  A recent analysis by one of the authors\cite{Perivolaropoulos:2016ucs} has
indicated the presence of a $2\sigma$ signal of spatially oscillating new force
residuals in the torsion balance data of the Washington experiment. We extend
that study and analyse the data of the Stanford Optically Levitated Microsphere
Experiment (SOLME) \cite{Rider:2016xaq} (kindly provided by the authors of
\cite{Rider:2016xaq}) searching for sub-mm spatially oscillating new force
signals. We find a statistically significant oscillating signal for a force
residual of the form $F(z)=\alpha \; cos(\frac{2\pi}{\lambda}\; z +c)$ where
$z$ is the distance between the macroscopic interacting masses (levitated
microsphere and cantilever). The best fit parameter values are $\alpha=(1.1 \pm
0.4)\times 10^{-17}N$, $\lambda=(35.2\pm 0.6)\mu m$. Monte Carlo simulation of
the SOLME data under the assumption of zero force residuals has indicated that
the statistical significance of this signal is at about $2\sigma$ level.
Private communication with members of the SOLME group has indicated that this
previously unnoticed signal is most probably due to a systematic effect
(diffraction of non-Gaussian tails of the laser beam). Thus it can only be
useful as an upper bound of the amplitude of new spatially oscillating forces
on sub-mm scales. Assuming gravitational origin emerging from a fundamental
modification of the Newtonian potential of the form
$V_{eff}(r)=-G\frac{M}{r}(1+\alpha_O \cos(\frac{2\pi}{\lambda}\;
r+\theta))\equiv V_{N}(r)+V_{osc}(r)$, we evaluate the source integral and
obtain a bound $\alpha_O < 10^7$ for $\lambda \simeq 35 \mu m$. Thus, we get no
useful constraints on the modified gravity parameter $\alpha_O$. However, the
constraints on the general phenomenological parameter $\alpha$ can be useful in
constraining other fifth force models related to dark energy (chameleon
oscillating potentials etc).
