Lecture #18 The Laser

1. Lecture #18The Laser March, 30th

2. First, a review of some of the basic aspects of light emission by gases, from the previous lectures. 1) The energy values of electrons bound to atoms are discrete. That is, their allowed values are restricted to very specific numbers. These values are the fingerprints of the atom. We can tell what type of atom we have, by examining the light it produces.

3. 2) Light is emitted from an atom only if its atomic energy is lowered. This is called de-excitation. By conservation of energy, the energy of the light emitted (photon energy) is exactly the energy lost by the atom. 3) For each pair of atomic levels (energies) there is one energy difference.

4. Conclude: There is one photon energy value for each pair of levels Efinal and Einitial. The photon energy is Ephoton = Ef - Ei . 1)             The frequency f of the emitted photon must solve Ephoton = hf.

5. The Laser Light Amplification by Stimulated Emission of Radiation A beam of laser light is a)intense b)narrow c) of a single frequency. d)coherent. Coherent means: We choose any cross-section of the beam. Then all parts within it have the same phase.

6. The Processes in a Laser There are three processes: 1.absorption of light. 2.spontaneous emission. 3.stimulated emission. The third process is new. Consider two energy states. The lower-energy one has value E1. The other state (upper state) has energy Eu.

7. Examples of the three processes: AAbsorption. The electron is initially in state E1. A photon meets the atom.  Suppose the photon energy is Ephoton = Eu - E1.  Then, absorption can occur. That is, the atom can absorb the photon. If so, it “jumps” to the upper state of energy Eu.. The photon energy has been given to the atom. This process is an example of resonance. Resonance occurs when there is a match between the properties of an external driver and that of the system acted on. In this case, the system acted on is the atom. The driver is the photon. The photon energy matches the energy difference of the two atomic states. Consequence of resonance: A strong interaction between driver and system, (e.g., absorption).

8. Spontaneous Emission This process is the reverse of absorption. In this emission process, the atom starts out in the upper state of energy Eu. Initially, there is no photon.  The atom makes a transition to the lower energy state E1. This occurs spontaneously.  A photon is emitted in the process. (Otherwise, energy is not conserved.) So, the photon emitted must have energy  Ephoton = Eu - E1. This is the same energy as required for the absorption process. The light you see from “neon” signs is produced by spontaneous emission.

9. 3) Stimulated Emission This is the key process in laser action. This process was proposed by Einstein in his famous 1917 paper of the theory of radiation.  Many decades later, the idea was put into practical use by the invention of the laser.  In this process, the atom again must be in an excited state, initially. Let its energy be Eu .  A photon comes along, with “just the right energy”, namely Ephoton = Eu - E1 .  It then stimulates the transition of the atom into the lower energy state E1.

10. Resonance and Stimulated Emission Simulated emission is an example of resonance Why? The original photon has energy matching the energy difference Eu - E1 . So, we expect a strong interaction between driver (i.e., the photon) and the system. The strong interaction is the stimulated emission of the second photon, in energy of the atom. But now, unlike absorption, a photon is created, not destroyed.

11. Example of a Simple Laser The ruby laser (invented in 1960). The basic material (sapphire) is Al O3 Added to the sapphire are Cr3+ ions. We call the material ruby. The Cr3+ replace some of the Al atoms. The Cr ions have a ground state (lowest energy). At room temperature, with no excitation, practically all the Cr ions are in the ground state. Choose the zero of energy to be that of the ground state. At energy of 2.25 eV, there are states present.  _________________ Energy E2 of value 2.25 eV. ________________ Zero Energy (ground state) Incident light is applied. Its photon energy matches is chosen to be 2.25 eV. This process is called pumping.

12. Absorption – The First Process The incident photons are absorbed, as they have just the right energy (resonance). Result: The Cr ions are now in the state of energy 2.25 eV. Let this energy be called E2. Key point about the ruby material: There is a state just below E2. It has energy E1 of value 1.8 eV. By spontaneous emission, the electrons jump down to the lower energy value E1.

13. Outcome of Stimulated Emission The result is that two photons emerge. The first photon is the original (stimulating) one. The second photon is one that must be produced to conserve energy. (The atom has lost energy Eu - E1.) These two photons have the same energy. Hence, they have the same frequency (by E = hf). Also, they travel in the same direction. They also have the same phase. We say that the two photons are coherent.

14. Laser Action Starts A few Cr ions jump down to the ground state, by spontaneous emission. They emit photons in the process. These photons produce stimulated emission of the other atoms. Laser action has begun! The photons emitted have energy of 1.8 eV. Diagram:  ______________ E1 = 1.8 eV (Metastable State) ______________ E0 = 0 (Ground State)

15. Metastable State A crucial requirement: The state of energy E1 must be metastable. That is, the transition rate to the ground state by spontaneous emission must be relatively small. Otherwise, the inverted population will not occur. Reason: If not, the atoms would then not remain long enough in the state of energy E1 to allow for it to be populated more than the ground state.

16. Observations About Lasers • They produce narrow beams of intense light • They often have pure colors • They are dangerous to eyes • Reflected laser light has a funny speckled look

17. Spontaneous Emission • Excited atoms normally emit light spontaneously • Photons are uncorrelated and independent • Incoherent light

18. Stimulated Emission • Excited atoms can be stimulated into duplicating passing light • Photons are correlated and identical • Coherent light

19. Laser Amplification • Stimulated emission can amplify light • Laser medium contains excited atom-like systems • Photons must have appropriate wavelength, polarization, and orientation to be duplicated • Duplication is perfect; photons are clones

20. Laser Oscillation • Laser medium in a resonator produces oscillator • A spontaneous photon is duplicated over and over • Duplicated photons leak from semitransparent mirror • Photons from oscillator are identical

21. Properties of Laser Light • Coherent – identical photons • Controllable wavelength/frequency – nice colors • Controllable spatial structure – narrow beams • Controllable temporal structure – short pulses • Energy storage and retrieval – intense pulses • Giant interference effects • Apart from these issues, laser light is just light

22. Types of Lasers • Gas (HeNe, CO2, Argon, Krypton) • Powered by electricity • Solid state (Ruby, Nd:YAG, Ti:Sapphire, Diode) • Powered by electricity or light • Liquid (Dye, Jello) • Powered by light • Chemical (HF) • Nuclear

23. Supplementary - textbook: Chapter 28 pp. 803-806; No supplementary materials No homework

24. Quiz #3 1 (3 points). The green light of a laser has =514 nm. Will green light with this wavelength be able to eject electrons from Cs, if the minimum energy for electron ejection is 3.0510-19 J?2 (3 points). What is the wavelength of an electron with velocity v=6106 m/s? The electron mass is 9.110-31 Kg.3 (3 points). What is the energy that corresponds to n=4 for the hydrogen atom? The energy that corresponds to the ground (or fundamental) state is -13.6 eV. 4 (3 points). What is the necessary energy for ionization of a hydrogen atom, which is already excited at the level n=3?