390 likes | 416 Views
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. Parabola: curve at equal distance from a point (F) and line.
E N D
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
Parabola: curve at equal distance from a point (F) and line y = ax2 F B A O x d E D
Parabolic mirror: why do all rays perpendicular to the directrix converge at the focus F? F y=2ax A x x O 2 C d D E …because ACF is isoceles, hence AF=CF and AE=y+d so OF = d
Group delay Wave front and energy front db tan g = l db = angular dispersion g = tilt of energy front dl dl Group velocity dispersion There is also a relation between GVD and angular dispersion
S’W Q S0, SW PW rW a L r0 P0 S’0 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.
S’W Q S0, SW PW rW a L r0 P0 S’0
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.
a h L A B L g C (R)
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 B q2 q1 D t2 W t W+dW q6 q4 q5 q0 B’ = q3 A’ A’’ a u O’ s
ceo Phase delay
O H A q0 q3 B q2 q1 D t2 W t W+dW q6 q4 q5 q0 B’ = q3 A’ A’’ a u O’ s
O q3 A B q2 t q4 B’ A’ W = q3 A’’ t2 W+dW a O’ s
dq3 q6 q5 q7 = q0 B’ A’ Q 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 A’’ q1 O’’’ g
Angular Glass:
O H A q3 B q1 L D W q6 q4 q5 q0 B’ = q3 A’ a O’
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
OC Oscillators M2 TS To Timing Logic M1 G P1 S PD FM P2 S EM
Mode-Matched Stretched Seed s-polarized TS p-polarized Relay Imaged Pump Beam TFP PC
Output to compressor Relay-Imaged Nd:YAG Pump TS Divergence-adjusted seed from Regenerative Amplifier Relay-Imaged Nd:YAG Pump Multipass amplifier
Compressor Top View G G M