Photonic bandgap reflector-suppressor

• US 20070145046A1
• Filed: 12/23/2005
• Published: 06/28/2007
• Est. Priority Date: 12/23/2005
• Status: Active Grant

• Current Assignee: National Research Council Canada
• Original Assignee: National Research Council Canada
• Inventors: Vatsya, S.
• Granted Patent: US 7,332,697 B2
• Time in Patent Office: Days
• US Class Current: 219/745
• CPC Class Codes: H05B 6/74 Mode transformers or mode stirrers

Abstract

A computer-based design methodology for photonic bandgap devices that permits determination of both the upper and lower bandgap edges in either a one-dimensional or two-dimensional photonic crystal. Using this methodology, a one-dimensional crystal may be created for use in a waveguide-fed microwave oven as a radiation reflector-suppressor, particularly for undesirable higher harmonic frequencies of about 12 GHz. By conceptually arranging multiple reflectors in a desired geometry, a two-dimensional crystal may be created that is particularly useful as a waveguide or splitter. The waveguide or splitter thus created has especially high efficiency for microwave wavelength ranges of about 9 GHz as compared with the prior art and is particularly useful in communications applications.

Claims

1. A radiation reflector for a microwave oven comprising a photonic bandgap crystal having a plurality of cells,

a) each cell comprising:

i. two layers of a first material having a first thickness and a first dielectric constant;

ii. a second material having a second thickness and a second dielectric constant less than the first dielectric constant, the second material sandwiched between the two layers of the first material and in intimate contact therewith;

iii. each cell abutting and in intimate contact with an adjacent cell to create a periodic structure having a plurality of interleaving first and second materials; and

,

b) the crystal reflecting at least 75% of microwave power incident to the reflector at a frequency of from 10 to 15 GHz.

2. The reflector of claim 1, wherein at least 90% of incident microwave power is reflected at a frequency of from 12 to 13 GHz

3. The reflector of claim 1, wherein the photonic bandgap crystal is a one-dimensional crystal.

4. The reflector of claim 1, wherein the shield comprises at least 5 cells.

5. The reflector of claim 1, wherein the first dielectric constant is at least 7.

6. The reflector of claim 5, wherein the second dielectric constant is about 1.

7. The reflector of claim 6, wherein the shield comprises 7 cells.

8. The reflector of claim 7, wherein at least 98% of incident microwave power is reflected at a frequency of from 12 to 13 GHz.

9. The reflector of claim 8, wherein the first thickness is about 1.5 mm.

10. The reflector of claim 9, wherein the second thickness is about 4 mm.

11. A waveguide comprising a photonic bandgap crystal for use in directing or splitting incident photonic radiation, the waveguide comprising:

a) a block of a first material having a first dielectric constant, the block having a length, a width and a thickness;

b) a guide path for directing or splitting photonic radiation through the crystal, the guide path having a starting point on the width and at least one ending point on the length or width;

c) a plurality of cylindrical holes, each having a longitudinal axis parallel to the thickness and a radius perpendicular thereto, the holes provided along the length and width of the block outside the guide path and arranged in a triangular lattice having a lattice constant, the holes containing a second material having a second dielectric constant less than the first dielectric constant;

d) wherein the first dielectric constant is from 7.4 to 25, the second dielectric constant is from 0.9 to 1.1 and the ratio of the radius to the lattice constant is from 0.45 to 0.495.

12. The waveguide of claim 11, wherein the waveguide has an efficiency of at least 70%

13. The waveguide of claim 11, wherein the first dielectric constant is about 12, the second dielectric constant is about 1 and the ratio of the radius to the lattice constant is 0.475.

14. The waveguide of claim 13, wherein the guide path is straight, bent, Y-shaped or pitchfork shaped, the frequency of the photonic radiation is from 9 to 13 GHz and wherein the waveguide has an efficiency of at least 44%.

15. The waveguide of claim 13, wherein the guide path is straight, the frequency of the photonic radiation is 9.3 GHz and wherein the waveguide has an efficiency of at least 85%.

16. A method of determining an upper and a lower boundary of a photonic bandgap using a computer, the method comprising:

a) providing a set of co-ordinates relating to physical dimensions of a photonic bandgap crystal in from a one-dimensional space to a three-dimensional space;

b) providing a dielectric constant for the photonic bandgap crystal;

c) numerically solving Maxwell'"'"'s equations at both the upper and lower boundaries of the photonic bandgap using a Fourier expansion of solutions to the Maxwell'"'"'s equations along with an extended Fejé

r summation for resolving discontinuities in the Fourier expansion at the upper and lower boundaries of the bandgap, the extended Fejé

r summation producing a set of Fejé

r weights;

d) multiplying each term of the Fourier expansion by selected Fejé

r weights from the set of Fejé

r weights to thereby improve convergence of the Fourier expansion at the upper and lower boundaries of the bandgap; and

,

e) displaying a value for the upper and lower boundaries of the bandgap.

17. The method according to claim 16, wherein a trans-electric polarization mode is de-coupled from a trans-magnetic polarization mode.

18. The method according to claim 17, wherein each Fourier coefficient is multiplied by a composite Fejé

r weight comprising the square root of the product of the selected Fejé

r weights, the number of terms in the product equal to twice the dimension of the crystal.

19. The method according to claim 18, wherein, for a two dimensional crystal, the composite Fejé

r weight, ζ

_mn, is calculated according to the following formula;

ζ

_mn=√

{square root over (ζ

_mx ζ

_my ζ

_nx ζ

_ny )}

wherein,

ζ

_mx is an m_x^th Fejé

r weight of the set of Fejé

r weights;

ζ

_my is an m_y^th Fejé

r weight of the set of Fejé

r weights;

ζ

_nx is an n_x^th Fejé

r weight of the set of Fejé

r weights; and

,

ζ

_ny is an n_y^th Fejé

r weight of the set of Fejé

r weights.

20. The method according to claim 18, wherein, for a one dimensional crystal, the composite Fejé

r weight, <sub>ζ

mn</sub>, is calculated according to the following formula;

ζ

_mn=√

{square root over (ξ

_m ξ

_n)}

wherein,

ζ

_m is an m^th Fejé

r weight of the set of Fejé

r weights; and

,

ζ

_n is an n^th Fejé

r weight of the set of Fejé

r weights.