Optimization of Non-diffractive Beam Propagation in Random Media

Formed by Annular Beam

Ziqi Peng and Tatsuo Shiina

Graduate School of Advanced Integration Science, Chiba University,

1-33 Yayoi-cho, Inage-ku, Chiba-shi, Chiba, 263-8522, Japan

Keywords: Annular Beam, Non-diffractive Beam, Scattering, Random Media, Propagation.

Abstract: Light is quite difficult to propagate a long distance in random media such as human tissue or atmospheric

dense cloud because of its scattering and absorption. For optical sensing, it is important to increase

propagation efficiency which means expanding the sensing range. An annular beam can transform its

waveform into a non-diffractive beam due to its propagation in a long distance. In our previous work, we

found the annular beam also had non-diffractive effect when it propagated in diluted milk solution of a few

tens centimetres at the concentration of less than 1%. In this study, to clear up how to control and optimize

the non-diffractive effect of the annular beam in random media, numerical calculation of propagation

characteristics of annular beam in air was estimated. The narrow annular beam with a small diameter would

generate a high intensity non-diffractive beam at a short distance. We also had three sets of experiments of

annular beam propagation in random media with the same view point as the calculation, but its propagation

characteristics was evaluated by milk concentration. They showed the same variation of a non-diffractive

beam with the result of numerical calculation in air. These results provide us a hint of optimization for annular

beam propagation in random media.

1 INTRODUCTION

Optical sensing is widely used in environmental

observation, medical examination, military and other

industrial fields as a non-invasive and non-contact

sensing technology (Shiina, 2007) (Aruga, 1999). But

for visible light and near-infrared light, it is very hard

to propagate a long distance in random media (

Craig,

1998

) such as human tissue and atmospheric dense

cloud because of its light absorption and scattering,

especially when the size of the scattering particle is

close to the wavelength of the light (Profio, 1989)

(Ishimaru, 1989) (Diruan, 1991). For optical sensing,

it is important to increase propagation efficiency to

expand the sensing range.

We focused on the self-transformation of the

annular beam through its propagation (Voelz, 2009)

(Chen 2008) (Eyyuboglu, 2006). The annular beam

can be easily created from a Gaussian beam by a pair

of axicon prisms. Comparing with other types of

annular beams, this type is high efficiency because

none of the light is cut down (Shiina, 2007). The

annular beam with the diameter of 40mm can

transform its waveform into the non-diffractive beam

(quasi-Bessel beam) at the propagation distance of

210m. Comparing to the Gaussian beam, the non-

diffractive beam has better resistance to air

fluctuation when it propagate in air (Rao, 2008)

(Gercekcioglu, 2010) (Baykal, 2005) (Eyyuboglu,

2008) (Shiina, 2005). In our previous work, we found

the annular beam also had the non-diffractive effect

when it propagated in random media, the milk

solution at concentration of less than 1% with the

length of tens centimeters (Peng, 2011).

In this study, for the purpose of controlling and

optimizing non-diffractive effect of the annular beam

in random media, we had numerical calculation and

three sets of experiments. In Chap. 2, theory of the

annular beam and propagation characteristics were

discussed when propagation distance, ring thickness

and diameter of annular beam were varied. In Chap.

3, it showed experimental results with the same

viewpoint as the calculation shown in Chap. 2. The

calculation and the experimental results were

compared in criterion of propagation distance and the

concentration of random media.

Peng, Z. and Shiina, T.

Optimization of Non-diffractive Beam Propagation in Random Media Formed by Annular Beam.

DOI: 10.5220/0005683300620068

In Proceedings of the 4th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2016), pages 64-70

ISBN: 978-989-758-174-8

2 THEORY ANALYSIS

Because the non-diffractive beam formed from the

annular beam is decided by not only its propagation

distance, but also the incident beam characteristics

such as the thickness and the diameter of the annular

beam. It is also affected by the concentration of the

random media.

2.1 Annular Beam

and Non-Diffractive Beam

The annular beam we used was created from

Gaussian beam by a pairs of Axicon prisms

(Fedotowsky, 1974) (Scott, 1992) (Aruga, 1997)

(Aruga 1999) (Kono, 1997).The conversion function

from an incident beam to an annular beam is shown

by formula (1) and (2).

)](exp[

)(

rg −⋅=

(1)

)()( rRg

ra −⋅

−

(2)

g(r) is an intensity function of Gaussian

distribution, and a(r) is an intensity function of an

annular beam. h is a distance from the center to the

point of beam radius, where the intensity becomes

1/e

of the center value. R is the external radius of the

annular beam decided by the interval between Axicon

prisms, and r is the internal radius of the annular beam

decided by width of g(r). The radius of the incident

beam could be expressed as R-r

Using Fresnel diffraction equation (3), we

calculated propagation characteristics of the Gaussian

and the annular beam in air.

dxdyiklyxf

yxu



= )exp(),(),(

(3)

u(x

, y

) is a diffractive beam function, f(x, y) is an

amplitude function of the incident beam, λ is a

wavelength, L is a propagation distance, k is a wave

number, and l is the distance from the incident point

, y

) to the target point (x, y). Figure 1 (a) shows

the intensities of the Gaussian beam and the annular

beam calculated by formula (1) and (2). They have

the same total light intensity. Figure 1 (b) shows the

intensity of the Gaussian beam and the annular beam

after they propagated at 210m in air. Although the

Gaussian beam diffused because of diffraction, the

annular beam changed its wave shape into the non-

diffractive beam after its propagation. As the width

of the main peak of the non-diffractive beam becomes

(a) Incident Gaussian and annular beam.

(b) Gaussian and transformed non-diffractive beam after

the propagation.

Figure 1: Propagation characteristics of Gaussian and

annular beam. (h=1.8mm, R=20mm.).

Figure 2: Center intensity of non-diffractive beam against

propagation distance in air. (h=1.8mm, R=20mm.).

narrow, it is an advantage of high resolution for

optical sensing. Figure 2 shows variation of the center

intensity of the non-diffractive beam against the

propagation distance in air. The center intensity

hadthe maximum when the annular beam propagated

at the distance of 210m, where the non-diffractive

beam was transformed completely. This distance

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

-30 -20 -10 0 10 20 30

Intensity(a.u.)

Position

(

)

Gaussian mode

Annular mode

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-30 -20 -10 0 10 20 30

Intensity(a.u.)

Position(mm)

Gaussian mode after 210m

propagation

Annular mode after 210m

propagation

0.2

0.4

0.6

0.8

1.2

0 100 200 300 400 500 600 700 80

Normalized intensity (a.u.)

Propagation distance (m)

Optimization of Non-diffractive Beam Propagation in Random Media Formed by Annular Beam

would be changed when the annular beam had the

other diameter or the thickness of the ring.

Figure 3: Variation of the non-diffractive beam with

different thickness (R=12mm).

Figure 3 shows the maximum intensity of the non-

diffractive beam while the annular beam had the same

diameter and the different ring thickness. The

transformed beam had the higher center intensity with

a main peak when the thickness of the annular beam

was narrower, but the distance where the non-

diffractive beam was obtained became short when the

thickness of annular beam became narrow. The width

of the main peak of the non-diffractive beam was

about twice of the ring thickness of the incident

annular beam.

Figure 4 shows the variation of the intensity of the

non-diffractive beam while the annular beam had the

same ring thickness and the different diameters. All

the main peaks of the non-diffractive beams had the

same width. The high center intensity was obtained

when the diameter of the annular beam was small.

The distance where the non-diffractive beam was

maximum became short due to the decrease of the

diameter of the annular beam.

2.2 Propagation in Random Media

At the previous study, non-diffractive effect was

confirmed in the diluted milk solution at the

concentration of less than 1% when the annular beam

propagated at 20cm. We considered the annular beam

remained its coherency after it scattered several times

in the forward direction with a narrow scattering

angle, and converted into a non-diffractive beam.

When the multiple scattering occurred in random

media, the incident light will change its propagation

direction several times when it hits the scatters. The

transport mean free path is defined as the average

distance light travelled between successive impacts.

It can be written as formula (4),

sca

Cgn

)1(

−

(4)

n is the number of scattering particles in unit volume,

g is the anisotropy parameter, and C

sca

is the

scattering cross-section. According to Mie theory, the

Figure 4: Variation of the non-diffractive beam with

different Diameter (Thickness=0.75mm).

Figure 5: Center intensity of non-diffractive beam against

the propagation distance in air (with lens effect,

Thickness=3mm, R=20mm.).

transport mean free path can be expressed by the

concentration of the random media R

as formula (5).

292.4

−

×=

(5)

In our experiment, the transport mean free path would

be about 5cm when the concentration was 0.8%.

When the length of the random media was set as 20cm,

4 or 5 times scattering would be occured according to

0.05

0.1

0.15

0.2

0.25

0.3

-4-3-2-101234

Intensity （a.u.）

Position（ｍm）

Thickness=0.75mm L=85m

Thickness=0.6mm L=60m

Thickness=0.3mm L=35m

0.02

0.04

0.06

0.08

0.1

0.12

-4 -3 -2 -1 0 1 2 3 4

Intensity （a.u.）

Position（ｍm）

R=12mm L=85m

R=16mm L=110m

R=20mm L=135m

0 50 100 150 200 250 300

Normalized center intensity (a.u.)

Propagation distance (m)

PHOTOPTICS 2016 - 4th International Conference on Photonics, Optics and Laser Technology

transport mean free path of 5cm. So the maximum

total optical path would become about 1m (20cm*4

or 5) when the scattered light travelled to the forward

direction. For the annular beam with diameter of

40mm, the non-diffractive effect is originally

emerged after the propagation of a few hundred

meters in air. We considered that scattering particles

act as a lens in the random media. The light spread its

travel direction by keeping its polarization. This lens

effect is depended on number of scattering particles

in unit volume of the random media.

Figure 5 shows the center intensity variation of

non-diffractive beam in air when we set a lens to

made annular beam focus at each distance. Center

intensity was high when it focus in a short distance.

3 EXPERIMENT

3.1 Measurement System

Figure 6 and Table 1 shows the structure of

measurement system and the specification of the

optical elements in our measurement system,

respectively.

A high power DPSS laser was introduced, and the

pulsed beam was used to increase the efficiency of

non-diffractive effect in random media. An ND filter

was used to adjust the optical intensity. A beam

expander and a pair of axicon prisms helped to control

the thickness and the diameter of the annular beam.

To change the propagation distance, three sizes of

media tanks were used. The processed milk with

1.8% fat was chosen as the random media. The fat

particles in the milk have the scattering coefficient

similar with human tissue, so that we can model the

human tissue by adjusting the concentration of the

milk. The absorption in the milk solution is very weak,

which can be ignored to compare with the effect of

scattering. The combination of a collimate lens and a

multiple mode optical fiber made a narrow view angle

of 5.5mrad, which helped to catch up the forward

scattering light, and this combination was set on a

mechanical stage controlled by PC with the resolution

of 0.1mm at horizontal-axis. A photo multiplier tube

(PMT) was used as a detector to obtain the weak

optical signal through the random media, and a

sampling oscilloscope was used to monitor the pulsed

electric signal from PMT.

Table 1: Specification of the experiment system.

Light source

DPSS laser CryLas, 1Q532-1:

Wavelength: 532nm;

Pulse width: 2ns;

Peak power: 4.6kW;

Repetition: 15kHz.

Annular beam

converter

Axicon prims:

Zenith angle: 150° (±10′);

Diameter: 50.8mm;

Annular beam diameter range:

24mm~42mm

Random media

Media tank:

Material: Tempax glass;

Size: W*H*L

20cm*20cm*(10,20,30)cm;

Media:

Processed milk with 1.8% fat;

Fat size: 1.1µm;

Diluted range: 0.1%~1.0%;

Receiver

Optical elements:

Optical Fiber: Multiple mode

Diameter.: 50µm;

Collimate lens N.A.:0.55

View angle: 5.5mrad;

PMT:

Hamamatsu R-636;

Response time: 0.78ns

Sampling oscilloscope:

Agilent, DCA-J 86100C with

83484A module

Bandwidth: 50GHz

3.2 Result

In the three sets of experiments, the milk concentration

Figure 6: The experiment system to analyze light propagation characteristics in random media.

Optical fiber

Axicon prisms

Media tank

Sampling

Oscilloscope

Photo Multiplier

Tube

Power Supply

Photon Diode

DPSS Laser

Dilutedmilksolution

Glass Plate

ND Filter

Pin Hole

Beam Expander

R-r

Collimate Lens

Optimization of Non-diffractive Beam Propagation in Random Media Formed by Annular Beam

was set as 0.1%~1.0% in steps of 0.1%. The observed

waveforms were combined two parts. The first part

was an isotropic intensity distribution caused by

multiple scattering. This part covered in all of the

scattering angle. Another part was non-diffractive

effect as a small peak at the center on the waveform.

The width of the center peak is about 6mm. For

comparison of the waveform, first, the intensity of non-

diffractive beam at 20mm away from center was

normalized as 1. The non-diffractive effect was

evaluated by the intensity ratio between the center

intensity and the intensity at 3mm away from center,

where was the foot of the peak of non-diffractive beam.

3.2.1 Propagation Distance

In the first experiment, a propagation distance was set

as 10, 20 and 30cm by using the different media tanks.

Figure 7 shows the different non-diffractive beams

converted by the annular beams with the same ring

thickness, the diameter, and the different propagation

distances. The waveform of 10cm and 20cm

propagation were added 0.02 and 0.01 in intensities

respectively, to facilitate visualization. These three

non-diffractive beams at the different propagation

distance obtained maximum in the concentration of

0.4%, 0.6% and 1.0%. Figure 8 shows the intensity

ratio of the non-diffractive effect when the isotropic

intensity was subtracted. The center intensity ratios

were 1.8%, 1.2% and 0.85% at the propagation

distance of 10, 20 and 30cm, respectively. As we

considered the scattering particles act as lens, this

result shows the non-diffractive beam has a high

intensity in short distance propagation with high

concentration. It has the same tendency with the

calculated result shown in Fig. 5, the non-diffractive

beam had a high intensity in a short distance when a

lens effect with short focal distance was considered.

Figure 7: Scattering wave fronts of annular beam with

different distance (Diameter: 40mm, Thickness: 3mm).

Figure 8: Intensity ratio of non-diffractive beam against

propagation distance in random media.

Figure 9: Scattering waveforms of annular beam with

different thickness (Diameter: 40mm; Distance: 20cm).

3.2.2 Annular Beam Thickness

As the next experiment, the ring thickness of annular

beam was set as 3 and 6mm. Figure 9 shows the

difference between two non-diffractive beams

converted by the annular beams with the same

diameter and the same propagation distance but with

the different ring thickness. The waveform intensity

obtained by the annular beam of ring thickness of

3mm has been added 0.01 for visualization. In the

case of the annular thickness of 3mm, the width of the

main peak of the obtained waveform is narrower than

that of the case of 6mm. Both widths of the main

peaks are about twice of the thickness of the incident

annular beams. The two non-diffractive beams were

transformed in the concentration of 0.6%. The center

intensities ratios of the non-diffractive beams are

1.2% and 1.0%. This result shows the annular beam

with the narrow thickness would generate a narrow

width and a high intensity of the non-diffractive beam

in random media. These variation had agreement with

the numerical calculation in Fig.3.

1.02

1.04

1.06

1.08

1.1

1.12

-20 -15 -10 -5 0 5 10 15 20

Normalized intensity (a.u.)

Position (mm)

Distance 30cm 0.4%

Distance 20cm 0.6%

Distance 10cm 1.0%

0.4

0.6

0.8

1.2

1.4

1.6

1.8

0 1020304050

Intensity ratio of non-diffractive beam (%)

Propagation distance in random media (cm)

1.02

1.04

1.06

1.08

-20 -15 -10 -5 0 5 10 15 20

Normalized intensity (a.u.)

Position (mm)

Thickness 6mm 0.6%

Thickness 3mm 0.6%

PHOTOPTICS 2016 - 4th International Conference on Photonics, Optics and Laser Technology

3.2.3 Annular Beam Diameter

In the third experiment, annular beam diameter was

set as 24, 32 and 40mm, respectively. Figure 10

shows the non-diffractive beams converted by the

annular beams with the same ring thickness and the

same propagation distance but with the different

diameter. The waveform converted by annular beams

with the diameter of 24mm and 32mm were added

0.02 and 0.01 in intensity for visualization. The

center intensities were 3.7%, 2.9% and 1.2% higher

than the intensity around away from center, and the

widths of the main peaks are 5~6mm. Figure 11

shows the intensity ratio between the non-diffractive

beam and the main peaks widths against the diameter

of the annular beam. They show that the non-

diffractive beam with the high intensity would be

transformed at the low concentration of the random

media when the annular beam diameter is small, but

the width of the main peak was kept in around 5~6mm

when the ring thickness of the annular beam was

3mm. Comparing to the numerical calculation, the

width of main peak was considered to be twice of the

annular beam thickness. These results were coincided

with the theory numerical calculation in Fig.4.

4 CONCLUSIONS

In this study, we considered that the propagation

characteristics of the annular beam in air was

associated with its experimental results in the random

media. They showed agreement in non-diffractive

beam propagation characteristics. For the same

incident annular beam, the random media at a short

propagation distance with a high concentration could

generate a high intensity non-diffractive beam. And

Figure 10: Scattering waveforms of annular beam with

different diameters (Thickness: 3mm; Distance: 20cm).

Figure 11: Variation of intensity ratio and main peak width

of non-diffractive beam. (Thickness: 3mm; Distance:

20cm).

for the same random media, the annular beam with

the narrow thickness or the small diameter could

generate a high intensity non-diffractive beam. The

width of the non- diffractive beam would be twice of

the thickness of the annular beam. And the non-

diffractive effect was generated in the random media

and had the same tendency with its propagation in air.

The results of the calculation and the experiment were

coincide with each other.

In future, further analysis of annular beam

propagation in random media should be explained by

diffusion and scattering theory, and the mathematical

relationship between non-diffractive beam waveform

and parameters such as the ring thickness or the

diameter of the annular beam should be cleared up.

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1.02

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1.14

-20 -15 -10 -5 0 5 10 15 20

Normalized intensity (a.u.)

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PHOTOPTICS 2016 - 4th International Conference on Photonics, Optics and Laser Technology