Fourier Transform

The Fourier transform, named after Joseph Fourier, is a mathematical transformation employed to transform signals between time (or spatial) domain andfrequency domain, which has many applications in physics and engineering. It is reversible, being able to transform from either domain to the other. The term itself refers to both the transform operation and to the function it produces.

This is the basic mathematical tool used for the calculation of difficult mathematical problems, specially, when the problem is related to any domain. like time domain, frequency domain, space domain and others.

Fourier transform converts every domain to s domain which has real and negative part. The poles and zeros are on either real part or on imaginary part. If they are on real axis and at negative side then the system is stable, If the are on positive side then system is unstable. If they are on imaginary axis then system is marginal stable.

Fourier transform gives the relation between time domain to frequency domain, so we can easily convert a signal in other domains.  In frequency domain it is very easier to solve and complex problem. but in time domain it very easier to design the system. So for system designing and its performance characterization we need Fourier Transform.

Fourier transform is the natural mechanism used by the nature to solve the optical problem as the lens give the Fourier transform of any signal at its focus, when signal is originated from its other focus. It can be so simple in the solving a differentiation or integral problem. Since it is in the form of exponential and differentiation and integration of the exponential is exponential.

The Fourier Transform is extensively used in the field of Signal Processing. In fact, the Fourier Transform is probably the most important tool for analyzing signals in that entire field. So what exactly is signal processing? I'll try to give a one paragraph high level overview. A signal is any waveform (function of time). This could be anything in the real world - an electromagnetic wave, the voltage across a resistor versus time, the air pressure variance due to your speech (i.e. a sound wave), or the value of Apple Stock versus time. Signal Processing then, is the act of processing a signal to obtain more useful information, or to make the signal more useful. How can a signal be made better? Suppose that you are listening to a recording, and there is a low-pitched hum in the background. By applying a low-frequency filter, we can eliminate the hum. Or suppose you have a digital photograph, and it is very noisy (that is, there are random specs of light everywhere). We can use signal processing and fourier transforms to filter out this undesirable "noise".

Fiber Bragg Grating

"FBG is a simple device used for the separation of wavelength from a group of wavelengths."  Rayc


A fiber Bragg grating (FBG) is a type of distributed Bragg reflector constructed in a short segment of optical fiber that reflects particular wavelengths of light and transmits all others. This is achieved by creating a periodic variation in the refractive index of the fiber core, which generates a wavelength specific dielectric mirror. A fiber Bragg grating can therefore be used as an inline optical filter to block certain wavelengths, or as a wavelength-specific reflector.

The first in-fiber Bragg grating was demonstrated by Ken Hill in 1978. Initially, the gratings were fabricated using a visible laser propagating along the fiber core. In 1989, Gerald Meltz and colleagues demonstrated the much more flexible transverse holographic inscription technique where the laser illumination came from the side of the fiber. This technique uses the interference pattern of ultraviolet laser light to create the periodic structure of the fiber Bragg grating.

Fiber Bragg gratings are created by "inscribing" or "writing" systematic (periodic or aperiodic) variation of refractive index into the core of a special type of optical fiber using an intense ultraviolet(UV) source such as a UV laser. Two main processes are used: interference and masking. The method that is preferable depends on the type of grating to be manufactured. Normally agermanium-doped silica fiber is used in the manufacture of fiber Bragg gratings. The germanium-doped fiber is photosensitive, which means that the refractive index of the core changes with exposure to UV light. The amount of the change depends on the intensity and duration of the exposure as well as the photosensitivity of the fibre. To write a high reflectivity fiber Bragg grating directly in the fiber the level of doping with germanium needs to be high. However, standard fibers can be used if the photosensitivity is enhanced by pre-soaking the fiber in hydrogen. More recently, fiber Bragg gratings have also been written in polymer fibers, this is described in the PHOSFOS entry

Fiber bragg grating can easily designed by using a simple fiber in presence of the interference of two ultravoilet light beam. Which give constructive and destructive interferences. At constructive interference refractive index decrease and at destructive interference refractive index remains same so we get two different refractive indices. Which periodically makes FBG.

FBG  are of two types:

1. Simple FBG 

2. Chirped FBG

 Simple FBG  in this refractive index of the dense medium is fixed. In this reflected light is the function of length of a period of refractive index.

 Chirped FBG in this refractive index of the dense medium is getting denser.In this refracted light is combination of different wavelengths are refracted at different time intervals.

Fiber Bragg Gratings are made by laterally exposing the core of a single-mode fiber to a periodic pattern of intense ultraviolet light. The exposure produces a permanent increase in the refractive index of the fiber's core, creating a fixed index modulation according to the exposure pattern. This fixed index modulation is called a grating.

At each periodic refraction change a small amount of light is reflected. All the reflected light signals combine coherently to one large reflection at a particular wavelength when the grating period is approximately half the input light's wavelength. This is referred to as the Bragg condition, and the wavelength at which this reflection occurs is called the Bragg wavelength. Light signals at wavelengths other than the Bragg wavelength, which are not phase matched, are essentially transparent.

Therefore, light propagates through the grating with negligible attenuation or signal variation. Only those wavelengths that satisfy the Bragg condition are affected and strongly back-reflected. The ability to accurately preset and maintain the grating wavelength is a fundamental feature and advantage of fiber Bragg gratings.

The central wavelength of the reflected component satisfies the Bragg relation: λrefl=2nΛ, with n the index of refraction and Λ the period of the index of refraction variation of the FBG. Due to the temperature and strain dependence of the parameters n and Λ, the wavelength of the reflected component will also change as function of temperature and/or strain, see Figure 2. This dependency is well known what allows determining the temperature or strain from the reflected FBG wavelength.

There have been many advances in the methods used to perform strain measurements. The three most prevalent technologies today are electrical foil gages, electrical vibrating wire, and fiber Bragg grating (FBG) optical sensors. 

For most standard strain sensing applications, electrical sensing has been and will continue to be the best and most effective solution. However, optical sensors can offer an important alternative in traditionally challenging applications. Harsh environments, distributed systems, or long-term deployments are a few examples where the characteristics of an optical sensing system can make it a more effective solution compared to conventional electrical sensors. 

Applications often require measurement solutions that encompass the benefits and attributes of multiple sensing technologies. It is therefore important to consider a hybrid approach. This paper provides a brief overview of each technology and weighs their benefits and drawbacks.

Electrical Sensing: Metal Foil Gages

Foil strain gages use the relationship between electrical resistance and conductor length to measure changes in strain. As the foil is stretched, its length is increased, which translates into a minute increase in resistance. To accurately measure these small changes in resistance, additional signal conditioning is necessary, often in the form of a Wheatstone bridge resistance network. A constant voltage is applied across the resistance network, and the varying proportional drop in voltage across the foil can be translated to strain.

Gradient Force

"Gradient" refers to how rapidly a quantity (such as pressure or temperature) changes in a given distance. It can be thought of as measure of "steepness", like the topography on a contour plot.

The pressure gradient force is the force which results when there is a difference in pressure across a surface. In general, a pressure is a force per unit area, across a surface. A difference in pressure across a surface then implies a difference in force, which can result in an acceleration according to Newton's second law, if there is no additional force to balance it. The resulting force is always directed from the region of higher-pressure to the region of lower-pressure. When a fluid is in an equilibrium state (i.e. there are no net forces, and no acceleration), the system is referred to as being in hydrostatic equilibrium. In the case of atmospheres, the pressure gradient force is balanced by the gravitational force, maintaining hydrostatic equilibrium. In the Earth's atmosphere, for example, air pressure decreases at increasing altitudes above the Earth's surface, thus providing a pressure gradient force which counteracts the force of gravity on the atmosphere

In optical tweezer Gradient force is used to compensate Scattering force.

In cases where the diameter of a trapped particle is significantly greater than the wavelength of light, the trapping phenomenon can be explained using ray optics. As shown in the figure, individual rays of light emitted from the laser will be refracted as it enters and exits the dielectric bead. As a result, the ray will exit in a direction different from which it originated. Since light has a momentum associated with it, this change in direction indicates that its momentum has changed. Due to Newton's third law, there should be an equal and opposite momentum change on the particle.

Most optical traps operate with a Gaussian beam (TEM₀₀ mode) profile intensity. In this case, if the particle is displaced from the center of the beam, as in the right part of the figure, the particle has a net force returning it to the center of the trap because more intense beams impart a larger momentum change towards the center of the trap than less intense beams, which impart a smaller momentum change away from the trap center. The net momentum change, or force, returns the particle to the trap center.

If the particle is located at the center of the beam, then individual rays of light are refracting through the particle symmetrically, resulting in no net lateral force. The net force in this case is along the axial direction of the trap, which cancels out the scattering force of the laser light. The cancellation of this axial gradient force with the scattering force is what causes the bead to be stably trapped slightly downstream of the beam waist.

This is the output when beam is linear.

If the particle is located at the center of the beam, then individual rays of light are refracting through the particle symmetrically, resulting in no net lateral force. The net force in this case is along the axial direction of the trap, which cancels out the scattering force of the laser light. The cancellation of this axial gradient force with the scattering force is what causes the bead to be stably trapped slightly downstream of the beam waist.

This is the output, when beam is focused.

The standard tweezers works with the trapping laser propagated in the direction of gravity and the inverted tweezers works against gravity.

Wind is simply air in motion relative to the earth's surface. We normally think of the wind as the horizontal motion of the air, although air actually moves in three dimensions. The vertical component of the wind is generally quite small, except in thunderstorm updrafts. The vertical motion of air, however, is very important in determining our weather. Air that is rising cools, which may cause it to reach saturation and form clouds and precipitation. Conversely, air that is sinking warms, which causes clouds to evaporate and produce clear weather.

Surface maps usually have H's and L's at various locations. The H's and L's represent high and low pressure systems. On weather maps highs and lows are surrounded by lines called isobars. Isobars are lines of constant pressure; they connect every location that has the same value of pressure. When isobars are packed close together, the pressure is changing rapidly over a small distance. The closer the isobars are packed together, the stronger thepressure gradient (the rate of pressure change over a given distance.) Also, notice that (in the Northern Hemisphere) the wind blows clockwise around a high pressure system and also slightly outward from its center. Around a low pressure system, the wind blows counterclockwise and slightly in towards its center.

Diffraction Limit

An ideal optical system would image an object point perfectly as a point. However, due to the wave nature of radiation, diffraction occurs, caused by the limiting edges of the system’s aperture stop. The result is that the image of a point is a blur, no matter how well the lens is corrected. This is the diffraction blur or Airy disk, named in honor of Lord George Biddel Airy, a British mathematician (1801–1892). Its cross section and its appearance are shown in the figure below.

Airy disk, energy distribution and appearance.

If an image is made through a small aperture, there is a point at which the resolution of the image is limited by the aperture diffraction. As a matter of general practice in photographic optics, the use of a smaller aperture (larger f-number) will give greater depth of field and a generally sharper image. But if the aperture is made too small , the effects of the diffraction will be large enough to begin to reduce that sharpness, and you have reached the point of diffraction-limited imaging.

If you are imaging two points of light, then the smallest separation at which you could discern that there are two could reasonably be used as the limit of resolution of the imaging process. Presuming that diffraction is the determining factor, then the generally accepted criterion for the minimum resolvable detail is the Rayleigh criterion.

This shows the intensity curves for the radial distribution of the diffracted light for different separations. Your eye sees the characteristic bulls eye distribution of light as illustrated below.

For modern digital photography where the images are projected onto a CCD, the information is collected on pixels of the digital detector. At left is an attempt to show the effect of diffraction on such imaging in cases where the diffraction is the phenomenon that limits the resolution. If the image is in focus and free of visible affects of lens aberrations, then it may be that it will fit on one pixel. But if the aperture is small enough, then diffraction can spread the image onto neighboring pixels and constitute the limit on the resolution of the image.

Diffraction of any image reduces its sharpness and losses the frequency component inside it. Since there is lot much noise comes in even scent modes.

Tweezer

Optical tweezer is a device used to trap the micro level particles by using Laser, since laser have very high intensity with a high coherence length to trap the particle. In this method, we impose optical beam on a particle and beam is scattered by the particle and the particle is trapped due to the forces applied in this.

There are two types of particle can be trap by using this technique

 particle smaller than the 1 micro meter Mie particle

 particle bigger than the 1 micro meter Raleigh particle

For trapping micron level particle we need scattering force, gradient force and gravitational force. For trapping sub-micron level particle, we need scattering force, gradient force, thermal heating and gravitational force, which works on the particle and cancel out each other, so the total force on he particle is zero.Since in case of nano particle the differection limit of the source is very important parameter which depends on the wavelength.

This is the schemetic diagram of system.

 A new technology called haptic optical tweezers allows microscope users to manipulate samples by sight and touch, which could improve dexterity of micromanipulation and microassembly. 

The tweezers “will become an invaluable tool for force feedback micromanipulation of biological samples and nano- and microassembly parts,” said Dr. Cécile Pacoret of Université Pierre et Marie Curie (UPMC), a co-author of the study. 



There are two type of particles .
micron particles 
sub micron particles


Micron Particles: In this type of particles Scattering and gradient forces. Scattering force is applied in the direction of propagation of optical beam. Where as gradient force is applied towards the center of the focus. When gradient force is greater than scattering force we can trap the particle.

Mitty

As we all knows the world has begin with dust particle and whole world has been created. So we are just rearranging the things. There are some property in the soil which is yet not demonstrated, related to optics.

There are different type of waves, which generates due to the mass of any particle that can be related to mitty.

Latest

To Touch the Microcosmos: New Haptic Microscope Technique Allows Researchers to 'Feel' Microworld

Sep. 13, 2013 — What if you could reach through a microscope to touch and feel the microscopic structures under the lens? In a breakthrough that may usher in a new era in the exploration of the worlds that are a million times smaller than human beings, researchers at Université Pierre et Marie Curie in France have unveiled a new technique that allows microscope users to manipulate samples using a technology known as "haptic optical tweezers."

Communication

Maximum high load communication on today's date is done by optical fibers. Because they can wear a very high load and provide a high duty period. Since optical frequency is very high so they provides a very high bandwidth and can easily sustain very high load.

This can be done by using two methods 

• By single laser and detector 
• By dual laser and detector

Single laser

This is done with the help of mirrors, since mirrors are passive element so they do not provides any time dependent noise.

This site provides an overview of new 4th generation Free Space Optics wireless bridges used to connect buildings and towers with Gigabit capacity, license-free, interference-free data transmission capability.

In the news: NASA launching Earth-to-Moon/Satellite Free Space Optics link (video below). For more information on NASA laser communications,

The Lunar Laser Communication Demonstration (LLCD) is NASA's first high-rate, two-way, space laser communication demonstration.

What is LLCD? 

NASA is venturing into a new era of space communications using laser communications technology and it's starting with the LLCD mission. For decades NASA has launched and operated satellites in order to expand our understanding of earth and space science. In order to sustain this vision, satellites have increased their observation capabilities, transmitting data over greater distances, with a corresponding increase in data downlink rate and data volume. In an effort to address these challenges and enhance the Agency's communications capability, NASA has directed the Goddard Space Flight Center (GSFC) to lead the Lunar Laser Communication Demonstration (LLCD).

LLCD will be NASA's first-step in creating a high performance space-based laser communications system. The LLCD mission consists of a space terminal that will reach lunar orbit as a payload aboard the LADEE spacecraft; and a robust ground segment that consists of three ground terminals in optimal locations around the globe.

Laser communications set for Moon mission

An advanced laser system offering vastly faster data speeds is now ready for linking with spacecraft beyond our planet following a series of crucial ground tests. Later this year, ESA’s observatory in Spain will use the laser to communicate with a NASA Moon orbiter.

The laboratory testing paves the way for a live space demonstration in October, once NASA’s Lunar Atmosphere and Dust Environment Explorer – LADEE – begins orbiting the Moon.

LADEE carries a terminal that can transmit and receive pulses of laser light. ESA’s Optical Ground Station on Tenerife will be upgraded with a complementary unit and, together with two US ground terminals, will relay data at unprecedented rates using infrared light beams at a wavelength similar to that used in fiber-optic cables on Earth.


Optic fiber line to give China access to Pak military networks

BEIJING: Work on lying a fiber optic cable line linking China to Pakistan is set to begin soon. 

Sources said that the link will give China access to Pakistani military's communication networks. Radio Pakistan reported that a team of exports have visited parts of the area to be covered by the line and plan to begin work soon. 

Telecom experts recently carried out inspection in Sost and Khunjarab in the upper Hunza area of Gilgit Baltistan, Radio Pakistan said quoting officials of the communication department in the area. 

The new lines will also connect Rawalpindi, the military headquarters of Pakistan and Gilgit Baltistan including areas in Pakistan Occupied Kashmir, sources said. 

Pakistani experts have talked about the security challenges faced by the project including the possibility of the communication lines being monitored and disrupted by Taliban militants but they have not expressed any worry about the access it would give to Chinese authorities, observers said. This may be because Pakistan regards China as an all-weather and trusted friend, they said. 

China and Pakistan signed an agreement for the optic fiber project by the Chinese company Huawei during the visit of Prime Minister Nawaz Sharif to Beijing in July. 

The fiber cable connecting Rawalpindi and Khunjarab on the Pakistan-China border will be 820 km long and will cost $44 million. 

Both neighbors have opted for additional measures to mitigate security challenges because voice and data traffic along the militant infested border could be monitored and disturbed, sources said. Erratic climatic conditions in the area also pose a challenge. 

The project planners have provided for an alternative link between Pakistan and Trans-Asia Europe cable in China to ensure connectivity with the international telecom traffic in case of disruption, APP, the Pakistani news agency reported.

Logic Gates

These devices and Boolean logic are not limited to electronics. They have been demonstrated with optics in many different implementations with various switching mechanisms. The interest the optics community has in these devices has spawned from the fact that conventional computational speeds are approaching limits.

Optical logic gates can be made by using basic optical phenomena like, refraction, reflection, Interference, dispersion and absorption. Currently maximum optical gates are working in Non linear optics. This could also be made by using Electrooptic and accoustooptic  crystals. this will provide very cheap and fast optical communication, since optical to electrical conversion will be removed for optical processing.

Few Optical gates are working with loop reflector, Machzender and Michelson intereferometer.

Optical NAND Gate could be made by using OLCR method in the optical domain, which is design by  me.
For more detail contact me, I will reply for your questions.

Optical gates can be made by two types:-

1. By using Optical passive devices
2. By using Optical active devices

BY Passive optical device, in this we can use the basic element like fiber couplers. 

By Active optical devices, in this we use nonlinear material like etalon.



Interference
In this two waves are interacting each other and making interference, this is basic optical phenomenon. This will depend upon the frequencies and optical path difference of both beams.

Bi-stability
Bi-stable system is a system, which is stable in both two states, means changing of states from one states two other state is possible only when any input is applied to the input terminal, device will not change its any state automatically, which is very useful phenomenon. Since system is holding its state it could be considered  as memory element and when we are applying input it is changing state according to input so it is working like a logic gate depending upon input not the time.

Two features required for making a bistable device: Non-linearity and Feedback. An optical bistable system can be realized by use of a nonlinear optical element, whose output beam is used in a feedback system to control the transmission of light trough the element itself.

Bistable Optical Devices
Numerous schemes can be used for the optical implementation of the foregoing basic principle. Two types of nonlinear optical elements can be used

•  Dispersive nonlinear element, for which the refractive index n is a function of optical intensity.
• Dissipative nonlinear element, for which the absorption coefficient alpha is a function of the optical intensity.

Dissipative Nonlinear Element
A dissipative nonlinear material has an absorption coefficient that is dependent on the optical intensity I.  The saturable absorber in which the absorption coefficient is nonlinear function of I,

Suppose that the saturable absorber is replaces by an amplifying medium with a saturable gain
The system is nothing but optical amplifier with feedback. In some sense, the dispersive bistable optical system is the nonlinear-index-of-refraction analog of the laser.



Optical And gate
In this method we use two pulses as input. The binary data is represented by pulses that are added and their sum used as input to bistable device. With and appropriate choice of the pulse height in relation to the threshold, the device can be made to switch to high only when both pulses are present, so that it act as an AND gate. The AND logic gate is a digital device with two binary inputs and one binary output. Both input must be in the "1" state for the output to be in the "1" state. Otherwise, the output will be "0" state.
\par this is as simple as addition of two signals and making threshold greater than both but less than summation of both signals.


 all-optical reversible gates, namely, Feynman, Toffoli, Peres, and Feynman double gates, with optically controlled microresonators. To demonstrate the applicability, a bacteriorhodopsin protein-coated silica microcavity in contact between two tapered single-mode fibers has been used as an all-optical switch. Low-power control signals (<200 μW) at 532 nm and at 405 nm control the conformational states of the protein to switch a near infrared signal laser beam at 1310 or 1550 nm. This configuration has been used as a template to design four-port tunable resonant coupler logic gates. The proposed designs are general and can be implemented in both fiber-optic and integrated-optic formats and with any other coated photosensitive material. Advantages of directed logic, high Q-factor, tunability, compactness, low-power control signals, high fan-out, and flexibility of cascading switches in 2D/3D architectures to form circuits make the designs promising for practical applications.

Metamaterial

Metamaterials are artificial media structured on a size scale smaller than the wavelength of external stimuli.^[3] Materials of interest exhibit properties not found in nature, such as negative index of refraction. They are cellular assemblies of multiple elements fashioned from materials including metals and plastics, arranged in periodic patterns. Metamaterials gain their properties not from their constituents, but from their exactingly-designed structures. Their precise shape, geometry, size, orientation and arrangement can affect light or sound in a manner that is unachievable with conventional materials

A material which turns the light in opposite direction of Snell’s law is called left handed material. This material has negative refractive index. Refractive index is the square root of multiplication of relative permittivity and relative permeability. Relative permittivity is the coefficient related to the propagation of electric field and relative permeability is related to the propagation of magnetic field. When either relative permeability or relative permitivity is negative, material has real and imaginary refractive index. When both permitivity and permeability is negative material has negative refractive index.This type of material has taken a very high attention in current scenario of optical communication. This will provide us subwavelength imaging.

Metamaterials are exotic composite materials that display properties beyond those available in naturally occurring materials. Instead of constructing materials at the chemical level, as is ordinarily done, these are constructed with two or more materials at the macroscopic level. One of their defining characteristics is that the electromagnetic response results from combining two or more distinct materials in a specified way which extends the range of electromagnetic patterns because of the fact that they are not found in nature.

The term was coined in 1999 by Rodger M. Walser of the University of Texas at Austin. He defined metamaterials as

macroscopic composites having a manmade, three-dimensional, periodic cellular architecture designed to produce an optimized combination, not available in nature, of two or more responses to specific excitation.

In a paper published in 2001, Rodger Walser from the University of Texas, Austin, coined the termmetamaterial to refer to artificial composites that "...achieve material performance beyond the limitations of conventional composites." The definition was subsequently expanded by Valerie Browning and Stu Wolf of DARPA (Defense Advanced Research Projects Agency) in the context of the DARPA Metamaterials program that started also in 2001. Their basic definition: Metamaterials are a new class of ordered composites that exhibit exceptional properties not readily observed in nature. While the original metamaterials definition encompassed many more material properties, most of the subsequent scientific activity has centered on the electromagnetic properties of metamaterials gains its properties from its structure rather than directly from its composition."

Electromagnetics researchers often use the term metamaterials more narrowly, for materials which exhibit negative refraction. W. E. Kock developed the first metamaterials in the late 1940s with metal-lens antennæ and metallic delay lenses.

With a negative refractive index researchers have been able to create a device known as a cloaking device, or an invisibility cloak, which is not possible with natural materials. Refraction is the bending of light as it moves through some transparent medium, such as the lenses of eyeglasses, or a glass of water. Something such as a finger through the glass may look greater or smaller. A pencil stuck in a glass of water seems to sharply bend at an angle. At each bend the light through the glass brakes inward, and the index of refraction in natural materials has a positive value. A negative refractive index is when light brakes outward, and bends outward in a thicker medium. In 1967, when metamaterials were first theorized by Victor Veselago, they were thought to be bizarre and preposterous. Usually when a beam of light is bent entering a glass of water it keeps faring in a straight line at the angle that it entered, and the index of refraction is constant. Suppose one could shape the index over the medium's span: With metamaterials it can be controlled so that the object becomes invisible—a negative refraction index. Ames Laboratory in Iowa created a metamaterial of index of −0.6 for red light (780 nanometers). Previously, physicists were only successful in bending infrared light with a metamaterial at 1,400 nm, which is outside the visible range.

Metamaterial cloaking is the usage of metamaterials in an invisibility cloak. This is accomplished by manipulating the paths traversed by light through a novel optical material. Metamaterials direct and control the propagation and transmission of specified parts of the light spectrum and demonstrate the potential to render an object seemingly invisible. Metamaterial cloaking, based on transformation optics, describes the process of shielding something from view by controlling electromagnetic radiation. Objects in the defined location are still present, but incident waves are guided around them without being affected by the object itself.

Star Wars fans know it's best not to get on the dark side of Darth Vader. The infamous Sith Lord would regularly choke those who had annoyed him from a distance with a determined and gravity-defying stranglehold.But a new photo meme is encouraging hundreds of internet users to also master the ways of the force, or at least appear to. The new online craze requires at least two participants to recreate Darth Vader's signature move. One person needs to extend their hand in attack, the other to make a huge jump in the air while holding their neck and looking pained. The trend makes for some impressive and hilarious results

Surface Plasmon Resonance

In current scenario optical communication is playing important role and small particle study and subwavelength study is enhancing domains. In SPR light is launched from the one port of the device and the controlled output is taken from the other port of the device, so at the other port light is controlled and also it aperture is also possible in the subwavelength size, since light is travelling inside the boundary betweem metal and dielectric. So it can be decoupled from any small size so that we can overcome diffraction limitation.

When a light fall on the boundary of metal and dielectric, some part of light got trap inside metal-dielectric boundary, because light excites electrons of metal and make them free to flow inside the medium. These electrons make cloud and moves along the boundary. This cloud is known as surface plasmon polariton and frequency of surface plasmon politron is called surface plasmon resonance.

Since the permittivity of the metal are negative. They also have a positive part of permittivity that is imaginary so called gives positive and imaginary refractive index.

Because of surface plasmon some part of light is trapped between metal and dielectric and this light can be guided through the medium and can be used for small power communication and sub-wavelength imaging. 

This can be done in two formate

1. Otto configuration
2. Kreschmann configuration

Otto configuration

In this there is a air gap between metal and dielectric.

Kreshtchmann configuration

in this there is no air gap between metal and dielectric.

SPR can be generated by using gold silver aluminium and also with iron.

Excitation of surface plasmons is based on total internal reflection when an incident beam of p-polarized light strikes an electrically conducting gold layer at the interface of a glass sensor with high RI (Refractive Index) and an external medium (gas or liquid) with low RI. At a given angle, the excitation of surface plasmons takes place resulting in a reduced intensity of the reflected light. (Fig.1). A slight change at the interface (e.g. a change in refractive index or formation of a nanoscale film thickness) will lead to a change in SPR signal, allowing precise measurements of thin film properties as well as surface molecular interactions in real-time.

Surface Plasmon Resonance (SPR) is a physical process that can occur when plane-polarized light hits a metal film under total internal reflection conditions(1).

When a light beam hits a half circular prism, the light is bend towards the plane of interface, when it is passing from a denser medium to a less dense one. Changing the incidence angle (Θ) changes the outcoming light until a critical angle is reached. At this point, all the incoming light is reflected within the circular prism. This is called total internal reflection (TIR).

Although no light is coming out of the prism in TIR, the electrical field of the photons extends about a quarter of a wavelength beyond the reflecting surface.

Now the prism is coated with a thin film of a noble metal on the reflection site. In most cases, gold is used because it gives a SPR signal at convenient combinations of reflectance angle and wavelength. In addition, gold is chemically inert to solutions and solutes typically used in biochemical contexts(1). When the energy of the photon electrical field is just right it can interact with the free electron constellations in the gold surface. These are the outer shell and conduction-band electrons. The incident light photons are absorbed and the energy is transferred to the electrons, which convert into surface plasmons.

Photon and electron behaviour can only be described when they have both wave and particle properties. In accordance with the quantum theory, a plasmon is the particle name of the electron density waves. Therefore, when in a TIR situation the quantum energy of the photons is right, the photons are converted to plasmons leaving a 'gap' in the reflected light intensity.

perfectly matched layer (PML)

A perfectly matched layer (PML) is an artificial absorbing layer for wave equations, commonly used to truncate computational regions in numerical methods to simulate problems with open boundaries, especially in the FDTD and FE methods. The key property of a PML that distinguishes it from an ordinary absorbing material is that it is designed so that waves incident upon the PML from a non-PML medium do not reflect at the interface—this property allows the PML to strongly absorb outgoing waves from the interior of a computational region without reflecting them back into the interior.

PML was originally formulated by Berenger in 1994 for use with Maxwell's equations, and since that time there have been several related reformulations of PML for both Maxwell's equations and for other wave equations. Berenger's original formulation is called a split-field PML, because it splits the electromagnetic fields into two unphysical fields in the PML region. A later formulation that has become more popular because of its simplicity and efficiency is called uniaxial PML or UPML (Gedney, 1996), in which the PML is described as an artificial anisotropic absorbing material. Although both Berenger's formulation and UPML were initially derived by manually constructing the conditions under which incident plane waves do not reflect from the PML interface from a homogeneous medium, both formulations were later shown to be equivalent to a much more elegant and general approach: stretched-coordinate PML (Chew and Weedon, 1994; Teixeira and Chew, 1998). In particular, PMLs were shown to correspond to a coordinate transformation in which one (or more) coordinates are mapped to complex numbers; more technically, this is actually an analytic continuation of the wave equation into complex coordinates, replacing propagating (oscillating) waves by exponentially decaying waves. This viewpoint allows PMLs to be derived for inhomogeneous media such as waveguides, as well as for other coordinate systems and wave equations.

As molecules are immobilized on a sensor surface, the refractive index at the interface between the surface and a solution flowing over the surface changes, altering the angle at which reduced-intensity polarized light is reflected from a supporting glass plane.

The change in angle, caused by binding or dissociation of molecules from the sensor surface, is proportional to the mass of bound material and is recorded in a sensorgram.

When sample is passed over the sensor surface, the sensorgram shows an increasing response as molecules interact. The response remains constant if the interaction reaches equilibrium. When sample is replaced by buffer, the response decreases as the interaction partners dissociate.

Complete profiles of recognition, binding and dissociation are generated in real time. From these profiles, data such as specificity, affinity, kinetic behavior and sample concentration can be determined.
For most applications, a dextran matrix covering the gold layer enables molecules to be immobilized to a sensor surface and provides a hydrophilic environment for interactions. Surface specificity is determined by the nature of the immobilized molecule.

Since light does not penetrate the sample, interactions can be followed in colored, turbid or opaque samples. No labels are required and detection is instantaneous.

This is the full model of SPR generation can be used for the focusing light into very small and thin films, which are smaller as compare to the wavelengths focused inside it.

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Gradient Force: The Gaussian beam has every angle from -180° to 180° so its gradient have a curve, which is negative for positive direction and positive for negative direction on x-axis. So because of Brownian motion of the particle when it comes in this region of intensity gradient, it is always forced toward the center of laser beam. This force ,which attract the particle towards the center of the beam is called as Gradient force. When this gradient force is sufficiently larger as compared to scattering force, the particle will be trapped inside the trap volume.

For Rayleigh particle, the gradient force can be given as:

F_grad = - n_b³r³ /2 (m ²-1/ m ²-2) grad(E²)

Thermal Force:- Mie particles are moving with Browne motion in the open atmosphere so they possase a momentum because of their speed. So they are having a force inside them called as thermal force, since it increases with the temperature. Sice we are woking in very small particles so small change in temperature will require change in Gradient force to trap them.

Thermal force applied to the particle is

|F(f)|² = 4γk_BT

By this we can see that force applied to the particle is depending on the temperature, so if temperature will increase thermal force will also increase and we have to control it so that particle will be trap inside the system. The wave vector because of the Brauny motion is

|X(F)|² = K_BT/ γ(f_c-f)²