Light Forcing: Mechanisms in Optics and Climate

• Light forcing is the use of electromagnetic radiation to bias system dynamics by transferring momentum, energy, and altering material states.
• Direct optical forcing employs radiation pressure and multipole interference to control motion, demonstrating phenomena like tractor beams and lateral deflections.
• Indirect methods such as phototaxis, photophoresis, and radiative climate forcing harness light to drive changes from microscale flows to planetary energy budgets.

Across optics, soft matter, and climate physics, light forcing denotes the use of electromagnetic radiation—or radiation-mediated exchange of momentum, energy, chemical state, or irradiance—as an external driver of motion, transport, or energy balance. In one class of problems, light acts directly through radiation pressure and multipolar scattering; in another, it acts indirectly by inducing phototaxis, photophoresis, diffusio-osmotic slip, or thermally generated recoil. A distinct usage in climate science treats changes in solar irradiance as radiative forcing of the atmosphere. These literatures collectively show that light can function as a reversible control field, a propulsion mechanism, a source of fluctuation-induced stresses, and a constraint on planetary energy budgets.

1. Conceptual scope and mechanistic classes

The central unifying feature of light forcing is that illumination does not merely reveal a system; it alters its dynamics. In direct optical forcing, the relevant quantity is momentum flux carried by incident and scattered photons. In indirect forcing, light modifies internal state variables—temperature, chemical composition, or swimmer orientation—which are then converted into force or flow. Examples include backward optical pulling through multipole interference, photophoretic repulsion of absorbing droplets, diffusio-osmotic transport generated by photosensitive surfactants, phototactic steering of micro-algae in shear flow, and spontaneous acceleration by asymmetric thermal radiation exchange (Chen et al., 2011, Esseling et al., 2012, Arya et al., 2020, Garcia et al., 2013, Deop-Ruano et al., 2024).

A recurring misconception is that optical forcing is determined solely by the local Poynting vector or by intensity gradients. The literature surveyed here rejects both reductions. Negative Poynting vector is neither necessary nor sufficient for optical pulling, and several “exotic” forces vanish at leading dipole order in the Rayleigh limit, appearing instead through interference between multipole orders. This places channel structure, beam geometry, and material response at the center of the theory of light-driven motion (Ruffner et al., 2015).

2. Direct optical forcing: radiation pressure, pulling, lateral deflection, and optimal control

The most familiar direct effect is forward radiation pressure, but several works show that this intuition is incomplete. For a propagation-invariant beam such as a Bessel beam, the axial force can be written as

$$F = W_{\mathrm{sca}}\,c^{-1}\left(\cos\theta_0-\cos\theta\right),$$

where $W_{\mathrm{sca}}$ is the scattered power, $\theta_0$ characterizes the incident beam components, and $\cos\theta$ is the weighted mean direction of the scattered radiation. A plane wave has $\theta_0=0$, so it cannot pull. By contrast, a beam whose photon momentum projection along the propagation direction is small can generate a backward scattering force if multipole interference makes the scattered field more strongly forward-directed than the incident axial momentum budget permits. The necessary condition is simultaneous excitation of multiple multipoles; the effect is favored in the Mie regime, with large cone angle, near impedance matching, and low absorption (Chen et al., 2011).

A closely related formulation uses a strongly non-paraxial vector Bessel beam. There the decisive parameter is the cone angle $\alpha$, with strong non-paraxiality corresponding to small longitudinal wavenumber $\beta$. In the magnetodielectric Rayleigh regime, the axial force contains a positive radiation-pressure term proportional to $\beta$ and a negative term proportional to $$\mathrm{Re}(\alpha_e)\mathrm{Re}(\alpha_m)\mathrm{Re}(P_z)$$. Attraction requires small $\beta$, the presence of a magnetic dipole moment, and large positive $W_{\mathrm{sca}}$0. The same study emphasizes that even a large negative axial Poynting vector does not by itself guarantee a negative force, and that purely dipolar non-magnetic particles are always pushed, although non-magnetic non-Rayleigh particles can be attracted through higher-order electric moments (Novitsky et al., 2011).

The Rayleigh-limit theory clarifies why these effects are exceptional. For optically isotropic particles, first-order electric- and magnetic-dipole forces contain conservative gradient terms and nonconservative phase-gradient terms, but no spin-curl contribution. Tractor-beam action in propagation-invariant beams therefore vanishes at leading order. It reappears only in second-order interference terms such as

$W_{\mathrm{sca}}$1

which introduce momentum-density and polarization-structure effects absent from the leading approximation. In this formulation, spin-dependent forces, spin-curl forces, and tractor-beam behavior are emergent second-order scattering phenomena rather than generic consequences of local light momentum (Ruffner et al., 2015).

Surface-assisted forcing introduces another symmetry channel. A chiral particle near a substrate can experience a lateral force $W_{\mathrm{sca}}$2 perpendicular to the incident photon momentum even when the substrate itself does not break left-right symmetry. The mechanism is coupling between structural chirality and the substrate-reflected near field; opposite handedness yields opposite lateral deflection, and for a helical gold particle above gold the lateral force can reach about $W_{\mathrm{sca}}$3 times the forward scattering force. The effect weakens with particle–substrate separation and oscillates with dielectric substrate thickness through Fabry–Perot structure (Wang et al., 2013).

At a more general level, optical force and torque can be cast as quadratic forms in incoming and outgoing scattering channels: $W_{\mathrm{sca}}$4 Within this framework, $W_{\mathrm{sca}}$5 and $W_{\mathrm{sca}}$6 emerge as force and torque constants, and the reverse problem—finding the globally optimal illumination field for a fixed scatterer—reduces to a generalized eigenvalue problem. The study also shows that spherically symmetric structures cannot generally saturate plane-wave force and torque bounds, and that wavefront shaping can produce $W_{\mathrm{sca}}$7–$W_{\mathrm{sca}}$8 torque enhancement for a silver nanocube at fixed incident intensity (Liu et al., 2018).

3. Indirect forcing through absorption, heating, and photochemistry

A major branch of light forcing is mediated rather than direct. In photophoresis, an absorbing object in an inhomogeneous light field develops temperature gradients across the particle and in the surrounding gas, producing a force away from the high-intensity region. For single airborne ink droplets of radius $W_{\mathrm{sca}}$9, illuminated by a $\theta_0$0 frequency-doubled Nd:YAG laser shaped into a thin light sheet, low power around $\theta_0$1 yields negligible deflection, whereas above about $\theta_0$2 the droplets rebound and follow quasi-ballistic trajectories. Using a Gaussian estimate with $\theta_0$3 and $\theta_0$4, the peak intensity at $\theta_0$5 is

$\theta_0$6

and the required intensity for visible manipulation is reported as $\theta_0$7. Inferred lower-bound forces are $\theta_0$8 normal to the sheet and $\theta_0$9 along the propagation direction, about two orders of magnitude larger than in typical optical tweezers (Esseling et al., 2012).

Another indirect route is photochemical forcing at interfaces. In water containing small additives of azobenzene-containing cationic surfactant, illumination changes the trans/cis ratio near a charged wall, thereby modifying ionic concentration in the electrostatic diffuse layer and generating a diffusio-osmotic flow. The diffuse-layer excess is estimated as

$\cos\theta$0

and the corresponding diffusio-osmotic velocity as

$\cos\theta$1

Nonporous silica particles act as passive tracers with $\cos\theta$2, whereas porous silica colloids actively participate in flow generation by absorbing surfactant ions and releasing cis-isomers from their pores under illumination. UV, green, blue, and red light play distinct roles: UV drives trans $\cos\theta$3 cis, green drives cis $\cos\theta$4 trans, blue shifts the balance more weakly, and red is essentially inactive for isomerization. Beam size and beam shape then determine whether particles are expelled, trapped, packed into dense monolayers and multilayer crystalline structures, or arranged into dilute lattices of well-separated particles (Arya et al., 2020).

Thermal radiation can itself become a forcing mechanism without an external source of illumination. For a planar structure with asymmetric optical response placed in an environment at temperature $\cos\theta$5, the exchanged thermal photon flux produces a force

$\cos\theta$6

with $\cos\theta$7 the asymmetry in reflectance of the two sides. In the ideal limit of a perfect absorber on one side and a perfect reflector on the other,

$\cos\theta$8

so $\cos\theta$9. The same work reports forces up to about $\theta_0=0$0 for several hundred kelvin temperature differences, maximum accelerations of order $\theta_0=0$1 for $\theta_0=0$2-thick structures, and a terminal velocity in the ideal case

$\theta_0=0$3

This suggests a self-powered radiation-pressure mechanism driven by thermal imbalance rather than an applied beam (Deop-Ruano et al., 2024).

4. Light forcing in active suspensions: phototaxis and shear-coupled migration

In active matter, light can force motion by repeatedly resetting the swimming direction of self-propelled organisms. In suspensions of Chlamydomonas reinhardtii flowing through square PDMS microchannels of $\theta_0=0$4, phototaxis and Poiseuille vorticity combine to produce reversible cross-stream migration. The minimal model writes the swimmer trajectory as

$\theta_0=0$5

with

$\theta_0=0$6

in a Poiseuille flow

$\theta_0=0$7

Without illumination, swimmers undergo oscillatory cross-stream trajectories but no net migration averaged over a full rotation period; the suspension remains homogeneous across the channel (Garcia et al., 2013).

Illumination breaks that neutrality. When the light source is placed upstream, the cells repeatedly reorient toward the source while the flow continues to rotate them, and the resulting bias drives migration toward the channel center. When the light is placed downstream, the same mechanism drives them toward the walls. Self-focusing is observed for

$\theta_0=0$8

with the narrowest focused band at $\theta_0=0$9, where the band width is about $\alpha$0 of the channel width. Below this range the flow is too weak to rotate the cells effectively; above it the rotation is too rapid for reorientation toward light before the cells are turned again (Garcia et al., 2013).

Intermittent forcing demonstrates reversibility and sets the timescale. Using $\alpha$1 cycles with $\alpha$2 light followed by $\alpha$3 dark, the half-band width varies linearly and reversibly in time, and the average transverse speed is about

$\alpha$4

for $\alpha$5, consistent with the swimming speed $\alpha$6. When the light is switched off from the focused state, the algae remix and refill the channel at roughly the same characteristic speed. This makes the forcing field clean and reversible, and it also clarifies that the concentration dynamics are driven by active swimming rather than slow hydrodynamic diffusion. The study proposes applications in algae concentration for hydrogen production and in pollutant biodetection, because phototactic migration is sensitive to contaminants such as copper ions or PCP (Garcia et al., 2013).

5. Disordered media, coherent transport, and fluctuation-induced light forcing

In random media, light forcing acquires a mesoscopic and statistical character. Wavefront shaping through a strongly scattering $\alpha$7-thick ZnO layer shows that controlling the back-surface intensity over a chosen optimization region does more than create a local focus. Using a $\alpha$8 HeNe laser, a Holoeye Pluto SLM, and the partitioning algorithm, the optimization radius $\alpha$9 is increased so that the number of open transmission channels,

$\beta$0

grows with area $\beta$1. The target enhancement

$\beta$2

reaches about $\beta$3 for a single speckle spot, but falls to about $\beta$4 at $\beta$5, corresponding to $\beta$6 open transmission channels. At the same time, total transmitted enhancement rises from about $\beta$7 to about $\beta$8, total reflected enhancement decreases to about $\beta$9, and the intensity outside the optimization region grows to about $\beta$0. The authors interpret this as energy redistribution between transmission and reflection channels, together with qualitative evidence of a long-range reflection-transmission correlation (Ojambati et al., 2016).

A different disorder-induced mechanism yields genuine mechanical force fluctuations. In a weakly disordered dielectric, coherent multiple scattering produces long-range mesoscopic intensity correlations that act as a non-equilibrium noise source. The diffusive light current is written as

$\beta$1

with noise covariance

$\beta$2

and an Einstein relation $\beta$3. The force variance on an immersed plate takes the form

$\beta$4

where $\beta$5 is a geometry-dependent dimensionless conductance. Because the force scales as $\beta$6, reducing conductance enhances the coherent fluctuation-induced force. For visible light with $\beta$7, $\beta$8, $\beta$9, square plates of size $$\mathrm{Re}(\alpha_e)\mathrm{Re}(\alpha_m)\mathrm{Re}(P_z)$$0, and intensity $$\mathrm{Re}(\alpha_e)\mathrm{Re}(\alpha_m)\mathrm{Re}(P_z)$$1, the predicted forces reach tens to hundreds of piconewtons (Soret et al., 2019).

Random fields can also generate effective interparticle attraction. For two identical absorbing particles in a homogeneous isotropic random light field, tuned to the Fröhlich resonance where

$$\mathrm{Re}(\alpha_e)\mathrm{Re}(\alpha_m)\mathrm{Re}(P_z)$$2

the interaction reduces to

$$\mathrm{Re}(\alpha_e)\mathrm{Re}(\alpha_m)\mathrm{Re}(P_z)$$3

a non-oscillatory attractive inverse-square law from near to far field. The interpretation is mutual shadowing: each particle scatters or absorbs part of the isotropic radiation, thereby shielding the other from some incoming flux. Off resonance or for nonabsorbing particles, the force becomes oscillatory or crosses over to other power laws, so the clean gravity-like behavior is specific to resonant absorption-dominated response (Luis-Hita et al., 2018).

6. Radiative forcing in climate science

In climate physics, “light forcing” appears in the distinct sense of radiative forcing: changes in the atmospheric energy balance caused by variations in solar irradiance. Long-term stellar photometry has been used to place observational limits on this quantity by treating the Sun as a member of an ensemble of Sun-like stars. Using 72 stars observed at Fairborn Observatory between 1993 and 2017, and focusing on 22 stars with $$\mathrm{Re}(\alpha_e)\mathrm{Re}(\alpha_m)\mathrm{Re}(P_z)$$4, one study obtains an ensemble mean gradient of about

$$\mathrm{Re}(\alpha_e)\mathrm{Re}(\alpha_m)\mathrm{Re}(P_z)$$5

which is converted to irradiance using

$$\mathrm{Re}(\alpha_e)\mathrm{Re}(\alpha_m)\mathrm{Re}(P_z)$$6

for $$\mathrm{Re}(\alpha_e)\mathrm{Re}(\alpha_m)\mathrm{Re}(P_z)$$7. The inferred effective solar forcing since 1750 is

$$\mathrm{Re}(\alpha_e)\mathrm{Re}(\alpha_m)\mathrm{Re}(P_z)$$8

but the emphasized result is the bound

$$\mathrm{Re}(\alpha_e)\mathrm{Re}(\alpha_m)\mathrm{Re}(P_z)$$9

to be compared with the IPCC anthropogenic forcing estimate $\beta$0 (2002.04633).

The argument rests on three explicit assumptions: most brightness variations occur within the average time-series length of $\beta$1 years; the Sun seen from the ecliptic behaves as an ensemble of middle-aged solar-like stars; and Strömgren $\beta$2 and $\beta$3 photometry is linearly proportional to total solar irradiance. The authors identify the first as the most important and most testable through longer observations. This usage of forcing differs from mechanical light forcing, but it shares the same structural idea: radiation acts as an externally imposed driver, and the scientific problem is to quantify both the forcing amplitude and the system response (2002.04633).

7. Significance, limitations, and recurring design principles

Several general principles recur across these otherwise heterogeneous literatures. First, forcing efficiency depends on mode structure and asymmetry rather than on intensity alone. Backward optical forces require multipole interference and reduced axial photon momentum; lateral chiral forces require reflection-induced asymmetry; fluctuation-induced forces depend on conductance $\beta$4; thermal self-propulsion requires asymmetric optical response; and diffusio-osmotic forcing requires controlled trans/cis concentration gradients (Chen et al., 2011, Wang et al., 2013, Soret et al., 2019, Deop-Ruano et al., 2024, Arya et al., 2020).

Second, reversibility is system-dependent. Phototactic self-focusing in channel flow is explicitly reversible under intermittent illumination, whereas photophoretic droplet rebound depends on absorption, evaporation, and interaction time, and thermal radiation propulsion is intrinsically tied to the irreversible relaxation of a temperature difference (Garcia et al., 2013, Esseling et al., 2012, Deop-Ruano et al., 2024).

Third, apparent anomalies usually reflect hidden channel balances rather than violations of momentum conservation. Tractor beams do not require “negative momentum” in the beam; chiral lateral forces do not require a geometrically chiral substrate; and fluctuation-induced forces in random media do not require a nonzero disorder-averaged force. In each case, the controlling variable is redistribution of momentum or energy across scattering, reflection, absorption, emission, or transport channels (Chen et al., 2011, Wang et al., 2013, Soret et al., 2019).

This suggests a broad but technically precise characterization: light forcing is not a single mechanism but a family of forcing strategies in which electromagnetic radiation biases dynamics by coupling to material response, transport geometry, and non-equilibrium state variables. Its implementations range from optical micromanipulation and active-matter control to mesoscopic force generation and planetary radiative-budget inference.