Lecture 13: Wavelength Separators

Dispersing Systems

Separate/disperse radiation as a function of frequency, energy, wavelength, etc.

Types of spatially dispersive systems

Monochromator, polychromator, spectrometer, spectrograph

Monochromator

single colour device

Polychromator

Multiple wavelength device

Spectrometer

detector needed, ID

Spectrograph

2D information (wavelength and intensity)

Image forming/transfer optics

lenses, mirrors

Dispersion optics

prisms, gratings

What does the first optic (L1) do?

collects light from the source, focuses light into the entrance slit, (de)magnifies light from source

What does second optic (M1) do?

collimates/makes divergent rays parallel

What does dispersion optic (G1) do?

separates rays based on frequency

What does third optic (M2) do?

refocuses light onto exit slit, detector placed after

Snell’s Law

n1sin(theta1)=n2sin(theta2)

What does refractive index (n) vary with?

wavelength

Critical angle

when theta1 and theta 2 =90,

theta 1> theta c

no light transmitted (all reflected)

Total internal reflectance

basis of fiber optics, ATR

Prism

separation in space

Maximum Resolving Power

R=d(dn/dwavelegnth)

Where does max resolving power occur?

minimum deviation angle (D), light inside prism parallel to base

Diffraction

every point where plane wave encounters object, creates spherical wave. Most pronounced when obstacle ~ wavelength

Huygens-Fresnel Principle

Every point on a propagating wavefront acts as a source of secondary spherical wavelets, and the new wavefront at any subsequent time is the result of the mutual interference of these wavelets

Double-slit experiment

collimated, monochromatic beam interacts with two slits, each slit creates propogating spherical waves, which interfere constructively and destructively

Braggs Law

need to type equation

Braggs law eq (write)

m=diffraction order, d=spacing between slits (normal incidence of light)

Diffraction Grating

optic with multiple, evenly space obstacles, best if obstacle and spacing ~ wavelegnth

Transmission Grating

obstacles=slits/holes

Reflection grating

obstacles=reflective grooves

Diffraction grating equation

write equation

Equation for non-normal incidence

equation write out

Resolving power for grating

R=mN, N=# of grooves (obstacles)

Plate Factor (P)

wavelegnth/f tan

Free Spectral Range (FSR)

delt wavelegnth=wavelenth/m=wavelegnth²/dsintheta

Transmission Grating

Can involve refraction, used in high-res applications

Ruled grating

mechanically formed grooves

Blazed (sawtooth) gratings

angled faces improve efficiency in certain order, angle of zero order based on grating normal, diffraction based on groove normal

Blaze angle

angle of groove wrt grating surface

Equation for echellette

write eq

Czerny-Turner Monochromator

uses planar grating, EMR dispersed across a plane

Czerny-Turner spectrograph

x axis-wavelegnth, y axis=vertical position

Rowland Circle

utilizes curved grating has diameter=radius of curvature of grating, results in focal curve, slit placed anywhere on rowland circle is imaged somewhere else on circle

Echelle Grating

large spacing (d) and also larger order

Problems with chelle grating

FSR very small, overlap of orders occurs and can’t distinguish overlapping orders

Cross/pre-dispersion

Normal grating or prism in one direction (poor res), echelle in other dimension (high res)