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Resumo aula anterior Conectores, acopladores e adaptadores tanto para comunicações qto tb para outros propósitos. Interruptores ópticos 20110523.

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Apresentação em tema: "Resumo aula anterior Conectores, acopladores e adaptadores tanto para comunicações qto tb para outros propósitos. Interruptores ópticos 20110523."— Transcrição da apresentação:

1 Resumo aula anterior Conectores, acopladores e adaptadores tanto para comunicações qto tb para outros propósitos. Interruptores ópticos

2 Tarefas? Design and Simulation of Planar Electro-optic Switches in Ferroelectrics M. Krishnamurthi, L. Tian and V. Gopalan, Appl. Phys. Lett., (2008). PDF ou PDF2 Interruptor de 60ns: NanonaTM High Speed & Low Loss Optical Switch Semiconductor optical switches reach the speed of light April 29, 2011 Ctistis, G., Yuce, E., Hartsuiker, A., Claudon, J., Bazin, M., Gérard, J., & Vos, W. (2011). Ultimate fast optical switching of a planar microcavity in the telecom wavelength range Applied Physics Letters, 98 (16) DOI: / switch a light beam within a semiconductor device at speeds of 0.3 picosecond 2 Tarefa: como detectar?

3 Light Cloak http://news.bbc.co.uk/2/hi/science/nature/7553061.stm
Page last updated at 00:53 GMT, Monday, 11 August :53 UK Invisibility cloak 'step closer' Invisibility Cloak One Step Closer: New Metamaterials Bend Light Backwards Invisibility Cloak for Almost-Visible Light

4 A última sobre light cloak
Presentation QTuG5 "Three-dimensional invisibility carpet cloak at 700 nm wavelength," by Joachim Fischer et al. is at 11 a.m. Tuesday, May 3. Fischer et al. will also present CML1, "Three-Dimensional Laser Lithography with Conceptually Diffraction-Unlimited Lateral and Axial Resolution," at 10:15 a.m. Monday, May 2. Appearing in CLEO: QELS - Fundamental Science category was a paper demonstrating a full 3-D invisibility cloak in visible light by a research team from the Karlsruhe Institute of Technology in Germany. Ainda não publicado extensivamente

5 AMPLIFICADOR ÓPTICO O QUE É PARA QUE É QUE TIPOS HÁ

6 Exemplo de comunicação óptica

7 Antigamente Tradicionais repetidores eletrônicos

8 Objetivos dos amplificadores

9 Parte das perdas são atribuídas a diferentes tipos de acoplamentos Lembremos

10 Eficiência de Acoplamento Sensitividade ao desalinhamento transversal
SMF núcleo SMF núcleo ∆x SMF ωo = 5.15µm ωo = 25µm η(∆x) = e –(∆x/ωo)2

11 Eficiência de acoplamento Sensitividade de desalinhamento angular
SMF núcleo Ө SMF ωo = 5.15µm ωo = 25µm η(Ө) = e -(ΠӨωo/λ)2 Modo expandido melhora a sensitividade de desalinhamento transversal, mas aumenta a sensitividade angular. Modo limitado pelas dimensões da fibra -> bom compromisso Expanded mode improves transverse mis-alignment sensitivity, but increases angular sensitivity Mode size constrained by fiber dimensions  good compromise Low loss mode size converter from 0.3 µm square Si wire waveguides to singlemode fibres Electronics Letters -- 5 December Volume 38, Issue 25, p T. Shoji,1 T. Tsuchizawa,1 T. Watanabe,1 K. Yamada,1 and H. Morita1 1NTT Corporation, NTT Telecommunications Energy Laboratories, Kanagawa Pref., Japan (Received 24 June 2002) A novel integrated mode size converter for single-mode Si wire waveguides is presented. The mode size converter is constructed with two-dimensional tapered Si waveguides and overlaid high-index polymer waveguides. We calculated the proposed mode size converter characteristics, and fabricated 1.09 mm length Si wire waveguides with the converters. The measured loss of the mode size converter was 0.8 dB per conversion, and the total insertion loss through the sample with an Si wire waveguide was 3.5 dB.

12 Eficiência de acoplamento
Sensitividade por desalinhamento longitudinal SMF núcleo SMF núcleo ∆z η(z) = 1/(1+λz/(1+ Πz/2ωo2)2 For “large” ∆z lensing is required SMF ωo = 5.15µm ωo = 25µm SMF ωo = 5.15µm ωo = 25µm

13 Pq há necessidade de um amplificador óptico?
Atenuação do sinal. De onde vem a atenuação do sinal? São várias as razões: longa distância, acoplamento entre outras. Qual a vantagem de ter um amplificador óptico? Principalmente amplificar um sinal óptico sem necessidade de converte-lo antes em elétrico.

14 Outros tipos de sistemas para acoplamento da luz com fibra para minimizar perdas

15 Lente no feixe O feixe Gaussiano pode ser caracterizado por sua fase e amplitude em qualquer ponto do feixe Para um acoplamento “perfeito” tanto a fase e amplitude devem estar casadas Componente óptico Gaussian beam can be characterized by a phase and amplitude at any point For “perfect” coupling both phase and amplitude must be matched

16 Lentes no feixe Aplicações Componentes passivos isoladores filtros
splitters circuladores WDM alguns são dispositivos com mais de 2 portas lasers receptores moduladores Projeção de feixe Solda a laser apontadores Componentes ópticos entre fibras Isolator Laser Passive components isolators filters splitters circulators WDMs… some are > 2 port devices Active components lasers receivers modulators Beam projection laser welding free-space pointing Tela

17 O que há em usar lentes discretas
Duram bastante tempo Alta performance Oferece desenho de dispositivos mais flexíveis Relativamente barato Continua a ser ”bons amigos” na industria MAS… A colocação de componentes adicionais, e.g., lentes reduce a robustes e confiabilidade aumento de custos de manipulação Maioria das lentes discretas são grandes em relação às fibras Aumento no tamanho das embalagens Aumento no tamanho do modo – OK para algumas aplicações mas não para outras WRT fibers With Respect To fibers

18 R - Radial Distance (au)
Graded-Index Lens GRIN lens very popular - high quality & cylindrical shape But, large and expensive Typical n(r) - Square Law R - Radial Distance (au) n(R) -Refractive Index (au) a R a GRIN Lens Fiber GRIN Lens

19 Imagem com sistema Fibra/Lente Grin
SM Fiber L=1/4 Pitch L > ¼ Pitch Graded Index MMF

20 Fibra-lente Fused “Collimated” Beam SMF Core (SMF) ¼ Pitch MMF Lens
Core (MMF) Fused “Collimated” Beam ¼ Pitch SMF Core (SMF) A graded index multi-mode fiber also has a square-law refractive index, thus is a small GRIN lens Fusing the appropriate length MMF to a SMF provides a lensed fiber in unitary structure

21 Fibras-Lentes Fundidas
Vantagens Podem ser fundidas em fibras Elimina a sensitividade do desalinhamento transversal de fibras SM Casamento de índice na interface – minimiza reflexões e perdas Tendo o mesmo diâmetro SMFsimplificação de desenho e empacotamento Custo da lente ~”zero” Oferece um bom compromisso entre sensitividades transversal e angular Altamente flexível: da expansão de modo simples para sistemas de focamento Podem ser fundidas em fibras Eliminates SM transverse mis-alignment sensitivity Index match at interface – minimizing reflections & loss Has same diameter as SMFdesign and packaging simplicity Lens cost is ~”zero” Provides a good compromise between transverse sensitivity and angular sensitivity Highly flexible: from simple mode expansion to focusing systems

22 Montagem da fibra-lente fundida Processos críticos
Core/core alignment Fiber eccentricity Core concentricity Reproducible fusion process Interface diameter control Bulging/necking Dopant diffusion control Means to polish endface Final length control Apex control Determination of beam parameters vs endface contour Relationship of endface contour and optical performance MMF SMF Fiber lens choice: Eccentricity Centricity of core Fusion compatability Uniformity & Flexibility) Accurate & reproducible lens length Post fusion After final polish 3. Fiber Lens Endface 2. Fiber Lens 1. Fiber/Lens Fused Interface

23 Outra opção de Fibra-Lente
The insertion of a silica “fiber section” between the SMF and the MMF lens adds additional flexibility to fiber-lens applications Silica Section SMF Core (SMF) MMF Lens Core (MMF)

24 Lembrem-se mais uma aquela da lente esférica formato de bola na frente da fibra

25 Acoplamento fibra-esfera/fibra-fibra
Understanding Ball Lenses Ball lenses are great optical components for improving signal coupling between fibers, emitters and detectors. They are also used in endoscopy, bar code scanning, ball pre-forms for aspheric lenses and sensor applications. Ball lenses are manufactured from a single substrate of glass and can focus or collimate light, depending upon the geometry of the input source. Half-ball lenses are also common and can be interchanged with (full) ball lenses if the physical constraints of an application require a more compact design. Essential Equations for Using Ball Lenses Figure 1: Key Parameters There are five key parameters needed to understand and use ball lenses (Figure 1): Diameter of Input Source (d), Diameter of Ball Lens (D), Effective Focal Length of Ball Lens (EFL), Back Focal Length of Ball Lens (BFL) and Index of Refraction of Ball Lens (n). EFL is very simple to calculate (Equation 1) since there are only two variables involved: Diameter of Ball Lens (D) and Index of Refraction (n). EFL is measured from the center of the ball lens, indicated by R in Figure 1. BFL (Equation 2) is easily calculated once EFL and D are known. Numerical Aperture NA (Equation 3) is dependent on EFL and d. It is a commonly referenced term and often used in lieu of d/D. (1) (2) (3) Since NA is often used, Figure 2 illustrates how it increases as the Diameter of the Input Source (d) also increases. Figure 2: Numerical Aperture vs. Diameter for Ball Lens Glass Types offered by Edmund Optics®. Application Examples Figure 3: Laser to Fiber Coupling Example 1: Laser to Fiber Coupling When coupling light from a laser into a fiber optic, the choice of ball lens is dependent on the NA of the fiber and the diameter of the laser beam, or the input source. The diameter of the laser beam is used to determine the NA of the ball lens. The NA of the ball lens must be less than or equal to the NA of the fiber optic in order to couple all of the light. The ball lens in contact with the fiber as shown in Figure 3. Initial Parameters Diameter of Input Laser Beam = 2mm Index of Refraction of Ball Lens = Numerical Aperture of Fiber Optic = 0.22 Calculated Parameter Diameter of Ball Lens (4) A N-BK7 ball lens (index of refraction of 1.517) of 6-8mm in diameter would be ideal for coupling a 2mm laser source into a 0.22NA fiber optic. One can easily try different indices of refraction in order to find the best ball lens for a laser to fiber coupling application. Figure 4: Fiber to Fiber Coupling Example 2: Fiber to Fiber Coupling To couple light from one fiber optic to another fiber optic of similar NA, two identical ball lenses are used. Place the two ball lenses in contact with the fibers as shown in Figure 4. If the fiber optics have the same NA, then the same logic as in Example 1 can be applied. Related Products

26 Amplificadores Ópticos

27 Diferentes tipos de Amplificadores Ópticos
Semicondutor (SOA) (= Semiconductor Optical Amplifier) SOA convencional GC-SOA (Gain-Clamped SOA) LOA (Linear Optical Amplifier) Fibra Óptica (FOA) Fibras dopadas com Terras Raras Erbium-Doped Fiber Amplifiers (EDFA) : C, L-Band Thulium-Doped Fiber Amplifiers (TDFA) : S-Band Praseodymium-Doped Fiber Amplifiers (PDFA) : O-Band Banda l(nm) Banda C (conventional) Banda L (long) Banda S (short) Conversosr de frequência  comprimento de onda

28 Conversosr de frequência  comprimento de onda http://www. ee. byu
Equation: f * λ = c where: f = frequency in Hertz (Hz = 1/sec) λ = wavelength in meters (m) c = the speed of light and is approximately equal to 3*108 m/s Frequency / Wavelength Calculator If you want to convert wavelength to frequency enter the wavelength in microns (μm) and press "Calculate f". The corresponding frequency will be in the "frequency" field in GHz. OR enter the frequency in gigahertz (GHz) and press "Calculate λ" if you want to convert to wavelength. Wavelength will be in μm. Wavelength: (λ) [μm] Frequency: (f) [GHz] **see nomograph below

29 http://www. teleco. com. br/tutoriais/tutorialdwdm/pagina_4
desde ha um tempo

30 Mapa atualizado (2011?) Do livro Advances in Optical Amplifiers, Edited by Paul Urquhart, 2011

31 Hoje TX representa o transmissor do sinal
Amplificadores a diodo laser Amplificadores a fibra dopada (Er, operam em 1,55m m ). O Amplificador Óptico a Fibra Dopada com Érbio (AFDE) pode funcionar como amplificador de potência para aumentar o nível do sinal de saída do transmissor; posicionado na entrada do receptor, como pré-amplificador, para aumentar a sensitividade na recepção; ou como repetidor ou amplificador de linha para amplificar o sinal já atenuado ao longo do enlace óptico. TX representa o transmissor do sinal RX representa o receptor do sinal, SMF representa a Fibra Monomodo Padrão (Standard Monomode Fibers) sendo o meio de transmissão, AFDE que representa o Amplificador a Fibra Dopada com Érbio.

32 Diagrama de blocos de um repetidor regenerativo
Uma das grandes vantagens dos amplificadores ópticos está no fato de um único amplificador poder substituir todo o complexo circuito que compõe um repetidor regenerativo. CAG representa o Controlador de Aumento e Ganho do repetidor regenerativo A conseqüência imediata é o aumento da velocidade de transmissão. Outro ponto importante é que esses amplificadores são transparentes à taxa de bits e pode-se aumentar a taxa de transmissão, por exemplo: de 155Mbps para 622Mbps, sem que seja necessário alterar o sistema de amplificação.

33 Componentes de um EDFA ou AFDE
laser semicondutor de bombeamento, operando em uma das bandas de absorção do Érbio, 980nm ou 1480nm por um acoplador que opera com multiplexação por divisão de comprimento de onda (WDM), cuja função é acoplar em uma mesma fibra a potência óptica do laser de bombeamento e o sinal óptico a ser amplificado um trecho limitado de fibra dopada com érbio (FDE), responsável pelo processo de amplificação.

34 Diagrama de níveis de energia do Er3+

35 Tipos de emissão: Estimulada e espontânea

36 Como opera o EDFA Um EDFA consiste de uma extensão curta de fibra(~ 10m) dopada com uma pequena quantidade controlada de Er3+. Os íons de Er3+ tem vários estados de energia (meta-estados). Quando o Er está num estado excitado, um fóton de luz poderá estimular para que ceda algo de sua energia na forma de luz voltando para um estado de menor energia mais estável. A medida que o sinal de entrada está sendo alimentado no sistema, um laser diodo gera um sinal de bombeio (10 a 200 mW)(l = 980nm ou 1480nm) de tal forma que os íons de Er absorverão os fótons indo para estados excitados.

37 Princípios do Amplificador Óptico 1
ERBIUM ELECTRONS IN FUNDAMENTAL STATE PUMP PHOTON 980 nm PUMP PHOTON 980 nm ENERGY ABSORPTION ERBIUM ELECTRONS IN EXCITED STATE IN FUNDAMENTAL STATE

38 Princípios do Amplificador Óptico 2
PUMP PHOTON 980 nm TRANSITION METASTABLE STATE EXCITED STATE FUNDAMENTAL STATE NR

39 Princípios do Amplificador Óptico 3
PUMP PHOTON 980 nm TRANSITION METASTABLE STATE SIGNAL PHOTON 1550 nm STIMULATED PHOTON FUNDAMENTAL STATE EXCITED STATE

40 Perfil do Ganho do Amplificador Óptico
ASE = Amplified Spontaneous Emission

41 ASE = Amplified Spontaneous Emission
O que é ASE Efeitos da ASE sobre sistemas em cascata Como atenuar a ASE Aplicações positivas da ASE

42 Amplificador Óptico: Amplificação de Multi-Comprimentos de Onda

43 Configurações de montagens de EDFA
OI = Optical Isolator WSC = Wavelength Selective Coupler (a) Bombeamento co-propagado – baixo ruído baixa potência de saída (b) Bombeamento contra-propagado – maior potência de saída mas maior ruído (c)Bombeamento dual

44 Melhor bombear com 980nm ou 1480nm?
Baixo ASE, amplificador de ruído bx Com 1480nm Laser de bombeio maior Maior potência de saída Não tão eficiente Grau de inversão de população é menor

45 Quais fontes de laser para bombear?

46 Outro exemplo GFF = Gain-Flattening Filters

47 Em sistemas de transmissão usamos unidades de potência em dB. Assim........

48 DECIBEL (dB)– num sistema de transmissão
Potência de Entrada = Pin Potência de Saída = Pout Transmissão do Sistema : Exemplos: -10dB é Pout = Pin/10 -40dB é Pout = Pin10-4 Transmissão em dB: dBm é a Potência em dB relativo a 1mW Exemplos: -10dBm é P = 0,1W +40dB é P = 10W

49 Ganho do EDFA O ganho do EDFA depende do comprimento da fibra. O ganho começa a decrescer após certo comprimento devido a que o bombeio não tem potência suficiente para criar a inversão de população. Assim a região não bombeada absorve o sinal Gmax = exp(rsL) s é a seção transversal da emissão do sinal r é a concentração de Er L é o comprimento do amplificador de fibra

50 Ganho e ruído nas configurações anteriores

51 Emissão Espontânea Amplificada (ASE)
A fonte dominante de ruído num amplificador óptico é a Emissão Espontânea Amplificada (ASE) Alguns dos íons de Er excitados decaem para o estado fundamental com emissão espontânea antes que tenha tempo de se encontrar com um fóton do sinal de entrada. Assim o fóton é emitido com a fase randômica e direção Uma fração muito pequena dos fótons emitidos ocorrerão na mesma direção da fibra e confinados

52 Potência de saída vs comprimento de onda
ASE = Amplified Spontaneous Emission Amplificação entre 1.53 e 1.56 mm.

53 Largura de banda de ganho de amplificadores ópticos

54 Uma das formas para atenuar ASE

55 Referências Fiber-Optic Communication Systems, Govind Agrawal, 2nd Edition, 1997. Erbium-Doped Fiber Amplifiers: Fundamentals and Technology, P.C. Becker, 1999. Fiber Optic Test and Measurement, D. Dercikson, 1998 Optical Fiber Amplifiers: Materials, Devices and Applications, Sudo Shoichi, 1997. Rare-Earth-Doped Fiber Lasers and Amplifiers, Michel J. F. Digonnet, 2001. Semiconductor Optical Amplifier, Michael J. Connelly, 2002. Advances in Optical Amplifiers, Edited by Paul Urquhart, 2011.

56 Notação de alguns AO de fibra
EDFA (do Inglês: Erbium Doped Fibre Amplifier ) EYDFA ( do Inglês: Erbium Ytterbium Doped Fibre Amplifier ) PDFFA (do Inglês: Praseodymium Doped Fluoride Fibre Amplifier ) TDFFA (do Inglês: Thulium Doped Fluoride Fibre Amplifier ) RA (do Inglês: Raman Amplifier ) Híbridos

57 Notação de alguns AO de guia de onda planar – OWGA – Optical WaveGuide Amplifier
EDWA (do Inglês: Erbium Doped Waveguide Amplifier ) SOA (do Inglês: Semiconductor Optical Amplifier ) LOA (do Inglês: Linear Optical Amplifier ) TIA (do Inglês: Transimpedance Integrated Amplifier )

58 SOA Uma corrente elétrica passa através do dispositivo, com a finalidade de excitar elétrons na região ativa. Quando os fótons se propagam através da região ativa pode fazer com que alguns destes elétrons percam energia na forma de fótons que coincidam com os comprimentos de onda daqueles incidentes. Assim o sinal que passa através da região ativa é amplificada e dizemos que houve ganho. Silicon or semiconductor fiber optic amplifiers (SOA) function in a similar way to a basic laser. The structure is much the same, with two specially designed slabs of semiconductor material on top of each other, with another material in between them forming the 'active layer.’ An electrical current is set running through the device in order to excite electrons which can then fall back to the non-excited ground state and give out photons.  Incoming optical signal stimulates emission of light at its own wavelength.  SOA can be classified into two groups, Fabry-Perot Amplifiers (FPA) and Traveling Wave Amplifiers (TWA).  The difference is the reflectivity coefficient value of both mirror surfaces.

59 Dispositivo

60 Optical Amplifiers: Internal Design
Optical amplification is a key DWDM enabling technology Amplifiers use wavelength band separation (bands : BLUE, RED, IR) to minimize gain tilt Optimized multi-stage amplifier design 1st stage optimized for low noise figure 2nd stage optimized for high output power

61 Multiestágios de AO PUMP Input Output Signal 1st Active Stage
Er3+ Doped Fiber Optical Isolator 1st Active Stage Co-pumped 2nd Active Stage Counter-pumped Nf 1st/2nd stage = Pin - SNRo [dB] - 10 Log (hc2 / 3) Nftotal = Nf1+Nf2/G1

62 Referências

63 Distributed Raman Amplifier (DRA)
DRA está baseado sobre espalhamento Raman. Um bombeamento maior é co-lançado num comprimento de onda menor daquele do sinal a ser amplificado.

64 Espectroscopia Raman Basic theory
The Raman effect occurs when light impinges upon a molecule and interacts with the electron cloud of the bonds of that molecule. The amount of deformation of the electron cloud is the polarizability of the molecule. The amount of the polarizability of the bond will determine the intensity and frequency of the Raman shift. The photon (light quantum), excites one of the electrons into a virtual state. When the photon is released the molecule relaxes back into vibrational energy state. The molecule will typically relax into the first vibration energy states, and this generated Stokes Raman scattering. If the molecule was already in an elevated vibrational energy state, the Raman scattering is then called Anti-Stokes Raman scattering.

65 Complementação sobre AO
ERBIUM-DOPED PLANAR OPTICAL AMPLIFIERS A. Polman Publicado em: Proc. 10th European Conference on Integrated Optics (ECIO) Paderborn, Germany, April , 2001, p. 75 (2001)

66 Transferência de energia Er - Eu
0.19at.%Er 0.19at.%Er, 0.44at%Eu We present an investigation of Er3+ photoluminescence in Y2O3 waveguides codoped with Eu3+. As a function of europium concentration we observe an increase in decay rate of the erbium 4I11/2 energy level and an increase of the ratio of photoluminescence emission from the 4I13/2 and 4I11/2 states. Using a rate equation model, we show that this is due to an energy transfer from the 4I11/2 to 4I13/2 transition in erbium to europium. This increases the branching ratio of the 4I11/2 state towards the 4I13/2 state and results in a higher steady state population of the first excited state of erbium. Absolute intensity enhancement of the 4I13/2 emission is obtained for europium concentrations between 0.1 and 0.3 at. %. In addition, the photoluminescence due to upconversion processes originating from the 4I11/2 state is reduced. Using such state-selective energy transfer the efficiency of erbium doped waveguide amplifiers can be increased. False color image of the green emission of Er31 with and without europium. The green emission from the Er31 4S3/2 state is represented in black. 980 nm light is coupled into the planar waveguide from a fiber ~left hand side of the images!. In the presence of 0.44 at. % europium, the green upconversion emission is reduced considerably. 4I11/2=> 4I15/2 = 980nm 4I13/2=>4I15/2 = 1540nm J. Appl. Phys., Vol. 88, No. 8, 15 October 2000

67 Níveis de energia do Er3+

68 Transferência de energia de QD de Si e Er

69

70 Outros detalhes sobre EDFA

71 Fim sobre AO

72 Diversas formas e/ou dispositivos para realizar acoplamentos de multiplexagem

73 Multiplexagem em WDM

74 Acopladores

75 Acopladores

76 Acopladores

77 Acoplador baseado em micro-óptica

78 Acoplador bicônico e derivados
Razão de Divisão de Potência:

79 Acoplador com fibras deslocadas lateralmente

80 Acoplador com núcleo sobreposto

81 Acoplador com núcleo sobreposto

82 Acoplador com divisor de feixe

83 Acoplador em X

84 Acoplador em Z

85 Defeitos em sólidos, centros de cor e Redes de Bragg
Próxima aula Defeitos em sólidos, centros de cor e Redes de Bragg

86 DECIBEL (dB)– num sistema de transmissão
Potência de Entrada = Pin Potência de Saída = Pout Transmissão do Sistema : Exemplos: -10dB é Pout = Pin/10 -40dB é Pout = Pin10-4 Transmissão em dB: dBm é a Potência em dB relativo a 1mW Exemplos: -10dBm é P = 0,1W +40dB é P = 10W

87 Modos numa fibra Fig.: Electric field contour lines for all the guided modes of a fiber with a top-hat refractive index profile (→ step index fiber). The two colors indicate different signs of electric field values. The lowest-order mode (l = 1, m = 0, called LP01 mode) has an intensity profile which is similar to that of a Gaussian beam. In general, light launched into a multimode fiber will excite a superposition of different modes, which can have a rather complicated shape. Fiber Modes – Single-Mode vs. Multimode Fibers A fiber can support one or several (sometimes even many) propagation modes the intensity distributions of which are located at or immediately around the fiber core, although some of the intensity may propagate within the fiber cladding. Other modes are not restricted to the core region and all called cladding modes. The power in these is usually lost after some distance of propagation, but can in some cases propagate over longer distances. Outside the cladding, there is typically a protective polymer coating, which gives the fiber improved mechanical strength and protection against moisture, and also determines the losses for cladding modes. An important distinction is that between single-mode and multimode fibers: Single-mode fibers usually have a relatively small core (with a diameter of only a few micrometers) and can guide only a single spatial mode (disregarding the fact that there are two different polarization directions), the profile of which in most cases has roughly a Gaussian shape. Changing the launch conditions only affects the launched power, while the spatial distribution of the light exiting the fiber is fixed. Efficiently launching light into a single-mode fiber usually requires a laser source with good beam quality and precise alignment of the focusing optics in order to achieve mode matching. There are actually also large mode area fibers with single-mode guidance, where the alignment tolerances are lower in terms of position but higher in terms of angle (which is less of a problem). Multimode fibers usually have a larger core and/or a larger index difference between core and cladding, so that they support multiple modes with different intensity distributions (see the figure below). In this case, the spatial profile of light exiting the fiber core may depend on the launch conditions, which determine the distribution of power among the spatial modes. Long-range optical fiber communications systems usually use single-mode fibers, because the different group velocities of different modes would mess up the data at high data rates; for shorter distances, however, multimode fibers are more convenient as the demands on light sources and component alignment are lower. Therefore, local area networks (LANs), except those for highest bandwidth, normally use multimode fiber. Single-mode fibers are also normally used for fiber lasers and amplifiers. Multimode fibers are often used e.g. for the transport of light from a laser source to the place where it is needed, particularly when the light source has a poor beam quality and/or the high optical power requires a large mode area. Different modes of a fiber can be coupled via various effects, e.g. by bending, or often by irregularities in the refractive index profile. These may be unwanted or purposely introduced, e.g. as fiber Bragg gratings. Waveguide theory shows that an important factor for the coupling between different fiber modes is the difference of their wavenumbers, which for efficient coupling has to match the wavenumber of a coupling disturbance. Main Parameters The design of a step-index fiber can be characterized with only two parameters, e.g. the core radius a and the refractive index difference Δn between core and cladding. Typical values of the core radius are a few microns for single-mode fibers and tens of microns or more for multimode fibers. Instead of the refractive index difference, one usually uses the numerical aperture, defined as which is the sine of the maximum acceptable angle of an incident beam with respect to the fiber axis (considering the launch from air into the core in a ray-optic picture). The NA also basically quantifies the strength of guidance. Typical values are of the order of 0.1 for single-mode fibers, even though actual values vary in a relatively large range. For example, large mode area single-mode fibers can have low numerical apertures below 0.05, while some rare-earth doped fibers have values of 0.3 and higher for a high gain efficiency. NA values around 0.3 are typical for multimode fibers. The sensitivity of a fiber to bend losses strongly diminishes with increasing NA, which causes strong confinement of the mode field to the core. Another frequently used parameter is the V number which is a kind of normalized frequency. Single-mode guidance is achieved when the V number is below about Multimode fibers often have huge V values.

88 Fiber Modes – Single-Mode vs. Multimode Fibers
A fiber can support one or several (sometimes even many) propagation modes the intensity distributions of which are located at or immediately around the fiber core, although some of the intensity may propagate within the fiber cladding. Other modes are not restricted to the core region and all called cladding modes. The power in these is usually lost after some distance of propagation, but can in some cases propagate over longer distances. Outside the cladding, there is typically a protective polymer coating, which gives the fiber improved mechanical strength and protection against moisture, and also determines the losses for cladding modes. An important distinction is that between single-mode and multimode fibers: Single-mode fibers usually have a relatively small core (with a diameter of only a few micrometers) and can guide only a single spatial mode (disregarding the fact that there are two different polarization directions), the profile of which in most cases has roughly a Gaussian shape. Changing the launch conditions only affects the launched power, while the spatial distribution of the light exiting the fiber is fixed. Efficiently launching light into a single-mode fiber usually requires a laser source with good beam quality and precise alignment of the focusing optics in order to achieve mode matching. There are actually also large mode area fibers with single-mode guidance, where the alignment tolerances are lower in terms of position but higher in terms of angle (which is less of a problem). Multimode fibers usually have a larger core and/or a larger index difference between core and cladding, so that they support multiple modes with different intensity distributions (see the figure below). In this case, the spatial profile of light exiting the fiber core may depend on the launch conditions, which determine the distribution of power among the spatial modes.

89 Fig.: Electric field contour lines for all the guided modes of a fiber with a top-hat refractive index profile (→ step index fiber). The two colors indicate different signs of electric field values. The lowest-order mode (l = 1, m = 0, called LP01 mode) has an intensity profile which is similar to that of a Gaussian beam. In general, light launched into a multimode fiber will excite a superposition of different modes, which can have a rather complicated shape. Long-range optical fiber communications systems usually use single-mode fibers, because the different group velocities of different modes would mess up the data at high data rates; for shorter distances, however, multimode fibers are more convenient as the demands on light sources and component alignment are lower. Therefore, local area networks (LANs), except those for highest bandwidth, normally use multimode fiber. Single-mode fibers are also normally used for fiber lasers and amplifiers. Multimode fibers are often used e.g. for the transport of light from a laser source to the place where it is needed, particularly when the light source has a poor beam quality and/or the high optical power requires a large mode area. Different modes of a fiber can be coupled via various effects, e.g. by bending, or often by irregularities in the refractive index profile. These may be unwanted or purposely introduced, e.g. as fiber Bragg gratings. Waveguide theory shows that an important factor for the coupling between different fiber modes is the difference of their wavenumbers, which for efficient coupling has to match the wavenumber of a coupling disturbance. Main Parameters The design of a step-index fiber can be characterized with only two parameters, e.g. the core radius a and the refractive index difference Δn between core and cladding. Typical values of the core radius are a few microns for single-mode fibers and tens of microns or more for multimode fibers. Instead of the refractive index difference, one usually uses the numerical aperture, defined as                      which is the sine of the maximum acceptable angle of an incident beam with respect to the fiber axis (considering the launch from air into the core in a ray-optic picture). The NA also basically quantifies the strength of guidance. Typical values are of the order of 0.1 for single-mode fibers, even though actual values vary in a relatively large range. For example, large mode area single-mode fibers can have low numerical apertures below 0.05, while some rare-earth doped fibers have values of 0.3 and higher for a high gain efficiency. NA values around 0.3 are typical for multimode fibers. The sensitivity of a fiber to bend losses strongly diminishes with increasing NA, which causes strong confinement of the mode field to the core. Another frequently used parameter is the V number                                    which is a kind of normalized frequency. Single-mode guidance is achieved when the V number is below about Multimode fibers often have huge V values.


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