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

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Nanophotonics Class 6 Microcavities


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slide1

Nanophotonics

Class 6

Microcavities

optical microcavities
Optical Microcavities

Vahala, Nature 424, 839 (2003)

Microcavity characteristics: Quality factor Q, mode volume V

simplest cavity fabry perot etalon
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.

free spectral range
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

interpretation of free spectral range in the time domain

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

quality factor q
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

2 definition of q via resonance bandwidth
2. Definition of Q via resonance bandwidth:

Fourier

Time domain

Frequency domain

1

1/e

Lorentzian

2/

The two definitions for Q are equivalent !

finesse f
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

quality factor vs finesse
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.
application low threshold lasing
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 !

application low threshold lasing11

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:

differences between microcavities
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…

differences between cavities
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

critical coupling
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)

sensing example d 2 o detection
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)

summary
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.