Planar lightwave Fabry-Perot filter

1. An optical filter comprising:

a first mirror;

a cavity coupled to said first mirror; and

a second mirror coupled to said cavity;

wherein said first and second mirrors each comprise a plurality of trenches etched into the surface of a waveguide, a desired propagation mode of the waveguide is selected by selecting a height of the waveguide, a width of the waveguide, a refractive index of the waveguide, and/or a refractive index of the surrounding medium, according to:

M

≈

π

4

⁢

(

2

⁢

d

λ

0

)

2

⁢

(

n

1

2

-

n

2

2

)

where M is the desired propogation mode, d is the width and the height of the waveguide, n 1 is the refractive index of the waveguide, n 2 is the refractive index of a surrounding medium and λ 0 is a center wavelength of the mirrors.

2. The optical filter of claim 1 , wherein said trenches are periodic.

3. The optical filter of claim 1 , wherein said cavity comprises a region of the waveguide without the plurality of trenches.

4. The optical filter of claim 1 , wherein the waveguide is coupled to a lower cladding layer.

5. The optical filter of claim 4 , wherein the waveguide is coupled to an upper cladding layer.

6. The optical filter of claim 4 , wherein said lower cladding layer is coupled to a substrate.

7. The optical filter of claim 1 , wherein the trenches are filled with a material having a different refractive index than the waveguide.

8. The optical filter of claim 1 , wherein the cavity comprises one of a solid, liquid, gas or vacuum.