Parametric process (optics)

<h2 id="temporal-characteristics">Temporal characteristics</h2>
<p>Because a parametric process prohibits a net change in the energy state of the system, parametric processes are "instantaneous".  For example, if an atom absorbs a <a href="/facts/Photon/mFNhAEzA">photon</a> with energy E, the atom's energy increases by ΔE = E, but as a parametric process, the quantum state cannot change and thus the elevated energy state must be a temporary <a href="/facts/Virtual_state_(physics)/EJYUzxfl">virtual state</a>.  By the <a href="/facts/Uncertainty_principle/UUSoSp4T">Heisenberg Uncertainty Principle</a> we know that ΔEΔt~ħ/2, thus the lifetime of a parametric process is roughly Δt~ħ/2ΔE, which is appreciably small for any non-zero ΔE.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>
</p>
<h2 id="parametric-versus-non-parametric-processes">Parametric versus non-parametric processes</h2>
<h3>Linear optics</h3>
<p>In a linear optical system the dielectric <a href="/facts/Polarization_(electrostatics)/2oQv9EHx">polarization</a>, P, responds linearly to the presence of an <a href="/facts/Electric_field/tt4MooBs">electric field</a>, E, and thus we can write
</p>

P
          
        
        =
        
          ε
          
            0
          
        
        χ
        
          
            E
          
        
        =
        (
        
          n
          
            r
          
        
        +
        i
        
          n
          
            i
          
        
        
          )
          
            2
          
        
        
          
            E
          
        
        ,
      
    
    {\displaystyle {\mathbf {P} }=\varepsilon _{0}\chi {\mathbf {E} }=(n_{r}+in_{i})^{2}{\mathbf {E} },}

<p>where ε0 is the <a href="/facts/Electric_constant/gWRUhPGY">electric constant</a>, χ is the (<a href="/facts/Complex_number/2w7mqI7e">complex</a>) <a href="/facts/Electric_susceptibility/TumGY966">electric susceptibility</a>, and nr(ni) is the real(imaginary) component of the <a href="/facts/Refractive_index/yjkzvgeE">refractive index</a> of the medium.  The effects of a parametric process will affect only nr, whereas a nonzero value of ni can only be caused by a non-parametric process.
</p><p>Thus in linear optics a parametric process will act as a lossless <a href="/facts/Dielectric/PnVt9P2G">dielectric</a> with the following effects:
</p>
<ul><li><a href="/facts/Refraction/S8kvSKzM">Refraction</a></li>
<li><a href="/facts/Diffraction/Mk80xXHT">Diffraction</a></li>
<li><a href="/facts/Scattering/nMou7lEH">Elastic scattering</a>
<ul><li><a href="/facts/Rayleigh_scattering/o0MQtPMM">Rayleigh scattering</a></li>
<li><a href="/facts/Mie_theory/5mJc3SrT">Mie scattering</a></li></ul></li></ul>
<p>Alternatively, non-parametric processes often involve loss (or gain) and give rise to:
</p>
<ul><li><a href="/facts/Absorption_(electromagnetic_radiation)/xBYKt7yS">Absorption</a></li>
<li><a href="/facts/Scattering/nMou7lEH">Inelastic scattering</a>
<ul><li><a href="/facts/Raman_scattering/obhSpgrR">Raman scattering</a></li>
<li><a href="/facts/Brillouin_scattering/bnCg0jDW">Brillouin scattering</a></li></ul></li>
<li>Various optical emission processes
<ul><li><a href="/facts/Photoluminescence/L1u2PJIa">Photoluminescence</a></li>
<li><a href="/facts/Fluorescence/qsJVT2qP">Fluorescence</a></li>
<li><a href="/facts/Luminescence/1QkIWyUj">Luminescence</a></li>
<li><a href="/facts/Phosphorescence/WshJFsKV">Phosphorescence</a></li></ul></li></ul>
<h3>Nonlinear optics</h3>
<p class="note">Main article: <a href="/facts/Nonlinear_optics/maerngXd">Nonlinear optics</a></p>
<p>In a <a href="/facts/Nonlinear_optics/maerngXd">nonlinear media</a>, the dielectric <a href="/facts/Polarization_(electrostatics)/2oQv9EHx">polarization</a> P responds nonlinearly to the <a href="/facts/Electric_field/tt4MooBs">electric field</a> E of the light.  As a parametric process is in general coherent, many parametric nonlinear processes will depend on <a href="/facts/Nonlinear_optics/maerngXd">phase matching</a> and will usually be <a href="/facts/Polarization_(waves)/fP33m0eD">polarization</a> dependent.
</p><p>Sample parametric nonlinear processes:
</p>
<ul><li><a href="/facts/Second-harmonic_generation/NzWSrT3J">Second-harmonic generation</a> (SHG), or <i>frequency doubling</i>, generation of light with a doubled frequency (half the wavelength)</li>
<li><a href="/facts/Third-harmonic_generation/JrzN8cs1">Third-harmonic generation</a> (THG), generation of light with a tripled frequency (one-third the wavelength) (usually done in two steps: SHG followed by SFG of original and frequency-doubled waves)</li>
<li><a href="/facts/High_harmonic_generation/xp3fJ3pt">High harmonic generation</a> (HHG), generation of light with frequencies much greater than the original (typically 100 to 1000 times greater)</li>
<li><a href="/facts/Sum-frequency_generation/0mPKGhN3">Sum-frequency generation</a> (SFG), generation of light with a frequency that is the sum of two other frequencies (SHG is a special case of this)</li>
<li>Difference frequency generation (DFG), generation of light with a frequency that is the difference between two other frequencies</li>
<li><a href="/facts/Optical_parametric_amplification/brn6XMuy">Optical parametric amplification</a> (OPA), amplification of a signal input in the presence of a higher-frequency pump wave, at the same time generating an <i>idler</i> wave (can be considered as DFG)</li>
<li><a href="/facts/Optical_parametric_oscillation/K6RBDNjY">Optical parametric oscillation</a> (OPO), generation of a signal and idler wave using a parametric amplifier in a resonator (with no signal input)</li>
<li><a href="/facts/Optical_parametric_generation/brn6XMuy">Optical parametric generation</a> (OPG), like parametric oscillation but without a resonator, using a very high gain instead</li>
<li><a href="/facts/Spontaneous_parametric_down-conversion/yLRBgEkH">Spontaneous parametric down-conversion</a> (SPDC), the amplification of the vacuum fluctuations in the low gain regime</li>
<li>Optical <a href="/facts/Kerr_effect/IoJN6wlW">Kerr effect</a>, intensity dependent refractive index</li>
<li><a href="/facts/Self-focusing/UvB7UP1N">Self-focusing</a></li>
<li><a href="/facts/Kerr-lens_modelocking/exJ3mYXj">Kerr-lens modelocking</a> (KLM)</li>
<li><a href="/facts/Self-phase_modulation/p7Dy5Vjv">Self-phase modulation</a> (SPM), a 
  
    
      
        
          χ
          
            (
            3
            )
          
        
      
    
    {\displaystyle \chi ^{(3)}}
  
 effect</li>
<li><a href="/facts/Soliton_(optics)/LPWgQ6AD">Optical solitons</a></li>
<li><a href="/facts/Cross-phase_modulation/KBCBvIrx">Cross-phase modulation</a> (XPM)</li>
<li><a href="/facts/Four-wave_mixing/0sRq9zld">Four-wave mixing</a> (FWM), can also arise from other nonlinearities</li>
<li><a href="/facts/Cross-polarized_wave_generation/fjov4p4y">Cross-polarized wave generation</a> (XPW), a 
  
    
      
        
          χ
          
            (
            3
            )
          
        
      
    
    {\displaystyle \chi ^{(3)}}
  
 effect in which a wave with polarization vector perpendicular to the input is generated</li></ul>
<p>Sample non-parametric nonlinear processes:
</p>
<ul><li><a href="/facts/Stimulated_Raman_scattering/obhSpgrR">Stimulated Raman scattering</a></li>
<li><a href="/facts/Raman_amplification/c2cNDHyc">Raman amplification</a></li>
<li><a href="/facts/Two-photon_absorption/BaEbrAKj">Two-photon absorption</a>, simultaneous absorption of two photons, transferring the <a href="/facts/Energy/wd8PrQM7">energy</a> to a single electron</li>
<li>Multiphoton absorption</li>
<li>Multiple <a href="/facts/Photoionisation/HIJK2mHo">photoionisation</a>, near-simultaneous removal of many bound electrons by one photon</li></ul>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Nonlinear_optics/maerngXd">Nonlinear optics</a></li></ul>
<h2 id="notes">Notes</h2>

<ul><li><a href="/facts/Robert_W._Boyd_(physicist)/9VQSz9ka">Boyd, Robert</a> (2008). <a href="https://books.google.com/books?id=uoRUi1Yb7ooC&pg=PA13">"1.2.10 Parametric versus Nonparametric Processes"</a>. <i>Nonlinear Optics</i> (3rd ed.). Academic Press. pp. 13–15. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-12-369470-6.</li>
<li>Paschotta, Rüdiger, <a href="http://www.rp-photonics.com/parametric_nonlinearities.html">"Parametric Nonlinearities"</a>, <i><a href="/facts/Encyclopedia_of_Laser_Physics_and_Technology/EkAHKqkM">Encyclopedia of Laser Physics and Technology</a></i></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>See Boyd 2008, pp. 13–15 1.2.10 Parametric versus Nonparametric Processes - Boyd, Robert (2008). "1.2.10 Parametric versus Nonparametric Processes". Nonlinear Optics (3rd ed.). Academic Press. pp. 13–15. ISBN 978-0-12-369470-6. <a href="https://books.google.com/books?id=uoRUi1Yb7ooC&pg=PA13" target="_blank">https://books.google.com/books?id=uoRUi1Yb7ooC&pg=PA13</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>See Boyd 2008, pp. 13–15 1.2.10 Parametric versus Nonparametric Processes - Boyd, Robert (2008). "1.2.10 Parametric versus Nonparametric Processes". Nonlinear Optics (3rd ed.). Academic Press. pp. 13–15. ISBN 978-0-12-369470-6. <a href="https://books.google.com/books?id=uoRUi1Yb7ooC&pg=PA13" target="_blank">https://books.google.com/books?id=uoRUi1Yb7ooC&pg=PA13</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
</ol>

Parametric process (optics) open-in-new

Parametric process (optics)