Chapter 7: Laser Diodes Optical resonators Stimulated emission and photon amplification Optical fiber amplifiers Gas lasers Laser oscillation conditions Laser diodes Vertical cavity surface emitting lasers Optical laser amplifiers PHYS5320 Chapter Seven 1 Optical Resonators When two mirrors are aligned to be perfectly parallel, light wave reflections between the two mirrors lead to interference of the waves within the cavity. The result is a series of stationary or standing EM waves. Since the electric field at the mirrors (metal coated) is zero, only an integer number of half wavelength of the waves can be fit in. c m L m m m f 2 2L m = 1,2,3,… m m1 m f Each particular allowed m for a f is known as the free given m defines a cavity mode. spectral range. PHYS5320 Chapter Seven 2 Optical Resonators Charles Fabry (18671945), left Alfred Perot (18631925), right This simple optical cavity with two mirrors, etalon, serves to store radiation energy only at certain frequencies and it is called a Fabry- Perot optical resonator. The mode peaks become broader as the reflection loss at the mirrors is increased. PHYS5320 Chapter Seven 3 Optical Resonators Consider a wave A traveling to the right. After one round trip this wave will be traveling again towards the right, but now as wave B, and so on. If the two mirrors are identical and have a reflection coefficient of magnitude r, then B has one round-trip phase difference of k(2L) and a magnitude r2 (two reflections) with respect to A. 2 ⋯ exp 2 exp 4 ⋯ 1exp 2 PHYS5320 Chapter Seven 4 Optical Resonators 2 2 2 Let R r Icavity Ecavity I0 A I0 Icavity 1 R 2 4Rsin 2 kL I0 Imax k L m 1 R 2 m The spectral width (full width at half maximum) of the Fabry-Perot etalon of an individual mode intensity can be calculated by R1/ 2 f F m F 1 R F is called the finesse of the resonator. Finesse is the ratio of mode separation (m = f) to spectral width (m). PHYS5320 Chapter Seven 5 Optical Resonators The Fabry-Perot optical cavities are widely used in lasers, interference filters, and spectroscopic applications. For interference filters, mirrors are replaced with plates that are partially reflecting and transmitting. If the incident beam has the wavelength corresponding to one of the cavity modes, it can sustain oscillations in the cavity and lead to a transmitted beam. 1 R 2 I transmitted Iincident 1 R 2 4Rsin 2 kL PHYS5320 Chapter Seven 6 Example: Consider a Fabry-Perot optical cavity of air of length 0.1 mm. The mirrors have a reflectance of 0.9. Calculate the cavity mode nearest to 900 nm, the separation of the modes, and the spectral width of each mode. 2 2 10 2L 2104 222.22 222 900.90nm 910 m m 222 c 3108 1.51012 Hz m f 2L 2104 1/ 2 1/ 2 12 R 0.9 f 1.510 10 F 29.8 5.0310 Hz 1 R 1 0.9 m F 29.8 2 c c 2 900.90109 m 5.031010 0.136nm m 2 m m 8 m m c 310 The above derivation can be extended to a medium with a refractive index n. If the incidence angle at the mirrors is not normal, we can resolve k to be along the cavity length direction. PHYS5320 Chapter Seven 7 Chapter 7: Laser Diodes Optical resonators Stimulated emission and photon amplification Optical fiber amplifiers Gas lasers Laser oscillation conditions Laser diodes Vertical cavity surface emitting lasers Optical laser amplifiers PHYS5320 Chapter Seven 8 Stimulated Emission and Photon Amplification In stimulated emission, the emitted photon is in phase with the incoming photon, it is in the same direction, it has the same polarization, and it has the same energy. Stimulated emission is the basis for obtaining photon amplification since one incoming photon results in two outgoing photons that are in phase with each other. PHYS5320 Chapter Seven 9 Stimulated Emission and Photon Amplification For light amplification to occur, the majority of the atoms must be at the energy level E2, which is called a population inversion. We can never achieve population inversion if there are only two energy levels because in the steady state, incoming photons will cause as many upward excitations as downward stimulated emissions. LASER: Light Amplification by Stimulated Emission of Radiation PHYS5320 Chapter Seven 10 Stimulated Emission Rate and Einstein CoefficientsThe image part with relationship ID rId3 was not found in the file. A useful laser medium must have a higher efficiency of stimulated emission compared with the efficiencies of spontaneous emission and absorption. Consider a medium with N1 atoms per unit volume with energy E1 and N2 atoms per unit volume with energy E2. The upward and downward transition rates will be h E E R12 B12 N1h R21 A21N2 B21N2 h 2 1 B12 is for absorption. A21 is for spontaneous emission. B21 is for stimulated emission. They all known as the Einstein coefficients. (h) is the photon energy density per unit frequency, representing the number of photons per unit volume with an energy h. To find the Einstein coefficients, we consider the medium in thermal equilibrium. There is no net change in the populations at E1 and E2. N E E 2 exp 2 1 R12 R21 N1 kBT PHYS5320 Chapter Seven 11 Stimulated Emission Rate and Einstein Coefficients In thermal equilibrium, (h) is given by Planck’s black body radiation distribution law: 8h 3 h h c3exp 1 kBT R12 R21 N1 N2 B12h A21 B21h B h E E 12 exp 2 1 A21 B21h kBT 3 3 A 8h / c h 21 E2 E1 / kBT h / kBT B12e B21 e 1 PHYS5320 Chapter Seven 12 Stimulated Emission Rate and Einstein Coefficients We obtain from the equation on the previous slide: 3 3 B12 B21 A21 / B21 8h / c Consider the ratio of stimulated emission to spontaneous emission and the ratio of stimulated emission to absorption: 3 R stim B h c R21stim N2 21 21 h 3 R absorp N R21spon A21 8h 12 1 There are two important conclusions. For stimulated emission to exceed photon absorption, we need to achieve population inversion. For stimulated emission to far exceed spontaneous emission, we must have a large photon concentration, which is achieved by building an optical cavity to contain the photons. The population inversion means that we depart from thermal equilibrium. The laser principle is based on non-thermal equilibrium. PHYS5320 Chapter Seven 13 Chapter 7: Laser Diodes Optical resonators Stimulated emission and photon amplification Optical fiber amplifiers Gas lasers Laser oscillation conditions Laser diodes Vertical cavity surface emitting lasers Optical laser amplifiers PHYS5320 Chapter Seven 14 Optical Fiber Amplifiers A light signal traveling along an optical fiber over a long distance suffers attenuation. It is necessary to regenerate the light signal at certain intervals for long haul communications (>1000 km). Instead of regenerating the signal by photodetection, conversion to an electrical signal, amplification, and then conversion back from electrical to light energy by a laser diode, it is more practical to amplify the signal directly by using an optical amplifier. One practical amplifier is erbium ion (Er3+) doped fiber amplifier (EDFA). PHYS5320 Chapter Seven 15 Optical Fiber Amplifiers The erbium doped fiber is inserted into the fiber communication line by splicing. It is pumped from a laser diode through a wavelength-selective coupler that allows only the pumping wavelength to be coupled. In the absence of the pumping light, erbium ions will absorb 1550-nm photons and act as an attenuator. The optical isolators inserted at the entry and exit end allow only the optical signals at 1550 nm to pass in one direction and prevent the 980 nm pumping light from the propagation into the communication system. PHYS5320 Chapter Seven 16 Chapter 7: Laser Diodes Optical resonators Stimulated emission and photon amplification Optical fiber amplifiers Gas lasers Laser oscillation conditions Laser diodes Vertical cavity surface emitting lasers Optical laser amplifiers PHYS5320 Chapter Seven 17 Gas Lasers: the He‐Ne Laser The HeNe laser consists of a gaseous mixture of He and Ne atoms in a gas discharge tube. An optical cavity is formed by end mirrors so that reflection of photons back into the lasing medium builds up the photon concentration in the cavity. By using dc or RF high voltage, electrical discharge obtained within the tube causes the He atoms to become excited by collisions with drifting electrons. PHYS5320 Chapter Seven 18 Gas Lasers: the He‐Ne Laser electron impact PHYS5320 Chapter Seven 19 Gas Lasers: the He‐Ne Laser The molar ratio of He to Ne in He-Ne lasers is typically 5 to 1 with a pressure of several torrs. The lasing emission intensity increases with the tube length since more Ne atoms are then used in stimulated emission. The intensity decreases as the tube diameter is increased because Ne atoms in the 2p53s1 state can return to the ground state only by collisions with the walls of the tube. Brewster windows are typically used at the ends of the tube to allow only polarized light to be transmitted and amplified within the cavity so that the output radiation is polarized. PHYS5320 Chapter Seven 20 The Doppler Broadening Effect The output radiation from a gas laser covers a spectrum of wavelengths with a central peak. One mechanism causing the line broadening is the Doppler effect. According to the kinetic molecular theory, gas atoms are in random motion with an average kinetic energy of (3/2)kBT.