1 / 16

Nanophotonics Class 6 Microcavities

Nanophotonics Class 6 Microcavities. Optical Microcavities. Vahala, Nature 424, 839 (2003). Microcavity characteristics: Quality factor Q , mode volume V. Simplest cavity: Fabry-Perot etalon.

clea
Download Presentation

Nanophotonics Class 6 Microcavities

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Nanophotonics Class 6 Microcavities

  2. Optical Microcavities Vahala, Nature 424, 839 (2003) Microcavity characteristics: Quality factor Q, mode volume V

  3. Simplest cavity: Fabry-Perot etalon Transmission peaks: constructive interference between multiple reflections between the two reflecting surfaces(wavelength fits an integer number of times in cavity). Next few slides: definition and interpretation of free spectral range , quality factor Q, and finesse F.

  4. Free spectral range  2 1  depends on cavity length: Eq. 1: Eq. 2: m: integer; n: refractive index The smaller d, the larger the free spectral range  !! Free spectral range (FSR)  is frequency (or wavelength) spacing between adjacent resonances. d T n R

  5. The time tRT to make 1 round trip 2d is then: Free spectral range  (divided by ) is a measure for the optical cycle time compared to the round trip time Interpretation of free spectral range  in the time domain: Consider traveling wave in the cavity: Optical cycletime Look at phase front that is at x = 0 at t = 0: k0x  0t = 0 The time t to travel a distance x is: Free-spacewavelength

  6. Quality factor Q 1. Definition of Q via energy storage: Consider the ‘ring-down’ of a microcavity: E = Electric field at acertain position u = Energy density 1 1/e 0 Energy density decay: 2/ Optical period T = 1/f0 = 2/0

  7. 2. Definition of Q via resonance bandwidth: Fourier  Time domain Frequency domain 1 1/e Lorentzian 2/ The two definitions for Q are equivalent !

  8. Finesse F This can be rewritten as: F See slide on Q See slide on FSR F is similar to Q except that optical cycletime T is replaced by round trip time tRT Definition of F via resonance bandwidth: F 2 1

  9. Quality factor vs. Finesse • Suppose mirror losses dominate cavity losses, then: • Q can be increased by increasing cavity length • F is independent of cavity length !! This shows that Q and F are different figures of merit for the light circulation capabilities of a microcavity • Quality factor: number of optical cycles (times 2) before stored energy decays to 1/e of original value. • Finesse: number of round trips (times 2) before stored energy decays to 1/e of original value.

  10. Application: Low-threshold lasing On threshold: Pin= 16 W. If all light is coupled into the cavity, then in steadystate: D = 40 mQ = 4  107 APL 84, 1037 (2004) with Pin= 16 W  Pcirc = 800 mW !!! 1. Ultra-high F leads to an extremely high circulating power relative to the input power !

  11. The light circulation concept is not only useful for lasing, but also for: • Nonlinear optics (e.g. Raman scattering) • Purcell effect • Strong coupling between light and matter • … See also: Vahala, Nature 424, 839 (2003), and www.vahala.caltech.edu Application: Low-threshold lasing 2. A small mode volume Vmode leads to strong confinement of the circulating power, and thus to a high circulating intensity:

  12. Differences between microcavities • Practical differences are related to: • Ease of fabrication • Connectivity to waveguides • Integration in larger circuits • Principle differences are related to the figure of merits: • Free spectral range (= spectral mode separation) • Quality factor (= temporal time) • Mode volume (= spatial confinement) One example: the cavity build-up factor See next slide…

  13. Differences between cavities Q/V = 102 Q/V = 103 Q/V = 104 Q/V in units(/n)3 Vahala, Nature 424, 839 (2003) Q/V = 105 Q/V = 106 Q/V = 106 Highest Q/V: geometries useful for fundamental researchon QED (Kimble, Caltech) but not practical for devices

  14. Critical coupling If  = 0 and ex = 0, then T = 0 !! If the intrinsic damping rate equals the coupling rate, then 100 % of the incoming light is transferred into the cavity(perfect destructive interference at output waveguide) ex Decay rates (s-1): 1/ex: coupling to waveguide 1/0: internal losses 0 For derivation, see: Kippenberg, Ph.D. Thesis, section 3.3.2 (http://www.mpq.mpg.de/~tkippenb/TJKippenbergThesis.pdf)

  15. Sensing example: D2O detection Subtle difference inoptical absorptions between D2O and H2O is magnified due to light circulationin cavity. Sensitivity: 1 part per million !!! Evanescent waves are essential for both sensing and fiber coupling Armani and Vahala, Opt. Lett. 31, 1896 (2006)

  16. Summary • Microcavities: Confinement of light to small volumes by resonant recirculation. • Applications: lasing, nonlinear optics, QED, sensing, etc. • FSR, Q, Vmode, and F characterize different aspects of the light recirculation capabilities of a microcavity. • Different microcavity realizations (e.g. micropost, microsphere) differ in FSR, Q, Vmode, and F.

More Related