Photonic bandgap phase modulator, optical filter bank, photonic computing system, and methods of use

1. A method for optical modulation, comprising, at an optical filter bank comprising a waveguide, a first photonic bandgap phase modulator (PhBPM) defining a first portion of the waveguide, and a second PhBPM defining a second portion of the waveguide:

applying a first electrical input to a first photonic crystal region of the first PhBPM, wherein the first photonic crystal region is operable to transition, based on the first electrical input, between:

a first mode, in which light of a first wavelength and light of a second wavelength propagates through the first photonic crystal region in a first photonic band defining a first refractive index; and

a second mode, in which light of the first wavelength propagates through the first photonic crystal region in a second photonic band defining a second refractive index substantially different from the first refractive index, and light of the second wavelength propagates through the first photonic crystal region in the first photonic band;

substantially concurrent with applying the first electrical input to the first photonic crystal region, applying a second electrical input to a second photonic crystal region of the second PhBPM, wherein the second photonic crystal region is operable to transition, based on the second electrical input, between:

a third mode, in which light of the second wavelength propagates through the second photonic crystal region in a third photonic band defining a third refractive index, and light of the first wavelength propagates through the second photonic crystal region in a fourth photonic band defining a fourth refractive index substantially different from the third refractive index; and

a fourth mode, in which light of the first wavelength and light of the second wavelength propagates through the second photonic crystal region in the fourth photonic band;

while applying the first electrical input to the first photonic crystal region and applying the second electrical input to the second photonic crystal region, at the waveguide, receiving a first optical input signal, the first optical input signal comprising a first portion having the first wavelength and a second portion having the second wavelength, wherein:

the first optical input signal propagates along the waveguide through the first and second PhBPMs;

the first PhBPM phase modulates the first portion based on the first electrical input and does not substantially phase modulate the second portion; and

the second PhBPM phase modulates the second portion based on the second electrical input and does not substantially phase modulate the first portion.

2. The method of claim 1 , wherein:

the optical filter bank further comprises:

a second waveguide; and

an output coupler that optically couples the waveguide to the second waveguide, the output coupler defining an optical output; and

the waveguide defines a first light propagation path, wherein the first and second portions of the waveguide precede the output coupler along the first light propagation path;

the method further comprising:

substantially concurrent with receiving the first optical input signal, at the second waveguide, receiving a second optical input signal, the second optical input signal comprising a third portion having the first wavelength and a fourth portion having the second wavelength;

after the first PhBPM phase modulates the first portion and the second PhBPM phase modulates the second portion, generating an optical output signal, comprising coupling the first optical input signal and the second optical input signal at the output coupler; and

outputting the optical output signal.

3. The method of claim 2 , further comprising, at an input coupler:

receiving a combined optical input signal;

splitting the combined optical input signal into the first and second optical input signals;

providing the first optical input signal to the waveguide; and

providing the second optical input signal to the second waveguide.

4. The method of claim 2 , wherein, before the first PhBPM phase modulates the first portion and the second PhBPM phase modulates the second portion, the first and second optical input signals are substantially identical.

5. The method of claim 2 , further comprising:

receiving a first modulation factor and a second modulation factor;

determining the first electrical input based on the first modulation factor; and

determining the second electrical input based on the second modulation factor;

wherein:

the optical output signal comprises a fifth portion having the first wavelength and a sixth portion having the second wavelength;

a first intensity ratio, defined by a fifth portion intensity divided by a first portion intensity, is substantially equal to the first modulation factor; and

a second intensity ratio, defined by a sixth portion intensity divided by a second portion intensity, is substantially equal to the first modulation factor.

6. The method of claim 1 , wherein:

the optical filter bank further comprises a third PhBPM defining a third portion of the waveguide;

the method further comprises, substantially concurrent with applying the first electrical input to the first photonic crystal region, applying a third electrical input to a third photonic crystal region of the third PhBPM, wherein the third photonic crystal region is operable to transition, based on the third electrical input, between:

a fifth mode, in which light of the third wavelength propagates through the third photonic crystal region in a fifth photonic band defining a fifth refractive index; and

a sixth mode, in which light of the third wavelength propagates through the third photonic crystal region in a sixth photonic band defining a sixth refractive index substantially different from the fifth refractive index;

the optical input signal further comprises a third portion having the third wavelength;

the optical input signal propagates along the waveguide through the third PhBPM;

the third PhBPM phase modulates the third portion based on the third electrical input and does not substantially phase modulate the first and second portions; and

the first and second PhBPMs do not substantially phase modulate the third portion.

7. The method of claim 6 , wherein:

the first wavelength is shorter than the second wavelength;

the second wavelength is shorter than the third wavelength;

at the first photonic crystal region, in the first mode and in the second mode, light of the third wavelength propagates through the first photonic crystal region in the first photonic band;

at the second photonic crystal region, in the third mode and in the fourth mode, light of the third wavelength propagates through the second photonic crystal region in the third photonic band;

at the third photonic crystal region, in the fifth mode and in the sixth mode, light of the first wavelength and light of the second wavelength propagates through the third photonic crystal region in the sixth photonic band.

8. The method of claim 7 , wherein:

the first wavelength is within 10 nm of the second wavelength; and

the third wavelength is within 10 nm of the second wavelength.

9. The method of claim 1 , wherein:

the optical input signal further comprises a third portion having an intermediate wavelength, wherein the intermediate wavelength is longer than the first wavelength and shorter than the second wavelength;

at the first photonic crystal region, in the first mode, light of the intermediate wavelength propagates through the first photonic crystal region in the first photonic band;

at the first photonic crystal region, in the second mode, light of the intermediate wavelength propagates through the first photonic crystal region in the second photonic band;

at the second photonic crystal region, in the third mode, light of the intermediate wavelength propagates through the second photonic crystal region in the third photonic band;

at the second photonic crystal region, in the fourth mode, light of the intermediate wavelength propagates through the second photonic crystal region in the fourth photonic band;

the first PhBPM phase modulates the third portion based on the first electrical input; and

the second PhBPM phase modulates the third portion based on the second electrical input.

10. The method of claim 9 , wherein:

the optical filter bank further comprises:

a second waveguide; and

an output coupler that optically couples the waveguide to the second waveguide, the output coupler defining an optical output; and

the waveguide defines a first light propagation path, wherein the first and second portions of the waveguide precede the output coupler along the first light propagation path;

the method further comprises:

substantially concurrent with receiving the first optical input signal, at the second waveguide, receiving a second optical input signal, the second optical input signal comprising a fourth portion having the first wavelength, a fifth portion having the second wavelength, and a sixth portion having the intermediate wavelength;

after the first PhBPM phase modulates the first and third portions and the second PhBPM phase modulates the second and third portions, generating an optical output signal, comprising coupling the first optical input signal and the second optical input signal at the output coupler; and

outputting the optical output signal;

the optical output signal comprises a seventh portion having the first wavelength, an eighth portion having the second wavelength, and a ninth portion having the intermediate wavelength;

a first intensity ratio, defined by a seventh portion intensity divided by a first portion intensity, is substantially equal to 1; and

a second intensity ratio is substantially equal to a third intensity ratio, wherein:

the second intensity ratio is equal to an eighth portion intensity divided by a second portion intensity; and

the third intensity ratio is equal to a ninth portion intensity divided by a third portion intensity.

11. The method of claim 1 , wherein:

the first electrical input maintains the first photonic crystal region in the first mode; and

the method further comprises, after applying the first electrical input to the first photonic crystal region, applying a third electrical input to the first photonic crystal region, wherein the third electrical input maintains the first photonic crystal region in the second mode.

12. The method of claim 11 , further comprising, substantially concurrent with applying the third electrical input to the first photonic crystal region, applying a fourth electrical input to the second photonic crystal region, wherein:

the fourth electrical input is substantially identical to the second electrical input;

the second electrical input maintains the second photonic crystal region in the fourth mode; and

the fourth electrical input maintains the second photonic crystal region in the fourth mode.

13. The method of claim 11 , wherein:

applying the first electrical input to the first photonic crystal region comprises substantially maintaining a reverse bias across a semiconductor junction of the first PhBPM, wherein the semiconductor junction comprises the first photonic crystal region; and

applying the third electrical input to the first photonic crystal region comprises not maintaining a substantial reverse bias across a semiconductor junction of the first PhBPM, wherein the semiconductor junction comprises the first photonic crystal region.

14. The method of claim 1 , wherein:

the first PhBPM further comprises a third photonic crystal region defining a photonic band structure substantially identical to the first photonic crystal region;

the second PhBPM further comprises a fourth photonic crystal region defining a photonic band structure substantially identical to the second photonic crystal region;

the method further comprises, substantially concurrent with applying the first electrical input to the first photonic crystal region and applying the second electrical input to the second photonic crystal region:

applying a third electrical input to the third photonic crystal region, wherein the third photonic crystal region is operable to transition, based on the third electrical input, between the first mode and the second mode; and

substantially concurrent with applying the third electrical input to the third photonic crystal region, applying a fourth electrical input to the fourth photonic crystal region, wherein the fourth photonic crystal region is operable to transition, based on the fourth electrical input, between the third mode and the fourth mode;

the first PhBPM further phase modulates the first portion based on the third electrical input; and

the second PhBPM further phase modulates the second portion based on the fourth electrical input.

15. The method of claim 1 , wherein:

the optical filter bank further comprises a continuous photonic crystal defining a substantially regular array of holes, the continuous photonic crystal comprising the first photonic crystal region, the second photonic crystal region, and a transition region defining a first end and a second end, wherein the first end abuts the first photonic crystal region and the second end abuts the second photonic crystal region;

in the first photonic crystal region, the holes of the array substantially define a first width;

in the second photonic crystal region, the holes of the array substantially define a second width substantially greater than the first width; and

in the transition region, a width of the holes of the array increases substantially monotonically from the first end to the second end.

16. The method of claim 1 , wherein:

the first and third refractive indices are greater than zero; and

the second and fourth refractive indices are less than zero.