July 2003 Chuck DiMarzio, Northeastern University 11140b-06-1 ECEG105 Optics for Engineers Course Notes Part 6: Interference Prof. Charles A. DiMarzio Northeastern University Fall 2007 August 2007

July 2003 Chuck DiMarzio, Northeastern University 11140b-06-2 Basic Equations of Interference Re E Im E

July 2003 Chuck DiMarzio, Northeastern University 11140b-06-3 Mach Zehnder (1) Gas Cell n>1 Example Straight-Line Layouts: Source, s M1 M2 BS1 BS2 s BS1BS2 s BS1M2BS2 s BS1M1BS2 s BS1M2BS2 Geometric M1 Transit Time

July 2003 Chuck DiMarzio, Northeastern University 11140b-06-4 Mach Zehnder (2) Straight-Line Layout: Transit Time s BS1BS2 s BS1M2BS2 M1  Diffuser

July 2003 Chuck DiMarzio, Northeastern University 11140b-06-5 Mach Zehnder (3)  

July 2003 Chuck DiMarzio, Northeastern University 11140b-06-6 Michaelson Interferometer Front = 50% R? Rear= AR BS M1 M2 Straight-Line Layout: Transit Time s BS s M2 M1 BS Geometric Optics Via M2 with Three Passes Through Beamsplitter and M1 with only one s BS s M2 M1 BS

July 2003 Chuck DiMarzio, Northeastern University 11140b-06-7 Interferometry: Conflicting Goals Match Optical Path Lengths (Transit Time) –Pulses must arrive simultaneously for interference, or –Paths must be within coherence length of the source (more on this later in the course) Match Wavefront Curvature (geom. opt.) –Fringes must be few enough to be within resolution of instrumentation Thus we can’t compensate for extra glass with extra path length.

July 2003 Chuck DiMarzio, Northeastern University 11140b-06-8 Compensator Plate BS s s M2 M1 BS s s M2 M1 BS Goal: Match Paths in Transit Time and Wavefront Curvature t source Power received Power C C C CC M1 M2

July 2003 Chuck DiMarzio, Northeastern University 11140b Optical Testing BS M1, Known Reference M2, Mirror Under Test Spheres 4-wave difference Same with 2-wave bump Flats with 8-wave tiltSame with 2-wave bump

July 2003 Chuck DiMarzio, Northeastern University 11140b Fabry-Perot Interferometer (1) I1I1 I4I4 Straight Line Model Multiple Sources, with decreasing amplitudes (usually) and increasing distances (and thus phases).

July 2003 Chuck DiMarzio, Northeastern University 11140b Fabry-Perot: Transmission Peaks f, Freq., THz T, Transmission 600nm 650nm 10  m FSR August 2007

July 2003 Chuck DiMarzio, Northeastern University 11140b Fabry-Perot: Resolution f, Freq., THz T, Transmission 600nm 650nm 10  m  f FSR August 2007 Max 1 1212 0.7 Max Graphical Analysis of I 4 /I 1 Denominator

July 2003 Chuck DiMarzio, Northeastern University 11140b Fabry-Perot: Extinction f, Freq., THz T, Transmission August nm 650nm 10  m

July 2003 Chuck DiMarzio, Northeastern University 11140b Interference Magnitudes

July 2003 Chuck DiMarzio, Northeastern University 11140b Coherent Detection P sig Signal 4kTB Quantum Noise x 10 4 P sig Dotted Lines: Higher LO

July 2003 Chuck DiMarzio, Northeastern University 11140b Amplitude Modulator Fiber Splitters E/O Modulator InputOutput Unused Alt. Output

July 2003 Chuck DiMarzio, Northeastern University 11140b Thin Films: Three Approaches Sum the multiple Reflections EAEA EBEB ECEC EDED Use Wave Equation and Boundary Conditions E1E1 Network Approach with Fresnel Coefficients E2E2 E3E3 E4E4 E’ 1 E’ 2 E’ 3 E’ 4

July 2003 Chuck DiMarzio, Northeastern University 11140b Thin Films: Fresnel Coefficients

July 2003 Chuck DiMarzio, Northeastern University 11140b Coherence Issues

July 2003 Chuck DiMarzio, Northeastern University 11140b Etalon Transmission Only Coherent Sources contribute to the fringes Re (1/  ) Im (1/  )

July 2003 Chuck DiMarzio, Northeastern University 11140b Thin Film Matrices (1)

July 2003 Chuck DiMarzio, Northeastern University 11140b Thin Film Matrices (2) M=M 1 M 2 M 3 M 4 M1M1 M4M4 November 2007

July 2003 Chuck DiMarzio, Northeastern University 11140b High Reflection Stack (1) November 2007

July 2003 Chuck DiMarzio, Northeastern University 11140b High Reflection Stack (2) Phase=0    Sign of Reflectivity is inverted on going from High to Low Index. L HHL November 2007

July 2003 Chuck DiMarzio, Northeastern University 11140b Anti-Reflection Coatings Quarter-Wave Coating Magnesium Flouride n=1.35 is a close match, low cost and durable. Phase =0  R 4% Examples Uncoated Glass Violet Red One Layer Two Layers Three Layers