Chip-scale optomechanical gravimeter

1. A method of determining a gravitational force, the method comprising:

providing at least one first radiation to at least one optomechanical oscillator, the at least one optomechanical oscillator being structured to deform under the gravitational force to cause a shift in resonance associated with the at least one optomechanical oscillator, wherein the at least one optomechanical oscillator includes a photonic crystal separated into a first portion and a second portion by an air slot, a width of the air slot is structured to be altered under the gravitational force;

receiving at least one second radiation from the at least one optomechanical oscillator, wherein the at least one second radiation is associated with the shift in the resonance, wherein the air slot forms a waveguide through which the first radiation and the second radiation travel; and

determining the shift in the resonance based on the first and second radiations, wherein the shift in the resonance is associated with the alteration of the width of the air slot through which the first and second radiations travel.

2. The method of claim 1 , further comprising determining a change in the gravitational force based on the shift in the resonance.

3. The method of claim 1 , wherein determining the shift comprises measuring modulation associated with an optomechanical cavity, the modulation being determined by comparing the first and second radiations.

4. The method of claim 3 , wherein measuring the modulation comprises measuring an amplitude and phase of the second radiation.

5. A non-transitory computer readable medium for determining a shift in a resonance associated with at least one optomechanical oscillator, the computer readable medium including instructions stored therein and accessible by a hardware processing arrangement, wherein, when the processing arrangement executes the instructions, the processing arrangement is configured to perform at least one procedure comprising:

directing at least one first radiation to at least one optomechanical oscillator, the at least one optomechanical oscillator being structured to deform under the gravitational force to cause a shift in resonance associated with the at least one optomechanical oscillator, wherein the at least one optomechanical oscillator includes a photonic crystal separated into a first portion and a second portion by an air slot, a width of the air slot is structured to be altered under the gravitational force;

receiving at least one second radiation from the at least one optomechanical oscillator, wherein the at least one second radiation is associated with the shift in the resonance, wherein the air slot forms a waveguide through which the first radiation and the second radiation travel; and

determining the shift in the resonance based on the first and second radiations, wherein the shift in the resonance is associated with the alteration of the width of the air slot through which the first and second radiations travel.

6. The computer readable medium of claim 5 , wherein the processing arrangement is further configured to determine a change in the gravitational force based on the shift in the resonance.

7. The computer readable medium of claim 5 , wherein determining the shift comprises measuring modulation associated with an optomechanical cavity, the modulation being determined by comparing the first and second radiations.

8. The computer readable medium of claim 7 , wherein measuring the modulation comprises measuring an amplitude and phase of the second radiation.

9. An apparatus for measuring gravitational force comprising:

at least one optomechanical oscillator, the at least one optomechanical oscillator having an initial resonance, and a second resonance when displaced by gravitational force;

at least one radiation source arrangement to direct at least one first radiation towards the at least one optomechanical oscillator;

at least one photonic crystal having:

at least one cavity coupling optical and mechanical degrees of freedom of the oscillator, and

at least one air slot separating the at least one photonic crystal into a first portion and a second portion, the at least one air slot forming a waveguide through which the at least first radiation travels, wherein a width of the at least one air slot is structured to be altered under the gravitational force;

at least one detecting arrangement to at least one of receive or detect at least one second radiation from the at least one at least one optomechanical oscillator; and

at least one hardware processing arrangement to determine:

the shift in the resonance associated with the at least one optomechanical oscillator based on the first and second radiations, wherein the shift in the resonance is associated with the alteration of the width of the at least one air slot, and

the gravitational force based on the shift in the resonance.

10. The apparatus of claim 9 , wherein the at least one cavity includes a high Q/V air-slot photonic crystal mode gap cavity.

11. The apparatus of claim 9 , further comprising a mass suspended by one or more tethers on which the at least one optomechanical oscillator is disposed.

12. The apparatus of claim 9 , wherein the at least one air slot is associated with an optomechanical cavity, and wherein a mass is coupled to the optomechanical cavity such that a change in the gravitational force impacts the mass by correspondingly changing a size of the optomechanical cavity to cause the shift in the resonance.

13. The apparatus of claim 9 , wherein the at least one optomechanical oscillator comprises a chip-scale optical oscillator employing a material having a nonlinear response to an optical field to cause the shift in resonance based on a nonlinear interaction coupling optical and mechanical modes.

14. The apparatus of claim 9 , wherein the at least one optomechanical oscillator comprises a chip-scale optical oscillator employing the photonic crystal defining the at least one air slot having holes formed in the photonic crystal on opposite sides of the at least one air slot for forming the waveguide for an optical signal to travel through the at least one air slot.

15. The apparatus of claim 14 , wherein a width of the air slot is changeable responsive to a change in the gravitational force such that a change in the width of the air slot causes the shift in the resonance, and wherein the shift in resonance is measured to provide an indication of the change in the gravitational force.