Design Concept of Free Space

Optics

Author and Presenter :Pritesh Jivan

Co-Authors : R. Kritzinger, J. Burger

Date: 25 September 2016

Outline

• What is Free Space Optics (FSO)

• Advantages and disadvantages of FSO

• Applications

• Theoretical study and Gaussian optics

• Results of derivations

• Confirmation of derivations

• Conclusion

What is Free Space Optics (FSO)

• Interchangeably known as Free Space Photonics (FSP) or Optical Wireless.

• Refers to the transmission of infrared and visible beams through the atmosphere.

• As with fiber, FSO uses lasers and LED to transmit data.

• Instead of transmission through a guided medium, FSO uses an unguided medium such as air.

Advantages of FSO

• Flexibility in terms of beam shaping.

• Compactness of optical systems.

• Wireless communication at the speed of

light, unlike RF.

• No licensing required, ease and speed of

deployment.

• Mounted inside buildings, no competition

for rooftops

Advantages of FSO

• Immunity to electromagnetic interference.

• Full duplex operation

• Offers a line of site path with an invisible beam, therefore providing difficulty in interception.

• Cannot be detected by spectrum analyzers and RF meters.

Disadvantages

• Heavy fog has the ability to attenuate the FSO signal

• Physical obstructions such as birds, may cause a disruption in signal transmittance.

• Pointing stability, building sway and tower movement combined may cause interference in a system.

• Points can not have an arbitrary distance between them.

Applications

• Used in free space optical communication, in various topologies, such as mesh, multipoint, etc.

• Military communication access, as it is easy to deploy and difficult to detect.

Applications

• Space observation and inter-space station communication

Applications

• Beam shaping in experimental photonics set-ups

Theoretical Study

• We wish to develop an optical time and frequency standard using a fiber laser.

• The system requires the use of a rubidium cell to absorb a specific wavelength spectrum.

• The cell requires the laser beam to be shaped, this requires the use of free space optics.

Gaussian Optics

• The characterisation and development of a free space optical system utilises Gaussian optics.

• An assumption is made that the 𝑀2factor is 1.

• The 𝑀2 factor is an indication of the beam divergence through free space.

5.62 M 5.22 M

Gaussian Optics

• Some important parameters of a free space optical system are:• Beam width.

• Rayleigh Range

• The beam width of a beam varies as it propagates through space.

• The position at which the width is the smallest is known as the beam waist.

Gaussian Optics

• The Rayleigh Range is the minimum value of the wavefrontradius and is half the focus depth.

• Equations are derived from first principles in order to assist with the design of a FSO system.

• These equations are aimed to assist in speeding up the design process and create a better understanding of Gaussian optics.

Derivation of equations

• Matrix optics is used to mathematically describe each component in the system.

• Propagation through free space is given by

𝑀1 =1 𝑑10 1

• Propagation through a thin lens is given by

𝑀2 =

1 0−1

𝑓1

• Matrix optics takes into account a variety of optical permutations such as mirrors and various lenses.

Derivation of equations

• A cascade form of representing the components is used.

• This allows for a full system representation to be made up by the product of each matrix.

𝑀𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 = 𝑀𝑁 . . . .𝑀2𝑀1 ,

• This simple system below is used as the basis to derive equations that may be used in more complex

Derivation of equations

• The following composite matrix results

𝑀 =

1 −𝑑2𝑓

𝑑1 + 𝑑2 −𝑑1𝑑2𝑓

−1

𝑓1 −

𝑑1𝑓

=𝐴 𝐵𝐶 𝐷

• The complex envelope of the Gaussian beam

𝑟 =𝐴1𝑞 𝑧

𝑒−𝑗𝑘

𝑝2

2𝑞 𝑧

Derivation of equations

• Using the composite system and the complex envelope of the Gaussian beam the following equations result.

𝑑2 = 𝑓 −𝑓2 𝑓 − 𝑑1

𝑧012 + 𝑓 − 𝑑1

2

𝑑1 = 𝑓 −𝑓2(𝑓 − 𝑑2)

𝑧022 + (𝑓 − 𝑑2)

2

• These equations are generic and may be used for any system containing an infinite set of lenses in free space.

Results

• The system which we wish to design is an optical system which will take a beam of a specific width and magnify/increase the width at the waist.

Collimating

lens

Focusing

lens

Distance =0

Input Beam Output Beam

w1 w2

d1 d2

w3

Results

• Using the derived equations the following table of system parameters are given, these are calculated using a varying Rayleigh range on the input beamRayleigh

range (Z01)

(cm)

Distance to

focus (d1)

(cm)

Beam waist at

focus (w1) (μm)

Beam waist at

collimating lens

(w2) (cm)

Rayleigh

range (2×zR)

(cm)

Beam waist

before

focusing lens

(cm)

Beam waist

after 7.5 cm

focusing lens

(μm)

7.50 7.50 136.284 0.019 15.00 0.019 86

5.00 13.09 111.275 0.031 10.00 0.031 58

3.75 14.00 96.367 0.037 7.50 0.037 49

2.50 14.57 78.684 0.047 5.00 0.047 40

1.00 14.93 49.764 0.075 2.00 0.075 25

0.50 14.98 35.188 0.110 1.00 0.110 17

0.25 15.00 24.882 0.150 0.50 0.150 12

0.05 15.00 11.123 0.330 0.10 0.330 5

Confirmation of results

• Paraxia software is used to confirm the results obtained using the derived equations.

Conclusion

• The two formulas derived from first principles were proven to work suitably well, this was backed up by computer software known as Paraxia.

• The use of these equations were less cumbersome and proved to be more flexible then Paraxia.

• These equations work well with composite optical systems as matrix optics allows for a variety of optical components.