Optical device having a Mach-Zehnder interferometer with improved linearity
Example optical devices having a Mach-Zehnder interferometer (MZI) with improved linearity are presented. An example optical device may include an MZI and a microring resonator (MRR) optically coupled to any one of a first optical waveguide arm or a second optical waveguide arm, where the MRR is operable in a resonance state and in an off-resonance state during operation of the optical device. The MZI includes a length difference between the first optical waveguide arm and the second optical waveguide arm thereby achieving a quarter-period phase delay between optical signals of the first optical waveguide arm and the second optical waveguide arm such that a superlinear transmission region of the microring resonator is aligned with peaks of an optical output of the MZI improving linearity of the optical output of the MZI.
1. An optical device comprising:
a Mach-Zehnder interferometer (MZI) comprising a first optical waveguide arm and a second optical waveguide arm; and
a microring resonator (MRR) configured to exhibit a superlinear response in phase change when an optical signal inside the MRR is at resonance, and wherein the MRR is optically coupled to any one of the first optical waveguide arm or the second optical waveguide arm,
wherein the MZI comprises a length difference between the first optical waveguide arm and the second optical waveguide arm thereby achieving a quarter-period phase delay between optical signals of the first optical waveguide arm and the second optical waveguide arm such that a superlinear transmission region of the superlinear response of the MRR is aligned with peaks of an optical output of the MZI to thereby improve linearity of the optical output of the MZI.
2. The optical device of claim 1 , wherein the MRR is optically coupled to a shorter one of the first optical waveguide arm and the second optical waveguide arm.
3. The optical device of claim 1 , wherein a coupling coefficient between the MRR and the MZI is greater than a normalized optical loss incurred inside the MRR.
4. The optical device of claim 1 , wherein the length difference (ΔL MZI ) between the first optical waveguide arm and the second optical waveguide arm is set to:
(
n
M
R
R
+
Δ
n
M
R
R
)
2
π
λ
×
L
r
wherein, λ is an operating wavelength of the MZI, n MZI is a refractive index of the MZI,
and m is any integer value.
5. The optical device of claim 1 , further comprising a phase shifter formed along a portion of the MRR, wherein the phase shifter is configured to receive a voltage and induce a refractive index change (Δn MRR ) in the MRR causing an MRR-induced phase (ϕ r ) in an optical signal within the MZI.
6. The optical device of claim 5 , wherein the MRR-induced phase (ϕ r ) is equal to
(
2
m
+
1
)
λ
4
n
MZI
wherein, λ is an operating wavelength of the MZI, n MRR is a refractive index of the MRR, and L r is a circumference of the MRR.
7. The optical device of claim 1 , wherein the alignment of the superlinear transmission region of the microring resonator with the peaks of the optical output of the MZI causes a standard deviation between the output of the MZI and a linear response to be more than two times lower compared to a standard deviation between an output of a conventional MZI and the linear response.
8. The optical device of claim 1 , wherein an improvement in the linearity of the optical output increases a bit precision of the optical device by more than two times compared to a conventional MZI.
9. An optical device comprising:
an MZI comprising a first optical waveguide arm and a second optical waveguide arm; and
an MRR optically coupled to any one of the first optical waveguide arm or the second optical waveguide arm,
wherein the MZI comprises a length difference between the first optical waveguide arm and the second optical waveguide arm, and wherein the length difference is based on an annular length of the MRR such that a superlinear transmission region of the MRR is aligned with peaks of an optical output of the MZI to thereby improve linearity of the optical output of the MZI.
10. The optical device of claim 9 , wherein the MRR is optically coupled to a shorter one of the first optical waveguide arm and the second optical waveguide arm.
11. The optical device of claim 9 , wherein a coupling coefficient between the MRR and the MZI is greater than a normalized optical loss incurred inside the MRR.
12. The optical device of claim 9 , wherein the length difference (ΔL MZI ) between the first optical waveguide arm and the second optical waveguide arm is set to half of the annular length of the MRR.
13. The optical device of claim 9 , further comprising a first phase shifter formed along a portion of the MRR, wherein the MRR is formed adjacent to the first optical waveguide arm, and wherein the first phase shifter is configured to receive a first voltage and induce a first refractive index change (Δn MRR ) in the MRR causing an MRR-induced phase (ϕ r ) in an optical signal within the MZI.
14. The optical device of claim 13 , wherein the MRR-induced phase (ϕ r ) caused is equal to
(
n
M
R
R
+
Δ
n
M
R
R
)
2
π
λ
×
L
r
wherein, λ is an operating wavelength of the MZI, n MRR is a refractive index of the MRR, and L r is the annular length of the MRR.
15. The optical device of claim 13 , further comprising a second phase shifter formed along a portion of the second optical waveguide arm, wherein the second phase shifter is configured to receive a second voltage and to induce a refractive index change (Δn MRR ) in the second optical waveguide arm causing an MZI arm induced phase (ϕ r ) in the optical signal within the MZI.
16. The optical device of claim 15 , wherein the MZI arm induced phase (θ) is equal to
(
n
MZI
+
Δ
n
MZI
)
2
π
λ
×
L
r
2
wherein, λ is an operating wavelength of the MZI, n MZI is a refractive index of the MZI, L r is an annular length of the MRR, and Δn MZI is the refractive index change caused by the second voltage applied to the second phase shifter.
17. The optical device of claim 9 , wherein the improvement in the linearity of the optical output increases a bit precision of the optical device by more than two times compared to a conventional MZI.
18. The optical device of claim 9 , wherein the optical device is implemented in one or more of a computer, a server, a storage system, a wireless access point, a network switch, a router, a docking station, a printer, or a scanner.
19. An electronic system, comprising:
a circuit board; and
a photonic integrated circuit mounted on the circuit board, wherein the photonic integrated circuit comprises an optical device comprising:
an MZI comprising a first optical waveguide arm and a second optical waveguide arm; and
an MRR optically coupled to any one of the first optical waveguide arm or the second optical waveguide arm,
wherein the MZI comprises a length difference between the first optical waveguide arm and the second optical waveguide arm, and wherein the length difference is based on an annular length of the MRR such that a superlinear transmission region of the MRR is aligned with peaks of an optical output of the MZI to thereby improve linearity of the optical output of the MZI.
20. The electronic system of claim 19 , wherein the length difference between the first optical waveguide arm and the second optical waveguide arm is set to half of the annular length of the MRR.