FOCUSING OPTICS Spherical lenses Achromatic doublets Parabolic mirrors

Chromatic Aberration only No aberration Slide 2 Cheap singlets may be better than expensive aspherics! Chromatic and spherical aberration

y = ax2 Parabola: curve at equal distance from a point (F) and line F

Parabolic mirror: why do all rays perpendicular to the directrix converge at the focus F? F y=2ax A x O x 2 C d D E …because ACF is isoceles, hence AF=CF and AE=y+d so OF = d

Off-axis parabolic mirror

Wave front and energy front Group delay Wave front and energy front db tan g = l db g = tilt of energy front = angular dispersion dl dl Group velocity dispersion There is also a relation between GVD and angular dispersion

Whether considering group delays or group velocity dispersion (GVD), we will consider sufficiently broad beams, and sufficiently short propagation distances Lp behind the element, such that diffraction effects can be neglected. Q S0, SW S’0 S’W a P0 PW rW r0 L

Q S0, SW S’0 S’W a P0 PW rW r0 L

The most widely used optical devices for angular dispersion are prisms and gratings. To determine the dispersion introduced by them we need to specify not only a(W), but also the optical surfaces between which the path is being calculated. The ``dispersion'' of an element has only meaning in the context of a particular application, that will associate reference surfaces to that element. Indeed, we have assumed in the previous calculation that the beam started as a plane wave (plane reference surface normal to the initial beam) and terminates in a plane normal to the ray at a reference optical frequency $\omega_\ell$. The choice of that terminal plane is as arbitrary as that of the reference frequency $\omega_\ell$ (cf. Chapter 1, Section~\ref{Fourier-rep}). After some propagation distance, the various spectral component of the pulse will have separated, and a finite size detector will only record a portion of the pulse spectrum.

a h L A B L g C (R)

2

For a collimated beam, a logical reference plane is normal to the beam Pairs of prisms 2nd Element (reversed) Reference plane B Reference plane A 1st Element

O H A q0 q3 q2 B q1 D t2 W t W+dW q6 q4 q5 B’ q0 = q3 A’ A’’ a u O’ s

ceo Phase delay

O H A q0 q3 q2 B q1 D t2 W t W+dW q6 q4 q5 B’ q0 = q3 A’ A’’ a u O’ s

O q3 A q2 B t q4 B’ A’ W = q3 A’’ t2 W+dW a O’ s

dq3 q6 q5 q7 = q0 B’ Q A’ a-q2 R B’’ T A’’ S q5 u q4 H’ B’’’ A’’’ a O’

W O Lg a X A’ q0 A W + dW q1 dq1 q1 A’’ O’’’ g

Angular Glass:

q3 H q5 q6 q0 O A B’ A’ O’ B D q1 = q3 q4 W a L

Paper of Fork WRONG, because implies that the separation between the prisms L has both a positive and negative effect. the only optical path considered is L or the path between the two prisms; the beam displacement after the second prism is not calculated. is only for the case of tip to tip propagation in the prisms

{ ceo Phase delay For a pair of prisms we found: For gratings, the simple rule applies also

4. Gratings pairs for pulse stretching – what are the adjustable Parameters? Wavelength? l Fixed Groove spacing d? Larger than l Diffraction angle large (Littrow configuration) Size of grating: pulse length. Grating order

db’ C P W d C0 P0 G2 b’ G1 b b A

Oscillators and Amplifiers

Oscillators M2 OC TS M1 To Timing Logic G P1 S PD FM P2 S EM

Stretcher

Mode-Matched Stretched Seed TS Relay Imaged Pump Beam TFP PC s-polarized TS p-polarized Relay Imaged Pump Beam TFP PC

Multipass amplifier Output to compressor Relay-Imaged Nd:YAG Pump TS Divergence-adjusted seed from Regenerative Amplifier Output to compressor Relay-Imaged Nd:YAG Pump TS

Compressor Top View G G M