Photonic crystals

by Szymon Krupinski

Course no. 320352 – Photonics and Optical Communication

Presentation plan● Revolution wave № 2● Physics of PCs● Examples

– 1-dimensional PC

– 2-dimensional PC

– 3-dimensional PC

● Tuning PCs● Applications of photonic crystals● So, will it work..?

Revolution wave № 2

● “If only it were possible to make dielectric materials in which electromagnetic waves cannot propagate at certain frequencies, all kinds of almost-magical things would be possible”

-- John Maddox, Nature 1990

● Tailoring optical properties the same way engineers designed custom semiconductors

● Integrated optics...?● Started late 80's, now turning into business

Physics of PCs

● Analogies between the semiconductors and PCs● Keywords in analyzing PCs:

– mixed dielectric medium➔ drill holes in crystals, change n by UV exposure, ...

– scalability properties➔ every wavelength can be used!➔ analogy: Bragg diffraction

– symmetries in crystals➔ allow to classify the modes

Physics of PCsMixed Medium & Symmetries

A composite of regions of homogeneous dielectric material with no internal charge and currents

● is generalised

● described by Maxwell eqns.

● can extended in dimensions and decomposed into modes

Cavities and dielectric regions can be symmetric in 1,2 or 3 dim.

● special modes which are sustained (see waveguides), introduces mode symmetry

● tremendously simplifies the eqns. derived from the M.E.

● the heart of the idea of PC!

Examples1-dimensional PC

● We already know

this structure– Fiber Brag

grating uses

the same principle!

● Easy to make● Limitation: does not

work for every direction

Examples1-dimensional PC in operation

Otherwise, the wave quickly dies out after consecutive reflections/interferences

=> Blocking

The incoming wave is not attenuated if it period is coherent with the spacing of the dielectric regions

=> Acceptance

Examples2-dimensional PC

● The same principle, working in two directions● Harder to manufacture● Can also be made by drilling holes● Possible material: diamond

Examples3-dimensional PC

● Yes, a crystal is also

a 3-dimensional PC by itself– M.E. scalability confirmed

– but: quantum effects at this level!

– Bragg diffraction, used in crystalography

● Already existing example:

Yablonovite, made by

drilling holes in 3 directions

differing by 35º

Tuning crystals - defects

● The band-gap properties can be further tuned by introducing exceptions to the regular structure

● This can introduce localized modes and evanescent states

Making defects in YablonoviteDefects in a simple 1-d PC

Applications of PCs

● Nature● Band-gap optical fibers● Nanoscale lasers● Pigments● Antennae, reflectors● LEDs● Photonic integrated circuits● ...

done :-)

done

lab only

done, costs!

lab only

done

underconstruction

So, will it work..?Drawbacks of PCs

● No holistic and accurate theoretical background– a number of assumptions has to be made while

deriving the formulas

– for now, only “cooking recipes” are known

● Expensive!– how to drill 500,000 nanometer scale holes precisely,

quickly and cheap?

– often there exists a competing technology

References

(1) “Photonic Crystals: Molding the Flow of Light”, J.D. Joannopoulos, R.D. Meade, J. N. Winn; Princeton University Press, 1995

(2) “Photonic Crystals: Semiconductors of Light”, E. Yablonovitch; Scientific American, 2001