Free-space Optical Links Using Phase Singularity

Bharat Kumar Yadav and Hem Chandra Kandpal

Optical Radiation Standards

National Physical Laboratory (Council of Scientific and Industrial Research)

Dr. K.S. Krishnan Road, New Delhi – 110012, India

byadav@mail.nplindia.ernet.in, hckandpal@mail.nplindia.ernet.in

Abstract— In this paper, we demonstrate novel type of free-

space optical links. It is a contrived idea but has a great

potential for realization. The links may be exploited to

exchange information in free-space.

Keywords-Free-space optical links; spectral switching;

optical communication; phase singularity

I. INTRODUCTION

Spectral switching [1] has been studied extensively [1-3]

in last few years and now it is a well-known phenomenon. It

is a peculiar behavior of polychromatic light waves that is

studied in the domain of singular optics [4]. It might have

number of potential applications in science and engineering.

Recently, its potential applications have been demonstrated

for information encoding [5] and transmission of

information in free space [6]. In addition, the spectral

switching may find potential applications in the field of

optical computing. Recently, we have proposed novel type

of spectral switching based techniques to develop spectrum-

selective optical interconnects, and the research has been

communicated elsewhere for publication.

In this paper, we elaborate the concept of free-space

optical link using phase singularity region of diffracted

polychromatic light waves and hollow optical beams. It is a

new contrived idea but has a great potential for realization

and might find applications in the field of optical computing

[7] and broadband wireless optical communications [8]. In

addition, on the basis of the research carried out so far, we

present a new scheme to produce a novel and secure optical

link using hollow Gaussian beam (HGB) to exchange

information in free-space.

II. ORIGIN OF THE CONCEPT

Spectral switching results basically in the vicinity of dark

fringes, referred as phase singularity region of the diffraction

pattern when the polychromatic light passes through an

aperture [1-3]. Phase singularity is a point or a very small

region where the intensity becomes zero and the phase

becomes indeterminate [4]. It has been observed that in a

particular direction, sometimes termed as critical direction

[2], the spectrum of diffracted light (in the vicinity of any

dark fringe) splits into two halves with respect to the source

spectrum. Either side of the critical direction, the spectrum

of diffracted light, shifts towards lower frequencies (redshift)

or towards higher frequencies (blueshift) or vice-versa. To

understand the concept, a schematic diagram of Fraunhofer

diffraction with notations is shown in Fig. 1.

Figure 1. Diffraction and diffracted light field propagation in free space.

Figure 2. Geometry of critical direction and related notations.

Suppose, polychromatic light having Gaussian spectral profile (indicated by G) comes from source S, and falls from left side on the aperture plane A. The diffraction takes place on the front side of the aperture (see Fig. 1). A 3D spectral profile of diffraction pattern is shown by Ap. Here, D1, D2, and D3 denote first, second and third critical direction respectively. The spectral anomalies can be observed in the vicinity of dark fringes of the diffraction pattern. To understand the concept more closely, the first dark ring of the diffraction pattern is broadened and shown in Fig. 2. In this figure, OE direction denotes the critical direction (the first critical direction shown by D1 in Fig. 1), where the source spectrum splits into two peaks spectrum (see inset in Fig. 2) after the diffraction of the polychromatic light. ABO indicates the formation of subtended area of phase singularity region in and around the critical direction when the diffracted waves propagate in free-space.

The shaded thick circle shows the first dark ring of the

diffraction pattern on the observation plane. θC represents

the critical angle which also indicates the critical direction.

Figure 3. Information encoding with spectral switching.

All spectral changes occur in the vicinity of the first (or any) dark ring. The logic behind information encoding with spectral shifts is also quite simple. An example of information encoding is shown in Fig. 3. Here a decimal number, (10)2 = “1010” is encoded. Information bits “1” and “0” are associated with redshift that occurs at diffraction angle θ = 1.14×10-3 rad and blueshift at diffraction angle θ = 1.16×10

-3 rad respectively. For this particular numerical

example (calculation is done using formulae given in [2]), the diffracted light spectrum splits into two peak spectrum with respect to the source spectrum at diffraction angle (critical angle), θC = 1.15×10

-3. R and B denote redshift and

blueshift respectively.

III. FREE-SPACE OPTICAL LINKS USING PHASE

SINGULARITY

Free-space optical links are the primary requirement for

optical computing [7] as well as for wireless

communications [8]. Several types of systems and schemes

have been proposed and discussed so far in this connection.

Every scheme may have some advantages and some

challenges. Generally, in these types of optical

communications, lasers are used to establish the optical links

but in the last few years, the broadband light has become

quite popular for optical communications.

Despite some typical limitations broadband light has

advantages over the laser based communication. Our focus

of the study is to demonstrate a secure, reliable, and safe

optical link using polychromatic light (broadband light). We

propose a novel type of free-space optical link based on

phase singularity region of the diffracted light field and

hollow optical beams. Recently, we have demonstrated the

possibility of such links [6]. Here, we extend and elaborate

the concepts. In addition, we present a realizable contrived

idea to form and establish the free-space optical link. As we

have discussed earlier, spectral switching takes place in a

particular direction i.e., critical directions. We may exploit

these directions to establish free-space optical links [6].

These links may be utilized not only for board to board

optical communication in optical computing but they may

also be used in communications for larger distances, e.g.,

local area networks. We have developed a model to study

these optical links. Related paper has been communicated

elsewhere. On the basis of the studies carried out so far on

spectral switching [1-3] and their applications [5, 6], we may

categorize these phase singularity based free-space optical

links into two types namely shielded and unshielded optical

links. Both links may be studied for near field (board to

board communication) and for far field (for few meters).

A. Optical links in diffracted light field

This type of optical links may be achieved through the

phase singularity region (propagating dark fringes) resulting

after diffraction (or interference) of broadband light field.

For the sake of convenience, we may treat these links as

unshielded (or unprotected) optical links. In this type of

optical links, although, the diffraction (or interference)

pattern maintains self similarity during propagation in the far

field but there is no proper cover around the link to prevent

information distortion. Overlapping layers of bright and dark

fringes propagate after diffraction (or interference) and are

distorted after traveling certain distances. Signal to noise

ratio is always a constraint in such links.

B. Optical links in Hollow Gaussian Beam

Hollow Gaussian Beam (HGB) [9-11] is a special kind

of optical beam having a dark region (phase singularity

region) in the core. Until now, the hollow beams have been

studied for atom trapping, micro partial trapping and to

design optical tweezers. Our study may add new application

as the hollow optical beams may be used in the field of

optical computing and free-space optical communications.

Recently, it has been demonstrated that the spectral

switching can be produced using HGB [11]. The so called

critical direction falls in the middle of the optical beam

because the dark region, i.e., phase singularity region, is

situated in the core of the beam and is surrounded by the

intensity distribution. To understand the internal structure of

the HGB, let us take longitudinal cross section of the optical

beam (see Fig. 4). In near zone the core of the beam will be a

very small region (almost a point). However, it spreads to a

very small extent with distance during propagation along the

z-axis (the direction of light field propagation). Because of

this spreading, the redshift region (cross hatching), two-

equal-peak region (dark gray), and blueshift region (vertical

hatching) spread accordingly and become sufficiently

broadened in the far field to resolve the spectral changes.

The imaginary directions (directions where blueshift, two-

equal-peak and redshift take place) along with the subtended

area (where the spectral anomalies occur) of each direction

may be treated as optical link.

The interesting thing in this optical link is the light

intensity distribution around the link and dense phase

singularity region in the core. The intensity distribution

around the link may work like a protection shield while the

phase singularity region may work as a carrier of

information. Theoretically, it has already been demonstrated

that after 5 m the HGB becomes unable to maintain its shape

and gradually looses its inherent optical properties [9]. On

the other hand, experimentally spectral switching has been

observed up to 5 m [6]. It means, phase singularity based

optical links using HGB may be realizable up to 5 m

distance and the information may be exchanged over it.

Future research may help increasing the length of the optical

link.It is evident that for shorter distances, only the signal to

noise ratio may affect the quality of the communication

while in the case of larger distances (< 5 m), atmospheric

turbulence may add additional complexity to the system. In

these optical links, the core part (phase singularity region) of

the light beam that carries the information is protected by

intensity distribution. Therefore, the optical link may be

termed as shielded (or protected) optical link. Such links

prove to be more secure and might be least affected by the

atmospheric turbulence over large distances.

C. Optical setup to form HGB based optical link

Fig. 5 illustrates an optical setup to generate optical link

using HGB. Here, the source and control system of HGB

consist of broadband light source, S, spatial coherence

modulator (SCM) [12], and a 4f system [10] to generate

HGB. Different spectral shifts may be achieved by changing

the spatial coherence in a predefined manner. The SCM with

control system will synthesize and change the spatial

coherence of the light and 4f system will shape the light into

HGB for propagation in free-space. This optical setup may

be used in the general communication model [6] for spectral

switching based communication. We are not giving the

processing details as it has already been discussed with the

general model. To understand the behavior of the beam

propagation in free-space, we may divide the optical links

into S1, S2 and S3 sub-sections. From section S1 to S2, the

HGB may be almost uniformly cylindrical (for few

centimeters to few meters depending on the optics) but form

section S2 to S3, the beam deviates from the cylindrical

shape. The critical direction is indicated by Cd and the thick

arrows show the spreading direction of the HGB. The study

[9] reveals that the HGB shows very good propagation

stability in the near zone. With further increase of

propagation distance (in z-axis), the intensity distribution

diverges and the dark region across the HGB decreases. In

the far field, the dark region disappears and the on-axis

intensity becomes maximum. Despite some limitations, the

optical links formation scheme using HGB (or any hollow or

bottle optical beam) is quite significant and interesting. It

may be exploited to establish secure and realizable free-

space optical links to exchange information in near zone

(board to broad) as well as in far zone (indoor or outdoor)

communication.

Figure 4. Schematics of optical link using Hollow Gaussian Beam.

Figure 5. Schematics of optical setup and link formation using HGB.

Some challenges to be addressed by future research are listed below:

• The stability of the optical beam reduces during propagation in the far field and a good broadband light source like the so called white light laser may significantly improve the quality of signal, signal to noise ratio and the transmission distance but it is still at research stage.

• In the existing technological scenario, the speed of spatial coherence modulator (at transmitter) and the scanning speed of high resolution monochromator (at receiver) may limit the speed of communication. The best speed of SCM demonstrated so far is 1µs and the best scanning speed of spectrometer claimed by different renowned companies is 1000 nm/s.

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