RECONSTRUCTION OF NONLINEAR WAVE PROPAGATION
First Claim
1. A method for characterizing a nonlinear medium, said method comprising:
- providing a known input waveform to said nonlinear medium such that said input waveform propagates through said nonlinear medium, said input waveform representative of two or more dimensional spatial information;
characterizing an output waveform emerging from said nonlinear medium; and
computationally propagating said output waveform through said nonlinear medium so as to obtain an estimated waveform that sufficiently matches said input waveform, said computational propagation depending on one or more properties of said nonlinear medium such that obtaining of said estimated waveform results in characterization of said one or more properties of said nonlinear medium.
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Abstract
Disclosed are systems and methods for characterizing a nonlinear propagation environment by numerically propagating a measured output waveform resulting from a known input waveform. The numerical propagation reconstructs the input waveform, and in the process, the nonlinear environment is characterized. In certain embodiments, knowledge of the characterized nonlinear environment facilitates determination of an unknown input based on a measured output. Similarly, knowledge of the characterized nonlinear environment also facilitates formation of a desired output based on a configurable input. In both situations, the input thus characterized and the output thus obtained include features that would normally be lost in linear propagations. Such features can include evanescent waves and peripheral waves, such that an image thus obtained are inherently wide-angle, farfield form of microscopy.
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Citations
59 Claims
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1. A method for characterizing a nonlinear medium, said method comprising:
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providing a known input waveform to said nonlinear medium such that said input waveform propagates through said nonlinear medium, said input waveform representative of two or more dimensional spatial information; characterizing an output waveform emerging from said nonlinear medium; and computationally propagating said output waveform through said nonlinear medium so as to obtain an estimated waveform that sufficiently matches said input waveform, said computational propagation depending on one or more properties of said nonlinear medium such that obtaining of said estimated waveform results in characterization of said one or more properties of said nonlinear medium. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
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13. An optical system, comprising:
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a nonlinear optical medium configured to receive a first waveform and yield a second waveform; a processor configured so as to obtain information about two of said nonlinear optical medium, first waveform, and second waveform and generate characterization of the remaining one of said nonlinear optical medium, first waveform, and second waveform, said generated characterization comprising numerical propagation of one of said first and second waveforms through said nonlinear optical medium. - View Dependent Claims (14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39)
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40. A computer-readable medium containing machine-executable instructions that, if executed by a device having one or more processors, causes the device to perform operations comprising:
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obtaining a digital representation of a measured output waveform resulting from propagation of an input waveform through a nonlinear medium; and computationally propagating said digital representation of said measured output waveform through said nonlinear medium so as to reconstruct a digital representation of said input waveform, said computational propagation depending on one or more properties of said nonlinear medium, information about said one or more properties stored in said computer-readable medium or accessible by said machine-executable instructions. - View Dependent Claims (42)
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41. A method for characterizing nonlinear wave propagation, said method comprising:
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providing a known input waveform to propagate through a first nonlinear environment so as to yield a first intensity distribution; providing said known input waveform to propagate through a second nonlinear environment so as to yield a second intensity distribution; determining an output waveform based at least in part on a difference between said first and second intensity distributions; and computationally propagating said output waveform through one of said first and second nonlinear environments to reconstruct an approximation of said input waveform. - View Dependent Claims (43, 44)
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45. An optical system, comprising:
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a nonlinearity component configured to provide first and second nonlinear propagation environments for an input waveform to respectively yield first and second output waveforms; an imaging device configured to detect at least intensity portions of said first and second output waveforms and generate first and second intensity distributions, respectively; and a processor configured to determine an output waveform based at least in part on a difference between said first and second intensity distributions. - View Dependent Claims (46, 47, 48, 49, 50, 51, 52)
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53. An apparatus, comprising:
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a nonlinear element configured so as to provide a nonlinear propagation environment for a wave passing therethrough, said nonlinear element dimensioned to receive an input and yield an output; and a computer-readable medium containing instructions that calculates one of said input and output if given the other, said calculation achieved numerically in an iterative manner using one or more parameters that characterize said nonlinear propagation environment. - View Dependent Claims (54, 55, 56, 57, 58, 59)
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Specification