Download presentation

Presentation is loading. Please wait.

Published byHeather Cramton Modified over 2 years ago

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

5
Consider traveling wave in the cavity: Look at phase front that is at x = 0 at t = 0 : k 0 x 0 t = 0 The time t to travel a distance x is: The time t RT 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 Optical cycle time Free-space wavelength Interpretation of free spectral range in the time domain:

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

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

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

9
Quality factor vs. Finesse 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. 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

10
On threshold: P in = 16 W. If all light is coupled into the cavity, then in steady state: 1.Ultra-high F leads to an extremely high circulating power relative to the input power ! APL 84, 1037 (2004) with D = 40 m Q = 4 10 7 Application: Low-threshold lasing P in = 16 W P circ = 800 mW !!!

11
Application: Low-threshold lasing 2.A small mode volume V mode leads to strong confinement of the circulating power, and thus to a high circulating intensity: 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

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 = 10 2 Q/V = 10 3 Q/V = 10 4 Q/V = 10 6 Q/V = 10 5 Q/V in units ( /n) 3 Highest Q/V: geometries useful for fundamental research on QED (Kimble, Caltech) but not practical for devices Vahala, Nature 424, 839 (2003)

14
Critical coupling For derivation, see: Kippenberg, Ph.D. Thesis, section 3.3.2 (http://www.mpq.mpg.de/~tkippenb/TJKippenbergThesis.pdf) Decay rates (s -1 ): 1/ ex : coupling to waveguide 1/ 0 : internal losses 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 00

15
Sensing example: D 2 O detection Subtle difference in optical absorptions between D 2 O and H 2 O is magnified due to light circulation in cavity. Sensitivity: 1 part per million !!! Armani and Vahala, Opt. Lett. 31, 1896 (2006) Evanescent waves are essential for both sensing and fiber coupling

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

Similar presentations

Presentation is loading. Please wait....

OK

Chapter 10. Laser Oscillation : Gain and Threshold

Chapter 10. Laser Oscillation : Gain and Threshold

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on means of communication in olden days Best ppt on history of cricket Ppt on blood groups in humans Ppt on db2 introduction to physics Ppt on cross site scripting error Ppt on superstition in indian culture Hrm ppt on recruitment and selection Ppt on order of operations Ppt on power line communication chip Ppt on area related to circle class 10