Slide 1

1Resumo aula anteriorConectores, acopladores e adaptadores tanto para comunicaes qto tb para outros propsitos.Interruptores pticos20110523Tarefas?2Design and Simulation of Planar Electro-optic Switches in FerroelectricsM. Krishnamurthi, L. Tian and V. Gopalan, Appl. Phys. Lett., 93 052912 (2008). PDF ou PDF22

switch a light beam within a semiconductor device at speeds of 0.3 picosecondSemiconductor optical switches reach the speed oflightApril 29, 2011Ctistis, G., Yuce, E., Hartsuiker, A., Claudon, J., Bazin, M., Grard, J., & Vos, W. (2011). Ultimate fast optical switching of a planar microcavity in the telecom wavelength range Applied Physics Letters, 98 (16) DOI: 10.1063/1.3580615 Tarefa: como detectar?Interruptor de 60ns: NanonaTM High Speed & Low Loss Optical Switch 3Light Cloakhttp://news.bbc.co.uk/2/hi/science/nature/7553061.stmPage last updated at 00:53 GMT, Monday, 11 August 2008 01:53 UKInvisibility cloak 'step closer' http://www.sciencedaily.com/releases/2008/08/080811092450.htmInvisibility Cloak One Step Closer: New Metamaterials Bend Light Backwardshttp://www.newsguide.us/education/science/Invisibility-Cloak-for-Almost-Visible-Light/Invisibility Cloak for Almost-Visible Light

A ltima sobre light cloak4

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 no publicado extensivamente5AMPLIFICADOR PTICOO QUE PARA QUE QUE TIPOS H6Exemplo de comunicao ptica

7Antigamente Tradicionais repetidores eletrnicos

8Objetivos dos amplificadores

9Parte das perdas so atribudas a diferentes tipos de acoplamentosLembremos10SMFncleoSMFncleoxEficincia de AcoplamentoSensitividade ao desalinhamento transversal(x) = e (x/o)2

SMFo = 5.15mSMFo = 25mwww.worldtechconsultants.com 1011SMFncleoSMFncleo Eficincia de acoplamentoSensitividade de desalinhamento angular() = e -(o/)2 Modo expandido melhora a sensitividade de desalinhamento transversal, mas aumenta a sensitividade angular. Modo limitado pelas dimenses da fibra -> bom compromisso

SMFo = 5.15mSMFo = 25m11Expanded mode improves transverse mis-alignment sensitivity, but increases angular sensitivityMode size constrained by fiber dimensions good compromiseLow loss mode size converter from 0.3m square Si wire waveguides to singlemode fibresElectronics Letters -- 5 December 2002 -- Volume 38, Issue 25, p. 1669-1670 T. Shoji,1 T. Tsuchizawa,1 T. Watanabe,1 K. Yamada,1 and H. Morita11NTT 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 1.09mm length Si wire waveguides with the converters. The measured loss of the mode size converter was 0.8dB per conversion, and the total insertion loss through the sample with an Si wire waveguide was 3.5dB.12SMFncleoSMFncleo z(z) = 1/(1+z/(1+ z/2o2)2 Eficincia de acoplamentoSensitividade por desalinhamento longitudinalFor large z lensing is required

SMFo = 5.15mSMFo = 25m

SMFo = 5.15mSMFo = 25m1213Pq h necessidade de um amplificador ptico?Atenuao do sinal.De onde vem a atenuao do sinal?So vrias as razes: longa distncia, acoplamento entre outras.Principalmente amplificar um sinal ptico sem necessidade de converte-lo antes em eltrico.Qual a vantagem de ter um amplificador ptico?14Outros tipos de sistemas para acoplamento da luz com fibra para minimizar perdas15 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 Lente no feixeComponenteptico15 Gaussian beam can be characterized by a phase and amplitude at any point

For perfect coupling both phase and amplitude must be matched 16Lentes no feixeAplicaes Componentes passivos isoladores filtros splitters circuladores WDM alguns so dispositivos com mais de 2 portas lasers receptores moduladores Projeo de feixe Solda a laser apontadores Componentes pticos entre fibrasLaser IsolatorTela16Passive components isolators filters splitters circulators WDMs some are > 2 port devices Active components lasers receivers modulators Beam projection laser welding free-space pointing

17O que h em usar lentes discretas Duram bastante tempoAlta performanceOferece desenho de dispositivos mais flexveisRelativamente baratoContinua a ser bons amigos na industria A colocao de componentes adicionais, e.g., lentes reduce a robustes e confiabilidade aumento de custos de manipulao Maioria das lentes discretas so grandes em relao s fibras Aumento no tamanho das embalagens Aumento no tamanho do modo OK para algumas aplicaes mas no para outrasMAS17WRT fibers With Respect To fibers18Graded-Index Lens

FiberGRIN LensTypical n(r) - Square Law R - Radial Distance (au)0n(R) -Refractive Index (au)aa GRIN lens very popular - high quality & cylindrical shape But, large and expensiveRaGRIN Lens1819Imagem com sistema Fibra/Lente Grin

L > PitchSM Fiber

L=1/4 Pitch

Graded Index MMF1920Fibra-lente SMFCore (SMF)MMF LensCore (MMF)FusedCollimated Beam Pitch20A graded index multi-mode fiber also has a square-law refractive index, thus is a small GRIN lensFusing the appropriate length MMF to a SMF provides a lensed fiber in unitary structure21 Podem ser fundidas em fibras Elimina a sensitividade do desalinhamento transversal de fibras SM Casamento de ndice na interface minimiza reflexes e perdas

Tendo o mesmo dimetro SMFsimplificao de desenho e empacotamento Custo da lente ~zero

Oferece um bom compromisso entre sensitividades transversal e angular

Altamente flexvel: da expanso de modo simples para sistemas de focamento Fibras-Lentes FundidasVantagens 21Podem ser fundidas em fibras Eliminates SM transverse mis-alignment sensitivity Index match at interface minimizing reflections & loss

Has same diameter as SMFdesign 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

22Montagem da fibra-lente fundidaProcessos crticos1. Fiber/Lens Fused Interface2. Fiber Lens3. Fiber Lens EndfaceMMFSMF Core/core alignment Fiber eccentricity Core concentricity Reproducible fusion process Interface diameter control Fiber eccentricity Bulging/necking Dopant diffusion control Fiber lens choice: Eccentricity Centricity of core Fusion compatability Uniformity & Flexibility) Accurate & reproducible lens length Post fusion After final polish Means to polish endface Final length control Apex control Determination of beam parameters vs endface contour Relationship of endface contour and optical performance23Outra opo de Fibra-LenteThe insertion of a silica fiber section between the SMF and the MMF lens adds additional flexibility to fiber-lens applications

SilicaSection SMFCore (SMF)MMF LensCore (MMF)2324Lembrem-se mais uma aquela da lente esfrica formato de bola na frente da fibraAcoplamento fibra-esfera/fibra-fibra25

http://www.edmundoptics.com/technical-support/optics/understanding-ball-lenses/?&viewall

Understanding Ball LensesBall 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 ParametersThere 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 CouplingExample 1: Laser to Fiber CouplingWhen 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 ParametersDiameter of Input Laser Beam = 2mmIndex of Refraction of Ball Lens = 1.517Numerical Aperture of Fiber Optic = 0.22Calculated ParameterDiameter 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 CouplingTo 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

2526Amplificadores pticos27Diferentes tipos de Amplificadores pticosSemicondutor (SOA) (= Semiconductor Optical Amplifier)SOA convencional GC-SOA (Gain-Clamped SOA)LOA (Linear Optical Amplifier)

Fibra ptica (FOA)Fibras dopadas com Terras RarasErbium-Doped Fiber Amplifiers (EDFA) : C, L-BandThulium-Doped Fiber Amplifiers (TDFA) : S-BandPraseodymium-Doped Fiber Amplifiers (PDFA) : O-BandBandal(nm)Banda C (conventional)1525 - 1565 Banda L (long)1570 - 1610 Banda S (short)1450 - 1490 Conversosr de frequncia comprimento de onda http://www.ee.byu.edu/photonics/fwnomograph.phtml 2728Conversosr de frequncia comprimento de onda http://www.ee.byu.edu/photonics/fwnomograph.phtmlEquation: f * = c

where: f = frequency in Hertz (Hz = 1/sec) = wavelength in meters (m) c = the speed of light and is approximately equal to 3*108 m/s Frequency / Wavelength CalculatorIf you want to convert wavelength to frequency enter the wavelength in microns (m) 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 " if you want to convert to wavelength. Wavelength will be in m. Wavelength: ()[m] Frequency: (f)[GHz] **see nomograph below29http://www.teleco.com.br/tutoriais/tutorialdwdm/pagina_4.asp desde ha um tempo

Mapa atualizado (2011?)30

Do livro Advances in Optical Amplifiers, Edited by Paul Urquhart, 20113031Hoje Amplificadores a diodo laser Amplificadores a fibra dopada (Er, operam em 1,55m m ). O Amplificador ptico a Fibra Dopada com rbio (AFDE) pode funcionar como amplificador de potncia para aumentar o nvel do sinal de sada do transmissor; posicionado na entrada do receptor, como pr-amplificador, para aumentar a sensitividade na recepo; ou como repetidor ou amplificador de linha para amplificar o sinal j atenuado ao longo do enlace ptico.

TX representa o transmissor do sinal RX representa o receptor do sinal, SMF representa a Fibra Monomodo Padro (Standard Monomode Fibers) sendo o meio de transmisso, AFDE que representa o Amplificador a Fibra Dopada com rbio. 32Diagrama de blocos de um repetidor regenerativoUma das grandes vantagens dos amplificadores pticos est no fato de um nico amplificador poder substituir todo o complexo circuito que compe um repetidor regenerativo.CAG representa o Controlador de Aumento e Ganho do repetidor regenerativo

A conseqncia imediata o aumento da velocidade de transmisso. Outro ponto importante que esses amplificadores so transparentes taxa de bits e pode-se aumentar a taxa de transmisso, por exemplo: de 155Mbps para 622Mbps, sem que seja necessrio alterar o sistema de amplificao. 33Componentes de um EDFA ou AFDElaser semicondutor de bombeamento, operando em uma das bandas de absoro do rbio, 980nm ou 1480nmpor um acoplador que opera com multiplexao por diviso de comprimento de onda (WDM), cuja funo acoplar em uma mesma fibra a potncia ptica do laser de bombeamento e o sinal ptico a ser amplificado um trecho limitado de fibra dopada com rbio (FDE), responsvel pelo processo de amplificao.

34

Diagrama de nveis de energia do Er3+

35Tipos de emisso: Estimulada e espontnea

36Como opera o EDFAUm EDFA consiste de uma extenso curta de fibra(~ 10m) dopada com uma pequena quantidade controlada de Er3+.Os ons de Er3+ tem vrios estados de energia (meta-estados). Quando o Er est num estado excitado, um fton de luz poder estimular para que ceda algo de sua energia na forma de luz voltando para um estado de menor energia mais estvel. A medida que o sinal de entrada est 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 ons de Er absorvero os ftons indo para estados excitados.37ERBIUM ELECTRONSIN FUNDAMENTAL STATEPUMP PHOTON980 nmPrincpios do Amplificador ptico 1PUMP PHOTON980 nmENERGY ABSORPTIONERBIUM ELECTRONSIN EXCITED STATEERBIUM ELECTRONSIN FUNDAMENTAL STATE3738Princpios do Amplificador ptico 2PUMP PHOTON980 nmTRANSITIONMETASTABLE STATEEXCITEDSTATEFUNDAMENTAL STATE

NR39Princpios do Amplificador ptico 3PUMP PHOTON 980 nmTRANSITIONMETASTABLE STATE SIGNAL PHOTON 1550 nmSTIMULATEDPHOTON1550 nmFUNDAMENTAL STATEFUNDAMENTAL STATEEXCITEDSTATE3940Perfil do Ganho do Amplificador ptico

ASE = Amplified Spontaneous Emission41ASE = Amplified Spontaneous EmissionO que ASEEfeitos da ASE sobre sistemas em cascataComo atenuar a ASEAplicaes positivas da ASE42Amplificador ptico:Amplificao de Multi-Comprimentos de Onda

4243Configuraes de montagens de EDFA

(b) Bombeamento contra-propagado maior potncia de sada mas maior rudo(a) Bombeamento co-propagado baixo rudo baixa potncia de sada(c)Bombeamento dualOI = Optical IsolatorWSC = Wavelength Selective CouplerMelhor bombear com 980nm ou 1480nm?44

Com 980nmBaixo ASE, amplificador de rudo bxCom 1480nmLaser de bombeio maiorMaior potncia de sadaNo to eficienteGrau de inverso de populao menorQuais fontes de laser para bombear?45

46Outro exemplo

http://www.furukawa.co.jp/review/fr020/fr20_05.pdf GFF = Gain-Flattening FiltersEm sistemas de transmisso usamos unidades de potncia em dB. Assim........4748DECIBEL (dB) num sistema de transmissoSistemaPotncia de Sada = PoutPotncia de Entrada = PinTransmisso do Sistema :

Transmisso em dB:

Exemplos: -10dB Pout = Pin/10-40dB Pout = Pin10-4dBm a Potncia em dB relativo a 1mW

Exemplos: -10dBm P = 0,1W+40dB P = 10W49Ganho do EDFA

O ganho do EDFA depende do comprimento da fibra. O ganho comea a decrescer aps certo comprimento devido a que o bombeio no tem potncia suficiente para criar a inverso de populao. Assim a regio no bombeada absorve o sinalGmax = exp(rsL)s a seo transversal da emisso do sinalr a concentrao de Er L o comprimento do amplificador de fibra50Ganho e rudo nas configuraes anteriores

51Emisso Espontnea Amplificada (ASE)A fonte dominante de rudo num amplificador ptico a Emisso Espontnea Amplificada (ASE)Alguns dos ons de Er excitados decaem para o estado fundamental com emisso espontnea antes que tenha tempo de se encontrar com um fton do sinal de entrada. Assim o fton emitido com a fase randmica e direoUma frao muito pequena dos ftons emitidos ocorrero na mesma direo da fibra e confinados

52Potncia de sada vs comprimento de onda

Amplificao entre 1.53 e 1.56 mm.52ASE = Amplified Spontaneous Emission

53Largura de banda de ganho de amplificadores pticos

5354Uma das formas para atenuar ASE

55RefernciasFiber-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, 1998Optical 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.

56Notao de alguns AO de fibraEDFA (do Ingls: Erbium Doped Fibre Amplifier )EYDFA ( do Ingls: Erbium Ytterbium Doped Fibre Amplifier )PDFFA (do Ingls: Praseodymium Doped Fluoride Fibre Amplifier )TDFFA (do Ingls: Thulium Doped Fluoride Fibre Amplifier )RA (do Ingls: Raman Amplifier )Hbridos 57Notao de alguns AO de guia de onda planar OWGA Optical WaveGuide AmplifierEDWA (do Ingls: Erbium Doped Waveguide Amplifier )SOA (do Ingls: Semiconductor Optical Amplifier )LOA (do Ingls: Linear Optical Amplifier )TIA (do Ingls: Transimpedance Integrated Amplifier ) 58SOA

Uma corrente eltrica passa atravs do dispositivo, com a finalidade de excitar eltrons na regio ativa.Quando os ftons se propagam atravs da regio ativa pode fazer com que alguns destes eltrons percam energia na forma de ftons que coincidam com os comprimentos de onda daqueles incidentes.Assim o sinal que passa atravs da regio ativa amplificada e dizemos que houve ganho.58Silicon 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. 59Dispositivo

60Optical Amplifiers:Internal DesignOptical amplification is a key DWDM enabling technologyAmplifiers use wavelength band separation (bands : BLUE, RED, IR) to minimize gain tiltOptimized multi-stage amplifier design 1st stage optimized for low noise figure 2nd stage optimized for high output power61Multiestgios de AONftotal = Nf1+Nf2/G1Nf 1st/2nd stage = Pin - SNRo [dB] - 10 Log (hc2 / 3)PUMPPUMPInputSignalOutputSignalEr3+ Doped FiberOpticalIsolatorOpticalIsolatorOpticalIsolator1st Active StageCo-pumped2nd Active StageCounter-pumpedEr3+ Doped Fiber62Referncias http://www.pad.lsi.usp.br/ipt-redes-2k3/aula10/cisco/cavanaugh1.ppthttp://www.light.utoronto.ca/vmehta/ase.pdf63Distributed Raman Amplifier (DRA)DRA est baseado sobre espalhamento Raman.Um bombeamento maior co-lanado num comprimento de onda menor daquele do sinal a ser amplificado.

64Espectroscopia Raman

64Basic theoryThe 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.65Complementao sobre AOERBIUM-DOPED PLANAR OPTICAL AMPLIFIERS A. Polman Publicado em: Proc. 10th European Conference on Integrated Optics (ECIO) Paderborn, Germany, April , 2001, p. 75 (2001)

66Transferncia de energia Er - Euhttp://kik.creol.ucf.edu/publications.html

4I11/2=> 4I15/2 = 980nm

4I13/2=>4I15/2 = 1540nm0.19at.%Er0.19at.%Er, 0.44at%EuJ. Appl. Phys., Vol. 88, No. 8, 15 October 200066We 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 withouteuropium. The green emission from the Er31 4S3/2 state is represented inblack. 980 nm light is coupled into the planar waveguide from a fiber ~lefthand side of the images!. In the presence of 0.44 at. % europium, the greenupconversion emission is reduced considerably.

67Nveis de energia do Er3+

68Transferncia de energia de QD de Si e Er

69

70Outros detalhes sobre EDFA

71Fim sobre AO72Diversas formas e/ou dispositivos para realizar acoplamentos de multiplexagem73Multiplexagem em WDM

74Acopladores

75Acopladores

76Acopladores

77Acoplador baseado em micro-ptica

78Acoplador bicnico e derivados

Razo de Diviso de Potncia:79Acoplador com fibras deslocadas lateralmente

80Acoplador com ncleo sobreposto

81Acoplador com ncleo sobreposto

82Acoplador com divisor de feixe

83Acoplador em X

84Acoplador em Z

85Prxima aulaDefeitos em slidos, centros de cor e Redesde Bragg86DECIBEL (dB) num sistema de transmissoSistemaPotncia de Sada = PoutPotncia de Entrada = PinTransmisso do Sistema :

Transmisso em dB:

Exemplos: -10dB Pout = Pin/10-40dB Pout = Pin10-4dBm a Potncia em dB relativo a 1mW

Exemplos: -10dBm P = 0,1W+40dB P = 10W87Modos numa fibra

87Fig.: 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 FibersA 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 ParametersThe design of a step-index fiber can be characterized with only two parameters, e.g. the core radius a and the refractive index difference n 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 2.405. Multimode fibers often have huge V values.88Fiber Modes Single-Mode vs. Multimode FibersA 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.

89Fig.: 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 ParametersThe design of a step-index fiber can be characterized with only two parameters, e.g. the core radius a and the refractive index difference n 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 2.405. Multimode fibers often have huge V values.