Gaussian Beam Thin Lens Calculator
Transform a paraxial Gaussian beam through one ideal thin lens and calculate new waist and downstream beam radius.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Apply the complex Gaussian q-parameter thin-lens transform, then propagate to the entered downstream plane.
qbefore=z+i zR; qafter=qbefore/(1−qbefore/f); new waist location=−Re(qafter)
Worked example
At the lens plane, calculated beam radius remains continuous through an ideal zero-thickness lens. A negative transformed waist distance denotes an upstream virtual waist.
Assumptions and input details
Ideal M²=1 paraxial Gaussian beam in air, one thin lossless lens. Waist and absolute focal length must be at least ten wavelengths. No aperture clipping, aberration, lens thickness, nonlinear effects or actual laser alignment procedure.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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