Laser Technology: Nonlinear Optics - Workspace

Laser Technology Course Lecturers: Professor Michael Damzen (Part 1. Laser Device Technology) and Professor John Tisch (Part 2. Nonlinear Optics) Aims: To provide the student with principles & practice of laser device and nonlinear optical technology. The course will provide an understanding of the key physical concepts underlying laser and nonlinear optics and their contemporary applications and equip the students with sufficient knowledge to be able to use and understand lasers and nonlinear optical processes in their subsequent research or commercial careers. Objectives: Part 1. Laser Device Technology After attending the course, the student should:  Know key laser applications and commercially-important lasers  Be able to match laser properties and laser systems to best fit application needs  Know how to control (and in some cases, design) key laser parameters  Be able to quantify some case studies of laser applications (e.g. speed of laser cutting) Part 2. Nonlinear Optics After attending the course, the student should:  Have an appreciation of the historical developments leading to modern nonlinear optics (NLO).  Know in general terms what the main scientific and technological applications of NLO processes are.  Have a good mathematically-based understanding of the interaction of light and matter in the linear regime, including the nature of the electromagnetic force on charges in the medium.  Be able to define the induced dipole moment and the polarisation of a medium.  Be able to write down Maxwell’s inhomogeneous wave equation and understand the significance of the polarisation source term and the conditions for the generation of new frequencies.  Understand the Lorentz Oscillator model and be able to derive the linear polarisation response and linear susceptibility of a medium within this model.  Know the physical significance of the complex refractive index and its relation to the linear susceptibility.  Understand what is meant by dispersion and be able to identify different features in the dispersion curve of a medium.  Have a good understanding of the physical origin of the nonlinear optical response in matter.  Be able to write down the polarisation as a power series expansion in the electric field and understand the physical significance of the different terms in this expansion.  Have an appreciation of the electric field strengths and corresponding optical intensities required to induce a significant nonlinear response. Be able to calculate the parameters required of different lasers to achieve these.  Know what other properties of laser radiation are important for NLO.  Know what is meant by a centro-symmetric medium.  Be able to show mathematically the origin of a range of NLO processes, including second harmonic generation (SHG), third harmonic generation (THG), the Pockels Effect and the Optical Kerr Effect.  Know what conditions must be met in order for these effects to be significant.  Have an understanding of SHG in the photon picture and be able to derive the phase-matching condition for SHG.  Know how to use the complex representation of fields in nonlinear differential equations.  Be able to derive the coupled wave equations for the complex field amplitudes.  Understand what is meant by pump depletion and how to solve the coupled wave equations for SHG in the limit of low pump depletion.

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Be able to derive and physically interpret expressions for the second harmonic intensity and conversion efficiency. Have a good understanding of the wave vector mismatch and the coherence length for SHG and be able to generalise these concepts to other NLO processes. Have an appreciation of the consequences of symmetry in NLO. Have a physical and mathematical understanding of birefringence in uniaxial crystals. Understand how birefringence can be used to phase-match SHG. Have a detailed understanding of Type I and Type II phase-matching of SHG in uniaxial crystals. Be able to sketch the geometry of these interactions and write down their wave vector mismatches and phase-matching conditions. For Type I phase-matching be able to derive an analytic expression for the phase-matching angle. Understand the problem of beam walk-off and how it can be avoided using non critical phasematching (NCPM). Know how temperature tuning can be used to achieve NCPM. Have an appreciation of the required and desirable properties of NLO crystals. Have some familiarity with the names, chemical formulae and production methods of common NLO crystals. Have an understanding of the issues arising when real laser sources are used for NLO, specifically those stemming from the divergence and frequency bandwidth of the radiation. Understand what is meant by the phase-matching acceptance angle and the limitations it imposes. Be able to derive a general expression for this quantity and specify it for SHG. Understand what is meant by pulse walk-off and the phase-matching bandwidth and the limitations they impose. Be able to derive an expression for these quantities for SHG. Be able to derive the origin of the intensity dependence of the refractive index arising from a third order nonlinear response and be aware of the symmetry issues in this response. Know what is meant by the nonlinear refractive index is of a material and have a feel for the typical values of this quantity in various media. Have good physical understanding of effects arising from the intensity dependent refractive index, including self-focusing and self-guiding of laser beams and self-phase modulation of laser pulses. Be able to write down the formula for the B-integral and understand how it is used to assess the extent of nonlinear phase accumulation. Be able to derive the formula for the critical power for nonlinear self-focusing of a laser beam and be able to apply it to various situations. Be able to derive the formula for the spectral bandwidth generated by self-phase modulation and be able to apply it to various situations. Have an appreciation of the applications of self-phase modulation for continuum generation and pulse compression. Be able to write down and identify the various terms arising in the second order nonlinear polarisation driven by two fields of different frequencies (frequency mixing). For sum-frequency generation (SFG) and difference frequency generation (DFG), be able to write down the relationship between the frequencies and wavelengths of the fields. To be able to use these relationships to analyse or devise frequency generation schemes and to have an appreciation of the applications of these processes. Be able to write down the wave-vector mismatches and phase-matching conditions for SFG and DFG. Have a familiarity with the scaling of the intensity of the generated field with relevant parameters. Be able to apply Type I and Type II phase-matching concepts to SGF and DFG. Understand the connection between DFG and optical parametric amplification (OPA). Know what is meant by the terms signal, idler and pump fields in OPA. Have an appreciation of the differences between OPA and conventional laser amplification. Know what is meant by optical parametric oscillation and be able to draw a practical scheme to implement an optical parametric oscillator.

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