Fundamentals of Nonlinear Optics. ECED Lecture Notes c Sergey A. Ponomarenko. January 11, Preface to the Second Edition xv. Preface to the First Edition xvii. 1. The Nonlinear Optical Susceptibility. 1. Introduction to Nonlinear Optics. Why Study Nonlinear Optics? It is good fundamental physics. It leads to important applications. It is a lot of fun. Demonstrate these features with examples in.
|Language:||English, Spanish, French|
|ePub File Size:||19.71 MB|
|PDF File Size:||17.26 MB|
|Distribution:||Free* [*Regsitration Required]|
Parametric amplification. - Third-order nonlinearity. - Kerr effect. - Self- and cross- phase modulation. - Four-wave mixing. Outline. Introduction to Nonlinear Optics. PDF | On Oct 22, , B. D. Guenther and others published Nonlinear Optics. Changing its shape in space and time. • Mixing different laser pulses. • Create ultrashort laser pulses In nonlinear optics the superposition principle.
Lecture 18 pdf kb Module 4: Chapter 8. Self Fousing and Self Phase Modulation It turns out that most of the available materials do not meet the simultaneous require- ments of large as well as fast nonlinearity required for the practical devices. Mechanisms and Materials et al, ; Solli, et al ; Agrawal, ]. Module 5:
Self Fousing and Self Phase Modulation 7. This causes a beam of light to get focussed to a point in a nonlinear optical medium without the help ok of any external optical component such as a lens or a mirror. It is bo convenient to describe this effect in terms of an intensity-dependent refractive index.
Self focusing can lead to possible damage of opti- d cal media due to the increased intensity within the medium as an he extremely narrow beam of high intensity light passes through the is medium as a result of self focusing. On the other hand, this can be bl used to obtain an extremely narrow pencil of intense light in media pu that can withstand such intensities.
It can also be used in compen- sating for the natural beam divergence due to diffraction and thus a obtaining trains of optical pulses that maintain their shape, with of obvious application in optical communication. Self focusing leads to an intensity modulation of the e beam along its path and can lead to nonlinear absorption of light pl by the media which can be used in a variety of applications [Boyd, m ].
Sa Consider a monochromatic beam of light, with a Gaussian cross section traveling through a medium such as air, with a negligible value of n2 and entering another transparent medium with a reason- ably significant value of n2.
The corresponding wave front is plane parallel while in air, but starts getting distorted as the beam be- gins to propagate in the medium. The intensity modulation across the beam leads to a corresponding modulation in the refractive in- dex due to the intensity-dependent contribution.
The intensity and hence the refractive index are larger at the center of the beam than Some pages are not included here among these sample pages. Chapter 7. Unchirped pulse ok bo d he is bl pu a of s ge Figure 7. The origin of chirp pa 7. Thus the trailing edge of the pulse is blue-shifted. Thus the leading edge of the pulse is redshifted while the trailing edge of is blueshifted and chirping leads to a spectral broadening, which can be studied by analyzing the spectral content of the pulse by Fourier transform techniques.
This is called a positive chirp as the instantaneous frequency increases with time. A compari- Some pages are not included here among these sample pages.
Self Fousing and Self Phase Modulation What kind of chirping do you expect when a pulse travels through a medium of negative n2? What would happen to the pulse the medium also has a positive GVD? The concept of a soliton is very interesting as well as useful. The idea of compensating for the effect of one physical process ok on pulse propagation exactly by the effect of by another pro- bo cess is quite fascinating.
A lot of research has gone into the mathematical aspects of obtaining soliton solutions for non- d linear differential equations [Porsezian, ].
On the other he hand, a lot of work has been done in exploring the scope of soliton propagation in fiber optic communications [Agrawal, is and ]. You can take the help of popular mathe- bl matical software to explore the influence of designing systems pu with different values of LD and LN and visualize soliton prop- agation.
This may help to arrive at design parameters for a practical systems based on realistic materials available. Mechanisms and Materials 8. The response of a dispersive dielectric to an incident electromagnetic wave is described in terms of the dielectric constant of the medium, which is a complex quantity. The real part of di- electric constant governs its dispersive behavior and the imaginary part is responsible for optical absorption in the medium. An inter- esting consequence of the fact that the electric field in a material at any given instant is determined by the polarization which oc- ok curred at all preceding times is that the real and imaginary parts bo of the dielectric constant are related to each other.
The equations governing the relation between the processes of dispersion and ab- d sorption are known as Kramers-Kronig relations and are discussed he in standard textbooks on solid state physics [Kittel, ; Ashcroft is and Mermin, ]. The scope of these relations extend also to bl nonlinear optical absorption as well as dispersion. The changes in pu nonlinear absorption due to optical excitation processes are nor- mally limited to a range of frequencies and hence can be measured a more easily than changes in dispersion and hence the relation be- of tween absorption and dispersion becomes very useful [Hutchings et al, ; Peiponen et al, ; Lucarini et al, ].
A variety of s physical mechanisms can lead to absorption, excitation and disper- ge sion processes in different materials. Thus a systematic analysis of pa the known types of nonlinear materials and the underlying domi- nant mechanisms of light-matter interaction in these materials is a e very important frontier area of research. We have seen in previous chapters that certain non-linearities can be exhibited only by single crystals.
It is also possible to distinguish nonlinear optical materials as per their well- known standard classification: Space limitation does not permit us to make a compre- hensive account of all these aspects and hence we give an instructive perspective of some of the relevant features in this chapter. Chapter 8. We summarize these and then give a brief account of each to follow. Of course all these mechanisms do not operate in all materials and some are spe- cific to some type of materials while some have a universal character.
Experimental investigations can disclose which mechanism operates in a given material and for a given nonlinear optical process. The various mechanisms are: Some of these variations are known to enhance the nonlinearity of the basic polymer by way of extending the spatial spread of electrons and hence enlarging the linear as well as nonlinear susceptibilities [Vijaya et al, ; Martino et al, ] A second example is that of structure variation studies in por- phyrins, phthalocyanines etc which also has yielded interesting re- sults [Unnikrishnan, et al, ;Venkatram, et al, ].
Porphyrins allow for incorporation of various ligands and different core metal ions, which alter the susceptibilities dramatically. Incorporation of ok porphyrins into solid polymer membranes is found to enhance non- bo linearity, besides stabilizing the materials against photodegradation and providing a convenient solid matrix. Composites of optical d materials with different kinds of mechanisms and several other ma- he terials in solid, liquid and film state appear to hold promise from the device application point of view [Chemla, ; Chemla and is Zyss, ; Gupta et al, , ].
These include semiconductors, poly- e mers, inorganic crystals and liquid crystals, which are being used pl widely as conventional materials for applications in nonlinear op- m tics.
The most important limitation in the technology of nonlinear Sa optics has been the non-availability of ideal materials for exploiting the potential of nonlinear optical processes to their fullest extent. This is known as the materials bottleneck. It turns out that most of the available materials do not meet the simultaneous require- ments of large as well as fast nonlinearity required for the practical devices.
Thus recent research has focused on design and develop- ment of artificial materials with fast as well as large nonlinearity. Mechanisms of non- linearity in a variety of low dimensional materials such as semicon- ductor quantum dots, quantum wells, quantum wires, nanohybrids and composites, functionalized carbon nanotubes, graphene hybrids is being studied in this context. Quantum wells are made by confin- ing electrons to a plane, in quasi-two-dimensional structures.
This can be achieved by placing a thin layer of a semiconductor material ok sandwiched between two layers of an insulating material or even bo some other semiconductor a larger value of the bandgap.
Thus the electrons in the middle layer experience a potential when they try d to move in a direction perpendicular to the plane while they are he free to move within the plane. These are now being used in several is devices.
Electrons can be confined further to one dimension by em- bl bedding a semiconductor wire or a conducting polymer chain in a pu material of larger band gap.
The surrounding material provides the confining potential ge while also holding the material in place. These are practical real- pa izations of particle in a box whose optical properties depend on the particle size. Several techniques of obtaining such monosize clus- e ters have been perfected by materials scientists. However, a major pl problem with free standing nanoclusters disperse in solutions is the m lack of stability in view of the fact that individual quantum dots Sa to cluster together, become heavier and get precipitated eventually, often within a few hours after preparation.
The techniques used to prevent this include the use of a capping agent or a shell over the quantum dot or embedding them in appropriate insulating host media. Other techniques are ion-implantation, monolayer building and molecular beam epitaxy also are being used widely to produce strongly confined quantum dots.
Embedding semiconductor quan- tum dots in appropriate transparent insulating media such as Nafion ionomer [Nandakumar et al, ] has been shown to hold promise in obtaining highly stable quantum dots in a format convenient for Some pages are not included here among these sample pages.
Mechanisms and Materials ok bo d Figure 8. Optical absorption spectrum of nanocrystalline CdS. Mechanisms and Materials ok bo d he Figure 8. A skectch of the plot between frequency and the mag- is nitude of wave vector, showing photonic bandgap; inset: Apart from their su- perior efficiency in comparison with conventional fibers in commu- of nications, the nonlinear optical response of photonic crystal fibers s is also of considerable interest [Agrawal, ].
This is an effect based on an interplay of various nonlinear Sa optical mechanisms that occur when a optical pulse of a very high intensity and a very short duration interacts with matter, which eventually results in the generation of laser emission with a broad spectral band with reasonably high intensities [Alfano, ; Dud- ley et al ].
Apart from functioning as tunable laser sources on wavelength filtering, such media are also very useful for applications such as multi-wavelength microscopy, optical information process- ing and high resolution imaging. NLO provides: Applications in information processing and storage seem less mature.
Cundiff, Daniel J.
Express 19 23 Express 1 7 Amar R. Bhagwat and Alexander L. Gaeta Opt.
Express 16 7 Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Supradeepa and J. Durfee, T. Storz, J. Garlick, S. Hill, J. Squier, M. Kirchner, G. Taft, K. Shea, H. Kapteyn, M. Murnane, and S. Cong, X.
Zhang, Q. Wang, Z. Liu, X. Chen, S. Fan, X. Zhang, H. Zhang, X. Tao, and S. Wang, K. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R.
Norwood, M. Yamamoto, and N. Hollemeyer, W. Altmeyer, E. Heinzle, and C.