edited report partm2

8/12/2019 Edited Report Partm2

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1.3 WORKING OF PHOTONIC BAND GAP:

n a photonic crystal light entering the perforated material will reflect and refract off

interfaces between glass and air. *he comple4 pattern of overlapping beams will lead to

cancellation of a band of wavelengths in all directions leading to prevention of propagation of

this band into the crystal. *he resulting photonic band structure can be modified by filling in

some holes or creating defects in the otherwise perfectly periodic system.

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Chapter-2

TYPES AND FABRICATION OF PHOTONIC CRYSTAL

PCs are classified mainly into three categories according to its nature of structure periodicity,that is, +ne imensional "(#, *wo imensional "2#, and *hree imensional "3# PCs.

2.1 ONE DIMENSIONAL PC:

n (PCs, the periodic modulation of the refractive inde4 occurs in one direction only while

the refractive inde4 variations are uniform for other two directions of the structure. *he P!G

appears in the direction of periodicity for any value of refractive inde4 contrast i.e. difference

between the dielectric constant of the materials. n other words, there is no threshold for

dielectric contrast for the appearance of a P!G. 7or smaller values of inde4 contrast, the

width of the P!G appears very small and vice versa. @owever, the P!Gs open up as soon as

the refractive inde4 contrast is greater than one "n(/n2 (#, where n( and n2 are the

refractive inde4 of the dielectric materials. A defect can be introduced in a (PCs, by ma$ing

one of the layers to have a slightly different refractive inde4 or width than the rest.

7igure 2.( +ne dimensional PC

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2.2 TWO DIMENSIONAL PC:

PC structure"s# that are periodic in two different directions and homogeneous in third

direction are called 2PC which is shown in 7igure (."b# and 2"b#. n most of the 2PCs, the

P!G occurs when the lattice has sufficiently larger inde4 contrast. f the refractive inde4contrast between the cylinders "rods# and the bac$ground "air# is sufficiently large, 2 P!G

can occur for propagation in the plane of periodicity perpendicular to the rod a4is.

Generally, 2PCs consist of dielectric rods in air host "high dielectric pillars embedded in a

low dielectric medium# or air holes in a dielectric region "low dielectric rods in a connected

higher dielectric lattice# as shown in 7igures 3"a# and 3"b#. *he dielectric rods in air host give

P!G for the *ransverse =agnetic "*=# mode where the % field is polarized perpendicular to

the plane of periodicity. *he air holes in a dielectric region give "*ransverse %lectric# *%

modes where @ field is polarized perpendicular to the plane of periodicity.

7igure 2.2 *wo dimensional PC

2.3 THREE DIMENSIONAL PC:

A 3PCs is a dielectric structure which has periodic permittivity modulation along three

different a4es, provided that the conditions of sufficiently high dielectric contrast and suitable

periodicity are met, a P!G appears in all directions. 5uch 3 P!Gs, unli$e the ( and 2

ones, can reflect light incident from any direction. n other words, a 3 P!G material

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behaves as an omnidirectional high reflector. As an e4ample, 7igure 9 depicts the 3

woodpile structure. ue to the challenges involved in fabricating high-uality structures for

the scale of optical wavelengths, early PCs are performed at microwave and mid-infrared

freuencies B(, 2:.


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factor of J K L3L. @ere we try different approach in order to fabricate the I6odaI Cavity. n

the first fabrication step, the diamond crystal is undercut by turning side-on and etching to

obtain a 2::nm thic$ slab attached to the bul$ "a suspended slab#. n this stage the use of

platinum deposition, as described before, is crucial in order to obtain precise structures.


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which blue colour means low intensity and red colour means high intensity. !ecause there is

no "or less# etch damage in these regions. *his is an encouraging because it means that if

there were an 6FNcentre in the cavity we might be able to see it.


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O

"a# "b#

7igure 2. 5econdary electron image of a etched photonic crystal structure in the diamond

sampleD a# *ilted view of the cavity ta$en with 7! at different tilt magnitude.b# &argerimage of the membrane and the cavities.

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Chapter-3

DESIGN OF A NOVEL 2-D PHOTONIC CRYSTAL SUARE CAVITY

BASED BAND PASS FILTER

3.1 INTRODUCTION:

@ere we are designing a band pass filter for electromagnetic waves for which we are ta$ing

use of a 2- photonic crystal, we are ma$ing a waveguide and a suare cavity inside it by

introducing line defect, the four scatterer rods are situated on four corners of the suare

cavity, so it is a application of photonic crystal as a filter. n selecting a particular freuency

band there is a big role of scatterer and coupling roads of the photonic crystal, in our 2-

photonic crystal due to interaction of reflected waves from rods inside crystal having

different phases causes the cancellation of waves which are outside a particular freuency

band.

*he designed band pass filter can behave as a wavelength selective narrow band pass filter

with the introduction of scatterer rods at all the four corners of suare cavity. *his filter is

useful for wavelength division multiple4ing "


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!oth point and line defects are utilized to design this band pass filter. As observed from

figure ( that there are two in-lines uasi waveguides and a resonant suare cavity placed

between them consisting of three rings.

7igure 3.( Photonic crystal suare cavity based band pass filter

*his resonant suare cavity possesses dielectric scatterer rods at all the four corners which

provide high spectral selectivity. *he coupling rods are positioned between the in-line uasi

waveguide and resonant cavity. A Gaussian modulated continuous wave signal is inected by

vertical input plane at the input port and the output is observed by placing the observation

point at the output port. *he analysis of this photonic crystal based band pass filter "PC!P7#

is done by varying the radius of coupling rods and scatterer rods.

3.3 SIMULATION AND RESULTS:

A 2- 32 bit simulation is performed to obtain the response of this filter. *he simulation

runs for L::: time steps "result finalized#. *he result shown is of transverse electric "*%#

polarization. *he normalized transmission spectrum of output port is obtained using

freuency fast fourier transform "77*# calculations of the field by finite difference time

domain "7*# method. 7igure 2 shows the normalized transmission spectrum when the

radius of the coupling rods K :.(>m and scatterer rods K :.(2>m. *he normalization has been

done with respect to input plane.

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7igure 3.2 *he normalized transmission spectrum

7irst, one of the important design parameter i.e. the radius of the coupling rods is varied

$eeping all other parameters same. !y doing so, some other pass bands are also observed

with lesser 77* values. *he desire to achieve greater elevating heights and to operate at

higher temperature led to the development of the belt incorporating polyester and steel cable

reinforcing elements. *his has resulted in general change in high capacity buc$et elevator

engineering.

R!"#$% &' ()* +&$,#/ 0&"% # N&0!#*" (0!%#%%#& !$*

5.56 5.2178

5.57 5.4943

5.59 5.4943

5.1 5.4943

5.11 5.3563

5.12 5.3563

5.13 5.28:4

*able 3.( 'adius of the coupling rods and normalized *ransmission value of the suarecavity based band Pass filter

t is evident from table that as we increase or decrease the radius of coupling rods in the

vicinity of calculated value i.e. :.(>m, the normalized transmission value decreases. *he

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ma4imum value is :.993 for coupling rod radius K :.(>m.t is also observed that if we

further increase the coupling rod radius then this filter does not shows the freuency selective

property and other bands along with maor pass band are also observed. !ut it is further

possible to increase the transmission efficiency by varying the radius of the scatterer rods,

wafer dimension etc. n the second part of analysis, the other design parameter, i.e. radius of

the scatterer rods is varied by $eeping all other parameters same. *he output result is

summarized in table .

R!"#$% &'

%+!((*0*0 N&0!#*" C*(*0 ;!*-*/()

0&"% # (0!%#%%#& !-$* #

5.57 5.8172 5.44165.1 5.4943 5.4815

5.12 5.1449 5.4651

5.14 5.5378 5.4996

*able 3.2 'adius of the scatterer rods, normalized transmission value and center wavelengthof the suare cavity based band pass filter

t is observed that the center wavelength for scatterer rod radius :.:)>m, :.(>m, :.(2>m, and

:.(9>m is (.99(>m, (.9L(:>m, (.9:(>m and (.9 >m respectively. *his shows that the

centre wavelength of the bands shifted into higher wavelength when the radius of the

scatterer rods is increased. A good normalized transmission value is achieved for scatterer rod

radius K :.(2>m. *he bandwidth is about (:nm.

Chapter-9

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APPLICATIONS OF PHOTONIC CRYSTAL

*he ability to control and manipulate the spontaneous emission by introducing defects in

PCs, and related formation of defect state within P!G has been used for designing the optical

devices for different applications that are directed towards the integration of photonic

devices.

4.1 BRAGG MIRRORS:

%arliest e4ample of photonic crystal initial applications include mirrors for vcsels "vertical

cavity surface emitting lasers# consists of alternating uarter wavelength optical thic$ness

high and low refractive inde4 materials.

7igure 9.( !ragg mirror

4.2 PHOTONIC WAVEGUIDES:


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waveguide has some very interesting properties such as the ability to guide the light around

sharp corners that is not possible through conventional methods. *his effect has been used to

create waveguide splitters that can split a beam of light with the resultant beams being

transmitted in opposite directions to each other.

*he second consists of two types of fibers where photonic effects are used for guidance. +ne

where the refractive inde4 of the core is higher than the surrounding cladding, the other where

the core inde4 is lower such as the fibers which have a hollow core. 7igure 2 shows a cross-

section of such a fiber, and shows demonstrates how propagation occurs. *he method used

for the construction of such fibers has already been outlined in the section on the +ptical

'egime. As well as the continuing wor$ in constructing these fibers, wor$ is also being

conducted into how the they achieve their specific effect. B), 1. Canning, 2:::


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that meet the !ragg conditions R K " 2.n.S.sinT #/m are permitted to propagate along the fibre.

+nly single-mode behaviour is allowed because an angular photonic band gap is generated by

the structure which is used to prevent the propagation of additional modes. *hese band gaps

are controlled by the physicals properties of the fibre and so fibres can be constructed to

specific reuirements in much the same way as tradition fibre are today.

4.3 PERFECT REFLECTORS:

+mni directional mirrors have many applications, such as the walls of laser cavities.

=etallic mirrors are freuently used, however, at freuencies in the optical regime they have

large dissipative losses. *his problem can be addressed through the use of photonic crystals

as proposed by 0ablonovitch. A 3 photonic crystal behaves as an omnidirectional reflector

with little or no loss. @owever, as has been outlined earlier in this report the fabrication of 3

structures for the reuired wavelengths has many serious problems that have yet to be

overcome.


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&% we can forbid all modes for photons e4cept those which would normally escape the

crystal. As spontaneous emission in other modes is forbidden, all the energy will then go into

those modes which can escape. n this way we can have &%s which actually ta$e advantage

of the high internal uantum efficiency.

4.8 PHOTONIC CRYSTAL LASERS:

t has been speculated that photonic crystals can be used to produce lasers with an e4tremely

low lasing threshold. *his would allow lasers to operate at much higher efficiencies and with

much less power being lost as heat. @igh efficiency lasers would be very useful in the

photonic circuitry, or any application which involved a large number of lasers in a small

space.

As mentioned earlier, photonic crystals have the property of suppressing spontaneous

emission inside the photonic bandgap. t is forbidden for photons to propagate inside the

photonic bandgap, and hence it is forbidden for atoms in the crystal to emit photons with

these energies. n order for lasing to occur, a defect must be introduced into the material. *his

defect produces a freuency inside the bandgap at which photons can propagate. *his defect

should also be directional so that photons are permitted to propagate only in the desired

direction of the beam. *he energy which is pumped into the crystal may then only be emitted

by spontaneous or stimulated emission in a single direction. &asing action will then occur,

without any losses due to unwanted spontaneous emission.

7igure 9.3 Photonic crystal laser

+ne method which has been proposed is to use artificial opals. +pal consists of tiny spheres

of silica with a refractive of around (.9L. *hese spheres are arranged in an f.c.c. structure.

*his structure produces a periodic modulation in refractive inde4 and hence a photonic

crystal. *he space between the silica spheres can be filled with a laser die, to form the

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amplifying medium of the laser. *he use of photonic crystals, and in particular artificial opals

soa$ed in laser die, should allow the production of low threshold lasers, and be a maor

advantage in a range of technologies.

4. INTEGRATED PHOTONIC CIRCUITS:

7or a long time it has been hoped that photonics would follow electronics and create

integrated photonic circuitry. *he increase in data rates in optical communications produces a

considerable drive for ma4imum miniaturisation of photonic devices. @owever, there has

been little success in this area, both because of the large size of various components and the

difficult in guiding light around tight corners. n both these areas it should be possible to gain

considerable improvements through the use of photonic crystals. Photonic crystal waveguides

should allow for the introduction of much sharper corners than traditional optic fibres, and

the high efficiencies of &%s and lasers based on photonic crystals reduce the heat produced

by these devices and allows them to be pac$ed into a smaller space.

7igure 9.9 +ptical integrated circuits

Although, much research is on going, this area is still fairly speculative, and it is reasonable

to say that it shall be some time before integrated photonic circuitry is produced. @owever,

when it is,photonic crystals are li$ely to play a central role.

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CONCLUSION

n photonic crystals light localization occurs in carefully engineered dielectrics. Photonic

!and Gap formation is a synergetic interplay between microscopic and macroscopic

resonances. (- and 2- photonic crystals are easy to fabricate. Plane, line or point defectscan be introduced into photonic crystals and used for ma$ing waveguides, microcavities or

perfect dielectric mirrors by localization of light. Applications of photonic crystals includeY

photonic crystal fibers, lasers, waveguides, add drop filters, all-optical transistors, amplifiers,

routers photonic integrated circuits, optical computing.

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REFERENCES

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B( Anderson, !. . +., and 1. !. =oore, WA perfectly matched anisotropic absorber for use

as an absorbing boundary condition,X %%% *rans. Antennas and Propagation, vol. 93,

no. (2 pp.

B2 %li. 0ablonovitch., Inhibited spontaneous emission on solid-state physics and

electro-nics,IPhys. Rev. Lett., vol. L) "2:#, pp. 2:L-2:;2, ().

B3 A. Ghaffari, 7. =onifi, =. avid, and =. 5. Abrishamian, W@eterostructure

wavelength division demultiple4ers using photonic crystal ring resonatorsX, Optics

Communications, vol. 2)(, pp. 9:2)-9:32, 2::).

B9 A. =artinez, A. Griol, P. 5anchis and 1. =arti, W=ach-Uehnder interferometer

employing coupled-resonator optical waveguides, W+pt. &ett. 2), 9:L-9:"2::3#.

BL U. 5. 5ac$s, . =. Zingsland, '. &ee, and 1. 7. &ee, WA perfectly matched anisotropic

ab-sorber for use as an absorbing boundary condition,X %%% *rans. Antennas and

propogat-ion, vol. 93, no. (2, pp. (9;:Y(9;3, (L.

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