules and cells is one of the most relevant fields in Physics, Chemistry, and Biology. But, What about if all those studies lacked a half of the reality that one has to measure? So far, those works use the so-called conservation law of Maxwell’s stress tensor, which yields the real force, or radiation pressure, of light beams on objects. But a new study demonstrates the universal existence of a reactive force that counteracts, and thus impairs, this radiation pressure. 

In a new paper published in Light: Science & Applications, Manuel Nieto Vesperinas from the Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC, and Xiaohao Xu from the State Key Laboratory of Transient Optics and Photonics and Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, have demonstrated that the theory employed to date, which makes use of Maxwell’s stress tensor, only describes half the physics of radiation pressure. The other half, that they uncover and whose law they formulate, is described by the imaginary part of a complex stress tensor that they put forward, and of which Maxwell’s tensor is only its real part.

"We have discovered the existence of a universal phenomenon concerning electrodynamic forces, and optical in particular, exerted by light or other electromagnetic waves on a distribution of electric charges and currents in general, and of bodies and particles in particular”, the paper explains.

This discovery constitutes a new paradigm of the mechanic efficiency of light on the matter and completes the landscape of electromagnetic forces in photonics and electrodynamics”, add the investigators. Furthermore, this widens our understanding of the design of both illumination and matter, in optical manipulation and propulsión by light, so controlling the incident power, and thus also allowing us to reduce the dissipation and heat due to the interaction.

Nobel Prizes

It was in 1619 when Johannes Kepler proposed the hypothesis that the radiation pressure of solar light is responsible for the tail of comets pointing in opposite direction to the Sun. Two centuries and a half later, James Clerk Maxwell rigorously formulated, by establishing a stress tensor, the law that governs this force of light and other electromagnetic waves on surfaces.

Ever since, enormous progress has taken place in this field of Physics, among other things being recognized with four Nobel Prizes. Two of them are direct connected with the use of radiation pressure: in 1997 the demonstration of atom cooling by light beams, and in 2018 the invention of optical tweezers, nowadays of intensive usage in molecular and cell biology. The other two prizes are indirectly related to this force: that of 2001 to the confirmation of Bose-Einstein condensation, and in 2017 to the successful detection of gravitational waves.

In another of its prospective aspects, there is an increasing interest in handling and controlling radiation pressure in the design and experimentation of solar sails, which will constitute the propulsión systems of tomorrow's spacecraft.

To explain this, Nieto Vesperinas has been inspired by an analogous law of Electrodynamics: the Poynting theorem,  which governs the conservation of electromagnetic energy. According to it, energy transport is determined by two variables of the momentum of light: one is real, well-known, and currently observed; the other is imaginary, also known, and alternating since it depends on charges. However, the latter hinders the former; it is a workhorse of engineers designing circuits and antennas, known as reactive power or reactance.

All this may be better seen with an example: an antenna radiates a signal with an amount of energy. This would be the real variable of Poynting's theorem. However, very close to the antenna there exists a non-propagating electromagnetic field conveying reactive energy which is the imaginary variable, negatively interfering with the radiated field, thus impairing the antenna performance and giving rise to heating by dissipation of feeding power. Therefore, it is of paramount importance to know this reactive energy in order to control it, and hence to optimize the radiating efficiency. So, something analogous takes place with light and its force upon bodies, which has been ignored until this research discovered it.

The law of momentum conservation of electromagnetic waves interprets their mechanical interaction with matter. This law always works with a unique variable, which is real: the Maxwell stress tensor, which is the cornerstone of the whole theory of electromagnetic forces and optical manipulation, both at the macroscale and the nanoscale. Now, this new work shows that there exists, in addition, an imaginary part of the stress tensor. The latter is important as it fully touches the foundations of Electrodynamics in everything concerning matter propulsión by radiation pressure, the creation of optical binding (photonic molecules), and object manipulation by the action of light, which is, nowadays, one of the vibrant subjects of macro and nanoscience. "It is a so basic conservation law that it will likely be included in textbooks of undergraduate and doctoral studies in Physics and Engineering", adds Nieto Vesperinas.

"We have formulated the existence of a complex force in light-matter interactions which splits into two, either scaled or instantaneous", says the paper. "The real part is the well-known standard (or radiation pressure), which is time-averaged on detection times large versus the light oscillation frequency. On the other hand, the imaginary part, here established, stems from the instantaneous exchange of imaginary momentum, above mentioned, between the wave and matter”. This exchange also oscillates with the light frequency, being linked to the accretion of a new quantity that we have discovered and that we call “reactive strength of orbital momentum” of the light wave, which is given by the difference between its magnetic and electric orbital momenta.

This is fascinating, says Nieto Vesperinas, because it is precisely the orbital momentum of light responsible for radiation pressure, and this strength of orbital momentum involves a beautiful analogy with the reactive power, which is the difference between the electric and magnetic energy emitted by an antenna, let it be either a TV antenna, that of a mobile phone, or a nanoantenna. Hence, the role of electromagnetic energy as regards the power released by an emitter is undertaken by the orbital momentum of the wave in the electrodynamic force play.  As a consequence, the “imaginary stress tensor established in this work, constitutes the other side, so far ignored, of the dynamic effects in light-matter interactions”.

The study also details how to detect and control the novel imaginary part of the stress tensor, illustrating its effect on the effective radiation pressure. 

Therefore this reactive (imaginary) force counteracts the currently observed standard time-averaged force. Other researchers had previously found this kind of hindrance but had no explanation for it.  The cause here discovered is due to the dynamic reactance, namely, to the reactive --imaginary--, a force that light instantly exerts on bodies. 

The authors acknowledge the practical difficulties involved in accurately controlling propulsión and optical manipulation. However, they firmly believe "the fast advances and present maturity of the optical handling of matter now warrant the formulation of their theory”. From their point of view, this novel scenario completes an interpretative panorama of dynamics in the science of light and electrodynamics and may be useful in optimizing machinery. “In addition, it suggests the existence of reactive forces in the interaction of sound, fluids, and other matter waves, thus opening a new landscape of possible dynamic phenomena of waves on the matter”, they conclude.

-- Ángela R. Bonachera, ICMM Comunication (Photo: unsplash).