Waveguide for an electro-optic capacitive modulator
A waveguide including a substrate, an assembly of semiconductor regions consecutively extending on the substrate along a direction corresponding to a propagation direction of an electromagnetic wave having a wavelength noted λ, the semiconductor regions being electrically alternately doped with a first conductivity type and with a second conductivity type along the propagation direction, a dielectric layer interposed between two consecutive semiconductor regions, at least one pair of consecutive elementary structures having a dimensions along the propagation direction adapted to λ to form a grating where the light propagates with no diffraction effects.
1. A waveguide for a capacitive electro-optic modulator, the waveguide defining a propagation direction for an electromagnetic wave, the waveguide comprising:
a substrate;
an assembly of semiconductor regions consecutively extending on the substrate along the propagation direction of the electromagnetic wave, the semiconductor regions being electrically alternately doped with a first conductivity type and with a second conductivity type along the propagation direction;
an assembly of dielectric layers, each dielectric layer being formed between two consecutive semiconductor regions; the assembly of semiconductor regions and the assembly of dielectric layers forming a grating of structures consecutively comprising a first structure formed by a semiconductor region of the first conductivity type and an adjacent dielectric layer, and a second structure formed by a semiconductor region of the second conductivity type and an adjacent dielectric layer; the first and second structures respectively having first and second dimensions L A , L B along the propagation direction, the grating being configured to propagate optical modes of the electromagnetic wave having a wave number k in the grating;
a first layer in direct contact with the grating of first and second structures, the first layer being offset from the propagation direction of the electromagnetic wave, the first layer having a real part n env of an effective index such that the equation:
k 0 /k<1/n env is satisfied, where k 0 is a wave number of the electromagnetic wave propagating in vacuum.
2. The waveguide according to claim 1 , wherein the grating comprises photonic bandgaps defined for
Λ
BI
=
m
λ
2
n
eff
,
where:
Λ BI is a spatial period of the grating,
m is a non-zero natural integer,
n eff is a real part of an effective index of an optical mode propagating along the propagation direction,
λ is a wavelength of the electromagnetic wave;
and wherein the first and second structures form periodic patterns having a spatial period Λ p Λ p such that the optical modes allowed to propagate by the grating are outside of the photonic bandgaps.
3. The waveguide according to claim 2 , wherein the first and second structures form p-periodic gratings such that:
L
i
+
p
=
L
i
;
et
Λ
p
=
∑
j
=
0
p
-
1
L
i
+
j
where L i is a dimension of an i-th elementary structure along the propagation direction.
4. The waveguide according to claim 3 , wherein the first and second structures form bi-periodic gratings such that L i+2 =L i ; and Λ 2 =L A +L B .
5. The waveguide according to claim 4 , wherein the first and second structures form bi-periodic gratings such that Λ 2 <λ/n eff .
6. The waveguide according to claim 1 , wherein each dielectric layer has:
a relative permittivity, ∈ r , and
a length, l 0 , along the propagation direction,
and wherein each dielectric layer is configured so that
ɛ
r
l
o
≥
C
s
/
ɛ
0
,
where C s is a predetermined value representative of a surface capacitance, and ∈ 0 is permittivity of vacuum.
7. The waveguide according to claim 6 , wherein the length along the propagation direction of the dielectric layer of each first structure and each second structure is in the range of 5 nm to 50 nm.
8. The waveguide according to claim 1 , wherein the dielectric layer of each first and second structure is configured so that a ratio between a thickness of the dielectric layer and a length along the propagation direction is in the range of 6-60.
9. The waveguide according to claim 1 , wherein the dielectric layer of each first and second structure is comprised of a material selected from the group consisting of SiO 2 , Si 3 N 4 , and HfO 2 .
10. The waveguide according to claim 1 , wherein the semiconductor regions are monocrystalline.
11. The waveguide according to claim 1 , wherein the semiconductor regions have a doping level of the first conductivity type and of the second conductivity type in the range from 10 16 cm −3 to 10 19 cm −3 .
12. The waveguide according to claim 1 , wherein each semiconductor region has a cross-section transversal to the propagation direction, the cross-section defining a base provided with a raised portion.
13. The waveguide according to claim 1 , wherein the propagation direction of the electromagnetic wave is curvilinear, and wherein L A and L B are curvilinear abscissas calculated from a central area of the waveguide.
14. A capacitive electro-optic modulator comprising the waveguide according to claim 1 .
15. The waveguide according to claim 1 , wherein the first layer is in direct contact with the first and second structures and with the assembly of dielectric layers.
16. The waveguide according to claim 1 , comprising a second layer in direct contact with the grating of structures, said second layer being offset from the propagation direction of the electromagnetic wave and separated from the first layer by the grating, the second layer having a real part n env of an effective index such that k 0 /k<1/n env .
17. The waveguide according to claim 16 , wherein the second layer is in direct contact with the first and second structures and with the assembly of dielectric layers.
18. A waveguide for a capacitive electro-optic modulator, the waveguide comprising:
at least one light source emitting an electromagnetic wave along a propagation direction, the electromagnetic wave having a wavelength noted A;
a substrate;
an assembly of semiconductor regions consecutively extending on the substrate along the propagation direction of the electromagnetic wave, the semiconductor regions being electrically alternately doped with a first conductivity type and with a second conductivity type along the propagation direction;
an assembly of dielectric layers, each dielectric layer being formed between two consecutive semiconductor regions; the assembly of semiconductor regions and the assembly of dielectric layers forming a grating of structures consecutively comprising a first structure formed by a semiconductor region of the first conductivity type and an adjacent dielectric layer, and a second structure formed by a semiconductor region of the second conductivity type and an adjacent dielectric layer; the first and second structures respectively having first and second dimensions L A , L B along the propagation direction, the grating being configured to propagate optical modes of the electromagnetic wave having a wave number k in the grating;
a layer in direct contact with the grating of first and second structures, said layer being offset from the propagation direction of the electromagnetic wave, the layer having a real part n env of an effective index such that k 0 /k<1/n env , with k 0 is a wave number of the electromagnetic wave propagating in vacuum.