Laserphysik. Prof. Yong Lei & Dr. Yang Xu. Fachgebiet Angewandte Nanophysik, Institut für Physik

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1 Laserphysik Prof. Yong Lei & Dr. Yang Xu Fachgebiet Angewandte Nanophysik, Institut für Physik Contact: Office: Heisenbergbau V 202, Unterpörlitzer Straße 38 (Tel: 3748) Meitnerbau , Gustav-Kirchhoff-Straße 5 (Tel: 4902)

2 Definition of the laser Light Amplification by Stimulated Emission of Radiation A laser is a device that amplifies light and produces a high directional, high-intensity beam, that often has a very pure frequency or wavelength. Size: from one tenth of the diameter of a human hair, to the size of a very large building Power: 10-9 to W Wavelength: from microwave ( Hz) to the soft-x-ray spectral regions ( Hz)

3 A laser 1,000,000 times as bright! 3 mm 1 m Radiating Amplifying medium/ gain medium Concentrating A normal light would normally radiate from a source in all directions concentrating - light into a beam travelling in a single direction

4 Spontaneous emission - radiative decay of excited states of isolated atoms Atom radiates electromagnetic energy when an excited electron jumps from an upper energy level (u) to a lower energy level (l), emitting a photon of frequency ν ul and wavelength λ ul corresponding to the energy difference ΔE ul between the two levels such that ΔE ul = hν ul = hc/ λ ul. N u : population density in level u (number per unit volume) A ul : radiative transition (decay) rate or transition probability (1/lifetime, reciprocal of lifetime) τ u : lifetime of electron at level u Radiative transition between levels u and l with its associated transition rate A ul.

5 Decay frequency: Decay wavelength (c: velocity of light in vacuum) If a photon is emitted in a medium such as a gas, the measured wavelength would be shifted to a value of η: index of refraction of a medium, so the velocity ν of the photon would be reduced to For all gas-medium lasers in this course, the index of refraction is near 1, and thus the wavelength shift is very slight. But for high-density medium lasers, this shall be considered. The radiative decay from level u to level l is referred as spontaneous emission, since it is a natural process without any external stimulus.

6 Change of the population density N u A ul (1/time): radiative transition rate Considering life time When t = τ u, N u has decayed to 1/e of its original value. τ u is referred to as the lifetime of level u.

7 He-Ne laser: A reasonable approximation of the lifetime of 38.6 ns simply by including the transition rate from the strongest transition (strongest laser) ns

8 Nonradiative decay of the excited states collisional decay Collisions cause the excited atoms to make a transition to a lower level without radiation A general term for the decay rate of an excited level u is the symbol γ u (1/second): A more general expression for the lifetime:

9 Collisional depopulation in atomic or molecular gases Collisional depopulation (electrons) of excited atoms in a gas state can occur when electrons, atoms, or molecules collide with the excited electrons, move the population of electrons to a lower level More common at high electron densities Sensitive to the energy difference between the two levels Sensitive to the gas pressure He-Ne laser: collision between the ground-state He atoms and Ne (neon) atoms in the upper laser level a laser should try to decrease the collisional depopulation

10 Transfer across The conservation of energy and momentum allow efficient transfer from one excited state to another state, but only if those two states have equal or nearly equal energy. He-Ne laser

11 Decay rates: radiative vs. collisional Radiative decay rate: A ul ν ul 2 Collisional decay rate: A ul ΔE ul 2

12 Lattice relaxations in high-density materials Collisional interactions in liquid and solids are due to rapid short-range movements of the closely spaced atoms of dense medium, which are vibrating at velocities associated with the temperature of medium. Collisional interaction in solids refers to as phonon or lattice relaxations and are due to the crystalline lattice vibrations.

13 Spontaneous and stimulated emission, absorption Spontaneous emission ν = (E 2 E 1 )/h

14 Stimulated emission The energy difference E 2 -E 1 is delivered in the form of a wave (e.m.) that adds to the incident one.

15 Spontaneous emission vs. stimulated emission There is a fundamental difference between these two processes. In spontaneous emission, atom emits a wave that has no definite phase relation with that emitted by another atom (between 2 atoms). Furthermore, the wave can be emitted in any direction. In simulated emission, since the process is forced by incident wave, the emission of any atom adds in phase to that of the incoming wave and along the same direction - the incoming radiation is amplified. This is the physical basis of light amplification in optical amplifiers & lasers.

16 Absorption 0 External stimulus ν 0 = (E 2 E 1 )/h The energy difference E 2 -E 1 required by the atom to undergo the transition is obtained from the energy of the incident wave.

17 Description in terms of photons Spontaneous emission The atom decays from level u to level l through the emission of a photon Stimulated emission (creating photons) The incident photon stimulates the u l transition and we have two photons. Absorption (annihilating photons) The incident photon is simply absorbed to produce the l u transition.

18 High reflector Laser pumping energy Output coupler Laser oscillator Gain medium Laser beam Gain medium (1): a material with properties that allow it to amplify light by stimulated emission. Light of a specific wavelength that passes through the gain medium is amplified (increases in intensity). Pumping (2): The energy is typically supplied as an electric current (electron pumping) or as light (optical pumping). Pump light may be provided by a flash lamp or by another laser.

19 High reflector Laser pumping energy Output coupler Laser oscillator Gain medium Laser beam Optical cavity (1+3+5): a pair of mirrors on both ends of the gain medium. Lights bounce back and forth between the mirrors, passing through the gain medium and being amplified each time. (Laser pumping has direction, both mirrors shall have high reflectivity, left 99.9%, right 95%) Most practical lasers contain additional elements that affect properties of the emitted light, such as the polarization, wavelength, and shape of the beam, etc.

20 Types of lasers Physical state of the active material Solid state lasers Liquid lasers Gas lasers Wavelength of the emitted radiation Infrared lasers Visible lasers UV and X-ray lases ~ 1 mm, millimeter waves ~ 1 nm, upper limit of hard X-rays

21 Wavelength chart

22 Output power (continuous wave (cw) lasers) A few mw: signal sources (optical communications or bar-code scanners) Tens of kw: material working (cutting) A few MW: some military applications (directed energy weapons) Output power (pulsed lasers): as high as 1 petawatt (10 15 W) Physical dimension (in terms of cavity length): as small as ~ 1μm for the shortest lasers; up to some km for the longest (e.g. 6.5 km long for geodetic studies)

23 Unique properties of laser beams Monochromaticity Coherence Directionality Brightness Short time duration

24 Monochromaticity Only an electromagnetic wave (photon) of frequency ν 0 given by E u -E l can be amplified Since the two-mirror arrangement forms a resonant cavity, oscillation can occur only at the resonance frequencies of this cavity

25 Coherence Spatial coherence Spatial coherence is typically expressed through the output being a narrow beam - diffraction-limited. Laser beams can be focused to very tiny spots, achieving a very high irradiance (laser cutting and lithography), or they can have very low divergence to concentrate their power at a great distance (laser points). A plane wave with an infinite coherence length. A wave with a varying profile (wavefront) and infinite coherence length. A wave with a varying profile (wavefront) and finite coherence length.

26 Temporal coherence Temporal coherence implies a polarized wave at a single frequency (a single color of light) whose phase is correlated over a relatively great distance along the beam. A beam produced by a thermal or other incoherent light source has an instantaneous amplitude and phase that vary randomly with respect to time and position, thus having a short coherence length.

27 Directionality Diffraction-limited! The direct consequence of the fact that the active medium is placed in a resonant cavity. Only a wave propagating in a direction orthogonal to the mirrors (or in a direction very near to it) can be sustained in the cavity. θ d = βλ/d Huyghens principle: divergence of a plane e.m. wave due to diffraction θ d : divergence (laser beam) β: a numerical coefficient of the order of the unity λ: wavelength of the beam D: diameter of the beam

28 Brightness B = 4P/(πDθ) 2 if the beam is diffraction limited, θ=θ d, considering θ d = βλ/d B = 4P/(βλπ) 2 This is the maximum brightness that a beam of power P can have. The high directionality of a laser beam (even with a moderate power, e.g. a few milliwatts) gives a brightness that is several orders of magnitude greater than that of the brightest conventional sources.

29 Short time duration Gas lasers: pulse-width ~ 0.1 s 1 ns (comparable to some flash lamps) Solid state and liquid lasers: pulse-width down to ~ 10 fs

30 Thank you!

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