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### ⚡ **LASERS** - **Laser**: Device that emits light by **stimulated emission** — coherent, directional, and often monochromatic. - **Stimulated Emission**: An incoming photon causes an excited atom to emit a **duplicate photon** (same phase, direction, energy).(gain, pumping, optical resonator) - **Population Inversion**: Condition where more atoms are in the excited state than in the lower state — required for amplification. - Q-Switching:Techniquetogenerateshort,high-peak-powerpulses (nanoseconds range) as the laser stores energy in the gain medium while preventing lasing. Then suddenly "opens" the optical cavity, releasing all that energy at once. deltav = c/2nd Mode-Locking: Technique to generate extremely short pulses (picoseconds to femtoseconds), as instead of blocking lasing, it makes all the different longitudinal modes oscillate in sync (same phase). This interference causes light to bunch into very short pulses. Requires lasers with wide gain bandwidth. -Laser modes:LongitudinalModesrefertotheallowedfrequenciesoflightthatcanform standing waves inside the laser cavity. These occur when an integer number of half-wavelengths fits exactly between the mirrors. They are discrete in frequency, and their spacing depends on the cavity length. Only those within the gain bandwidth of the laser medium will be amplified. Transverse Modes (or spatial modes, designated as TEMmn) describe the intensity distribution of the laser beam perpendicular to the propagation direction. TEM00 is the fundamental mode with a Gaussian profile, while higher-order modes (e.g., TEM01, TEM10) show more complex patterns. Transverse modes are influenced by the aperture size, mirror alignment, and gain region width. #### Formulas: - Photon energy: `E = hf = hc/λ` - Gain: `I = I0 · e^(g·L)` with `g = σ21 · (N2 − N1)` - Threshold gain: `gth = α + (1/2L) · ln[1 / (R1R2(1−a1)(1−a2))]` - Saturation intensity: intensity at which gain drops to half --- ### 📏 **RADIOMETRY (Physical Light Quantities)** - **Φe (Radiant Flux)**: Total power emitted [W] - **Ie (Radiant Intensity)**: Power per solid angle [W/sr] - **Ee (Irradiance)**: Power per area on surface [W/m2] - **Le (Radiance)**: Power per area per solid angle [W/(sr·m2)] - **Me (Radiant Exitance)**: Power emitted per surface area [W/m2] - **Lambertian Surface**: Ideal surface with uniform radiance in all directions. `Me = π·Le` #### Formula: - Inverse square law: `Ee = Ie / r2` --- ### 🔆 **PHOTOMETRY (Human Eye Response)** - **Φv (Luminous Flux)**: Perceived power [lm] - **Iv (Luminous Intensity)**: Perceived intensity in direction [cd] - **Ev (Illuminance)**: Flux per area [lux] - **Lv (Luminance)**: Perceived brightness per unit area and angle [cd/m2] - **Luminosity Function V(λ)**: Eye sensitivity vs wavelength (peaks at 555 nm) #### Formula: - `Φv = 683 · ∫ Φe,λ(λ)·V(λ) dλ` --- ### 🧪 **MEASUREMENT TECHNIQUES** - **Intensity**: `I ∝ |E|2`, measured using photodiodes, PMTs - **Wavelength**: Measured with spectrometers (gratings, prisms) - **Phase**: `Δφ = (2π/λ)·OPD`, measured with interferometry - n= c/v (refraction/dispersion indice) --- ### 🌈 **INTERFERENCE & DIFFRACTION** - **Interference**: Superposition of waves → constructive or destructive pattern - **Diffraction**: Bending and spreading of waves when passing through a slit or around an obstacle #### Formulas: - Constructive interference: `Δφ = 2π·m` - Destructive interference: `Δφ = (2m+1)π` - Young’s fringe spacing: `Δy = λ·L / d`(entre fentes) - Single-slit minima: `a·sinθ = m·λ` - micleson interformeter:Principle: Splits light into two beams via a beam splitter, reflects them off mirrors, then recombines them to produce interference fringes. Key use: Measures tiny distances, refractive index changes, or wavelengths via fringe shifts. Fringe condition: Constructive: path difference = m·λ Destructive: path difference = (2m+1)·λ/2 Fringe shift per λ: Moving one mirror by Δx causes shift of N = 2Δx / λ fringes. ### 🔍 **LENSES & OPTICAL SYSTEMS** - **Thin Lens Formula**: `1/f = (n−1)(1/R1 − 1/R2)` - **Image Formation**: `1/f = 1/do + 1/di` - **Magnification**: `M = −di / do` - **Power**: `P = 1/f` (in meters) → units in Diopters [D] #### ABCD Matrix (for ray tracing): - **Propagation (distance d)**: `[[1, d], [0, 1]]` - **Thin lens (focal length f)**: `[[1, 0], [−1/f, 1]]` ###aberrations -**Chromatic Aberrations**: Caused by dispersion (n depends on λ) Axial (longitudinal): Different colors focus at different depths Lateral (transverse): Colors shift sideways (color fringes) Fix: Achromatic doublet (2 lenses, cancels color spread) -**Monochromatic Aberrations**: Same wavelength, geometric imperfections Spherical: Edge rays focus differently than center rays Coma: Off-axis points blur like comets Astigmatism: Lines instead of points Field curvature: Flat object → curved image Distortion: Shape warping (barrel/pincushion) Fix: Aspheric lenses, stops, lens combinations ### 🎇 **LIGHT EMISSION & SPECTRA** - **Excitation**: Electron absorbs energy → jumps to higher level - **Emission**: Returns to lower level → emits photon - **Line Spectrum**: Discrete lines from gas atoms (e.g. H, Ne) - **Continuous Spectrum**: Broad, no gaps (e.g. sunlight, bulbs) - **Incandescent Light**: How it works: Electric current heats a filament (usually tungsten) until it glows. Spectrum: Broad continuous spectrum (like blackbody radiation). Color: Warm/yellowish light (~2700 K) Efficiency: Low — much energy lost as heat. Example: Classic light bulbs. -**Halogen Lamp**: Type of incandescent light. Contains halogen gas (like iodine or bromine) in a quartz envelope. Brighter and hotter than regular incandescent. Higher efficiency and longer life. Spectrum: Still continuous, peaks in visible/infrared. -**Fluorescent Ligh**: How it works: Electric discharge excites mercury vapor, emitting UV light. UV excites phosphor coating inside the tube → emits visible light. Spectrum: Combination of line spectra (from mercury) and broad bands (from phosphor). Efficiency: Much higher than incandescent. Color: Can vary — warm white to daylight (depends on phosphor mix). #### Formula: - `E = hf = hc/λ`