25-08-2017, 09:32 PM
Presented By-
Mr. Manish Baberwal
Mr. Kandarp D Shah
[attachment=12533]
ABSTRACT
We are at the edge of another industrial revolution, namely the information age.
Although we may have not noticed, the amount of information generated by humanity is doubling every few months. In order to respond to such a huge demand for information modern communications relies on fast digital optical fiber systems which are fast emerging as dominant transmission medium within the major industrialized societies.
Even in advanced fiber optics systems longer spans of fiber with higher bit rates are desired. Researchers have been constantly struggling since the development of optical fiber in early 60’s to achieve the dream seen with it’s developments but without much success till a couple of years back.
Optical communication system are no longer the pipedreams of the future with the advent of this new data transmission scheme in optics which has facilitated to transmit data at rates in excess of 50 Gb/s, at a distance of 19000 kms requiring no repeaters and with no errors. At this rate one bibble could be sent to everyone on earth--- 5.5(9) people--- in just 10 days.
The new technique utilizes something called “SOLITON PULSES”.
Optical Solitons are essentially “stable pulses” that travel without changing their shape: they do not disperse and robustly resist perturbations in the physical medium that supports them. They represent one of the most exciting and fascinating concepts in modern communications, arousing special interest due to their potential applications in Optical Fiber Communication.
With this presentation I have tried to focus on the explicit integration of analytical and experimental methods in non linear optics specially “Optical Soliton Communication”.
Brief History Of Soliton
Solitons are essentially “stable pulses” that travel without changing their shape: they do not disperse and robustly resist perturbations in the physical medium that supports them.
The phenomenon was first discovered in 1894 by a Scottish Engg., John Scott Russell.
He observed a well defined heap of water that continued forward on its course with great velocity along the channel without change of form or diminution of speed. Unfortunately the implication that so excited him were misunderstood by his contemporaries.
It was not until the mid 60’s and the use of digital computers to study non linear wave propagation that the soundness of Russell’s ideas was appreciated. Two Dutchman, Kurtweig and deVries derived an equation that related the spatial changes in the amplitude of the wave to its temporal changes and proposed a solution which confirmed Russell’s observations. This equation is known as KdV equation.
During this time between 1955 to 1975 theory of solitary wave propagation was developed by various researches and mathematicians which confirmed the existence of special localized waves which exhibited particle like behavior.
In 1973 Hasegawa and Tappert proposed that such solitons could be used for optical communication and Russell’s research hit the big time in modern communication systems when in 1980’s Mollenauer observed the first soliton pulses in a single mode fiber giving birth to the new break through technology.
WHAT IS A SOLITON PULSE?
Soliton is a bell shaped pulse of light -- of sufficient intensity and correct wavelength traveling through a non linear optical fiber. They are very short pulses of light that show the peculiar characteristic of maintaining their pulse width in the presence of chromatic dispersion as they propagate in the optical fiber.
Solitons, and any encoded information they carry have a strong resistance to interferences.
Solitons are essentially “stable pulses” that travel without changing their shape: they do not disperse and robustly resist perturbations in the physical medium that supports them.
Properties of Soliton:
* Solitons have very short pulse duration, a single soliton is only 1 picosecond long (1 million millionth of a second). They have high stability and can propagate independently along its course forever.
* Solitons can exist when dispersion and non linearity effect of the fiber counteract one another as a result they propagate without deterioration over many thousands of kilometers.
* Soliton dynamics are governed by the Nonlinear Schrodinger Equation. Split-step Fourier Method can be applied to efficiently numerically solve the Nonlinear Schrodinger equation.
* During collision between two soliton pulses, they pass through each other, coming out of the interaction retaining their identities. Since these pulses behave more like particles than waves, they are named as solitons.
* Since solitons are non linear waves, the Principle of Superposition does not hold due to the fact that the wave's sprrd depends on the amplitude.
* Recently solitons that have decayed, had been revitalized, restored and relaunched following a stage of amplification.
Mathematical Analysis of Soliton:
One of the most impressive and useful applications of mathematics is to nonlinear optics. Solitons refer to the functional form of the specific solutions of the nonlinear equation that describes light propagation in nonlinear optical media.
Throughout the late 1960’s Zabusky and Kruskal, worked on the problem of finding a general expression for the solution of the KdV equation, under the assumption that the initial profile of the non linear waves was known. They studied certain quantities which remained constant with time. In particular, they had discovered a technique to solve the KdV equation by relating it to another equation, the so-called Schroedinger equation of quantum mechanics. Using the mathematical theory, which had been known for some time, they were able to solve the initial value problem. The remarkable thing about this technique was that they were able to solve a non linear equation by solving several linear equations, which are much easier to solve .In 1968, Lax developed a theory that predicted that other equations could be solved in a similar way. Namely, given a certain pair of linear equations, the so called Lax Pair, it would be possible to solve an associated non linear equation in much the same manner as they had solved the KdV equation.
In 1974, a group of researchers showed how one could work in the reverse direction to find a large class of equations solvable by this “Inverse Scattering Method”. Using the right variables, the solutions of these equations could be written as a superposition of non linear normal modes. This collection of normal modes included soliton, explaining the behavior during collisions. Solitons may be considered as involving the continual balance along its path between the dispersive and nonlinear terms of the nonlinear Schroedinger equation. It may be derived by solving the wave equation given below in a nonlinear and dispersive medium.
The soliton theory has grown steadily ever since it's advent and acceptance. However, very little about the soliton theory has left academic circles, probably due to the highly mathematical nature of the field.
Propagation Of Optical Soliton
An optical soliton is created in a optical fiber due to the interaction between two contradictory properties of the wave exhibited while transmission -- “Dispersion” and “Non linear effects".
The medium for transmission of optical signal is the optical fiber which is a dielectric medium since it is made of glass. The physical principle used for this transmission is “Total Internal Reflection” which states that when light travels from one medium to another whose index of refraction is lower, there is a critical angle of incidence below which the light will be totally reflected back in the first medium with no light penetrating the interface.
Dispersion: Dispersion describes the dependence of the refractive index (n) of medium on the wavelength of light traveling through the medium so that n=n(). Thus dispersion implies changing the light velocity inside the medium, depending on it's wavelength causing pulse spread.
A light source, even the best radiates light of a finite spectral width.As a result an information carrying light pulse contains different wavelengths which travels within a fiber at different velocities and will arrive at the fiber end at different times even though they propagate the same path.
Fig 2. Pulse widening caused by dispersion.
Refractive Index, n=c/v
Since, the fiber's refractive index is less for longer wavelengths they travel faster as compared to shorter wavelengths.This results in the spreading of the output light pulse.
Intermodal dispersion(due to interaction among different modes) and intermodal dispersion (occurring within a single mode) play a major role in limiting the bandwidth and thus the bit rate of optical fiber.
Non Linear Effects: An optical effect is called no linear if it's parameter depends on the light intensity (power). When an electric field is applied to the dielectric the electrons are displaced and get aligned in the particular direction. This alignment is called polarization.
The refractive index of the medium results from the applied optical field (depends on the square of amplitude of applied electric field) perturbing the atoms or molecules of the medium to induce an oscillating polarization which radiates producing an overall perturbed field which exhibits non linear effects at high optical intensity.
The intensity dependent refractive index causes an intensity dependent phase shift in the fiber. Thus non linearities result in a different transmission phase for the peak of the pulse compared to the leading and trailing pulse edges. This effect is known as self phase modulation (SPM) which can alter and broaden the frequency spectrum of the pulse since frequency of a pulse is time derivative of the pulse.
For critical pulse shapes and at high optical power levels (intensity) pulse compression can be obtained within the fiber itself by applying the SPM.
Mr. Manish Baberwal
Mr. Kandarp D Shah
[attachment=12533]
ABSTRACT
We are at the edge of another industrial revolution, namely the information age.
Although we may have not noticed, the amount of information generated by humanity is doubling every few months. In order to respond to such a huge demand for information modern communications relies on fast digital optical fiber systems which are fast emerging as dominant transmission medium within the major industrialized societies.
Even in advanced fiber optics systems longer spans of fiber with higher bit rates are desired. Researchers have been constantly struggling since the development of optical fiber in early 60’s to achieve the dream seen with it’s developments but without much success till a couple of years back.
Optical communication system are no longer the pipedreams of the future with the advent of this new data transmission scheme in optics which has facilitated to transmit data at rates in excess of 50 Gb/s, at a distance of 19000 kms requiring no repeaters and with no errors. At this rate one bibble could be sent to everyone on earth--- 5.5(9) people--- in just 10 days.
The new technique utilizes something called “SOLITON PULSES”.
Optical Solitons are essentially “stable pulses” that travel without changing their shape: they do not disperse and robustly resist perturbations in the physical medium that supports them. They represent one of the most exciting and fascinating concepts in modern communications, arousing special interest due to their potential applications in Optical Fiber Communication.
With this presentation I have tried to focus on the explicit integration of analytical and experimental methods in non linear optics specially “Optical Soliton Communication”.
Brief History Of Soliton
Solitons are essentially “stable pulses” that travel without changing their shape: they do not disperse and robustly resist perturbations in the physical medium that supports them.
The phenomenon was first discovered in 1894 by a Scottish Engg., John Scott Russell.
He observed a well defined heap of water that continued forward on its course with great velocity along the channel without change of form or diminution of speed. Unfortunately the implication that so excited him were misunderstood by his contemporaries.
It was not until the mid 60’s and the use of digital computers to study non linear wave propagation that the soundness of Russell’s ideas was appreciated. Two Dutchman, Kurtweig and deVries derived an equation that related the spatial changes in the amplitude of the wave to its temporal changes and proposed a solution which confirmed Russell’s observations. This equation is known as KdV equation.
During this time between 1955 to 1975 theory of solitary wave propagation was developed by various researches and mathematicians which confirmed the existence of special localized waves which exhibited particle like behavior.
In 1973 Hasegawa and Tappert proposed that such solitons could be used for optical communication and Russell’s research hit the big time in modern communication systems when in 1980’s Mollenauer observed the first soliton pulses in a single mode fiber giving birth to the new break through technology.
WHAT IS A SOLITON PULSE?
Soliton is a bell shaped pulse of light -- of sufficient intensity and correct wavelength traveling through a non linear optical fiber. They are very short pulses of light that show the peculiar characteristic of maintaining their pulse width in the presence of chromatic dispersion as they propagate in the optical fiber.
Solitons, and any encoded information they carry have a strong resistance to interferences.
Solitons are essentially “stable pulses” that travel without changing their shape: they do not disperse and robustly resist perturbations in the physical medium that supports them.
Properties of Soliton:
* Solitons have very short pulse duration, a single soliton is only 1 picosecond long (1 million millionth of a second). They have high stability and can propagate independently along its course forever.
* Solitons can exist when dispersion and non linearity effect of the fiber counteract one another as a result they propagate without deterioration over many thousands of kilometers.
* Soliton dynamics are governed by the Nonlinear Schrodinger Equation. Split-step Fourier Method can be applied to efficiently numerically solve the Nonlinear Schrodinger equation.
* During collision between two soliton pulses, they pass through each other, coming out of the interaction retaining their identities. Since these pulses behave more like particles than waves, they are named as solitons.
* Since solitons are non linear waves, the Principle of Superposition does not hold due to the fact that the wave's sprrd depends on the amplitude.
* Recently solitons that have decayed, had been revitalized, restored and relaunched following a stage of amplification.
Mathematical Analysis of Soliton:
One of the most impressive and useful applications of mathematics is to nonlinear optics. Solitons refer to the functional form of the specific solutions of the nonlinear equation that describes light propagation in nonlinear optical media.
Throughout the late 1960’s Zabusky and Kruskal, worked on the problem of finding a general expression for the solution of the KdV equation, under the assumption that the initial profile of the non linear waves was known. They studied certain quantities which remained constant with time. In particular, they had discovered a technique to solve the KdV equation by relating it to another equation, the so-called Schroedinger equation of quantum mechanics. Using the mathematical theory, which had been known for some time, they were able to solve the initial value problem. The remarkable thing about this technique was that they were able to solve a non linear equation by solving several linear equations, which are much easier to solve .In 1968, Lax developed a theory that predicted that other equations could be solved in a similar way. Namely, given a certain pair of linear equations, the so called Lax Pair, it would be possible to solve an associated non linear equation in much the same manner as they had solved the KdV equation.
In 1974, a group of researchers showed how one could work in the reverse direction to find a large class of equations solvable by this “Inverse Scattering Method”. Using the right variables, the solutions of these equations could be written as a superposition of non linear normal modes. This collection of normal modes included soliton, explaining the behavior during collisions. Solitons may be considered as involving the continual balance along its path between the dispersive and nonlinear terms of the nonlinear Schroedinger equation. It may be derived by solving the wave equation given below in a nonlinear and dispersive medium.
The soliton theory has grown steadily ever since it's advent and acceptance. However, very little about the soliton theory has left academic circles, probably due to the highly mathematical nature of the field.
Propagation Of Optical Soliton
An optical soliton is created in a optical fiber due to the interaction between two contradictory properties of the wave exhibited while transmission -- “Dispersion” and “Non linear effects".
The medium for transmission of optical signal is the optical fiber which is a dielectric medium since it is made of glass. The physical principle used for this transmission is “Total Internal Reflection” which states that when light travels from one medium to another whose index of refraction is lower, there is a critical angle of incidence below which the light will be totally reflected back in the first medium with no light penetrating the interface.
Dispersion: Dispersion describes the dependence of the refractive index (n) of medium on the wavelength of light traveling through the medium so that n=n(). Thus dispersion implies changing the light velocity inside the medium, depending on it's wavelength causing pulse spread.
A light source, even the best radiates light of a finite spectral width.As a result an information carrying light pulse contains different wavelengths which travels within a fiber at different velocities and will arrive at the fiber end at different times even though they propagate the same path.
Fig 2. Pulse widening caused by dispersion.
Refractive Index, n=c/v
Since, the fiber's refractive index is less for longer wavelengths they travel faster as compared to shorter wavelengths.This results in the spreading of the output light pulse.
Intermodal dispersion(due to interaction among different modes) and intermodal dispersion (occurring within a single mode) play a major role in limiting the bandwidth and thus the bit rate of optical fiber.
Non Linear Effects: An optical effect is called no linear if it's parameter depends on the light intensity (power). When an electric field is applied to the dielectric the electrons are displaced and get aligned in the particular direction. This alignment is called polarization.
The refractive index of the medium results from the applied optical field (depends on the square of amplitude of applied electric field) perturbing the atoms or molecules of the medium to induce an oscillating polarization which radiates producing an overall perturbed field which exhibits non linear effects at high optical intensity.
The intensity dependent refractive index causes an intensity dependent phase shift in the fiber. Thus non linearities result in a different transmission phase for the peak of the pulse compared to the leading and trailing pulse edges. This effect is known as self phase modulation (SPM) which can alter and broaden the frequency spectrum of the pulse since frequency of a pulse is time derivative of the pulse.
For critical pulse shapes and at high optical power levels (intensity) pulse compression can be obtained within the fiber itself by applying the SPM.