Fiber lasers. 1 Introduction. 2 Optical bers. Rui Miguel Cordeiro (F141104) April 13, 2015

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Fiber lasers Rui Miguel Cordeiro (F141104) April 13, 2015 1 Introduction Fiber lasers are, by denition, lasers in which the gain media is an optical ber.

1 Fiber lasers Rui Miguel Cordeiro (F141104) April 13, Introduction Fiber lasers are, by denition, lasers in which the gain media is an optical ber. Sometimes, laser devices in which the output is transmitted and then transported through optical ber are also called ber lasers. In this work, we will study lasers in which the gain media is an optical ber, and in particular the Erbium-doped ber amplier (EDFA). 2 Optical bers An optical ber is a ber, usually made of some kind of glass, the most commonly used being silica (SiO2, silicon dioxide), which is fairly exible and can be very long, up to hundreds of kilometres. An optical ber can be used to propagate light through very long distances, and silica is generally used because it has extremely low propagation losses and very high mechanical resistance to pulling and bending. Optical bers are constituted by two main components, the core and the cladding. It also has a third component, a jacket (usually a polymer jacket) for protection of the ber. The core has a bigger refractive index than the cladding. This allows the light to propagate only through the core, using total reection, provided that the incident angle on the core-cladding interface is small enough. The index of refraction may vary along the core and the cladding. The simplest case is that of a step-index ber, where the refractive index is constant within the core and within the cladding. The dierence between the core and cladding refractive indices determines the numerical aperture of the ber NA = 1 n n 2 core n 2 cladding (1) The NA is typically small, so it happens that optical bers only accept small angles of propagation. This waveguiding, combined with low propagation losses, makes it possible that optical intensity can be maintained over long lengths of ber. Optical ber, displaying core and cladding (in lighter grey) 1

2 3 Fiber lasers- The EDFA When talking about ber lasers, the gain medium is a ber doped with rare earth ions such as erbium (Er3+), neodymium (Nd3+), ytterbium (Yb3+), thulium (Tm3+), or praseodymium (Pr3+). Normally the pump laser is one or several ber-coupled diode lasers. There is a plethora of dierent ber lasers. So, for this work, i will concentrate on one type, the Erbium-doped ber amplier (EDFA), in widespread use nowadays in optical telecommunication systems. Erbium-doped ber ampliers (EDFAs) are suited for today's communication technology, since the radiative transition of the Erbium ions (Er3+) at 1535 nm is exactly where the spectral region of lowest loss (0.2dB/km) is in silica ber. Furthermore, the Er ions absorb strongly at 980 nm, where compact semiconductor lasers with reasonable output powers are available. They are constituted by a pump laser, to optically pump the ions, an isolator (to stop backward waves from propagating) a coupler (to join the signal and the pump laser to the ber), a doped ber, and optionally a lter at the output (we could also put a lens there, for other purposes). Erbium doped ber amplier 4 Broadening There are two essential types of broadening: homogeneous and inhomogeneous. In this case, the two most important homogeneous broadening eects are natural broadening (lifetime associated Lorentzianshaped) and phonon broadening (by collisions with phonons, also Lorentzian-shaped). For the inhomogeneous broadening, we have Stark eect. Stark eect is a broadening of the spectral lines caused by an external electric eld. As the electric eld inside the ber is dierent from point to point, Erbium ions in dierent points will experience dierent broadening of their emission. In fact, this eect is so important that we can consider Erbium ions in glass to be pre-dominantly inhomogeneously broadened. 5 Energy scheme As we can see, the relevant transitions are between 4I 11/2, 4I 13/2 and 4I 15/2. The energy level scheme shows us that this is a 3 level system, in which we can optically pump atoms using a 980 nm pump laser to the 4I 11/2 level, wait for it to decay to 4I 13/2 and then stimulate emission from 4I 13/2 to 4I 15/2 (wavelenght around 1550 nm). It is also possible to use in-band pumping to the higher levels of the 4I 13/2 manifold, using radiation around 1480 nm. It will decay to the lower level of the 4I 13/2 manifold and can be lased again. 2

Erbium trivalent ion energy scheme Erbium trivalent ion pumping scheme 6 Cross section The gain coecient is given by Nσ g, being N the total population density and σ g the gain cross section

3 Erbium trivalent ion energy scheme Erbium trivalent ion pumping scheme 6 Cross section The gain coecient is given by Nσ g, being N the total population density and σ g the gain cross section (dependent of the wavelenght of the incoming radiation). However, there is also an absorption cross section Nσ a that also plays a role in modifying the total gain coecient. These two curves overlap, giving a more complex behaviour for the EDFA, particularly the fact that gain in certain wavelenghts (longer wavelenghts) will be dependent of the pumping rate. We can dene the net cross section by σ net = N 2 N σ g(λ) N 1 N σ a(λ) (2) in which N 1, N 2 are respectively the population densities of the ground and excited level. We obtain the following curves: The net gain coecient is given by Nσ net. For small signals, i.e, signals that have negligible inuence in the excited state population, a small signal gain formula can be derived: φ(na) 2 P p G[dB] 4.3 (3) 2π(2.4) 2 νhν p This formula is valid for a four lever laser, however, for small pump radiation intensity, it is also valid for a three level system like the one we're analysing. Here, ν is the FWHM of the gain cross section of the laser, P p is the pump power absorbed and φ is the fraction of the net pumping rate that reaches the upper level. Various assumptions were made for this formula, including V<2.4 (single transverse mode), mode area for both signals equal to the core area πa 2 and gain cross section in the area of interest approximated to half the maximum value. This formula implies that we can get high signal intensities (high output power) with small pump 3

4 a b Net gain in the EDFA - a: Wavelenght dependence of gain and absorption cross sections section for dierent values of excitation ratio N 2 N b: Net cross power, for instance approximately 10 Db per mw of pump power, which can be explained by the extremely small cross sectional area of the core (of the order of m 2 ). 7 Modes For linearly polarized (LP) modes, i.e, modes that propagate with very small eld components in the z-direction (the direction that accompanies the lenght of the ber), Gloge showed that the electric elds in the core and cladding are respectively: E core = E l J l (Ur/a) J l (U) E cladding = E l K l (W r/a) K l (W ) cos(lφ) (4) cos(lφ) (5) in which a is the core radius, J l and K l are respectively, Bessel functions of the rst kind and order l and the modied Bessel function of order l. E l is the transverse electric eld at the interface. W and U are respectively U = a n 2 1 k2 0 k2 z (6) W = a kz 2 n 2 2 k2 0 (7) V is dened by V = k 0 a n 2 1 n2 2 = k 0a(NA) (8) V is obviously dened in terms of W and U by V 2 = U 2 + W 2. V is an important quantity, since it determines the number of modes that can propagate within the ber. The boundary conditions impose that E most be continuous at the core-cladding interface. For some l, there are various ways to assure continuity, and each one imposes that J l has a specic number of zeros. Therefore, the modes not only depend on l, but also on the number of zeros of J l, which is translated by the parameter m. Therefor, we call the modes LP lm. The cut-o occurs when k z equals the wave number of the signal in the cladding, n 2 k 0, when the mode stops being guided only by the core. This implies W=0, which translates into the general cut-o condition J l 1 (V ) = 0. The LP 01 mode always propagates, and we nd out that V>2.405 is necessary for the propagation of the next mode, LP 11. Other values of V allow other modes. A ber with V<2.405 is a single mode ber, while for V>2.405 is a multimode ber. Multimode bers 4

$have the inconvenient of intermodal dispersion, although even single-mode bers are aected by dispersion, since the group velocity is a function of the refractive index, which is a function of$

5 have the inconvenient of intermodal dispersion, although even single-mode bers are aected by dispersion, since the group velocity is a function of the refractive index, which is a function of wavelenght. Some transverse modes 8 Saturation intensity Saturation intensity for a given laser gain medium is the optical intensity of an input required to reduce the gain to half of the gain that a small signal would have. For ideal 3 level systems, the saturation intensity is given by: I s ω l σ 21 τ 2 (9) In which σ 21 is the transition cross section and τ 2 is the radiactive lifetime of the upper level. However, this works, for homogeneously broadened lasers (in the right approximation, τ 1 τ 2 ). In this case, the laser is extremely inhomogenously broadened, as we previously discussed. However, it is still possible to discuss the evolution of beam intensity in an inhomogenously broadened laser amplier. The equation 1 di I dz = α I I s(0) (10) in which α 0 is the total gain experienced by the probe beam, and I s (0) is the saturation intensity for ω=ω 0, implies that, for I<<I s (0) I(z) I(0) exp (α 0 z) (11) which is an exponential gain on distance. For I>>I s (0), we get, instead 1 I(z) I(0) + I(0)α0 z (12) 2 which is a quadratical increase with distance, much dierent from the previous behaviour. 9 Recent experiment The EDFA is important mostly for its use in telecommunications today. However, it can still be used, and is used, for scientic purposes. For instance, the EDFA is used as a femtosecond pulsed laser for infrared spectroscopy. 5

6 10 References eperalta/academics/304_lab5.pdf Fundamentals of Fiber Lasers and Fiber Ampliers - Valerii (Vartan) Ter-Mikirtychev Laser Physics - Hooker, Simon ; Webb, Colin 6

Tentative Schedule: Date, Place & Time Topics Sep.4 (Mo) No classes Labor Day Holiday Exam 1 Exam 2 Over Chapters 4-6

Tentative Schedule: Date, Place & Time Topics 1 Aug. 28 (Mo) 394; 5:00-6:15 Introduction, Spontaneous and Stimulated Transitions (Ch. 1) Lecture Notes 2 Aug. 30 (We) 394; 5:00-6:15 Spontaneous and Stimulated