Optical eigenmode imaging

1. A method of optimizing in an optical system that has a laser, at least one optical measure of an optical output from the laser that is a quadratic function of a wavefunction, the method comprising:

superimposing a plurality of wavefunctions;

determining a relationship between the superimposed wavefunctions and the quadratic measure;

identifying, using a computer processor, the superimposed wavefunctions that provide a desired or optimized quadratic optical measure using the determined relationship; and

generating, using the laser, the identified superimposed wavefunctions that provide the desired or optimized quadratic optical measure.

2. A method as claimed in claim 1 wherein each superposition of wavefunctions has an amplitude and/or phase, and the method involves using the amplitude and/or phase to determine a relationship or function between superimposed wavefunctions and the quadratic measure.

3. A method as claimed in claim 2 wherein the relationship or function is a linear relationship or function of the wavefunction.

4. A method as claimed in claim 3 , wherein the linear relationship is decomposed or transformed to be represented by a series of eigenvectors/eigenvalues.

5. A method as claimed in claim 4 , wherein the optimized or desired measure is selected by choosing the maximum or minimum magnitude eigenvalue.

6. A method as claimed in claim 3 wherein the linear function is a linear operator of the wavefunction.

7. A method as claimed in claim 6 wherein the linear operator comprises a square matrix where each element is given by the quadratic measure corresponding to all the superpostions of the wavefunctions considered, to form a n by n matrix where n is the number of wavefunctions considered.

8. A method as claimed in claim 1 where constraints and/or symmetries are applied.

9. A method as claimed in claim 8 wherein one parameter is constrained to be constant and another optimized within that constraint.

10. A method as claimed in claim 9 , wherein intensity is constrained to be constant and spot size is minimized within that constraint.

11. A method as claimed in claim 1 comprising defining a region of interest and determining the relationship between the superimposed wavefunctions and the quadratic measure within the region of interest.

12. A method as claimed in claim 11 wherein the region of interest is user defined.

13. A method as claimed in claim 1 wherein the quadratic measure is selected from: spot size; energy; intensity; power; momentum; circular spin.

14. A method as claimed in claim 1 wherein the wavefunctions are orthogonal.

15. A method as claimed in claim 1 wherein the wavefunctions are electromagnetic wavefunctions.

16. A method as claimed in claim 1 wherein the method is carried out computationally to identify the superimposed wavefunctions that provide a desired or optimized quadratic measure.

17. A method as claimed in claim 1 wherein the method is carried out experimentally to identify the superimposed wavefunctions that provide a desired or optimized quadratic measure.

18. A computer program product for optimizing in an optical system that has a laser, located on a non-transitory computer readable medium comprising instructions for operation by a computing device, said instructions comprising:

instructions configured for superimposing a plurality of wavefunctions;

instructions configured for determining a relationship between the superimposed wavefunctions and the quadratic measure;

instructions configured for identifying the superimposed wavefunctions that provide a desired or optimized quadratic optical measure using the determined relationship; and

instructions configured for generating, using a laser, the identified superimposed wavefunctions that provide the desired or optimized quadratic optical measure.

19. A device adapted to cause superposition of a plurality of wavefunctions, so as to optimize a quadratic measure, the plurality of wavefunctions being determined using the following operations by said device:

superimposing a plurality of wavefunctions;

determining a relationship between the superimposed wavefunctions and the quadratic measure;

identifying the superimposed wavefunctions that provide a desired or optimized quadratic optical measure using the determined relationship; and

generating, using a laser, the identified superimposed wavefunctions that provide the desired or optimized quadratic optical measure.

20. A device as claimed in claim 19 comprising a diffractive optical element adapted to create the optimized plurality of wavefunctions.

21. A device as claimed in claim 19 adapted to create a sub-diffraction limit spot size.

22. A method for forming an image in an optical system that has a laser, the method comprising:

illuminating a target with a plurality of wavefunctions;

capturing light that has interacted with the target;

decomposing the captured light into a plurality of wavefunctions that together describe the target;

determining a relationship between the superimposed wavefunctions and a quadratic measure;

identifying the superimposed wavefunctions that provide a desired or optimized quadratic optical measure using the determined relationship; and

using the identified superimposed wavefunctions to create an image of the target.

23. A method as claimed in claim 22 wherein the light captured is transmitted through or reflected from or scattered from the target.

24. A method as claimed in claim 22 , wherein the wavefunctions are electromagnetic wavefunctions.

25. A computer-implemented method of optimizing a spot size of an optical beam, the method comprising:

superimposing a plurality of wavefunctions;

determining, using a computer processor, a relationship between the superimposed wavefunctions and the spot size;

identifying, using a computer processor, the superimposed wavefunctions that provide a desired or optimized spot size using the determined relationship; and

generating, using a laser, the identified superimposed wavefunctions that provide the desired or optimized spot size.

26. The computer-implemented method as claimed in claim 25 , wherein the optimized spot size is below a diffraction limit.

27. The computer-implemented method as claimed in claim 25 , wherein the optimized spot size is a focal point spot size and the focal point spot size is below a diffraction limit.

28. A computer-implemented method of optimizing, in an optical trapping system, at least one measure that is a quadratic function of a wavefunction, the method comprising:

superimposing a plurality of wavefunctions;

determining, using a computer processor, a relationship between the superimposed wavefunctions and the quadratic measure;

identifying, using a computer processor, the superimposed wavefunctions that provide a desired or optimized quadratic using the determined relationship; and

generating, using a laser, an optical trap for trapping at least one particle, wherein the optical trap generates the identified superimposed wavefunctions that provide the desired or optimized quadratic measure.

29. A device adapted to optimizing a spot size of an optical beam using the following operations:

superimposing a plurality of wavefunctions;

determining, using a computer processor, a relationship between the superimposed wavefunctions and the spot size;

identifying, using a computer processor, the superimposed wavefunctions that provide a desired or optimized spot size using the determined relationship; and

generating, using a laser, the identified superimposed wavefunctions that provide the desired or optimized spot size.

30. A device as claimed in claim 29 , wherein the optimized spot size is below a diffraction limit.

31. A device as claimed in claim 29 , wherein the optimized spot size is a focal point spot size and the focal point spot size is below a diffraction limit.

32. A device for optimizing, in an optical trapping system, at least one measure that is a quadratic function of a wavefunction using the following operations:

superimposing a plurality of wavefunctions;

determining, using a computer processor, a relationship between the superimposed wavefunctions and the quadratic measure;

identifying, using a computer processor, the superimposed wavefunctions that provide a desired or optimized quadratic using the determined relationship; and

generating, using a laser, an optical trap for trapping at least one particle, wherein the optical trap generates the identified superimposed wavefunctions that provide the desired or optimized quadratic measure.