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Accomplishment of the
Phenomenon of Perfect Optical
Cloaking Using A Multi-Lens System
Making Invisibility Possible
Muhammad Miqdad Khan
Dept. of Physics
NED UET
Rafey Iqbal Rahman
Dept. of Management
CloudSynergi, Karachi
Inspired perhaps by Harry Potter’s invisibility cloak, scientists have recently developed several ways—some simple
and some involving new technologies—to hide objects from view. The latest effort, developed at the University of
Rochester,
What is Cloaking?
• The term 'cloaking' is usually misunderstood in the sense that the phenomenon
involves a piece of cloth, usually known as the “invisibility cloak”, which tends to
hide the object placed under it as shown in the famous Harry Potter series.
However, cloaking is much more than that.
• The mind-boggling phenomenon of cloaking allows us to induce invisibility in
objects, both in a partial manner as well as a whole. What actually happens is that
the light passes through an object as if it is not there at the moment. Since the
scientists and physicists are still unable to fully 'uncloak' the cloaking
phenomenon, only a handful of applications possessing social and of course,
technological impact have been discovered. Even the inclusion and incorporation
of the nanotechnology intended for the expansion and enhancement of the
cloaking phenomenon has not contributed much.
Some Applications
• The applications and usage in the defense sector are still not
deciphered in particular, however, on the other hand, the enablers of
the researches, both past and ongoing, in science and technology
have disclosed
• its applications in the health care and automotive sectors in the form
of the aspired advent of careful, precision-based, error-reduced
human surgeries (health care) and road accident prevention
technologies (automotive)
Previous Attempts
Natural resources formed inside the earth's crust are observing a significant
decline in their quantity on a daily basis. Owing to the trend towards the
plunge and lacking, the scientific laboratories undertook the task of the
creation of artificial or man-made resources in order to cope up with the
population growth and its requirements and the enhancement of the
lifestyle of the man-in-the-street and the people, alongside curbing the
adverse effect being generated by the act of exploitation of the natural
resources. Such an artificial resource was created by the name of
"Metamaterial". The metamaterial was created in order to surpass the
characteristics that the naturally-occurring materials possess and exhibit.
An application of metamaterial is found in the metamaterial cloaking
technique. However, the creation of a metamaterial is quite difficult and
cumbersome, although many advances have been made in science and
technology. Therefore, in comparison, another technique possessing the
name of "paraxial ray cloaking" is deemed to be quite convenient.
Theory
2.1.1 Two Lens System
𝑭𝟏 = 𝑭𝟐 = 𝑭 (1)
L1 L2
R1
R2
F
𝒅 = 𝒇𝟏 + 𝒇𝟐 (2)
Figure.1 Diagrammatic representation of a two-lens system
MATLAB calculation for system ray transfer matrix
Cloaked Region
There exists a limitation that no matter how fine the lens is, the
phenomenon of spherical aberration is witnessed. The spherical
aberration refers to the phenomenon where the focus point is not
unique. The focal length somehow portrays a nature of
dependency on the wavelength of the light. So, on behalf of the
above-said statement, it can be confidently said that:
𝑽𝒄𝒚 = 𝝅𝒓𝟐𝒉 (3)
𝑽𝒄𝒚 = 𝟑𝑽𝒄 (5)
𝑽𝒄 = 𝝅𝒓𝟐 𝒉 𝟑 (4)
2𝑹𝑪𝑳 = 𝑹𝑼𝑪𝑳 (6)
2𝑹𝑪𝑳 ≤ 𝑹𝑼𝑪𝑳 (7)
Four Lens System
The formula for calculating the total length of the cloaking apparatus, as described in prior research is as follows:
𝐿 = 2𝑡1 + 𝑡2 (𝑓1 + 𝑓2) / (𝑓1 − 𝑓2) (8)
As described in Eq. (1), the focal lengths of the lenses used in this experiment hold the same value, 40 cm. Therefore, as stated
previously, due to the inclusion of heavy mathematical equations, the phenomenon of optical cloaking did not prove to be practical
and feasible. The impracticality driven by the above-stated Eq. (8) can be observed as:
𝐿 = 2𝑡1 + 𝑡2 (40 + 40) / (40 − 40)
This results in the observation of an infinite cloaked region, however, for a cloaking phenomenon to be physically feasible, the
cloaked region must be of a finite or determined value.
Also, as described in prior research, the distance between the two pairs of lenses (t2) is as follows6,14:
t2 = 2f2 (f1+ f2) / (f1−f2) (9)
Again, with the similar approach, as it is known as f1 = f2 = f = 40 cm, therefore Eq. (9) becomes:
𝑡2 = 2𝑓2 (40 + 40) / (40 − 40)
From Fig. it is also proved that the distance between the two pairs of lenses does not matter.
Experimental Setup
Similar to the two-lens approach, we
will use two sets of a pair of lenses (L1),
(L2), (L3) and (L4). As we can see in the
Fig. that the rays between the two sets of
lenses are parallel. Since the distance
poses no threat in this case and could be
of any value greater than zero. The
reason that the distance could not be kept
equal to zero is that the problem of the
combination of the lens will occur. Then
the whole system would be wrongly
perceived as a three-lens system.
Results Discussion
Perfect cloaking is achieved since the background formed is original and erect. The four-lens cloaking
technique is the perfect cloaking. If we scale up the diameters of the lenses, larger objects can be hidden
too. The experimental setup used allows perfect paraxial ray optical cloaking up to 15º.
CONCLUSIONS
The experiments performed regarding the perfect paraxial ray optical cloaking yielded satisfactory results
along with some limitations and future recommendations for further research on the subject and the area
of interest.
The conclusions drawn from this research can be reported as:
Perfect paraxial ray optical cloaking is achieved without providing any significant amount of
consideration to the distance between the lenses.
The research is limited to hiding or cloaking of an object smaller in size due to the small diameter of lens
used in the series of experiments and the prototyping.
ACKNOWLEDGEMENT
We are highly indebted to Dr. Muhammad Imran Ahmed Siddiqui of
University of Karachi for his guidance and constant supervision as well
as for providing necessary information regarding this research and also
for his support in completing this endeavor.
REFERENCES
1. D. Barnstone. (2014, Sep. 25). "‘Cloaking’ device uses ordinary lenses to hide objects across range of angles". rochester.edu [Online]. Available:
https://www.rochester.edu/newscenter/watch-rochester-cloak-uses-ordinary-lenses-tohide-objects-across-continuous-range-of-angles-70592/. [Accessed: 2019, Apr. 19].
2. A. Healy. (2019, Mar. 22). "Harry Potter’s ‘invisibility cloak’ cracked: University of Rochester scientists create masking device." syracuse.com [Online]. Available:
https://www.syracuse.com/news/2014/09/university_of_rochester_scientists_create_cloaking_device_rivals_harry_potter s_i.html. [Accessed: 2019, Apr. 19].
3. NBC News. (2014, Sep. 25). "Scientists Show You How to Make an Invisibility Cloak (Sort Of)". nbcnews.com [Online]. Available: https://www.nbcnews.com/science/weird-
science/scientists-show-you-how-make-invisibility-cloaksort-n21096. [Accessed: 2019, Apr. 19].
4. NBC News. (2011, Jul. 14). "Invisibility gets a reality check". cosmiclog.nbcnew.com [Online]. Available: http://cosmiclog.nbcnews.com/_news/2011/07/14/7085017-invisibility-gets-a-
reality-check. [Accessed: 2019, Apr. 19].
5. R. Santus. (2014, Sep. 26). "Scientist Show How to Make an Invisibility Cloak". Mashable [Online]. Available: https://mashable.com/2014/09/26/how-to-make-invisibility-cloak/. [Accessed:
2019, Apr. 19].
6. J.S. Choi and J.C. Howell, "Paraxial ray optics cloaking," Optics Express, vol. 22, no. 24, pp. 29465-29478, 2014.
7. Harvard Natural Sciences Lecture Demonstrations. "Paraxial Ray Optics Cloaking". sciencedemonstrations.fas.harvard.edu/ [Online]. Available:
https://sciencedemonstrations.fas.harvard.edu/presentations/paraxial-ray-optics-cloaking. [Accessed: 2019, Apr. 19].
8. S. Frizell. (2014, Sep. 28). "This Discovery Brings Us One Step Closer to Harry Potter’s Invisibility Cloak". Time [Online]. Available: https://time.com/3441875/invisibility-cloak-harry-potter-
lens-rochester/. [Accessed: 2019, Apr. 19].
9. J. Fingas. (2014, Sep. 29). "Scientists make an invisibility cloak using off-the-shelf optical lenses". Engadget [Online]. Available: https://www.engadget.com/2014/09/29/optical-lens-
invisibility-cloak/. [Accessed: 2019, Apr. 19].
10. P. Carpena and A.V. Coronado, "On the focal point of a lens: beyond the paraxial approximation," European Journal of Physics, vol. 27, no. 2, pp. 231-241, 2006.
11. J. Orwig. (2014, Oct. 01). "How To Make An ‘Invisibility Cloak’ At Home For Under $100". Business Insider [Online]. Available: https://www.businessinsider.in/How-To-Make-An-Invisibility-
Cloak-At-Home-For-Under100/articleshow/43921961.cms. [Accessed: 2019, Apr. 19].
12. W. Cai, U.K. Chettiar, A.V. Kildishev, and V.M. Shalaev, "Optical cloaking with metamaterials," Nature Photonics, vol. 1, no. 4, pp. 224-226, Apr. 2007.
13. J. Valentine, et. al., "Three-dimensional optical metamaterial with a negative refractive index," Nature, vol. 455, no. 7211, pp. 376-379, Sep. 2008.
14. J.S. Choi. (2016). "Practical Invisibility Cloaking". pas.rochester.edu [Online]. Available: http://www.pas.rochester.edu/~jhgroup/alumni_theses/choi_thesis.pdf. [Accessed: 2019, Apr. 19].
15. J. Brownlee. (2014, Jan. 10). "The First Practical Invisibility Cloak Is Here". Fast Company [Online]. Available: https://www.fastcompany.com/3036471/the-first-practical-invisibility-cloak-is-
here. [Accessed: 2019, Apr. 19].
16. T. Zhai, K. Ren, R. Zhao, J. Zhou, and D. Liu, "An effective broadband optical ‘cloak’ without metamaterials," IOP Science, vol. 10, no, 6, pp. 1-5, 2013.
17. D. Halliday, R. Resnick, and K. Krane, Physics. New Delhi: Wiley, 2018.
18. F.A. Jenkins and H.E. White, Fundamentals of Optics. New York City: McGraw-Hill, 2001
THANK YOU
ANY QUESTIONS !

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The Accomplishment of the Phenomenon of Perfect Optical Cloaking Using A Multi-Lens System

  • 1.
  • 2. Accomplishment of the Phenomenon of Perfect Optical Cloaking Using A Multi-Lens System Making Invisibility Possible Muhammad Miqdad Khan Dept. of Physics NED UET Rafey Iqbal Rahman Dept. of Management CloudSynergi, Karachi
  • 3. Inspired perhaps by Harry Potter’s invisibility cloak, scientists have recently developed several ways—some simple and some involving new technologies—to hide objects from view. The latest effort, developed at the University of Rochester,
  • 4. What is Cloaking? • The term 'cloaking' is usually misunderstood in the sense that the phenomenon involves a piece of cloth, usually known as the “invisibility cloak”, which tends to hide the object placed under it as shown in the famous Harry Potter series. However, cloaking is much more than that. • The mind-boggling phenomenon of cloaking allows us to induce invisibility in objects, both in a partial manner as well as a whole. What actually happens is that the light passes through an object as if it is not there at the moment. Since the scientists and physicists are still unable to fully 'uncloak' the cloaking phenomenon, only a handful of applications possessing social and of course, technological impact have been discovered. Even the inclusion and incorporation of the nanotechnology intended for the expansion and enhancement of the cloaking phenomenon has not contributed much.
  • 5. Some Applications • The applications and usage in the defense sector are still not deciphered in particular, however, on the other hand, the enablers of the researches, both past and ongoing, in science and technology have disclosed • its applications in the health care and automotive sectors in the form of the aspired advent of careful, precision-based, error-reduced human surgeries (health care) and road accident prevention technologies (automotive)
  • 6. Previous Attempts Natural resources formed inside the earth's crust are observing a significant decline in their quantity on a daily basis. Owing to the trend towards the plunge and lacking, the scientific laboratories undertook the task of the creation of artificial or man-made resources in order to cope up with the population growth and its requirements and the enhancement of the lifestyle of the man-in-the-street and the people, alongside curbing the adverse effect being generated by the act of exploitation of the natural resources. Such an artificial resource was created by the name of "Metamaterial". The metamaterial was created in order to surpass the characteristics that the naturally-occurring materials possess and exhibit. An application of metamaterial is found in the metamaterial cloaking technique. However, the creation of a metamaterial is quite difficult and cumbersome, although many advances have been made in science and technology. Therefore, in comparison, another technique possessing the name of "paraxial ray cloaking" is deemed to be quite convenient.
  • 7. Theory 2.1.1 Two Lens System 𝑭𝟏 = 𝑭𝟐 = 𝑭 (1) L1 L2 R1 R2 F 𝒅 = 𝒇𝟏 + 𝒇𝟐 (2) Figure.1 Diagrammatic representation of a two-lens system
  • 8. MATLAB calculation for system ray transfer matrix
  • 9. Cloaked Region There exists a limitation that no matter how fine the lens is, the phenomenon of spherical aberration is witnessed. The spherical aberration refers to the phenomenon where the focus point is not unique. The focal length somehow portrays a nature of dependency on the wavelength of the light. So, on behalf of the above-said statement, it can be confidently said that: 𝑽𝒄𝒚 = 𝝅𝒓𝟐𝒉 (3) 𝑽𝒄𝒚 = 𝟑𝑽𝒄 (5) 𝑽𝒄 = 𝝅𝒓𝟐 𝒉 𝟑 (4) 2𝑹𝑪𝑳 = 𝑹𝑼𝑪𝑳 (6) 2𝑹𝑪𝑳 ≤ 𝑹𝑼𝑪𝑳 (7)
  • 10. Four Lens System The formula for calculating the total length of the cloaking apparatus, as described in prior research is as follows: 𝐿 = 2𝑡1 + 𝑡2 (𝑓1 + 𝑓2) / (𝑓1 − 𝑓2) (8) As described in Eq. (1), the focal lengths of the lenses used in this experiment hold the same value, 40 cm. Therefore, as stated previously, due to the inclusion of heavy mathematical equations, the phenomenon of optical cloaking did not prove to be practical and feasible. The impracticality driven by the above-stated Eq. (8) can be observed as: 𝐿 = 2𝑡1 + 𝑡2 (40 + 40) / (40 − 40) This results in the observation of an infinite cloaked region, however, for a cloaking phenomenon to be physically feasible, the cloaked region must be of a finite or determined value. Also, as described in prior research, the distance between the two pairs of lenses (t2) is as follows6,14: t2 = 2f2 (f1+ f2) / (f1−f2) (9) Again, with the similar approach, as it is known as f1 = f2 = f = 40 cm, therefore Eq. (9) becomes: 𝑡2 = 2𝑓2 (40 + 40) / (40 − 40) From Fig. it is also proved that the distance between the two pairs of lenses does not matter.
  • 11. Experimental Setup Similar to the two-lens approach, we will use two sets of a pair of lenses (L1), (L2), (L3) and (L4). As we can see in the Fig. that the rays between the two sets of lenses are parallel. Since the distance poses no threat in this case and could be of any value greater than zero. The reason that the distance could not be kept equal to zero is that the problem of the combination of the lens will occur. Then the whole system would be wrongly perceived as a three-lens system.
  • 12.
  • 13. Results Discussion Perfect cloaking is achieved since the background formed is original and erect. The four-lens cloaking technique is the perfect cloaking. If we scale up the diameters of the lenses, larger objects can be hidden too. The experimental setup used allows perfect paraxial ray optical cloaking up to 15º. CONCLUSIONS The experiments performed regarding the perfect paraxial ray optical cloaking yielded satisfactory results along with some limitations and future recommendations for further research on the subject and the area of interest. The conclusions drawn from this research can be reported as: Perfect paraxial ray optical cloaking is achieved without providing any significant amount of consideration to the distance between the lenses. The research is limited to hiding or cloaking of an object smaller in size due to the small diameter of lens used in the series of experiments and the prototyping.
  • 14. ACKNOWLEDGEMENT We are highly indebted to Dr. Muhammad Imran Ahmed Siddiqui of University of Karachi for his guidance and constant supervision as well as for providing necessary information regarding this research and also for his support in completing this endeavor.
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