Multimode interference coupler and method for the structural configuration thereof
A multimode interference coupler includes at least one supply waveguide and at least one output waveguide, wherein the coupler has along its longitudinal extent in the direction of the supply waveguide at least one longitudinal section in which the refractive index has a locally oscillating profile in a direction running substantially at right angles to the direction of the supply waveguide. A method for the structural configuration of such a multimode interference coupler.
1. A multimode interference coupler having
at least one supply waveguide,
at least one output waveguide, and
at least one interference section which is coupled to the at least one supply waveguide and the at least one output waveguide, wherein
the refractive index of said interference section has an oscillating profile in a direction running substantially perpendicular to the direction of the supply waveguide, and wherein
the effective refractive index n eff of the modes being able to propagate inside said interference section decreases in an approximately quadratic manner with the mode number.
2. The multimode interference coupler according to claim 1 , wherein the refractive index n(x) can be described by the following equation:
n
2
(
x
)
=
n
0
2
(
x
)
+
∑
k
=
0
M
-
1
N
k
·
φ
k
(
x
)
,
where x denotes the spatial coordinate in a direction running substantially perpendicular to the direction of the supply waveguide, n 0 (x) denotes the refractive index of a known multimode interference coupler, M is the mode number of the mode being able to propagate inside the at least one interference section, N k are numerical coefficients and φ k (x) denotes a set of base functions.
3. The multimode interference coupler according to claim 2 , wherein the basic functions φ k (x) describe the field distribution of the modes inside the interference section of a multimode interference coupler with the refractive index n 0 (x).
4. The multimode interference coupler according to claim 1 , wherein maximum and minimum values of the refractive index profile are variable, wherein the maximum and minimum values increase from the center of the interference section towards its edge, and wherein two adjacent maxima or minima of the oscillating profile of the refractive index are spaced 50 nm up to 400 nm apart from each other.
5. The multimode interference coupler according to claim 1 , having
two supply waveguides, and
any of two or four output waveguides.
6. The multimode interference coupler according to claim 1 , having
exactly one supply waveguide, and
any of two, four or ten output waveguides.
7. The multimode interference coupler according to claim 1 , wherein two adjacent maxima or minima of the oscillating profile of the refractive index are spaced 50 nm up to 400 nm apart from each other.
8. The multimode interference coupler according to claim 1 , wherein the at least one supply waveguide, the at least one output waveguide, and the at least one interference section are formed from a laterally structured layer.
9. A multimode interference coupler having
at least one supply waveguide,
at least one output waveguide, and
at least one interference section which is coupled to the at least one supply waveguide and the at least one output waveguide, wherein
the refractive index of said interference section has an oscillating profile in a direction running substantially perpendicular to the direction of the supply waveguide, wherein
maximum and minimum values of the oscillating refractive index profile are variable, and
wherein the maximum and minimum values increase from the center of the interference section towards its edge.
10. The multimode interference coupler according to claim 9 , wherein the effective refractive index n eff of the modes being able to propagate inside said interference section decreases in an approximately quadratic manner with the mode number.
11. The multimode interference coupler according to claim 9 , wherein the refractive index n(x) can be described by the following equation:
n
2
(
x
)
=
n
0
2
(
x
)
+
∑
k
=
0
M
-
1
N
k
·
φ
k
(
x
)
,
where x denotes the spatial coordinate in a direction running substantially perpendicular to the direction of the supply waveguide, n 0 (x) denotes the refractive index of a known multimode interference coupler, M is the mode number of the mode being able to propagate inside the at least one interference section, N k are numerical coefficients and φ k (x) denotes a set of base functions.
12. The multimode interference coupler according to claim 11 , wherein the basic functions φ k (x) describe the field distribution of the modes inside the interference section of a multimode interference coupler with the refractive index n 0 (x).
13. The multimode interference coupler according to claim 9 , having
exactly two supply waveguides, and
any of two or four output waveguides.
14. The multimode interference coupler according to claim 9 , having
exactly one supply waveguide, and
any of two, four or ten output waveguides.
15. The multimode interference coupler according to claim 9 , wherein two adjacent maxima or minima of the oscillating profile of the refractive index are spaced 50 nm up to 400 nm apart from each other.
16. A method for the structural configuration of a multimode interference coupler, said coupler having
at least one supply waveguide,
at least one output waveguide, and
at least one interference section which is coupled to the at least one supply waveguide and the at least one output waveguide, wherein
the profile of the refractive index n(x) is determined by solving the following equation:
n
2
(
x
)
=
n
0
2
(
x
)
+
∑
k
=
0
M
-
1
N
k
·
φ
k
(
x
)
,
where x denotes the spatial coordinate in a direction running substantially perpendicular to the direction of the supply waveguide, n 0 (x) denotes the refractive index of a known multimode interference coupler, M is the mode number of the mode being able to propagate inside the at least one interference section, N k are numerical coefficients and φ k (x) denotes a set of base functions.
17. The method according to claim 16 , wherein the basic functions φ k (x) describe the field distribution of the modes which are able to propagate in the multimode interference coupler with the refractive index n 0 (x).
18. The method according to claim 16 , wherein the coefficients N k are determined in such a manner that the effective refractive index n eff for the modes which are able to propagate decreases in a quadratic manner with the number of modes.
19. The method according to claim 16 , wherein only a sub-set of the M modes which are able to propagate in said interference section is included in the calculation.
20. The method according to claim 16 , wherein the numerical coefficients N k are determined using any of a rigorous-mode solving method or a simulated annealing method.