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Lecture Two - Agenda

Lecture Two - Agenda. Brief review of last class (incl. some basic vocabulary) Maxwell’s equations from another perspective: why does light move? Paraxial solution Simplest case: ray optics Summary. energy. 1. Last class review. Components of a laser

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Lecture Two - Agenda

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  1. Lecture Two - Agenda • Brief review of last class (incl. some basic vocabulary) • Maxwell’s equations from another perspective: why does light move? • Paraxial solution • Simplest case: ray optics • Summary Laser Optics – Phys460

  2. energy 1. Last class review • Components of a laser • Light propagating in free space (Maxwell Eqn.’s) • Cavity – see i. but add boundary conditions • Optical gain and loss (light-matter interaction) Laser Optics – Phys460

  3. Er:glass Cr:Fosterite Diodes Ho:YAG Ti:sapphire ArF excimer Cr:LiSAF Quantum cascade laser 1. review, cont. – basic vocabulary ion Notation example: Er:glass matrix 1m 10m 100nm Add to Fig. 1.3 (pg 3) – Key laser systems See also Section 41 (Melles-Griot catalog) Laser Optics – Phys460

  4. Inhomogenous wave equation 2. Maxwell’s equations in a different light • Standard analysis • Intuitively – why does light move? • Early days – people thought there was medium that light moved in. • Pulse on a string: interplay between kinetic and potential energy. Laser Optics – Phys460

  5. E 2. Maxwell, cont. • But Michelson and Morley found no ether…. y B grows! x z E changes! “simulation”…. Laser Optics – Phys460

  6. r k k 3. Paraxial wave equation Homogenous vector wave equation Linear in E, apply superposition principle SO look for monochromatic solutions Helmholtz equation Two extreme solutions: 1) Beam source : infinite 2) Beam source: point source Laser Optics – Phys460

  7. Paraxial wave equation 3. Paraxial, cont.. z Want a beamlike solution! Try: Assume that beam profile (E0) and its derivative change slowly as a function of z. This is known as the slowly varying envelope approximation. Laser Optics – Phys460

  8. 3. Paraxial, cont.. Simplistic solution – consider small wavelength: Paraxial wave equation The envelope never changes as a function of z! z RAY OPTICS!! (also known as geometrical optics) Laser Optics – Phys460

  9. Example of unreal ray optics! https://www.drdynamics.com/products/laser/NaturesMiracle.swf Laser Optics – Phys460

  10. 4. Ray optics: ABCD matrices Ray travels distance d. r z Convenient notation: Ray is characterized by 21 matrix: Free-space propagation of length d transforms the ray Laser Optics – Phys460

  11. 4. Rays, cont. - other transformations Lens focal length of f Spherical mirror with radius of curvature R Spherical dielectric interface, with radius of curvature R First medium index: n1, second medium index: n2 Laser Optics – Phys460

  12. 4. Rays, cont. - resonator stability r d R1 R2 Define g-parameter For r to remain finite, we find that: Resonator stability condition Laser Optics – Phys460

  13. 4. Rays, cont. - problems d=f All the rays pass through focal point. Paraxial Wave optics – gaussian beams Laser Optics – Phys460

  14. 5. Summary • Basic vocabulary: examples of laser systems • Why does light move: E creates B, B creates E… • Useful solutions to Maxwell’s equations – ray optics • Next class, slightly relax assumptions: gaussian optics Laser Optics – Phys460

  15. Laser Optics – Phys460

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