Point-wise phase matching for nonlinear frequency generation in dielectric resonators
An optical resonator fabricated from a uniaxial birefringent crystal, such as beta barium borate. The crystal is cut with the optical axis not perpendicular to a face of the cut crystal. In some cases the optical axis lies in the plane of the cut crystal face. An incident (input) electromagnetic signal (which can range from the infrared through the visible to the ultraviolet) is applied to the resonator. An output signal is recovered which has a frequency that is an integer multiple of the frequency of the input signal. In some cases a prism is used to evanescently couple the input and the output signals to the resonator.
1. An optical resonator, comprising:
a birefringent crystal having an optical axis, said birefringent crystal cut so that said optical axis is disposed at an angle different from 0 degrees relative to a direction perpendicular to a cut face of said birefringent crystal, said birefringent crystal configured to operate in a whispering gallery mode of optical propagation, said birefringent crystal configured to receive an input electromagnetic signal having a first frequency f 1 and configured to provide in response to said input electromagnetic signal an output electromagnetic signal having a second frequency f 2 , said first frequency and said second frequency being related according to the relation
f 2 =N ×f 1
where N is an integer greater than 1.
2. The optical resonator of claim 1 , wherein said birefringent crystal is beta barium borate.
3. The optical resonator of claim 1 , wherein said optical axis is disposed at an angle of 90 degrees relative to a direction perpendicular to a cut face of said birefringent crystal.
4. The optical resonator of claim 1 , wherein said input electromagnetic signal is a TE mode electromagnetic signal.
5. The optical resonator of claim 1 , wherein said output electromagnetic signal is a TM mode electromagnetic signal.
6. The optical resonator of claim 1 , wherein said integer N=2.
7. The optical resonator of claim 1 , wherein said input electromagnetic signal is an infrared signal.
8. The optical resonator of claim 1 , wherein said input electromagnetic signal is a visible signal.
9. The optical resonator of claim 1 , wherein said input electromagnetic signal is an ultraviolet signal.
10. The optical resonator of claim 1 , further comprising a structure evanescently coupled to said birefringent crystal, said structure configured to couple said input electromagnetic signal into said birefringent crystal, and said structure configured to couple said output electromagnetic signal out of said birefringent crystal.
11. The optical resonator of claim 10 , wherein said structure evanescently coupled to said birefringent crystal is a prism.
12. A method of generating a harmonic of an electromagnetic signal, comprising the steps of:
providing a birefringent crystal having an optical axis, said birefringent crystal cut so that said optical axis is disposed at an angle different from 0 degrees relative to a direction perpendicular to a cut face of said birefringent crystal;
applying an input electromagnetic signal having a first frequency f 1 to said birefringent crystal;
operating said birefringent crystal in a whispering gallery mode of optical propagation; and
recovering from said birefringent crystal an output electromagnetic signal having a second frequency f 2 , said first frequency and said second frequency being related according to the relation
f 2 =N ×f 1
where N is an integer greater than 1.
13. The method of generating a harmonic of an electromagnetic signal of claim 12 , wherein said optical axis is disposed at an angle of 90 degrees relative to a direction perpendicular to a cut face of said birefringent crystal.
14. The method of generating a harmonic of an electromagnetic signal of claim 12 , wherein said input electromagnetic signal is a TE mode electromagnetic signal.
15. The method of generating a harmonic of an electromagnetic signal of claim 12 , wherein said output electromagnetic signal is a TM mode electromagnetic signal.
16. The method of generating a harmonic of an electromagnetic signal of claim 12 , wherein said integer N=2.
17. The method of generating a harmonic of an electromagnetic signal of claim 12 , wherein said input electromagnetic signal is an infrared signal.
18. The method of generating a harmonic of an electromagnetic signal of claim 12 , wherein said input electromagnetic signal is a visible signal.
19. The method of generating a harmonic of an electromagnetic signal of claim 12 , wherein said input electromagnetic signal is an ultraviolet signal.
20. The method of generating a harmonic of an electromagnetic signal of claim 12 , wherein at least one of said input electromagnetic signal and said output electromagnetic signal is evanescently coupled to said birefringent crystal by way of a prism.