Demultiplexing filter and method

1. A demultiplexed filtering method, comprising:

propagating an optical beam from an input optical fiber through a lens to a diffraction grating to produce:

(i) a first diffracted beam, a center-wavelength thereof equaling a first center-wavelength of a first channel of the optical beam, that propagates back toward the input optical fiber at a first diffracted angle determined in part by the first center-wavelength and a diffraction order m 1 of the first diffracted beam; and

(ii) a second diffracted beam, a center-wavelength thereof equaling a second center-wavelength of a second channel of the optical beam and exceeding the first center wavelength, that propagates back toward the input optical fiber at a second diffracted angle determined in part by the second center-wavelength and a diffraction order m 2 of the second diffracted beam that is less than the diffraction order m 1 ;

wherein the lens has a ray propagated therethrough without refraction, such that a propagation angle of the ray is the same on each side of lens;

coupling the first diffracted beam into a first optical fiber of a one-dimensional optical-fiber array that includes the input optical fiber; and

coupling the second diffracted beam into a second optical fiber of the one-dimensional optical-fiber array.

2. The method of claim 1 , further comprising:

collimating the optical beam with the lens located between a tip of the input optical fiber and the diffraction grating; and

said coupling comprising focusing first diffracted beam and the second diffracted beam with the lens.

3. The method of claim 1 , further comprising coupling the third diffracted beam into a third optical fiber of the one-dimensional optical-fiber array, wherein said propagating the optical beam to the grating also produces the third diffracted beam, a center wavelength thereof equaling the third center wavelength of a third channel of the optical beam and exceeding the second center wavelength, that propagates back toward the input optical fiber at a third diffracted angle determined in part by the third center-wavelength and a diffraction order m 3 of the third diffracted beam that is less than the diffraction order m 2 .

4. The method of claim 1 , further comprising

collimating the optical beam with the lens located between a tip of the input optical fiber and the diffraction grating;

a distance between the first optical fiber and an optical axis of the lens being equal to f eff ·tan(β out1 −θ axis ); where f eff is an effective focal length of the lens, β out1 is an angle between the first diffracted beam and a surface-normal of the diffraction grating, and θ axis is an angle between the surface-normal and the optical axis in a plane that includes the one-dimensional optical-fiber array, and β out1 =arcsin(m 1 λ 1 /Λ−sin [θ axis +arctan(y mp /f eff )]), where λ 1 is the first center wavelength, Λ is a period of the diffraction grating, and y mp is the distance between the input optical fiber and the optical axis; and

a distance between the second optical fiber and an optical axis of the lens being equal to f eff ·tan(β out2 −θ axis ); β out2 is an angle between the first diffracted beam and a surface-normal of the diffraction grating, and β out2 =arcsin(m 2 λ 2 /Λ−sin [θ axis +arctan(y mp /f eff )]), where λ 2 is the second center-wavelength.

5. The method of claim 4 , diffraction order m 2 being greater than one.

6. The method of claim 1 , further comprising:

propagating a multiplexed probe beam through a combustion zone, the optical beam being the multiplexed probe beam after transmission through the combustion zone; and

coupling the optical beam into the input optical fiber.

7. A demultiplexing filter, comprising:

an optical-fiber array comprising an input optical fiber having a fiber optical axis and an input fiber end-face, a surface thereof defining a fiber end-face plane;

a first output optical fiber having a first fiber end-face that is substantially coplanar to the fiber end-face plane, and a first optical axis that is parallel to and coplanar with the fiber optical axis; and

a second output optical fiber having a second fiber end-face that is coplanar to the fiber end-face plane to within a predetermined tolerance, and a second optical axis that is parallel to and coplanar with the fiber optical axis, the input fiber end-face, the first fiber end-face, and the second fiber end-face being collinear;

a diffraction grating having a blazed diffractive surface facing the fiber end-face plane and tilted, with respect to the fiber optical axis, by a tilt angle that deviates from a blaze angle of the blazed diffractive surface by between 0.05 and 0.5 degrees; and

a lens along an optical path between the optical-fiber array and the diffraction grating, having a lens optical-axis perpendicular to the fiber end-face plane and configured to propagate a ray therethrough without refraction, such that a propagation angle of the ray is the same on each side of lens, and the lens further configured to form an image of the blazed diffractive surface in a focal plane that is substantially coplanar with the fiber end-face plane.

8. The demultiplexing filter of claim 7 , a distance between the fiber end-face plane and a principal plane of the lens being substantially equal to an effective focal length of the lens.

9. The demultiplexing filter of claim 7 , at least one of the input optical fiber, the first output optical fiber and the second output optical fiber operating as a multi-mode fiber in a wavelength range between 1.3 micrometers and 2.5 micrometers.

10. The demultiplexing filter of claim 7 , at least one of the input optical fiber, the first output optical fiber, and the second output optical fiber having a fiber core diameter than exceeds fifty micrometers.

11. The demultiplexing filter of claim 7 , wherein:

the input optical fiber emits an optical beam including a first optical channel having a first center-wavelength and a second optical channel having a second center-wavelength exceeding the first center-wavelength;

the lens collimates the optical beam; and

the diffraction grating generates, from the collimated optical beam, (i) a first diffracted beam, a center-wavelength thereof equal to the first center-wavelength, that propagates back toward the optical-fiber array at a first diffracted angle between the first diffracted beam and a surface-normal of the diffraction grating determined by the first center-wavelength and a diffraction order m 1 of the first diffracted beam, and (ii) a second diffracted beam, a center-wavelength thereof equal to the second center-wavelength, that propagates back toward the optical-fiber array at a second diffracted angle between the second diffracted beam and the surface-normal determined by the second center-wavelength and a diffraction order m 2 of the second diffracted beam that is less than the diffraction order m 1 .

12. The demultiplexing filter of claim 11 , each of the first center-wavelength and the second center-wavelength being between 1.3 micrometers and 2.5 micrometers.

13. The demultiplexing filter of claim 11 , at least one of the first center-wavelength and the second center-wavelength corresponding to an absorption line of one of carbon monoxide, water, and carbon dioxide.

14. The demultiplexing filter of claim 11 ,

the input optical fiber having a core radius a 0 and a numerical aperture NA 0 such that a parameter 2π(a 0 /λ 2 )NA 0 is greater than or equal to 2.405 to ensure multi-mode operation at both the first center-wavelength and the second center-wavelength, denoted by λ 2 ;

the first output optical fiber having a core radius a 1 and a numerical aperture NA 1 such that a parameter 2π(a 1 /λ 1 )NA 1 is greater than or equal to 2.405 to ensure multi-mode operation at the first center-wavelength, denoted by λ 1 ;

the second optical fiber having a core radius a 2 and a numerical aperture NA 2 such that a parameter 2π(a 2 /λ 2 )NA 2 is greater than or equal to 2.405 to ensure multi-mode operation at the second center-wavelength.

15. The demultiplexing filter of claim 11 , diffraction order m 2 being greater than one.

16. The demultiplexing filter of claim 11 , the diffraction grating having a grating period greater than four times the second center-wavelength.

17. The demultiplexing filter of claim 11 , further comprising a plurality of lasers optically coupled to the input optical fiber, to generate the optical beam.

18. The demultiplexing filter of claim 11 ,

the emitted optical beam including a third optical channel having a third center-wavelength that exceeds the second center-wavelength;

the optical-fiber array including a third output optical fiber having a third fiber end-face that is coplanar to the fiber end-face plane to within the predetermined tolerance and collinear with the first and second fiber end-faces, and a third optical axis that is parallel to and coplanar with an input-fiber optical axis; and

wherein the diffraction grating generates, from the collimated optical beam, a third diffracted beam, a center-wavelength thereof equal to the third center-wavelength, that propagates back toward the optical-fiber array at a third diffracted angle determined in part by the third center-wavelength and a diffraction order m 3 of the third diffracted beam that is less than the diffraction order m 2 .

19. The demultiplexing filter of claim 11 , the diffraction grating having a period Λ, an ideal grating blaze-angle for Littrow-configuration operation at the first center-wavelength and the second center-wavelength being ϕ 1 =arctan (m 1 λ 1 /(2Λ)) and ϕ 2 =arctan (m 2 λ 2 /(2Λ)) respectively, where λ 1 and λ 2 denote the first and second center wavelengths respectively, the diffraction grating having a grating blaze-angle θ B that differs from each of grating blaze-angles ϕ 1 and ϕ 2 by less than five degrees.

20. The demultiplexing filter of claim 11 ,

a distance between the first output optical fiber and the lens optical-axis being equal to f eff ·tan (β out1 −θ axis ); where f eff is an effective focal length of the lens, where β out1 is the first diffraction angle, and θ axis is an angle between the surface-normal and the lens optical-axis in a plane that includes the optical-fiber array; and

a distance between the second output optical fiber and the lens optical-axis of the lens being equal to f eff ·tan(β out2 −θ axis ), where β out2 is the second diffraction angle.

21. The demultiplexing filter of claim 20 ,

the first diffracted angle β out1 equaling arcsin (m 1 λ 1 /Λ−sin [θ axis +arctan(y mp /f eff )]), where λ 1 is the first center wavelength, Λ is a period of the diffraction grating, and y mp is the distance between the input optical fiber and the lens optical axis; and

the second diffracted angle β out2 equaling arcsin(m 212 /Λ−sin [θ axis +arctan(y mp /f eff )]), where λ 2 is the second center-wavelength.

22. The demultiplexing filter of claim 20 ,

the emitted optical beam including a third optical channel having a third center-wavelength that exceeds the second center-wavelength;

the optical-fiber array including a third output optical fiber having a third fiber end-face that is coplanar to the fiber end-face plane to within the predetermined tolerance and collinear with the first and second fiber end-faces, and a third optical axis that is parallel to and coplanar with an input-fiber optical axis;

the diffraction grating configured to generate, from the collimated optical beam, a third diffracted beam, a center-wavelength thereof equal to the third center-wavelength, that propagates back toward the optical-fiber array at a third diffracted angle determined in part by the third center-wavelength and a diffraction order m 3 of the third diffracted beam that is less than the diffraction order m 2 ; and

a distance between the third output optical fiber and the lens optical-axis of the lens being equal to f eff ·tan(β out3 −θ axis ), where β out3 is the third diffraction angle.

23. The demultiplexing filter of claim 22 , the third diffraction angle β out3 equaling arcsin(m 3 λ 3 /Λ−sin [θ axis +arctan(y mp /f eff )]), where λ 3 is the third center-wavelength.

24. A method for measuring species concentration in a combustion zone, comprising:

propagating a multiplexed input probe beam through a lens in the combustion zone to produce an output probe beam, the combustion zone including (i) a first gas-phase species that has an absorption line at a first center-wavelength and (ii) a second gas-phase species that has an absorption line at a second center wavelength that exceeds the first center-wavelength, the lens having a ray propagated therethrough without refraction, such that a propagation angle of the ray is the same on each side of lens;

coupling the output probe beam into an input optical fiber;

propagating the output probe beam from the input optical fiber to a diffraction grating to produce;

(i) a first diffracted beam, a center-wavelength thereof equaling the first center-wavelength, that propagates back toward the input optical fiber at a first diffracted angle determined in part by the first center-wavelength and a diffraction order m 1 of the first diffracted beam; and

(ii) a second diffracted beam, a center-wavelength thereof equaling the second center-wavelength, that propagates back toward the input optical fiber at a second diffracted angle determined in part by the second center-wavelength and a diffraction order m 2 of the second diffracted beam that is less than the diffraction order m 1 ;

coupling the first diffracted beam into a first optical fiber of a one-dimensional optical-fiber array that includes the input optical fiber;

coupling the second diffracted beam into a second optical fiber of the one-dimensional optical-fiber array;

measuring (i) a first signal amplitude of the first diffracted beam output from the first optical fiber and (ii) a second signal amplitude of the second diffracted beam output from the second optical fiber;

determining (i) from the first signal amplitude, a concentration of the first gas-phase species and the second gas-phase species.