Photonic crystal surface-emitting lasers enabled by an accidental Dirac point
A photonic-crystal surface-emitting laser (PCSEL) includes a gain medium electromagnetically coupled to a photonic crystal whose energy band structure exhibits a Dirac cone of linear dispersion at the center of the photonic crystal's Brillouin zone. This Dirac cone's vertex is called a Dirac point; because it is at the Brillouin zone center, it is called an accidental Dirac point. Tuning the photonic crystal's band structure (e.g., by changing the photonic crystal's dimensions or refractive index) to exhibit an accidental Dirac point increases the photonic crystal's mode spacing by orders of magnitudes and reduces or eliminates the photonic crystal's distributed in-plane feedback. Thus, the photonic crystal can act as a resonator that supports single-mode output from the PCSEL over a larger area than is possible with conventional PCSELs, which have quadratic band edge dispersion. Because output power generally scales with output area, this increase in output area results in higher possible output powers.
1. A surface-emitting laser comprising:
a gain medium to emit an electromagnetic wave; and
a photonic crystal, electromagnetically coupled to the gain medium and having an energy band structure characterized by a Dirac point at or near a center of a Brillouin zone of the photonic crystal and at a frequency within a gain band of the gain medium, to support radiation of at least a portion of the energy in the electromagnetic wave in a direction substantially orthogonal to a plane of the photonic crystal.
2. The surface-emitting laser of claim 1 , wherein the gain medium comprises at least one of a quantum well, a quantum dot, a quantum wire, and an organic molecule.
3. The surface-emitting laser of claim 1 , wherein the gain medium comprises at least one of GaAs, AlGaAs, InGaAs, InGaAsP, GaN, Si, Ge, GaP, InAlGaN, InAs, InSb and SiN.
4. The surface-emitting laser of claim 1 , wherein the photonic crystal supports propagation of a single mode of the electromagnetic wave in the plane of the photonic crystal.
5. The surface-emitting laser of claim 4 , wherein the single mode is a first mode from the center of the Brillouin zone of the photonic crystal.
6. The surface-emitting laser of claim 5 , wherein:
the photonic crystal defines a two-dimensional surface with an area L 2 , through which the at least the portion of the energy radiates out of the photonic crystal; and
a spacing between the first mode and a second mode from the center of the Brillouin zone varies in proportion to L −1 .
7. The surface-emitting laser of claim 1 , wherein the Dirac point comprises an intersection of respective linear regions of at least two energy bands in the energy band structure of the photonic crystal.
8. The surface-emitting laser of claim 1 , wherein the Dirac point represents an intersection of respective linear regions of at least three energy bands in the energy band structure of the photonic crystal.
9. The surface-emitting laser of claim 1 , wherein the photonic crystal defines a plurality of holes having a radius r, a period a, and a first index n 1 in a dielectric material having a second index n 2 , and
wherein the ratio r/a is about 0 to about 0.5 and the ratio n 1 /n 2 is about 0.25 to about 1.0.
10. The surface-emitting laser of claim 1 , wherein the photonic crystal comprises a plurality of rods having a radius r, a period a, and a first index n 1 in a dielectric material having a second index n 2 , and
wherein the ratio r/a is about 0 to about 0.5 and the ratio n 1 /n 2 is about 1.0 to about 4.0.
11. The surface-emitting laser of claim 1 , wherein the photonic crystal comprises at least one of a plurality of holes and a plurality of rods arrayed in at least one of an oblique lattice, a rectangular lattice, a rhombic lattice, a hexagonal lattice, and a square lattice.
12. The surface-emitting laser of claim 1 , wherein the photonic crystal has a period a and an output surface of the surface-emitting laser has at least one dimension of about 10a to about 10,000a.
13. The surface-emitting laser of claim 12 , wherein the period a is about 150 nm to about 550 nm.
14. The surface-emitting laser of claim 1 , wherein the electromagnetic wave has a wavelength λ and the photonic crystal has a thickness of about λ/10 to about 10λ.
15. The surface-emitting laser of claim 1 , wherein the photonic crystal comprises at least one of GaAs, AlGaAs, InGaAs, InGaAsP, GaN, Si, Ge, GaP, InAlGaN, InAs, InSb, and SiN.
16. The surface-emitting laser of claim 1 , further comprising:
at least one electrode, in electrical communication with the gain medium, to stimulate emission of the electromagnetic wave from the gain medium.
17. The surface-emitting laser of claim 1 , further comprising:
a pump source, in optical communication with the gain medium, to optically pump the gain medium so as to stimulate emission of the electromagnetic wave from the gain medium.
18. A method of making a surface-emitting laser, the method comprising:
fabricating a photonic crystal having an energy band structure characterized by a Dirac point at a center of a Brillouin zone of the photonic crystal; and
disposing a gain medium in electromagnetic communication with the photonic crystal having an energy band structure characterized by a Dirac point at or near the center of a Brillouin zone of the photonic crystal and at a frequency within a gain band of the gain medium so as to support:
(i) propagation of a single mode of the electromagnetic wave in a plane of the photonic crystal, and
(ii) radiation of at least a portion of the energy in the electromagnetic wave in a direction substantially orthogonal to a plane of the photonic crystal.
19. The method of claim 18 , wherein the single mode is a first mode from the center of the Brillouin zone.
20. The method of claim 18 , wherein fabricating the photonic crystal comprises defining the photonic crystal to define:
a two-dimensional surface with an area L 2 , through which the at least a portion of the energy radiates out of the photonic crystal; and
a spacing between modes of the photonic crystal that varies in proportion to L −1 .
21. The method of claim 18 , wherein fabricating the photonic crystal comprises:
selecting at least one of hole radius, rod radius, hole pitch, rod pitch, lattice shape, thickness, refractive index, and period of the photonic crystal so as to form a degeneracy at the Dirac point of at least three energy bands of the photonic crystal.
22. The method of claim 18 , wherein fabricating the photonic crystal comprises:
forming a plurality of holes having a radius r, a period a, and a first index n 1 in a dielectric material having a second index n 2 ,
wherein the ratio r/a is about 0 to about 0.5 and the ratio n 1 /n 2 is about 0.25 to about 1.0.
23. The method of claim 18 , wherein fabricating the photonic crystal comprises:
forming a plurality of rods having a radius r, a period a, and a first index n 1 in a dielectric material having a second index n 2 ,
wherein the ratio r/a is about 0 to about 0.5 and the ratio n 1 /n 2 is about 1.0 to about 4.0.
24. The method of claim 18 , wherein fabricating the photonic crystal comprises:
forming at least one of a plurality of holes and a plurality of rods in at least one of an oblique lattice, a rectangular lattice, a rhombic lattice, a hexagonal lattice, and a square lattice.
25. The method of claim 18 , wherein fabricating the photonic crystal comprises selecting a period a of the photonic crystal, and further comprising:
setting at least one dimension of an output surface of the surface-emitting laser to be about 10a to about 10,000a.
26. The method of claim 25 , wherein the period a is about 150 nm to about 550 nm.
27. The method of claim 18 , wherein the electromagnetic wave has a wavelength λ and fabricating the photonic crystal comprises selecting a thickness of the photonic crystal to be about λ/10 to about 10λ.
28. The method of claim 18 , wherein fabricating the photonic crystal comprises:
etching at least one of GaAs, AlGaAs, InGaAs, InGaAsP, GaN, Si, Ge, GaP, InAlGaN, InAs, InSb and SiN.
29. The method of claim 18 , wherein disposing the gain medium in electromagnetic communication with the photonic crystal comprises:
forming at least one quantum well electromagnetically coupled to the photonic crystal.
30. The method of claim 18 , further comprising:
forming the gain medium from at least one of GaAs, AlGaAs, InGaAs, InGaAsP, GaN, Si, and SiN.
31. The method of claim 18 , further comprising:
forming the gain medium from an organic dye medium.
32. The method of claim 18 , wherein fabricating the photonic crystal comprises selecting a period a of the photonic crystal, and further comprising further comprising:
disposing at least one electrode in electrical communication with the gain medium; and
placing the at least one electrode in electrical communication with a power source.
33. A method of generating an electromagnetic wave having a single mode, the method comprising:
stimulating emission of the electromagnetic wave by a gain medium; and
coupling the electromagnetic wave into a photonic crystal having an energy band structure characterized by a Dirac point at or near a center of a Brillouin zone of the photonic crystal and at a frequency within a gain band of the gain medium so as to support:
(i) propagation of a single mode of the electromagnetic wave in a plane of the photonic crystal, and
(ii) radiation of at least a portion of the energy in the electromagnetic wave in a direction substantially orthogonal to a plane of the photonic crystal.
34. The method of claim 33 , wherein stimulating emission of the electromagnetic wave comprises applying at least one of electrically pumping the gain medium and optically pumping the gain medium.
35. The method of claim 33 , further comprising:
emitting the single mode of the electromagnetic wave via a surface of a surface-emitting laser that comprises the gain medium and the photonic crystal.