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Optics operators

88 operators in the optics category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

OperatorDescriptionEquation
OP1Snell's law of refraction relating angles and refractive indices at a material interface.n_1\sin\theta_1 = n_2\sin\theta_2
OP10Resolving power of a diffraction grating: minimum resolvable wavelength difference.\Delta\lambda = \frac{\lambda}{mN}
OP2Thin lens equation relating object distance, image distance, and focal length.\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}
OP3Diffraction grating equation: constructive interference condition for multiple slits.d\sin\theta = m\lambda
OP4Malus's law: intensity of polarized light through a polarizer varies as cosine squared of angle.I = I_0\cos^2\theta
OP5Photon energy: energy of a quantum of light equals Planck's constant times frequency.E = h\nu = \frac{hc}{\lambda}
OP554Zeq spectral optics operator 554: quantum state expansion in the optics eigenbasis at channel 554.\hat{O}_{554} = \sum_n c_n |n\rangle\langle n|
OP555Zeq spectral optics operator 555: quantum state expansion in the optics eigenbasis at channel 555.\hat{O}_{555} = \sum_n c_n |n\rangle\langle n|
OP556Zeq spectral optics operator 556: quantum state expansion in the optics eigenbasis at channel 556.\hat{O}_{556} = \sum_n c_n |n\rangle\langle n|
OP557Zeq spectral optics operator 557: quantum state expansion in the optics eigenbasis at channel 557.\hat{O}_{557} = \sum_n c_n |n\rangle\langle n|
OP558Zeq spectral optics operator 558: quantum state expansion in the optics eigenbasis at channel 558.\hat{O}_{558} = \sum_n c_n |n\rangle\langle n|
OP559Zeq spectral optics operator 559: quantum state expansion in the optics eigenbasis at channel 559.\hat{O}_{559} = \sum_n c_n |n\rangle\langle n|
OP560Zeq spectral optics operator 560: quantum state expansion in the optics eigenbasis at channel 560.\hat{O}_{560} = \sum_n c_n |n\rangle\langle n|
OP561Zeq spectral optics operator 561: quantum state expansion in the optics eigenbasis at channel 561.\hat{O}_{561} = \sum_n c_n |n\rangle\langle n|
OP562Zeq spectral optics operator 562: quantum state expansion in the optics eigenbasis at channel 562.\hat{O}_{562} = \sum_n c_n |n\rangle\langle n|
OP563Zeq spectral optics operator 563: quantum state expansion in the optics eigenbasis at channel 563.\hat{O}_{563} = \sum_n c_n |n\rangle\langle n|
OP564Zeq spectral optics operator 564: quantum state expansion in the optics eigenbasis at channel 564.\hat{O}_{564} = \sum_n c_n |n\rangle\langle n|
OP565Zeq spectral optics operator 565: quantum state expansion in the optics eigenbasis at channel 565.\hat{O}_{565} = \sum_n c_n |n\rangle\langle n|
OP566Zeq spectral optics operator 566: quantum state expansion in the optics eigenbasis at channel 566.\hat{O}_{566} = \sum_n c_n |n\rangle\langle n|
OP567Zeq spectral optics operator 567: quantum state expansion in the optics eigenbasis at channel 567.\hat{O}_{567} = \sum_n c_n |n\rangle\langle n|
OP568Zeq spectral optics operator 568: quantum state expansion in the optics eigenbasis at channel 568.\hat{O}_{568} = \sum_n c_n |n\rangle\langle n|
OP569Zeq spectral optics operator 569: quantum state expansion in the optics eigenbasis at channel 569.\hat{O}_{569} = \sum_n c_n |n\rangle\langle n|
OP570Zeq spectral optics operator 570: quantum state expansion in the optics eigenbasis at channel 570.\hat{O}_{570} = \sum_n c_n |n\rangle\langle n|
OP571Zeq spectral optics operator 571: quantum state expansion in the optics eigenbasis at channel 571.\hat{O}_{571} = \sum_n c_n |n\rangle\langle n|
OP572Zeq spectral optics operator 572: quantum state expansion in the optics eigenbasis at channel 572.\hat{O}_{572} = \sum_n c_n |n\rangle\langle n|
OP573Zeq spectral optics operator 573: quantum state expansion in the optics eigenbasis at channel 573.\hat{O}_{573} = \sum_n c_n |n\rangle\langle n|
OP574Zeq spectral optics operator 574: quantum state expansion in the optics eigenbasis at channel 574.\hat{O}_{574} = \sum_n c_n |n\rangle\langle n|
OP575Zeq spectral optics operator 575: quantum state expansion in the optics eigenbasis at channel 575.\hat{O}_{575} = \sum_n c_n |n\rangle\langle n|
OP576Zeq spectral optics operator 576: quantum state expansion in the optics eigenbasis at channel 576.\hat{O}_{576} = \sum_n c_n |n\rangle\langle n|
OP577Zeq spectral optics operator 577: quantum state expansion in the optics eigenbasis at channel 577.\hat{O}_{577} = \sum_n c_n |n\rangle\langle n|
OP578Zeq spectral optics operator 578: quantum state expansion in the optics eigenbasis at channel 578.\hat{O}_{578} = \sum_n c_n |n\rangle\langle n|
OP579Zeq spectral optics operator 579: quantum state expansion in the optics eigenbasis at channel 579.\hat{O}_{579} = \sum_n c_n |n\rangle\langle n|
OP580Zeq spectral optics operator 580: quantum state expansion in the optics eigenbasis at channel 580.\hat{O}_{580} = \sum_n c_n |n\rangle\langle n|
OP581Zeq spectral optics operator 581: quantum state expansion in the optics eigenbasis at channel 581.\hat{O}_{581} = \sum_n c_n |n\rangle\langle n|
OP582Zeq spectral optics operator 582: quantum state expansion in the optics eigenbasis at channel 582.\hat{O}_{582} = \sum_n c_n |n\rangle\langle n|
OP583Zeq spectral optics operator 583: quantum state expansion in the optics eigenbasis at channel 583.\hat{O}_{583} = \sum_n c_n |n\rangle\langle n|
OP584Zeq spectral optics operator 584: quantum state expansion in the optics eigenbasis at channel 584.\hat{O}_{584} = \sum_n c_n |n\rangle\langle n|
OP585Zeq spectral optics operator 585: quantum state expansion in the optics eigenbasis at channel 585.\hat{O}_{585} = \sum_n c_n |n\rangle\langle n|
OP586Zeq spectral optics operator 586: quantum state expansion in the optics eigenbasis at channel 586.\hat{O}_{586} = \sum_n c_n |n\rangle\langle n|
OP587Zeq spectral optics operator 587: quantum state expansion in the optics eigenbasis at channel 587.\hat{O}_{587} = \sum_n c_n |n\rangle\langle n|
OP588Zeq spectral optics operator 588: quantum state expansion in the optics eigenbasis at channel 588.\hat{O}_{588} = \sum_n c_n |n\rangle\langle n|
OP589Zeq spectral optics operator 589: quantum state expansion in the optics eigenbasis at channel 589.\hat{O}_{589} = \sum_n c_n |n\rangle\langle n|
OP590Zeq spectral optics operator 590: quantum state expansion in the optics eigenbasis at channel 590.\hat{O}_{590} = \sum_n c_n |n\rangle\langle n|
OP591Zeq spectral optics operator 591: quantum state expansion in the optics eigenbasis at channel 591.\hat{O}_{591} = \sum_n c_n |n\rangle\langle n|
OP592Zeq spectral optics operator 592: quantum state expansion in the optics eigenbasis at channel 592.\hat{O}_{592} = \sum_n c_n |n\rangle\langle n|
OP593Zeq spectral optics operator 593: quantum state expansion in the optics eigenbasis at channel 593.\hat{O}_{593} = \sum_n c_n |n\rangle\langle n|
OP594Zeq spectral optics operator 594: quantum state expansion in the optics eigenbasis at channel 594.\hat{O}_{594} = \sum_n c_n |n\rangle\langle n|
OP595Zeq spectral optics operator 595: quantum state expansion in the optics eigenbasis at channel 595.\hat{O}_{595} = \sum_n c_n |n\rangle\langle n|
OP596Zeq spectral optics operator 596: quantum state expansion in the optics eigenbasis at channel 596.\hat{O}_{596} = \sum_n c_n |n\rangle\langle n|
OP597Zeq spectral optics operator 597: quantum state expansion in the optics eigenbasis at channel 597.\hat{O}_{597} = \sum_n c_n |n\rangle\langle n|
OP598Zeq spectral optics operator 598: quantum state expansion in the optics eigenbasis at channel 598.\hat{O}_{598} = \sum_n c_n |n\rangle\langle n|
OP599Zeq spectral optics operator 599: quantum state expansion in the optics eigenbasis at channel 599.\hat{O}_{599} = \sum_n c_n |n\rangle\langle n|
OP6Critical angle for total internal reflection at a boundary between two media.\theta_c = \sin^{-1}\frac{n_2}{n_1}
OP600Zeq spectral optics operator 600: quantum state expansion in the optics eigenbasis at channel 600.\hat{O}_{600} = \sum_n c_n |n\rangle\langle n|
OP601Zeq spectral optics operator 601: quantum state expansion in the optics eigenbasis at channel 601.\hat{O}_{601} = \sum_n c_n |n\rangle\langle n|
OP602Zeq spectral optics operator 602: quantum state expansion in the optics eigenbasis at channel 602.\hat{O}_{602} = \sum_n c_n |n\rangle\langle n|
OP603Zeq spectral optics operator 603: quantum state expansion in the optics eigenbasis at channel 603.\hat{O}_{603} = \sum_n c_n |n\rangle\langle n|
OP604Zeq spectral optics operator 604: quantum state expansion in the optics eigenbasis at channel 604.\hat{O}_{604} = \sum_n c_n |n\rangle\langle n|
OP605Zeq spectral optics operator 605: quantum state expansion in the optics eigenbasis at channel 605.\hat{O}_{605} = \sum_n c_n |n\rangle\langle n|
OP606Zeq spectral optics operator 606: quantum state expansion in the optics eigenbasis at channel 606.\hat{O}_{606} = \sum_n c_n |n\rangle\langle n|
OP607Zeq spectral optics operator 607: quantum state expansion in the optics eigenbasis at channel 607.\hat{O}_{607} = \sum_n c_n |n\rangle\langle n|
OP608Zeq spectral optics operator 608: quantum state expansion in the optics eigenbasis at channel 608.\hat{O}_{608} = \sum_n c_n |n\rangle\langle n|
OP609Zeq spectral optics operator 609: quantum state expansion in the optics eigenbasis at channel 609.\hat{O}_{609} = \sum_n c_n |n\rangle\langle n|
OP610Zeq spectral optics operator 610: quantum state expansion in the optics eigenbasis at channel 610.\hat{O}_{610} = \sum_n c_n |n\rangle\langle n|
OP611Zeq spectral optics operator 611: quantum state expansion in the optics eigenbasis at channel 611.\hat{O}_{611} = \sum_n c_n |n\rangle\langle n|
OP612Zeq spectral optics operator 612: quantum state expansion in the optics eigenbasis at channel 612.\hat{O}_{612} = \sum_n c_n |n\rangle\langle n|
OP613Zeq spectral optics operator 613: quantum state expansion in the optics eigenbasis at channel 613.\hat{O}_{613} = \sum_n c_n |n\rangle\langle n|
OP614Zeq spectral optics operator 614: quantum state expansion in the optics eigenbasis at channel 614.\hat{O}_{614} = \sum_n c_n |n\rangle\langle n|
OP615Zeq spectral optics operator 615: quantum state expansion in the optics eigenbasis at channel 615.\hat{O}_{615} = \sum_n c_n |n\rangle\langle n|
OP616Zeq spectral optics operator 616: quantum state expansion in the optics eigenbasis at channel 616.\hat{O}_{616} = \sum_n c_n |n\rangle\langle n|
OP7Magnification of an optical system: ratio of image height to object height.m = \frac{h_i}{h_o} = -\frac{d_i}{d_o}
OP8Double-slit fringe spacing: wavelength times slit-to-screen distance divided by slit separation.\Delta x = \frac{\lambda L}{d}
OP9Fresnel reflection coefficient at normal incidence for light at a material interface.R = \frac{n_1 - n_2}{n_1 + n_2}
PHO1Photon energy with Zeq HulyaPulse modulation for resonance-enhanced optical processes.E = h\nu = \frac{hc}{\lambda} \quad (\text{photon mode})
PHO10Quality factor of an optical resonator: stored energy divided by energy lost per cycle.Q = \frac{\nu}{\Delta\nu}
PHO11Second-order nonlinear susceptibility for optical frequency conversion.\chi^{(2)}: P = \epsilon_0(\chi^{(1)}E + \chi^{(2)}E^2)
PHO12Sum-frequency generation: output frequency equals sum of two input frequencies.\omega_3 = \omega_1 + \omega_2
PHO13Phase matching condition for efficient nonlinear optical frequency conversion.\Delta k = k_3 - k_1 - k_2 = 0
PHO14Second-harmonic generation efficiency relative to fundamental power.\eta = \frac{P_{SHG}}{P_{fund}^2}
PHO15Coherence length for nonlinear optical interaction from phase mismatch.L_c = \frac{\pi}{|\Delta k|}
PHO2Group index of refraction: ratio of speed of light to group velocity in a dispersive medium.n_g = c/v_g = n - \lambda\frac{dn}{d\lambda}
PHO3Numerical aperture of an optical fiber: light-gathering ability from refractive index contrast.NA = n\sin\theta_{max} = \sqrt{n_1^2 - n_2^2}
PHO4Absorption coefficient relating extinction coefficient to wavelength.\alpha = \frac{4\pi k}{\lambda}
PHO5Beer-Lambert law: exponential attenuation of light intensity through an absorbing medium.I = I_0 e^{-\alpha z}
PHO6Optical gain coefficient: stimulated emission rate depending on population inversion.g = \sigma_{stim}(N_2 - N_1)
PHO7Laser threshold current density for a semiconductor laser diode.I_{th} = \frac{\alpha_{int} + \alpha_m}{\Gamma g_0}
PHO8Laser output power above threshold: slope efficiency times current above threshold.P_{out} = \eta_d \frac{h\nu}{q}(I - I_{th})
PHO9Laser longitudinal mode spacing: free spectral range of a Fabry-Perot cavity.\Delta\nu = \frac{c}{2nL}

Compute with one of these​

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["OP1"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

See also​