Chapter-4 Stimulated emission devices LASERS

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1 Semiconductor Laser Diodes Chapter-4 Stimulated emission devices LASERS The Road Ahead Lasers Basic Principles Applications Gas Lasers Semiconductor Lasers Semiconductor Lasers in Optical Networks Improvement in Basic Design Recent Advances Light Amplification by Stimulated Emission of Radiation Key Terms: Stimulated Emission Metastable State Population Inversion

2 Properties of Lasers Monochromaticity Coherence Beam Divergence High Irradiance Properties vary with type of Lasers: Gas, Solid, Semiconductor Spontaneous and Stimulated Emission An electron in an atom can be excited from an energy level to a higher energy level by absorption photon absorption hν =. hυ 6 Spontaneous and Stimulated Emission Two possibilities of emission (an electron moves/transits down in energy to an unoccupied energy level emits a photon). Spontaneous Induced Spontaneous emission: random direction random photon. Transition for to as if the electron is oscilating with E a frequency ν. 2 hυ Spontaneous and Stimulated Emission Stimulated emission: incoming photon of energy hν = stimulates the whole emission process by inducing the electron at to transit down to. Emitted photon: in phase, same direction, same polarization, same energy with incoming photon two outgoing photons. To obtain stimulated emission the incoming photon should not be absorbed by another atom at. hυ In hυ hυ Out 7 8

3 Spontaneous and Stimulated Emission Although we consider transitions of an electron in an atom, we could have just well described photon absorption, spontaneous and stimulated emission in term of energy transitions of the atom itself in which case and represent the energy levels of the atom. Consider the collection of atoms to amplify light we must have the majority of atoms at the energy level. Otherwise the incoming photon will be absorbed by the atom at. Population inversion: more atoms at than at. In steady state incoming photon will cause as many upward excitations as downward stimulated emissions for only two energy levels we never achieve atom population at greater than. 9 Absorption and Radiation Processes E 4 n 2 ρ 2 n ρ Thermal Equilibrium hν Absorption (Excitation) Random photons hν Spontaneous Emission Coherent photons hν in phase Stimulated Emission Absorption and Radiation Processes (ρ:density of State) E 4 n 2 ρ 2 n ρ Thermal Equilibrium Number of electron at Boltzmann Distribution n = ρ f ( E ) = ρ n2 n ( E2 E) > < ρ2 ρ n2 n If > can be achieved by pumping, ρ2 ρ [ ( E E f )/ kt ] e [ ( E2 E f )/ kt ] Number of electron at n2 = ρ2 f ( E2 ) = ρ2e f f ( E2 ) n2 ρ [ ( E2 E )/ kt ] = = e ( E) n ρ2 n n = e ρ 2 [ ( E2 E )/ kt ] 2 ρ Absorption and Radiation Processes hν in phase Stimulated Emission Coherent photons In phase Same energy Same direction Same polarization kt < (negative temperature: Population inversion)

4 Laser: Basic Principle Lasing Action hυ 32 E 4 E 4 exp(- E/kT) E Population inversion Laser transition hυ 3 Metastable state IN hυ 2 OUT hυ 2 Coherent photons between & Laser action Atoms in the ground state are pumped up to the energy level by incoming photons of energy hν 3 = -. Atoms at rapidly decay to the metastable state at energy level by emitting photons or emitting lattice vibrations; hν 32 = -. As the states at are long-lived, they quickly become populated and there is a population inversion between and. Basic requirement for Lasing action: Metastable state, Population inversion, Optical resonant cavity A random photon (from a spontaneous decay) of energy hν 2 = - can initiate stimulated emission. Photons from this stimulated emission can themselves further stimulate emissions leading to an avalanche of stimulated emissions and coherent photons being emitted. Optical Fiber Amplifier Energy 3 2 Pump Fast Laser Energy 3 2 Pump Fast Laser Fast A light signal travels in long distance will suffer attenuation. It is necessary to regenerate the light signal at certain intervals for long haul communications over several thousand miles. Practical optical amplifier is based on the erbium ion (Er 3+ ) doped fiber amplifier (EDFA). The core region of an optical fiber is doped with Er 3+ or with neodymium ion (Nd 3+ ). The host fiber material is a glass based on SiO 3 -GeO 2 or Al 2 O 3. Easily fused to a single mode long distance optical fiber by technique called splicing. 6

5 Optical Fiber Amplifier Er 3+ has energy level as indicated in the figure. Er 3+ is optically pumped from laser diode to excite them to. The Er 3+ ions decay rapidly from to (longlived) energy level ~ ms. The decay from E3 to E2 involves energy losses by radiationless transition (phonon emission). Energy of the Er 3+ ion in the glass fiber.54 ev.27 ev 98 nm 7 E 3 Non-radiative decay Pump.8 ev 55 nm In 55 nm Out Optical Fiber Amplifier The accumulated Er 3+ ions at leads to a population inversion between and. Signal photons at 55 nm have energy of.8 ev ( ), and give rise to stimulated transitions of Er 3+ ions from to. Meanwhile, any Er 3+ ions left at will absorb in incoming 55 nm photons to reach. Energy of the Er 3+ ion in the glass fiber.54 ev.27 ev 98 nm 8 E 3 Non-radiative decay Pump.8 ev 55 nm In 55 nm Out Optical Fiber Amplifier EDFA: Er-doped Optical Amplifier Energy of the Er 3+ ion in the glass fiber.54 ev.27 ev 98 nm Pump E 3 Non-radiative decay.8 ev 55 nm 55 nm In Energy diagram for the Er 3+ ion in the glass fiber medium and light amplification by stimulated emission from to. Dashed arrows indicate radiationless transitions (energy emission by lattice vibrations) Stimulated emission Out Optical Fiber Amplifier Thus, to achieve light amplification we must have stimulated emission exceeding absorption. Only possible if more Er 3+ ions at (N 2 ) than at (N ). The net optical gain G op G = K op : ( N 2 N) where K is constant which depends on th i Energy of the Er 3+ ion in the glass fiber.54 ev.27 ev 98 nm 2 E 3 Non-radiative decay Pump.8 ev 55 nm In 55 nm Out

6 Optical Fiber Amplifier Signal in Optical isolator Er 3+ -doped fiber ( - 2 m) Wavelength-selective coupler Splice Splice Optical isolator Signal out Laser: Basic Principle = 55 nm = 55 nm Pump laser diode = 98 nm Termination A simplified schematic illustration of an EDFA (optical amplifier). The erbium-ion doped fiber is pumped by feeding the light from a laser pump diode, through a coupler, into the erbium ion doped fiber. Optical oscillators are inserted at the entry and exit to allow ONLY the optical signals at 55 nm to pass in one direction and prevent the 98 pump light from propagating back or forward into the communication system. Energy level,, and are not single unit levels, but rather consists of closely spaced collection of several levels range of stimulated transitions from to ( nm) with 4 nm optical bandwidth wavelength division multiplexed system (WDM) systems. 2 Laser: Basic Principle Longitudinal Modes Laser: Basic Principle Transverse Modes TEM TEM A lot of wavelengths are produced, but only some are amplified. TEM2 TEM3 TEM3

7 Lasers: Gas Lasers He-Ne Lasers Flat mirror (Reflectivity =.999) Very thin tube He-Ne gas mixture Concave mirror (Reflectivity =.985) Laser beam Lasers: Gas Lasers He-Ne Lasers He (s 2s ) 2.6 ev Electron impact Collisions (2p 5 5s ) (2p 5 3p ) 2.66 ev (2p 5 3s ) Ne ~6 nm Collisions with the walls nm Lasing emission Fast spontaneous decay Current regulated HV DC/RF power supply He atom to become excited by collision with drifting electrons (s 2 ) Ground states The principle of operation of the He-Ne laser. He-Ne laser energy levels (for nm emission). (2p 6 ) He-Ne laser energy diagram Lasers: Gas Lasers He-Ne Lasers Electron impact He (s 2s ) 2.6 ev Collisions (s 2 ) Various Lasing Transitions in the He-Ne laser (s 2s ) (2p 5 4s ) nm 9.8 ev 523 nm Ground states (2p 5 5s ) 52 nm (2p 5 3p ) 8 nm (2p 6 ) Ne 3.39 µm Collisions with the walls Lasing emissions nm (2p 5 4p ) Fast spontaneous decay (2p 5 3s ~6 nm ) Overall efficiency = Optical Power Output Electrical Power Input % Typical commercial He-Ne laser characteristics Wavelength (nm) Green Yellow Red Infrared Optical output power (mw) Typical current (ma) Typical voltage Overall efficiency = P out /IV % % % % %

8 Lasers: Gas Lasers Ar + -ion Lasers 5.75 ev Energy 4p levels Pumping 4s Ar + -ion laser energy diagram 72 nm Ar + ion ground state 488. nm 54.5 nm Ar atom ground state Gas Lasers: The He-Ne LASER By using dc or RF high voltage, electrical discharge is obtained within the tube which causes the He atoms to become excited by collisions with the drifting electrons, He + e - He * + e - The excited He atom, He *, cannot spontaneously emit a photon large number of He * atoms build up during the electrical discharge. When He * collides with a Ne atom, it transfers its energy to the Ne atom by resonance energy exchange. He * + Ne He + Ne * A spontaneous emission of a photon from one Ne * atom gives rise to an avalanche of stimulated emission process lasing emission with a wavelength nm in the red. 3 Gas LASER Output Spectrum Doppler effect resulting the broadening of the emitted spectrum output radiation from gas laser covers a spectrum of wavelengths with a central peak. Given the average K.E. of (3/2)kT, radiation freq. υ o (as source frequency), due to Doppler effect, when gas atom is moving away from the observer, the latter detects a lower frequency υ : v υ = x υ o c where v x is the relative velocity of the atom along the laser tube (x-axis) with respect to observer. When atom moving towards the observer, the detected freq υ 2 is higher: v x υ 2 = υ o + c 3 Gas LASER Output Spectrum Since the atoms are in random motion the observer will detect a range of frequencies due to Doppler effect. Resulting the frequency or wavelength of the output radiation from a gas laser will have a linewidth υ = υ 2 υ. It is called Doppler broadened linewidth. Stimulated emission wavelength of lasing medium or optical gain has distribution around o = c/υ o. The full width at half maximum FWHM in the output intensity vs. frequency spectrum is: 2kT ln(2) Optical Gain υ / 2 = 2υ o 2 Mc (a) ο Doppler broadening where M is mass of lasing atom or molecule 32

9 Gas LASER Output Spectrum Let consider an optical cavity of length L with parallel end mirrors (etalon Fabry-Perot optical resonator). Mirror L Stationary EM oscillations Mirror Any standing wave in the cavity must have an integer number of half-wavelengths /2 that fit into the cavity length L, where m is mode number m = L of the standing wave. 2 Cavity mode: each possible standing wave within the cavity (laser tube) which satisfy the above equation. Axial (longitudinal) modes: existing modes along the cavity axis. 33 Gas LASER Output Spectrum The laser output thus has broad spectrum with peaks at certain wavelengths corresponding to various cavity modes existing within the Doppler broadened optical gain. (a) Allowed Oscillations (Cavity Modes) m(/2) = L (b) ο δ m Doppler broadening Mirror (c) L δ m Stationary EM oscillations Mirror The output spectrum is determined by satisfying (a) and (b) simultaneously. 34 Output Spectrum of Laser Optical Gain Optical Gain optical gain curve Doppler broadening Allowed Oscillations (Cavity Modes) L Relative intensity Optical gainbetween FWHM points (a) (b) δ m Cavity modes 5modes 4modes Number of laser modes depends on how the cavity modes intersect the optical gain curve. In this case we are looking at modes within the linewidth /2. Mirror Stationary EM oscillations Mirror δ m m(/2) = L δ m Output Spectrum

10 Fabry-Perot laser spectrum Example: A typical low power 5mW He-Ne laser tube operate at a DC voltage of 2V and carrier a current of 7mA. What is the efficiency of the laser? Solution: Efficiency=output light power/input Electric power =5 x -3 W/(7 x -3 A)(2V) =.36% Note that 5mW over a beam diameter of mm is 6.4kW/m The He-Ne Laser A particular He-Ne laser operating at nm has a tube that is 5 cm long. The operating temperature is 3 C a Estimate the Doppler broadened linewidth ( in the output spectrum. b What are the mode number m values that satisfy the resonant cavity condition? How many modes are therefore allowed? c What is the separation ν m in the frequencies of the modes? What is the mode separation m in wavelength. Solution a The central emission frequency is υo = c/o = (3 8 m s - ) / ( m) = s -. The FWHM width of the frequencies υ/2 observed will be given by Eq. (3) υ / 2 =2υ o 2k Tln(2) B =2( ) 2( )(3+273)ln(2) Mc 2 ( )(3 8 ) 2 =.55 GHz To get FWHM wavelength width /2, differentiate = c/ν d dυ = c 2 υ = υ so that /2 υ/2 /υ = (.55 9 Hz)( m) / ( s - ) or / m or.22 nm. This width is between the half-points of the spectrum.

11 b For = o = nm, the corresponding mode number mo is, mo = 2L / o = (2.5 m) / ( m) = and actual mo has to be the closest integer value to , that is Consider the minimum and maximum wavelengths corresponding to the extremes of the spectrum at the half-power points: min = o 2 = and max = o + 2 = c The frequency separation υm of two consecutive modes is υ m = υ m + υ m = c c c = c = c m + 2L 2L m 2L (m +) m or υ m = c 2L = 3 8 = 3 8 Hz. 2(.5) The wavelength separation of two consecutive modes is m = 2 m 2L = ( ) 2 = m or.44 pm. 2(.5) Note: Linewidth of spectrum Modes = Separation of two modes / pm = m.44 pm = 5.4. Lasers: Laser beam Divergence Output Spectrum of a Gas Laser Laser tube Laser radiation θ L θ The output laser beam has a divergence characterized by the angle 2θ (highly exaggerated in the figure) r=ltanɵ. What is the diameter of the beam at a distance of m, if divergence is mrad? r Optical Gain Optical cavity resonator Laser medium hυ Optical Gain g(υ o ) Reflecting surface R 2 P f E f P i E i Reflecting surface P δx (a) P+δP x υ υ ο (b) g(υ) υ 2 Steady state EM oscillations L R Cavity axis x (a) A laser medium with an optical gain (b) The optical gain curve of the medium. The dashed line is the approximate derivation in the text.

12 (N 2 N ) and P o P o = Lasing output power (N 2 N ) th N 2 N Threshold population inversion Threshold pump rate Pump rate Simplified description of a laser oscillator. (N 2 N ) and coherent output power (P o ) vs. pump rate under continuous wave steady state operation.

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