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Related Concept Videos

¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Nonlinear Pharmacokinetics: Overview01:19

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Nonlinear or dose-dependent pharmacokinetics is a phenomenon that occurs when the pharmacokinetic parameters of certain drugs deviate from linear pharmacokinetics at higher doses. These drugs do not follow the expected first-order kinetics, where the rate of drug elimination is directly proportional to the drug concentration. Instead, they exhibit a nonlinear relationship, which can be attributed to several factors.
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Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
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Gain01:15

Gain

Gain and phase shift are properties of linear circuits that describe the effect a circuit has on a sinusoidal input voltage or current. The circuit's behavior that contains reactive elements will depend on the frequency of the input sinusoid. As a result, it is observed that the gain and phase shift will all be frequency functions.
Gain:
Suppose Vin is the input and Vout is the output signal to a circuit.

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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Large nonlinear phase shifts in second-order nonlinear-optical processes.

G I Stegeman, M Sheik-Bahae, E Van Stryland

    Optics Letters
    |October 3, 2009
    PubMed
    Summary
    This summary is machine-generated.

    Nonlinear optical processes like second-harmonic generation and parametric mixing can induce significant, field-dependent phase shifts in light beams. These effects are observable across various experimental conditions, impacting light-matter interactions.

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    Area of Science:

    • Nonlinear Optics
    • Quantum Optics
    • Photonics

    Background:

    • Parametric processes in nonlinear media are fundamental to optics.
    • Understanding phase shifts is crucial for controlling light propagation and interactions.
    • Previous studies have explored phase shifts, but broad applicability requires further investigation.

    Purpose of the Study:

    • To demonstrate that nonlinear optical processes can cause substantial phase shifts in light beams.
    • To investigate the conditions under which these field-dependent phase shifts occur.
    • To highlight the general nature of these phenomena in parametric mixing.

    Main Methods:

    • Theoretical analysis of nonlinear optical interactions.
    • Simulation of second-harmonic generation and downconversion.
    • Examination of parametric mixing in diverse optical systems.

    Main Results:

    • Identified large, field-dependent phase shifts for input beams.
    • Confirmed these shifts occur in processes like second-harmonic generation and downconversion.
    • Showcased the general applicability of parametric mixing to induce phase shifts.

    Conclusions:

    • Nonlinear optical processes provide a robust mechanism for inducing significant phase shifts.
    • Field-dependent phase shifts are a general feature of parametric mixing under various conditions.
    • These findings have implications for controlling light in nonlinear optical systems.