Supplementary Information for “Dielectric or Plasmonic Mie Object at Air-Liquid Interface: The Transferred and the

Travelling Momentum of Photon”

M.R.C. Mahdy1,2*, Hamim Mahmud Rivy1, Ziaur Rahman Jony1, Nabila Binte Alam3, Nabila Masud1, Golam Dastegir Al Quaderi4, Ibraheem Muhammad Moosa5, Chowdhury Mofizur

Rahman6, M Sohel Rahman5*

1Department of Electrical & Computer Engineering, North South University, Bashundhara, Dhaka 1229, Bangladesh

2Pi Labs Bangladesh LTD, ARA Bhaban, 39, Kazi Nazrul Islam Avenue, Kawran Bazar, Dhaka 1215, Bangladesh

3 Department of Computer Science & Engineering, Military Institute of Science and Technology, Dhaka, Bangladesh

4Department of Physics, University of Dhaka, Dhaka, Bangladesh 5Department of Computer Science & Engineering, Bangladesh University of Engineering and

Technology ECE Building, West Palasi, Dhaka-1205 6

*Corresponding Authors:

Department of Computer Science & Engineering, United International University, Dhaka, Bangladesh

mahdy.chowdhury@northsouth.edu and msrahman@cse.Buet.ac.bd

mailto:mahdy.chowdhury@northsouth.edu�mailto:msrahman@cse.Buet.ac.bd�

S1: Optical force curves [both 2D and 3D] when the refractive index of the lower long background is 1.87 and there is a small air gap between the object and the long backgrounf medium.

Fig. 1s Diameter of the object is 4000 nm and time averaged force on the object has been calculated using Eq (1) in the main article. The force is always found to be a pushing force due to the small gap between the object and the long background medium, based on full wave simulations (a) The 2D case. (b) 3D case.

S2: Optical force curves [2D] when a lossy dielectric is placed in the air water interface and gradually increase the lossy part (k) of the refractive index.

Fig. 2s Diameter of the lossy dielectric object is 4000 nm and placed in half air-water interface. The real part of the refractive index (n=1.45) is fixed and we gradually increase the lossy part (k) of the refractive index. The force is found pulling for k= .008, .009, .001 and the force is found pushing for k= .002. It shows that due to the gradual increase of lossy part, the force converts from pulling to pushing.

It has been shown in ref [1] that: for dielectric materials, two different version of optical volumetric forces [i.e. Chu force and Einstein-Laub (EL) force] lead to the same total time averaged force (also known as Lorentz force [1]):

S3. Detail of Lorentz force analysis (in the lower lossless water background):

* *

Bulk 0 in in 0 in in1 1Re[ ( ) ] Re[ ( ){ }2 2 s

iε ω ε ε= ∇ ⋅ − − ×Ef E E B

- This force is known as Chu’s bulk force for dielectric material. Surface force of Chu for a dielectric material can be calculated based on this formula [2]:

{ } out in

*Surfac

n

e

*

out i ˆ ( ) ,2o

e avgσ=

+ = − ⋅

f E

E EE E n

In contrast, the bulk force of EL for dielectric material can be calculated based on this formula [1]:

* *Bulk in 0 in in

1 1Re[( . ) ] Re[ ( ){ }2 2 s

iω ε ε= ∇ − − ×Ef P E B

The surface force part of EL force for dielectric material [1]:

{ } out i*

Surn

outf ie nac ˆ( ) ,2o = − ⋅

E - Ef E E n

However, in [3], it has been argued that: the EL volumetric force somehow predicts the accurate force distribution (of water medium) for the experimental observation of Ashkin experiment. Considering this fact, we have employed the EL force based calculation to yield the time averaged volumetric force on water background in the main article. However, both of them (EL force and Chu force) lead to same time averaged total force: Total Volume Bulk Surf Bulk Surfacedv ds= = + = +∫ ∫F F F F f f Hence, there is no problem to choose either one of them for the calculation purpose. But the most notable issue here: the associated electromagnetic momentum density of both the formulations is none but the Abraham electromagnetic momentum density [3],[4]. As a result, we cannot ignore the fact that: though the transferred momentum to the half-immersed object can better be considered as the one of Minkowski (especially at the interface of two distinct media [5]), the travelling momentum of photon can better be modelled as the one of Abraham type. This same conclusion was also proposed in [6] considering the photon momentum inside an absorbing dielectric semiconductor.

S4. Sample data (prepared based on full wave simulations)

The training dataset in chart 1s (given below) has been prepared based on several full wave simulations. The varying parameters (i.e., features) used in the dataset are as follows: particle radius/lambda; particle loss; refractive index of the particle, background and short background; loss at long background and short background; and short background width. Thus, Chart 1s has the first 8 columns for the parameters with the last (i.e., 9th) column representing the time averaged force experienced by the particle; here ‘1’ (‘0’) represents optical pulling (pushing) force. This 9th

column is the ‘label’ of the training dataset. It should be noted that we have varied the incident angle of light from 0 degree to 90 degree; if the time averaged force is negative for most of the angles, we have defined it as ‘1’; and in contrast, if the time averaged force is positive for most of the angles, we have defined it as ‘0’.

Chart-1s

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

5 0.005 3 3.1 0.005 20 1.5 0.005 0

4.6 0.001 2.8 2.9 0.001 18 1.1 0.001 0

4 0.005 3 3.1 0.005 20 1.5 0.005 0

3.6 0.002 2.6 2.7 0.002 18 1.2 0.002 0

3.35 0.002 2.35 2.45 0.002 18.5 1.2 0.002 0

3 0.001 2 2.1 0.001 18 1.1 0.001 0

2.8 0.002 1.8 1.9 0.002 18.5 1.2 0.002 0

2.6 0.003 1.6 1.7 0.003 20 1.5 0.003 1

2.35 0.003 1.35 1.45 0.003 19 1.3 0.003 0

2 0 2 2.1 0 18.5 1.2 0.002 0

1.8 0 1.8 1.9 0 19 1.3 0.003 0

1.7 0 1.7 1.8 0 18 1.1 0.001 0

1.6 0 1.6 1.7 0 19.5 1.4 0.004 1

1.5 0 1.5 1.6 0 18.5 1.2 0.002 0

1.35 0 1.35 1.45 0 19.5 1.4 0.004 1

1.2 0 1.2 1.3 0 18 1.1 0.001 0

1 0 2 2.1 0 19 1.3 0.003 0

5 0.005 3 3.1 0.05 20 1.2 0.005 0

4.6 0.001 2.8 2.9 0.03 18 0.8 0.001 0

4 0.005 3 3.1 0.05 20 1.2 0.005 0

3.6 0.002 2.6 2.7 0.035 18 0.9 0.002 0

3.35 0.002 2.35 2.45 0.035 18.5 0.9 0.002 0

3 0.001 2 2.1 0.03 18 0.8 0.001 0

2.8 0.002 1.8 1.9 0.035 18.5 0.9 0.002 0

2.6 0.003 1.6 1.7 0.04 20 1 0.003 0

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

2.35 0.003 1.35 1.45 0.04 19 1 0.003 0

2 0 2 2.1 0.045 18.5 0.9 0.002 0

1.8 0 1.8 1.9 0.04 19 1 0.003 0

1.7 0 1.7 1.8 0.03 18 0.8 0.001 0

1.6 0 1.6 1.7 0.045 19.5 1.1 0.004 0

1.5 0 1.5 1.6 0.035 18.5 0.9 0.002 0

1.35 0 1.35 1.45 0.045 19.5 1.1 0.004 0

1.2 0 1.2 1.3 0.03 18 0.8 0.001 0

1 0 2 2.1 0.04 19 1 0.003 0

5 0.005 3 3.1 0.005 20 1.2 0.05 0

4.6 0.001 2.8 2.9 0.001 18 0.8 0.01 0

4 0.005 3 3.1 0.005 20 1.2 0.05 0

3.6 0.002 2.6 2.7 0.002 18.5 0.9 0.02 0

3.35 0.002 2.35 2.45 0.002 18.5 0.9 0.02 0

3 0.001 2 2.1 0.001 18 0.8 0.01 0

2.8 0.002 1.8 1.9 0.002 18.5 0.9 0.02 0

2.6 0.003 1.6 1.7 0.003 20 1 0.03 0

2.35 0.003 1.35 1.45 0.003 19 1 0.03 0

2 0 2 2.1 0 18.5 0.9 0.02 0

1.8 0 1.8 1.9 0 19 1 0.03 0

1.7 0 1.7 1.8 0 18 0.8 0.01 0

1.6 0 1.6 1.7 0 19.5 1.1 0.04 0

1.5 0 1.5 1.6 0 18.5 0.9 0.02 0

1.35 0 1.35 1.45 0 19.5 1.1 0.04 0

1.2 0 1.2 1.3 0 18 0.8 0.01 0

1 0 2 2.1 0 19 1 0.03 0

5 0.005 3 3.1 0.005 15 1.2 0.005 0

4.6 0.001 2.8 2.9 0.001 17 0.8 0.001 0

4 0.005 3 3.1 0.005 15 1.2 0.005 0

3.6 0.002 2.6 2.7 0.002 16.5 0.9 0.002 0

3.35 0.002 2.35 2.45 0.002 16.5 0.9 0.002 0

3 0.001 2 2.1 0.001 17 0.8 0.001 0

2.8 0.002 1.8 1.9 0.002 16.5 0.9 0.002 0

2.6 0.003 1.6 1.7 0.003 16 1 0.003 0

2.35 0.003 1.35 1.45 0.003 16 1 0.003 0

2 0 2 2.1 0 16.5 0.9 0.002 0

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

1.8 0 1.8 1.9 0 16 1 0.003 0

1.7 0 1.7 1.8 0 17 0.8 0.001 0

1.6 0 1.6 1.7 0 15.5 1.1 0.004 0

1.5 0 1.5 1.6 0 16.5 0.9 0.002 0

1.35 0 1.35 1.45 0 15.5 1.1 0.004 0

1.2 0 1.2 1.3 0 17 0.8 0.001 0

1 0 2 2.1 0 16 1 0.003 0

5 0.0005 3 3.1 0.0005 20 1.2 0.005 0

4.6 0.0001 2.8 2.9 0.0001 18 0.8 0.001 0

4 0.0005 3 3.1 0.0005 20 1.2 0.005 0

3.6 0.0002 2.6 2.7 0.0002 18.5 0.9 0.002 0

3.35 0.0002 2.35 2.45 0.0002 18.5 0.9 0.002 0

3 0.0001 2 2.1 0.0001 18 0.8 0.001 0

2.8 0.0002 1.8 1.9 0.0002 18.5 0.9 0.002 0

2.6 0.0003 1.6 1.7 0.0003 20 1 0.003 0

2.35 0.0003 1.35 1.45 0.0003 19 1 0.003 0

2 0 2 2.1 0 18.5 0.9 0.002 0

1.8 0 1.8 1.9 0 19 1 0.003 0

1.7 0 1.7 1.8 0 18 0.8 0.001 0

1.6 0 1.6 1.7 0 19.5 1.1 0.004 0

1.5 0 1.5 1.6 0 18.5 0.9 0.002 0

1.35 0 1.35 1.45 0 19.5 1.1 0.004 0

1.2 0 1.2 1.3 0 18 0.8 0.001 0

1 0 2 2.1 0 19 1 0.003 0

5 0.0005 3 3.1 0 15 0.4 0 1

4.6 0.0001 2.8 2.9 0 11 0.225 0 0

4 0.0005 3 3.1 0 15 0.4 0 1

3.6 0.0002 2.6 2.7 0 12 0.225 0 0

3.35 0.0002 2.35 2.45 0 12 0.225 0 0

3 0.0001 2 2.1 0 11 0.2 0 0

2.8 0.0002 1.8 1.9 0 12 0.225 0 0

2.6 0.0003 1.6 1.7 0 13 0.25 0 1

2.35 0.0003 1.35 1.45 0 13 0.25 0 1

2 0 2 2.1 0 12 0.225 0 0

1.8 0 1.8 1.9 0 13 0.25 0 0

1.7 0 1.7 1.8 0 11 0.2 0 0

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

1.6 0 1.6 1.7 0 14 0.275 0 1

1.5 0 1.5 1.6 0 12 0.225 0 0

1.35 0 1.35 1.45 0 14 0.275 0 1

1.2 0 1.2 1.3 0 11 0.2 0 0

1 0 2 2.1 0 13 0.25 0 0

5 0.0005 3 3.1 0.0005 0 0 0 0

4.6 0.0001 2.8 2.9 0.0001 0 0 0 0

4 0.0005 3 3.1 0.0005 0 0 0 0

3.6 0.0002 2.6 2.7 0.0002 0 0 0 0

3.35 0.0002 2.35 2.45 0.0002 0 0 0 0

3 0.0001 2 2.1 0.0001 0 0 0 0

2.8 0.0002 1.8 1.9 0.0002 0 0 0 1

2.6 0.0003 1.6 1.7 0.0003 0 0 0 1

2.35 0.0003 1.35 1.45 0.0003 0 0 0 1

2 0.0002 2 2.1 0.0002 0 0 0 0

1.8 0.0001 1.8 1.9 0.0001 0 0 0 1

1.7 0.0002 1.7 1.8 0.0002 0 0 0 1

1.6 0.0003 1.6 1.7 0.0003 0 0 0 1

1.5 0.0001 1.5 1.6 0.0001 0 0 0 1

1.35 0.0001 1.35 1.45 0.0001 0 0 0 1

1.2 0.0001 1.2 1.3 0.0001 0 0 0 1

1 0.0001 2 2.1 0.0001 0 0 0 1

5 0.0005 3 3.1 0.0005 5 1.5 0.5 0

4.6 0.0001 2.8 2.9 0.0001 3 1.1 0.1 0

4 0.0005 3 3.1 0.0005 5 1.5 0.5 0

3.6 0.0002 2.6 2.7 0.0002 3.5 1.2 0.2 0

3.35 0.0002 2.35 2.45 0.0002 3.5 1.2 0.2 0

3 0.0001 2 2.1 0.0001 3 1.1 0.1 0

2.8 0.0002 1.8 1.9 0.0002 3.5 1.2 0.2 0

2.6 0.0003 1.6 1.7 0.0003 4 1.5 0.3 0

2.35 0.0003 1.35 1.45 0.0003 4 1.3 0.3 0

2 0 2 2.1 0 3.5 1.2 6 0

1.8 0 1.8 1.9 0 4 1.3 6 0

1.7 0 1.7 1.8 0 3 1.1 6 0

1.6 0 1.6 1.7 0 4.5 1.4 6 0

1.5 0 1.5 1.6 0 3.5 1.2 0.2 0

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

1.35 0 1.35 1.45 0 4.5 1.4 0.004 1

1.2 0 1.2 1.3 0 3 1.1 0.001 0

1 0 2 2.1 0 4 1.3 0.003 1

5 0.005 3 3.1 6.5 0 0 0 0

4.6 0.001 2.8 2.9 2.5 0 0 0 0

4 0.005 3 3.1 6.5 0 0 0 0

3.6 0.002 2.6 2.7 3.5 0 0 0 0

3.35 0.002 2.35 2.45 3.5 0 0 0 0

3 0.001 2 2.1 2.5 0 0 0 0

2.8 0.002 1.8 1.9 3.5 0 0 0 0

2.6 0.003 1.6 1.7 4.5 0 0 0 0

2.35 0.003 1.35 1.45 4.5 0 0 0 0

2 0 2 2.1 3.5 0 0 0 0

1.8 0 1.8 1.9 4.5 0 0 0 0

1.7 0 1.7 1.8 2.5 0 0 0 0

1.6 0 1.6 1.7 5.5 0 0 0 0

1.5 0 1.5 1.6 3.5 0 0 0 0

1.35 0 1.35 1.45 5.5 0 0 0 0

1.2 0 1.2 1.3 2.5 0 0 0 0

1 0 2 2.1 4.5 0 0 0 0

5 0.0005 3 3.1 0.065 5 0.15 6.5 0

4.6 0.0001 2.8 2.9 0.025 3 0.35 2.5 0

4 0.0005 3 3.1 0.065 5 0.15 6.5 0

3.6 0.0002 2.6 2.7 0.035 3.5 0.3 3.5 0

3.35 0.0002 2.35 2.45 0.035 3.5 0.3 3.5 0

3 0.0001 2 2.1 0.025 3 0.35 2.5 0

2.8 0.0002 1.8 1.9 0.035 3.5 0.3 3.5 0

2.6 0.0003 1.6 1.7 0.045 4 0.25 4.5 0

2.35 0.0003 1.35 1.45 0.045 4 0.25 4.5 0

2 0 2 2.1 0.035 3.5 0.3 3.5 0

1.8 0 1.8 1.9 0.045 4 0.25 4.5 0

1.7 0 1.7 1.8 0.025 3 0.35 2.5 0

1.6 0 1.6 1.7 0.055 4.5 0.2 5.5 0

1.5 0 1.5 1.6 0.035 3.5 0.3 3.5 0

1.35 0 1.35 1.45 0.055 4.5 0.2 5.5 0

1.2 0 1.2 1.3 0.025 3 0.35 2.5 0

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

1 0 2 2.1 0.045 4 0.25 4.5 0

5 1 3 3.1 0 20 1 0.5 0

4.6 1.5 2.8 2.9 0 24 0.6 0.1 0

4 1 3 3.1 0 24 1 0.5 0

3.8 1.5 2.8 2.7 0 22 0.6 0.1 0

3.6 1.4 2.6 2.45 0 20 0.7 0.2 0

3.35 1.4 2.35 2.1 0 25 0.7 0.2 0

3 1.5 2 1.9 0 25 0.6 0.1 0

2.8 1.4 1.8 1.7 0 23 0.7 0.2 0

2.6 1.3 1.6 1.45 0 21 0.8 0.3 0

2.35 1.3 1.35 2.1 0 20 0.8 0.3 0

2 1.4 2 1.9 0 20 0.7 6 0

1.8 1.3 1.8 1.8 0 24 0.8 6 0

1.7 1.5 1.7 1.7 0 20 0.6 6 0

1.6 1.2 1.6 1.6 0 22 0.9 6 0

1.4 1 1.4 1.45 0 20 1 0.5 0

1.25 1.4 1.25 1.3 0 23 0.7 0.2 0

1 1.3 2 2.1 0 21 0.8 0.3 0

5 0.006 3 3.1 0 20 1 0.005 1

4.6 0.001 2.8 2.9 0 24 0.6 0.001 1

4 0.006 3 3.1 0 24 1 0.005 1

3.8 0.001 2.8 2.7 0 22 0.6 0.001 1

3.6 0.009 2.6 2.45 0 20 0.7 0.002 0

3.35 0.009 2.35 2.1 0 25 0.8 0.002 0

3 0.001 2 1.9 0 25 0.6 0.001 1

2.8 0.009 1.8 1.7 0 23 0.7 0.002 1

2.6 0.008 1.6 1.45 0 21 0.8 0.003 1

2.35 0.008 1.35 2.1 0 20 0.8 0.003 1

2 0.009 2 1.9 0 20 0.7 0.06 1

1.8 0.008 1.8 1.8 0 24 0.8 0.06 1

1.7 0.001 1.7 1.7 0 20 0.6 0.06 1

1.6 0.007 1.6 1.6 0 22 0.9 0.06 1

1.4 0.006 1.4 1.45 0 20 1 0.005 0

1.25 0.009 1.25 1.3 0 23 0.7 0.002 1

1 0.008 2 2.1 0 21 0.8 0.003 1

5 0.0005 3 3.1 0.0005 15 1.2 0 1

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

4.6 0.001 2.8 2.9 0.001 17 0.8 0 1

4 0.005 3 3.1 0.005 15 1.2 0 1

3.6 0.002 2.6 2.7 0.002 16.5 0.9 0 1

3.35 0.002 2.35 2.45 0.002 16.5 0.9 0 1

3 0.001 2 2.1 0.001 17 0.8 0 1

2.8 0.002 1.8 1.9 0.002 16.5 0.9 0 1

2.6 0.003 1.6 1.7 0.003 16 1 0 1

2.35 0.003 1.35 1.45 0.003 16 1 0 1

2 0 2 2.1 0 16.5 0.9 0 1

1.8 0 1.8 1.9 0 16 1 0 1

1.7 0 1.7 1.8 0 17 0.8 0 1

1.6 0 1.6 1.7 0 15.5 1.1 0 1

1.5 0 1.5 1.6 0 16.5 0.9 0 1

1.35 0 1.35 1.45 0 15.5 1.1 0 1

5 0.0005 3 3.5 0.065 25 1.5 0 0

4.6 0.0001 2.8 3.3 0.025 15 3.5 0 1

4 0.0005 3 3.5 0.065 25 1.5 0 0

3.6 0.0002 2.6 3.1 0.035 17.5 3 0 1

3.35 0.0002 2.35 2.85 0.035 17.5 3 0 1

3 0.0001 2 2.5 0.025 15 3.5 0 1

2.8 0.0002 1.8 2.3 0.035 17.5 3 0 1

2.6 0.0003 1.6 2.1 0.045 20 2.5 0 1

2.35 0.0003 1.35 1.85 0.045 20 2.5 0 1

2 0 2 2.5 0.035 17.5 3 0 1

1.8 0 1.8 2.3 0.045 20 2.5 0 1

1.7 0 1.7 2.2 0.025 15 3.5 0 1

1.6 0 1.6 2.1 0.055 22.5 2 0 1

1.5 0 1.5 2 0.035 17.5 3 0 1

1.35 0 1.35 1.85 0.055 22.5 2 0 1

1.2 0 1.2 1.7 0.025 15 3.5 0 1

1 0 2 2.5 0.045 20 2.5 0 1

5 1 3 3.5 0 20 5 0.05 0

4.6 0 2.8 3.3 0 24 3 0.01 1

4 0 3 3.5 0 24 5 0.05 1

3.6 0 2.6 3.1 0 20 3.5 0.02 1

3.35 0 2.35 2.85 0 25 3.5 0.02 1

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

3 0 2 2.5 0 25 3 0.01 1

2.8 0 1.8 2.3 0 23 3.5 0.02 1

2.6 0 1.6 2.1 0 21 4 0.03 1

2.35 0 1.35 1.85 0 20 4 0.03 1

2 0 2 2.5 0 20 3.5 0.02 1

1.8 0 1.8 2.3 0 24 4 0.03 1

1.7 0 1.7 2.2 0 20 3 0.01 1

1.6 0 1.6 2.1 0 22 4.5 0.04 1

1.5 0 1.5 2 0 24 3.5 0.02 1

1.35 0 1.35 1.85 0 21 4.5 0.04 1

1.2 0 1.2 1.7 0 24 3 0.01 1

1 0 1 1.55 0 21 4 0.03 1

4.9 0.007 2.95 3.05 0 21 4.5 0.004 1

4.8 0.008 2.9 3 0 22 4 0.003 1

4.7 0.009 2.85 2.95 0 23 3.5 0.002 1

4.5 0.006 2.75 2.85 0 25 5 0.005 1

4.4 0.007 2.7 2.8 0 20 4.5 0.004 1

4.3 0.008 2.65 2.75 0 21 4 0.003 1

4.2 0.009 2.6 2.7 0 22 3.5 0.002 1

4.1 0.001 2.55 2.65 0 23 3 0.001 1

3.95 0.007 2.95 3.05 0 25 4.5 0.004 1

3.9 0.008 2.9 3 0 20 4 0.003 1

3.85 0.009 2.85 2.95 0 21 3.5 0.002 1

1.15 0 1.15 1.25 0 15 6 0 1

1.1 0 1.1 1.2 0 15.5 5.5 0 1

1.3 0 1.3 1.4 0 16 5 0 1

1.25 0 1.25 1.35 0 16.5 4.5 0 1

1.45 0 1.45 1.55 0 17 4 0 1

1.4 0 1.4 1.5 0 15 6 0 1

1.95 0 1.95 2.05 0 17 4 0 1

1.9 0 1.9 2 0 15 6 0 1

1.85 0 1.85 1.95 0 15.5 5.5 0 1

2.3 0.002 1.3 1.4 0.002 16.5 4.5 0 1

2.25 0.001 1.25 1.35 0.001 17 4 0 1

2.2 0.005 1.2 1.3 0.005 15 6 0 1

2.15 0.004 1.15 1.25 0.004 15.5 5.5 0 1

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

2.1 0.003 1.1 1.2 0.003 16 5 0 1

2.55 0.002 1.55 1.65 0.002 16.5 4.5 0 1

2.5 0.001 1.5 1.6 0.001 17 4 0 1

2.45 0.005 1.45 1.55 0.005 15 6 0 1

2.4 0.004 1.4 1.5 0.004 15.5 5.5 0 1

2.75 0.001 1.75 1.85 0.001 17 4 0 1

2.7 0.005 1.7 1.8 0.005 15 6 0 1

2.65 0.004 1.65 1.75 0.004 15.5 5.5 0 1

2.95 0.005 1.95 2.05 0.005 15 6 0 1

2.9 0.004 1.9 2 0.004 15.5 5.5 0 1

2.85 0.003 1.85 1.95 0.003 16 5 0 1

3.3 0.001 2.3 2.4 0.001 17 4 0 1

3.25 0.005 2.25 2.35 0.005 15 6 0 1

3.2 0.004 2.2 2.3 0.004 15.5 5.5 0 1

3.15 0.003 2.15 2.25 0.003 16 5 0 1

3.1 0.002 2.1 2.2 0.002 16.5 4.5 0 1

3.55 0.001 2.55 2.65 0.001 17 4 0 1

3.5 0.005 2.5 2.6 0.005 15 6 0 1

3.45 0.004 2.45 2.55 0.004 15.5 5.5 0 1

3.4 0.003 2.4 2.5 0.003 16 5 0 1

4.9 0.004 2.95 3.05 0.045 19.5 1.1 0.004 0

4.8 0.003 2.9 3 0.04 19 1 0.003 0

4.7 0.002 2.85 2.95 0.035 18.5 0.9 0.002 0

4.5 0.005 2.75 2.85 0.05 20 1.2 0.005 0

4.4 0.004 2.7 2.8 0.045 19.5 1.1 0.004 0

4.3 0.003 2.65 2.75 0.04 19 1 0.003 0

4.2 0.002 2.6 2.7 0.035 18.5 0.9 0.002 0

4.1 0.01 2.55 2.65 0.03 18 0.8 0.001 0

3.95 0.004 2.95 3.05 0.045 19.5 1.1 0.004 0

3.9 0.003 2.9 3 0.04 19 1 0.003 0

3.85 0.002 2.85 2.95 0.035 18.5 0.9 0.002 0

3.8 0.001 2.8 2.9 0.03 18 0.8 0.001 0

3.75 0.005 2.75 2.85 0.05 20 1.2 0.005 0

3.7 0.004 2.7 2.8 0.045 19.5 1.1 0.004 0

3.65 0.003 2.65 2.75 0.04 19 1 0.003 0

3.55 0.001 2.55 2.65 0.03 18 0.8 0.001 0

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

3.5 0.005 2.5 2.6 0.05 20 1.2 0.005 0

3.45 0.004 2.45 2.55 0.045 19.5 1.1 0.004 0

3.4 0.003 2.4 2.5 0.04 19 1 0.003 0

3.3 0.001 2.3 2.4 0.03 18 0.8 0.001 0

3.25 0.005 2.25 2.35 0.05 20 1.2 0.005 0

3.2 0.004 2.2 2.3 0.045 19.5 1.1 0.004 0

3.15 0.003 2.15 2.25 0.04 19 1 0.003 0

3.1 0.002 2.1 2.2 0.035 18.5 0.9 0.002 0

2.95 0.005 1.95 2.05 0.05 20 1.2 0.005 0

2.9 0.004 1.9 2 0.045 19.5 1.1 0.004 0

2.85 0.003 1.85 1.95 0.04 19 1 0.003 0

2.75 0.001 1.75 1.85 0.03 18 0.8 0.001 0

2.7 0.005 1.7 1.8 0.05 20 1.2 0.005 0

2.65 0.004 1.65 1.75 0.045 19.5 1.1 0.004 0

2.55 0.002 1.55 1.65 0.035 18.5 0.9 0.002 0

2.5 0.001 1.5 1.6 0.03 18 0.8 0.001 0

2.45 0.005 1.45 1.55 0.05 20 1.2 0.005 0

2.4 0.004 1.4 1.5 0.045 19.5 1.1 0.004 0

2.3 0.002 1.3 1.4 0.035 18.5 0.9 0.002 0

2.25 0.001 1.25 1.35 0.03 18 0.8 0.001 0

2.2 0.005 1.2 1.3 0.05 20 1.2 0.005 0

2.15 0.004 1.15 1.25 0.045 19.5 1.1 0.004 0

2.1 0.003 1.1 1.2 0.04 19 1 0.003 0

1.95 0 1.95 2.05 0.03 18 0.8 0.001 0

1.9 0 1.9 2 0.05 20 1.2 0.005 0

1.85 0 1.85 1.95 0.045 19.5 1.1 0.004 0

1.45 0 1.45 1.55 0.03 18 0.8 0.001 0

1.4 0 1.4 1.5 0.05 20 1.2 0.005 0

1.3 0 1.3 1.4 0.04 19 1 0.003 0

1.25 0 1.25 1.35 0.035 18.5 0.9 0.002 0

3.95 0.004 2.95 3.05 0.004 19.5 1.1 0.04 0

3.9 0.003 2.9 3 0.003 19 1 0.03 0

3.85 0.002 2.85 2.95 0.002 18.5 0.9 0.02 0

3.8 0.001 2.8 2.9 0.001 18 0.8 0.01 0

3.75 0.005 2.75 2.85 0.005 20 1.2 0.05 0

3.7 0.004 2.7 2.8 0.004 19.5 1.1 0.04 0

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

3.65 0.003 2.65 2.75 0.003 19 1 0.03 0

3.1 0 1.5 1.35 0 0 0 0 1

3.2 0 1.5 1.35 0 0 0 0 1

3.2 0 1.45 1.35 0 0 0 0 1

3.1 0 1.5 1.4 0 0 0 0 1

3.15 0 1.45 1.4 0 0 0 0 1

3.18 0 1.5 1.45 0 0 0 0 1

3.12 0 1.45 1.4 0 0 0 0 1

3 0 1.5 1.4 0 0 0 0 1

3 0 1.45 1.4 0 0 0 0 1

3 0 1.48 1.35 0 0 0 0 1

3.15 0 1.45 11 0 0 0 0 1

3.2 0 1.4 9 0 0 0 0 1

3 0 1.5 8 0 0 0 0 1

3.15 0 1.5 9.5 0 0 0 0 1

3.2 0 1.48 11 0 0 0 0 1

3 0 1.4 10.5 0 0 0 0 1

3.15 0 1.5 10.5 0 0 0 0 1

3.2 0 1.45 8 0 0 0 0 1

3.2 0 1.5 6 0 0 0 0 1

3 0 1.48 5 0 0 0 0 1

3 0 1.47 4 0 0 0 0 1

3 0 1.47 3 0 0 0 0 1

3 0 1.5 3 0 0 0 0 1

3.18 0 1.4 1 0 10 1.35 0 1

3.1 0 1.45 1 0 10 1.4 0 1

3.2 0 1.46 1 0 12 1.3 0 1

3.15 0 1.47 1 0 10 1.36 0 1

3 0 1.45 1 0 10 1.37 0 1

3.17 0 1.4 1 0 12.5 1.3 0 1

3.12 0 1.41 1 0 11 1.34 0 1

3.13 0 1.4 1 0 10.5 1.37 0 1

3.14 0 1.45 1 0 11 1.36 0 1

3.2 0 1.46 1 0 10.5 1.38 0 1

3.1 0 1.48 1 0 11 1.39 0 1

3.18 0 1.5 1 0 12 1.37 0 1

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

3.17 0 1.4 1 0 11 1.4 0 1

3.16 0 1.41 1 0 11.5 1.35 0 1

3.2 0 1.42 1 0 10.5 1.36 0 1

3.16 0 1.4 1 0 11 1.37 0 1

3.16 0 1.41 1 0 11.5 1.35 0 1

3.12 0 1.42 1 0 11 1.35 0 1

3.14 0 1.46 1 0 12 1.35 0 1

3.18 0 1.47 1 0 11 1.33 0 1

3.15 0 1.4 1 0 10.5 1.33 0 1

3.15 0 1.42 1 0 10.5 1.33 0 1

3.17 0 1.43 1 0 10 1.34 0 1

3.16 0 1.45 1 0 10 1.42 0 1

3.17 0 1.44 1 0 10 1.41 0 1

3.16 0 1.49 1 0 12 1.42 0 1

3.18 0 1.44 1.33 0.42 28 1.33 0 1

3.11 0 1.41 1.34 0.38 29 1.34 0 1

3.15 0 1.44 1.31 0.43 32 1.35 0 1

3.16 0 1.45 1.36 0.4 34 1.31 0 1

3.14 0 1.46 1.35 0.42 31 1.38 0 1

3.18 0 1.44 1.37 0.41 30 1.37 0 1

3.18 0 1.48 1.35 0.42 29 1.33 0 1

3.12 0 1.45 1.38 0.42 28 1.32 0 1

3.11 0 1.41 1.35 0.39 31 1.31 0 1

3.15 0 1.4 1.32 0.38 32 1.36 0 1

3.16 0 1.44 1.3 0.37 33 1.31 0 1

3.16 0 1.45 1.39 0.5 35 1.32 0 1

3.13 0 1.41 1.31 0.5 28 1.33 0 1

3.18 0 1.48 1.32 0.52 28 1.35 0 1

3.18 0 1.44 1.35 0.4 31 1.33 0 1

3.14 0 1.44 1.33 0.42 0 0 0 0

3.18 0 1.41 1.34 0.38 0 0 0 0

3.12 0 1.44 1.31 0.43 0 0 0 0

3.11 0 1.45 1.36 0.4 0 0 0 0

3.18 0 1.46 1.35 0.42 0 0 0 0

3.17 0 1.44 1.37 0.41 0 0 0 0

3.16 0 1.48 1.35 0.42 0 0 0 0

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

3.12 0 1.45 1.38 0.42 0 0 0 0

3.17 0 1.41 1.35 0.39 0 0 0 0

3.16 0 1.4 1.32 0.38 0 0 0 0

3.19 0 1.44 1.3 0.37 0 0 0 0

3.2 0 1.45 1.39 0.5 0 0 0 0

3.1 0 1.41 1.31 0.5 0 0 0 0

3.15 0 1.48 1.32 0.52 0 0 0 0

3.15 0 1.44 1.35 0.4 0 0 0 0

3.12 0.1 1.41 1.33 0 0 0 0 0

3.13 0.12 1.4 1.34 0 0 0 0 0

3.14 0.13 1.45 1.31 0 0 0 0 0

3.2 0.11 1.46 1.36 0 0 0 0 0

3.1 0.15 1.48 1.35 0 0 0 0 0

3.18 0.1 1.5 1.37 0 0 0 0 0

3.17 0.12 1.4 1.35 0 0 0 0 0

3.16 0.13 1.41 1.38 0 0 0 0 0

3.2 0.11 1.42 1.35 0 0 0 0 0

3.16 0.15 1.4 1.32 0 0 0 0 0

3.16 0.1 1.41 1.3 0 0 0 0 0

3.12 0.12 1.42 1.39 0 0 0 0 0

3.14 0.13 1.46 1.31 0 0 0 0 0

3.18 0.11 1.47 1.32 0 0 0 0 0

3.15 0.15 1.4 1.35 0 0 0 0 0

3.15 0.1 1.42 1.33 0 0 0 0 0

3.17 0.12 1.43 1.34 0 0 0 0 0

3.16 0.13 1.45 1.31 0 0 0 0 0

3.17 0.11 1.44 1.36 0 0 0 0 0

3.16 0.15 1.49 1.35 0 0 0 0 0

3.19 0 1.44 1.3 0 30 1.55 0.7 0

3.2 0 1.45 1.39 0 29 1.35 0.6 0

3.1 0 1.41 1.31 0 28 1.65 0.5 0

3.15 0 1.48 1.32 0 31 1.4 0.65 0

3.15 0 1.44 1.35 0 32 1.45 0.68 0

3.12 0 1.41 1.33 0 33 1.48 0.7 0

3.13 0 1.4 1.34 0 35 1.68 0.6 0

3.14 0 1.45 1.31 0 28 1.42 0.65 0

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

3.2 0 1.46 1.36 0 28 1.41 0.65 0

3.1 0 1.48 1.35 0 31 1.42 0.58 0

3.18 0 1.5 1.37 0 30 1.58 0.7 0

3.17 0 1.4 1.35 0 29 1.34 0.6 0

3.16 0 1.41 1.38 0 28 1.35 0.75 0

3.2 0 1.42 1.35 0 31 1.31 0.65 0

3.16 0 1.4 1.32 0 32 1.38 0.58 0

3.16 0 1.41 1.3 0 33 1.37 0.7 0

3.12 0 1.42 1.39 0 35 1.33 0.6 0

3.14 0 1.46 1.31 0 28 1.62 0.68 0

3.18 0 1.47 1.32 0 28 1.31 0.65 0

3.15 0 1.4 1.35 0 31 1.56 0.65 0

3.15 0 1.42 1.33 0 33 1.31 0.7 0

3.17 0 1.43 1.34 0 35 1.32 0.6 0

3.16 0 1.45 1.31 0 28 1.33 0.75 0

3.17 0 1.44 1.36 0 28 1.55 0.65 0

3.16 0 1.49 1.35 0 31 1.43 0.75 0

3.19 3 0.06 1.3 0 30 1.55 0 0

3.2 4 0.7 1.39 0 29 1.35 0 0

3.1 5 0.09 1.31 0 28 1.65 0 0

3.15 2.5 0.04 1.32 0 31 1.4 0 0

3.15 1 0.8 1.35 0 32 1.45 0 0

3.12 3 0.5 1.33 0 33 1.48 0 0

3.13 4 0.4 1.34 0 35 1.68 0 0

3.14 5 0.07 1.31 0 28 1.42 0 0

3.2 2.5 0.06 1.36 0 28 1.41 0 0

3.1 1 0.075 1.35 0 31 1.42 0 0

3.18 3 0.06 1.37 0 30 1.58 0 0

3.17 4 0.7 1.35 0 29 1.34 0 0

3.16 5 0.09 1.38 0 28 1.35 0 0

3.2 2.5 0.04 1.35 0 31 1.31 0 0

3.16 1 0.8 1.32 0 32 1.38 0 0

3.16 3 0.5 1.3 0 33 1.37 0 0

3.12 4 0.4 1.39 0 35 1.33 0 0

3.14 5 0.07 1.31 0 28 1.62 0 0

3.18 2.5 0.06 1.32 0 28 1.31 0 0

r/lambda particle loss

particle ref index

background ref index

background loss

short background width

short background ref index

short background loss

Force

3.15 1 0.075 1.35 0 31 1.56 0 0

3.15 3 0.06 1.33 0 33 1.31 0 0

3.17 4 0.7 1.34 0 35 1.32 0 0

3.16 5 0.09 1.31 0 28 1.33 0 0

3.17 2.5 0.04 1.36 0 28 1.55 0 0

3.16 1 0.8 1.35 0 31 1.43 0 0

3.2 0 1.48 1.38 0 3 1 0 0

3.3 0 1.5 2.38 0 4 1 0 0

3.1 0 1.4 3 0 5 1 0 0

3.4 0 1.7 2.5 0 6 1 0 0

3.5 0 1.65 2.8 0 3 1 0 0

3.2 0 2 2 0 4 1 0 0

3.3 0 1.48 1.8 0 7 1 0 0

3.1 0 1.5 1.7 0 6 1 0 0

3.4 0 1.4 1.38 0 2 1 0 0

3.5 0 1.7 2 0 4 1 0 0

3.2 0 1.65 1.9 0 5 1 0 0

3.3 0 2 1.35 0 3.5 1 0 0

3.1 0 1.4 1.8 0 3 1 0 0

3.4 0 1.5 2.5 0 4 1 0 0

3.5 0 1.4 3 0 5 1 0 0

References

[1] M. Mansuripur, A. R. Zakharian, and J. V. Moloney, Equivalence of total force (and torque) for two formulations of the Lorentz law. Proc. of the SPIE Conf., 63260G-63260G (2006).

[2] Mahdy, M.R.C., Danesh, M., Zhang, T., Ding, W., Rivy, H.M., Chowdhury, A.B. and Mehmood, M.Q. Plasmonic Spherical Heterodimers: Reversal of Optical Binding Force Based on the Forced Breaking of Symmetry. Scientific reports, 8, 3164 (2018).

[3] M. Mansuripur, A.R. Zakharian, and E.M. Wright, Electromagnetic force distribution inside matter. Phys. Rev. A 88, 023826 (2013).

[4] Kemp, B. A. "Resolution of the Abraham-Minkowski debate: Implications for the electromagnetic wave theory of light in matter." Journal of Applied Physics 109, no. 11: 7 (2011).

[5] Barnett, S.M., Loudon, R. “The enigma of optical momentum in a medium,” Phil. Trans. R. Soc, A 368, 927 (2010).

[6] Mansuripur, M., Zakharian, A. R. “Whence the Minkowski momentum?” Opt. Commun., 283, 3557 (2010).