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Resumo da aula passada Complementação de outros acopladores ópticos, tipos de lentes de acoplamento com fibras. Amplificadores ópticos, motivação pelo.

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Apresentação em tema: "Resumo da aula passada Complementação de outros acopladores ópticos, tipos de lentes de acoplamento com fibras. Amplificadores ópticos, motivação pelo."— Transcrição da apresentação:

1 Resumo da aula passada Complementação de outros acopladores ópticos, tipos de lentes de acoplamento com fibras. Amplificadores ópticos, motivação pelo seu desenvolvimento e diferentes tipos, Processo de amplificação óptica na fibra dopada com Er , diagrama de energia do Er3+. Problemas com a emissão espontânea amplificada (ASE). Diversas configurações de montagem com amplificador óptico de fibra dopada com Er Amplificador óptico de estado sólido (SOA) dispoptic 2013

2 Antes de entrar sobre redes de Bragg, um pequeno parêntese sobre os materiais e o índice de refração. dispoptic 2013

3 Índice de refração negativo
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4 Índice de refração: Valor positivo – Valor negativo?
Positivo Conforme nos ensinaram (regra da mão direita) Negativo Nos dias de hoje (regra da mão esquerda) dispoptic 2013

5 Lembrando conforme nos ensinaram
Lei de refração Para n1 = 1 dispoptic 2013

6 Outras relações Lei de Snell dispoptic 2013

7 Índice de refração negativo
Termos usados Meio Veselago Material duplamente negativo Metamaterial (Meta = Além) Meio de mão esquerda Meio reverso dispoptic 2013

8 O que é? Em geral todo material possui dois parâmetros físicos que o caracterizam: - permitividade e - permeabilidade m Esses dois parâmetros determinam como o material irá interagir com a radiação eletromagnética. Normalmente ambos são positivos, no entanto no caso de índice de refração negativo, ambos são negativos (por isso material duplamente negativo). dispoptic 2013

9 Amfoterismo? - Amfotérico?
Feito de/ou que possui dois componentes Óxidos amfotéricos de Zn, Sn, Al, Be entre outros. E.g. O ZnO reage conforme o pH da solução: ZnO + 2H+ --> Zn2+ + H2O em solução ácida ZnO + H2O + 2OH- --> [Zn(OH)4] em solução básica dispoptic 2013

10 nmaterial = 1 nmaterial > 1 1 > nmaterial > 0
Refração do ar para o material Refractive index below 1 A widespread misconception is that since, according to the theory of relativity, nothing can travel faster than the speed of light in vacuum, the refractive index cannot be lower than 1. This is erroneous since the refractive index measures the phase velocity of light, which does not carry energy or information, the two things limited in propagation speed. The phase velocity is the speed at which the crests of the wave move and can be faster than the speed of light in vacuum, and thereby give a refractive index below 1. This can occur close to resonance frequencies, in plasmas, and for x-rays. In the x-ray regime the refractive indices are lower than but very close to 1 (exceptions close to some resonance frequencies).[4] As an example, water has a refractive index of 1−2.6×10−7 at a photon energy of 30 keV (0.04 nm wavelength).[4] Yes it is possible! In typical media such as glass, air, water, perspex etc, one expects to find a refractive index grater than one. Light travels through the medium by sequential absorption and re-emission by the particles in the media. Think of atoms as passing a photon along like a package in a human chain. It takes time for each atom to absorb and re-emit the photon so the speed of light is slower than in vacuum. The ratio of speed in and out of the media is the refractive index. So in almost all cases the refractive index is grater than one. However there are some cases where the refractive index of a media can be less than one. Plasma - the refractive index of plasma is less than one n(f)= [1-(w/f)^2]^1/2 Where n(f) is the refractive index as a function of the frequency of light which is propagating through the plasma, w = the plasma frequency. Metals - although not transparent at visible frequencies, metal is transparent to IR frequencies, and exhibits an index less than one. This is because there is a more complex mechanism used by the atoms to pass the photon through the medium. In conductors like metal, its very complicated as magnetism and moving electrons in atoms become important. NOTE: It is the phase velocity that becomes faster than the speed of light. The group velocity of light can never exceed the speed light! Information and energy travels with the group velocity and so violation of relativity or Maxwell's equations. Read more: Dielectric constant of a plasma A plasma is very similar to a gaseous medium, expect that the electrons are free: i.e., there is no restoring force due to nearby atomic nuclii. Hence, we can obtain an expression for the dielectric constant of a plasma from Eq. (1149) by setting to zero, and to the number density of electrons, . We obtain (1150) where the characteristic frequency (1151) is called the plasma frequency. We can immediately see that formula (1150) is problematic. For frequencies above the plasma frequency, the dielectric constant of a plasma is less than unity. Hence, the refractive index is also less than unity. This would seem to imply that high frequency electromagnetic waves can propagate through a plasma with a velocity which is greater than the velocity of light in a vacuum. Does this violate the principles of relativity? On the other hand, for frequencies below the plasma frequency, the dielectric constant is negative, which would seem to imply that the refractive index is imaginary. How should we interpret this? Consider an infinite plane-wave, of frequency, , greater than the plasma frequency, propagating through a plasma. Suppose that the wave electric field takes the form (1152) where it is understood that the physical electric field is the real part of the above expression. A peak or trough of the above wave travels at the so-called phase velocity, which is given by (1153) Now, we have also seen that the phase velocity of electromagnetic waves in a dielectric medium is , so (1154) It follows from Eq. (1150) that (1155) in a plasma. The above type of expression, which effectively determines the wave frequency, , as a function of the wave-number, , for the medium in question, is called a dispersion relation (since, amongst other things, it determines how fast wave-pulses disperse in the medium). According to the above dispersion relation, the phase velocity of high frequency waves propagating through a plasma is given by (1156) which is indeed greater than . However, the theory of relativity does not forbid this. What the theory of relativity says is that information cannot travel at a velocity greater than . And the peaks and troughs of an infinite plane-wave, such as (1152), do not carry any information. We now need to consider how we could transmit information through a plasma (or any other dielectric medium) by means of electromagnetic waves. The easiest way would be to send a series of short discrete wave-pulses through the plasma, so that we could encode information in a sort of Morse code. We can build up a wave-pulse from a suitable superposition of infinite plane-waves of different frequencies and wave-lengths: e.g., (1157) where , and is determined from the dispersion relation (1155). Now, it turns out that a relatively short wave-pulse can only be built up from a superposition of plane-waves with a relatively wide range of different values. Hence, for a short wave-pulse, the integrand in the above formula consists of the product of a fairly slowly varying function, , and a rapidly oscillating function, . The latter function is rapidly oscillating because the phase varies very rapidly with , relative to . We expect the net result of integrating the product of a slowly varying function and rapidly oscillating function to be small, since the oscillations will generally average to zero. It follows that the integral (1157) is dominated by those regions of -space for which varies least rapidly with . Hence, the peak of the wave-pulse most likely corresponds to a maximum or minimum of : i.e., (1158) Thus, we infer that the velocity of the wave-pulse (which corresponds to the velocity of the peak) is given by (1159) This velocity is called the group velocity, and is different to the phase velocity in dispersive media, for which is not directly proportional to . (Of course, in a vacuum, , and both the phase and group velocities are equal to .) The upshot of the above discussion is that information (i.e., an individual wave-pulse) travels through a dispersive media at the group velocity, rather than the phase velocity. Hence, relativity demands that the group velocity, rather than the phase velocity, must always be less than . What is the group velocity for high frequency waves propagating through a plasma? Well, differentiation of the dispersion relation (1155) yields (1160) Hence, it follows from Eq. (1156) that (1161) which is less than . We thus conclude that the dispersion relation (1155) is indeed consistent with relativity. Let us now consider the propagation of low frequency electromagnetic waves through a plasma. We can see, from Eqs. (1156) and (1161), that when the wave frequency, , falls below the plasma frequency, , both the phase and group velocities become imaginary. This indicates that the wave attenuates as it propagates. Consider, for instance, a plane-wave of frequency . According to the dispersion relation (1155), the associated wave-number is given by (1162) Hence, the wave electric field takes the form (1163) Indeed, it can be seen that for electromagnetic waves in a plasma take the form of decaying standing waves, rather than traveling waves. We conclude that an electromagnetic wave, of frequency less than the plasma frequency, which is incident on a plasma will not propagate through the plasma. Instead, it will be totally reflected. We can be sure that the incident wave is reflected by the plasma, rather than absorbed, by considering the energy flux of the wave in the plasma. It is easily demonstrated that the energy flux of an electromagnetic wave can be written (1164) For a wave with a real frequency and a complex -vector, the above formula generalizes to (1165) However, according to Eq. (1162), the -vector for a low frequency electromagnetic wave in a plasma is purely imaginary. It follows that the associated energy flux is zero. Hence, any low frequency wave which is incident on the plasma must be totally reflected, since if there were any absorption of the wave energy then there would be a net energy flux into the plasma. The outermost layer of the Earth's atmosphere consists of a partially ionized zone known as the ionosphere. The plasma frequency in the ionosphere is about 1MHz, which lies at the upper end of the medium-wave band of radio frequencies. It follows that low frequency radio signals (i.e., all signals in the long-wave band, and most in the medium-wave band) are reflected off the ionosphere. For this reason, such signals can be detected over the horizon. Indeed, long-wave radio signals reflect multiple times off the ionosphere, with very little loss (they also reflect multiple times off the Earth, which is enough of a conductor to act as a mirror for radio waves), and can consequently be detected all over the world. On the other hand, high frequency radio signals (i.e., all signals in the FM band) pass straight through the ionosphere. For this reason, such signals cannot be detected over the horizon, which accounts for the relatively local coverage of FM radio stations. Note, from Eq. (1151), that the plasma frequency is proportional to the square root of the number density of free electrons. Now, the level of ionization in the ionosphere is maintained by ultra-violet light from the Sun (which effectively knocks electrons out of neutral atoms). Of course, there is no such light at night, and the number density of free electrons in the ionosphere consequently drops as electrons and ions gradually recombine. It follows that the plasma frequency in the ionosphere also drops at night, giving rise to a marked deterioration in the reception of distant medium-wave radio stations. dispoptic 2013 1 > nmaterial > 0 nmaterial < 0

11 Metamaterial dispoptic 2013
A negative−index material will refract light through a negative angle. (a) In this simulation17 of a Snell's law experiment, a negative−index wedge with ε = −1 and μ = −1 deflects an electromagnetic beam by a negative angle relative to the surface normal: The beam emerges on the same side of the surface normal as the incident beam. Color represents intensity: red, highest; blue, lowest. (b) A positive−index wedge, in contrast, will positively refract the same beam. Red lines trace the path of the beams, and the surface normals are shown in black. Experiments confirm this behavior. (c) The deflection angle (horizontal axis) observed for a beam traversing a negative wedge as a function of frequency (vertical axis). (d) The deflection angle observed for a positive−index Teflon® wedge as a function of frequency. In the negative wedge there is strong dispersion with frequency: The condition ε = −1, μ = −1 is realized only over a narrow bandwidth around 12 GHz. dispoptic 2013

12 http://physicsworld.com/cws/article/print/17398 Physics in Action
May 1, 2003 Negative-index materials are now a reality, as a recent experiment at MIT has shown. (a) Light travelling upwards is refracted in the positive direction (right) when it leaves a Teflon wedge. (b) A metamaterial consisting of wires and rings causes light to be refracted in the opposite direction (left) when it exits, thereby demonstrating that it has a negative index of refraction. dispoptic 2013

13 Propagação no meio Mão esquerda Mão direita Outros modelos:
A) Pendrys_P_L_xy.wmv B) Pendrys_Perfect_Lens_3D.wmv dispoptic 2013

14 Metamaterial para microondas
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15 Outros sistemas ressonantes na geração de metamateriais para microondas
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16 Principio de Fermat Principio de Fermat: “A trajetória da luz, ao passar de um ponto para outro, é tal que o tempo do percurso é estacionário em relação a variações na trajetória.” Como abordar o principio de Fermat para o caso de índice de refração negativo? dispoptic 2013

17 dispoptic 2013

18 Forma não-convencional, n<0
Aplicação Forma clássica, n>0 Forma não-convencional, n<0                                                                                                                                         dispoptic 2013

19 Refração negativa - imagem
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20 Aplicações Normal n1 n2 Metamaterial n1 n2 dispoptic 2013

21 Lentes? Limites de observação com luz visível Superlentes Hiperlentes
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22 Superlente - Hiperlente
Conventional, positive-refractive-index lenses create images by capturing the light waves emitted by an object and then bending them. However, objects also emit "evanescent" waves that contain a lot of information at very small scales about the object. These waves are much harder to measure because they decay exponentially and never reach the image plane - a threshold in optics known as the diffraction limit. A drawing of nano-scale imaging using a silver superlens that achieves a resolution beyond the optical diffraction limit. The red line indicates the enhancement of "evanescent" waves as they pass through the superlens. (Image: Cheng Sun, UC Berkeley) HIPERLENTE: Schematic of an optical hyperlens that can magnify and project sub-diffraction-limited objects onto a far-field plane. The objects and the hyperlens are enlarged to show details; they are actually much smaller than a conventional lens. Images courtesy the Zhang Lab, UC Berkeley Scientists at the University of California, Berkeley, have developed a "hyperlens" that brings them one major step closer to the goal of nanoscale optical imaging. The new hyperlens, described in the Feb. 23 issue of the journal Science, is capable of projecting a magnified image of a pair of nanowires spaced 150 nanometers apart onto a plane up to a meter away. Currently, to capture details down to a few nanometers, scientists must use scanning electron or atomic force microscopes, which create images by scanning objects point by point. Scanning electron microscopes can take up to several minutes to get an image. Because the object must remain immobile and in a vacuum during this process, imaging is restricted to non-living samples. dispoptic 2013

23 Defeitos em sólidos, centros de cor e Redes de Bragg
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24 Redes de Bragg - Introdução
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25 Rede de Bragg em fibras ópticas
Materiais fotosensitivos Fundamentos. Ref.: Fiber Bragg grating technology fundamentals and overview, JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 15, NO. 8, AUGUST 1997 Características e propriedades fundamentais Fabricação de redes Aplicações Fiber Bragg Gratings, Raman Kashyap, Academic Press 1999 E-book Fiber Bragg Gratings dispoptic 2013

26 Materiais fotosensitivos
São materiais que mudam suas características físicas induzidas pela luz: Mudam de cor, podem ficar dicroicos ou não Mudam seu índice de refração, podem ficar birrefringentes ou não Podem expandir Podem contrair Podem ter características reversíveis ou irreversíveis Dependência com campos externos Dependência com temperatura Dependência com tempo de exposição Dependência com concentração de impurezas ou centros de defeitos Dependência com a intensidade da fonte causadora do efeito Diferentes tipos de materiais: xstalinos e amorfos Associação com efeitos não-lineares dispoptic 2013

27 Principais usos do material fotosensitivo
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28 Efeito da luz sobre o material: memória óptica, holografia
Variação de índice de refração fotoinduzida: refratividade fotoinduzida Efeito da luz sobre o material: memória óptica, holografia l n2 n1 Applications of photorefractive polymers in dynamic holographic data storage n1 > ou < n2 dispoptic 2013

29 O que pode ocorrer com o meio ao ser iluminado?
Além daqueles fenômenos vistos na interação da radiação com a matéria (ef. Compton, fotoelétrico, etc): Criação de defeitos pontuais Criação de centros de cor Mudanças estruturais fotoinduzidas: reversíveis e permanentes Fotoexpansão Fotocontração Materiais fotorefrativos Materiais fotocrômicos dispoptic 2013

30 Defeitos pontuais, centros
A presença de impurezas ou desarranjo estrutural local, constituem defeitos pontuais ou centros que no conjunto da matriz alteram propriedades físicas (ópticas, mecânicas, elétricas, magnéticas, etc) do material considerado puro. A dopagem de impurezas são consideradas como formadoras de defeitos pontuais ou centros Formação de centros ou defeitos também ocorrem da forma fotoinduzida dispoptic 2013

31 Alguns exemplos de defeitos pontuais
Naturais: existem nas pedras preciosas e semi-preciosas. Os defeitos pontuais são as impurezas Gema Cor Cristal Hospedeiro Impureza Cor s/impureza Rubi vermelho oxido de alumínio (Corundum) (Alumina) cromo transparente Esmeralda verde aluminosilicato de berílio Granada aluminosilicato de cálcio ferro Topázio amarelo fluorosilicato de alumínio Turmalina rosa-vermelho boroaluminosilicato de cálcio e lítio manganês Turquesa azul-verde fosfoaluminato de cobre cobre dispoptic 2013

32 Algumas pedras preciosas (gemas)
Yellow beryl (Heliodor) is colored by the presence of F3+ ions. Beryl includes emerald , aquamarine, and lesser known varieties: goshenite (colorless), morganite (pink), Heliodor (yellow), and bixbite (red). The formula usually given for the beryl group is Be3Al2Si6O18; however, the general formula may be expressed as A2-3B2Si5(Si,Al)O18, where A _ beryllium, magnesium or iron and B _ Aluminium scandium or iron. Red ruby. The name ruby comes from the Latin "Rubrum" meaning red (Al2O3:Cr3+). The ruby is in the Corundum group, along with the sapphire. The brightest red and thus most valuable rubies are usually from Burma. Violet The formula usually given for the beryl group is Be3Al2Si6O18; however, the general formula may be expressed as A2-3B2Si5(Si,Al)O18, where A _ beryllium, magnesium or iron and B _ Aluminium scandium or iron. Green emerald. The mineral is transparent emerald, the green variety of Beryl on calcite matrix (CaCO3). 2.5 x 2.5 cm. Coscuez, Boyacá, Colombia dispoptic 2013

33 2[Be3(Al,Cr)2Si6O18]:Cr3+/V3+
Rubi e esmeralda Al2O3:Cr3+ 2[Be3(Al,Cr)2Si6O18]:Cr3+/V3+ Cr3+ dispoptic 2013

34 1% de Al é substituído por Cr
Corundum(Al2O3), from Eheliyagoda, near Ratnapura, Sri Lanka (3.9 x 2.5 x 1.4 cm). ©Rob Lavinsky (irocks.com), used by permission. Ruby on white marble, from Jegdalik, Sorobi District, Afghanistan (2.1 x 1.4 x 1.3 cm), ©Rob Lavinsky (irocks.com), used by permission. Beryl(Be3Al2Si6O18) on albite, from Shigar Valley, Pakistan (4.9 x 3.7 x 3.2 cm). ©Rob Lavinsky (irocks.com), used by permission. Emerald on white marble, from Panjshir Valley, Afghanistan (2.1 x 1.7 x 1.1 cm). ©Rob Lavinsky (irocks.com), used by permission. dispoptic 2013

35 Espectro de absorção – pq vermelho – pq verde?
Spectra of a ruby from Chanthaburi, Thailand (red) and an emerald from Malyshevo, Ural, Russia (green). Data obtained from the Caltech Mineral Spectroscopy Server. dispoptic 2013

36 Alguns artifícios para “melhorar” a cor das gemas
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37 Como os defeitos se localizam ?
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38 Outra versão sobre defeitos pontuais
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39 Centros de Cor – elétrons em vacâncias negativas
Xstais hospedeiros de halogeneto alcalinos são transparentes, e.g. NaCl Existem vários processos através do qual podem-se obter centros de cor: Excesso de vapor alcalino, conforme figura acima Radiação eletromagnética, UV, raios-X, gama Injeção de elétrons Fonte de neutrons dispoptic 2013

40 Espectros de absorção de centros F
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41 Complexos de centros F M ou F2 R ou F3 Memória óptica? dispoptic 2013

42 Centros de Cor Fluoreto de litio LiF dispoptic 2013

43 Estrutura da fluorita (CaF2) e quartzo – centros F
Fig 3. Fluorite structure (schematic): (A) normal, (B) containing an "F-center" where a fluorine ion has been replaced by an electron. Fig. 4. Quartz structure (schematic): (A) normal, (B) containing Al3+ substituted for Si4+ with an H+ for charge neutrality. Radiation ejects one of a pair of electrons from an O2- and leaves a "hole" color center of smoky quartz. A.- Normal B.- Com centros F. Íon de flúor substituído por um elétron A.- Normal B.- Com centros F. Íon de Si4+ substituído por um Al3+. dispoptic 2013

44 Centro de cor associada a impureza
FA dispoptic 2013

45 Próxima aula continuação
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