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Related Concept Videos

Integrals of Powers of Sine and Cosine01:29

Integrals of Powers of Sine and Cosine

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Trigonometric integrals involve the integration of expressions containing powers of sine, cosine, and related functions. They are common in calculus problems and have applications in physics and engineering. The method for integrating expressions of the form sinm(x)cosn(x) depends on whether the exponents are odd or even.If the power of sine is odd, one sine factor is separated from the integrand, leaving an even power of sine. The remaining sine terms are rewritten in terms of cosine using the...
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Integrals of Powers of Secant and Tangent01:18

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Integrals involving powers of tangent and secant are commonly evaluated using substitution, with the strategy determined by the parity of the exponents. The method relies on pairing part of the integrand with the derivative of a suitable trigonometric function and rewriting the remaining factors using trigonometric identities.When the power of secant is even, tangent is chosen as the substitution variable. Since the derivative of tangent is secant squared, a factor of sec⁡2x can be...
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Harmonic Mean

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The arithmetic mean is usually skewed towards the larger values in the data set. Therefore, to avoid this inherent bias towards smaller values, the harmonic mean is used.
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Simple harmonic motion is the name given to oscillatory motion for a system where the net force can be described by Hooke's law. If the net force can be described by Hooke's law and there is no damping (by friction or other non-conservative forces), then a simple harmonic oscillator will oscillate with equal displacement on either side of the equilibrium position. To derive an equation for period and frequency, the equation of motion is used. The period of a simple harmonic oscillator is given...
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Harmonic Nanoparticles for Regenerative Research
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Low-power integrated optical amplification through second-harmonic resonance.

Devin J Dean1, Taewon Park1,2, Hubert S Stokowski1

  • 1Department of Applied Physics and Ginzton Laboratory, Stanford University, Stanford, CA, USA.

Nature
|January 28, 2026
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Summary
This summary is machine-generated.

We developed a low-power integrated optical parametric amplifier (OPA) on thin-film lithium niobate, achieving high gain with minimal input power. This breakthrough enables practical on-chip OPAs for advanced quantum and classical photonics applications.

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Area of Science:

  • Photonics and Optical Engineering
  • Quantum Information Science
  • Materials Science

Background:

  • Optical amplifiers are crucial for telecommunications, sensing, and quantum processing.
  • Existing technologies like erbium-doped and semiconductor amplifiers have limitations in wavelength coverage, noise, and distortion.
  • Optical parametric amplifiers (OPAs) offer broadband, quantum-limited amplification but require high power, hindering miniaturization.

Purpose of the Study:

  • To demonstrate a miniaturized, low-power optical parametric amplifier (OPA) integrated on a thin-film lithium niobate platform.
  • To overcome the high power requirements that have limited the practical deployment of OPAs.
  • To achieve high gain and broadband amplification with significantly reduced input power for next-generation photonic applications.

Main Methods:

  • Developed a second-harmonic-resonant integrated OPA design on thin-film lithium niobate.
  • Utilized pump recirculation to enhance pump generation efficiency (95% conversion) and power utilization.
  • Implemented a resonant architecture to effectively increase pump power and multiplex signal and pump without sacrificing bandwidth.

Main Results:

  • Achieved >17 dB gain with <200 mW input power, an order of magnitude improvement over previous OPAs.
  • Demonstrated flat, near-quantum-limited noise performance across an 110 nm bandwidth.
  • The resonant design effectively increased the pump power by nearly an order of magnitude compared to single-pass designs.

Conclusions:

  • The demonstrated low-power, integrated OPA on thin-film lithium niobate overcomes previous power limitations.
  • This technology enables practical on-chip OPAs, paving the way for advancements in quantum and classical photonics.
  • The resonant design offers efficient amplification with broadband, low-noise characteristics suitable for diverse photonic applications.