Hermite–Gaussian Mode Profile

Evaluate low-order Hermite–Gaussian transverse-mode intensity at a normalized coordinate.

Description

Low-order Hermite–Gaussian profiles multiply polynomial factors by a Gaussian intensity envelope.

Low-order Hermite–Gaussian profiles multiply polynomial factors by a Gaussian intensity envelope. The coordinates are normalized to waist radius.^[1]

Evaluate low-order Hermite–Gaussian transverse-mode intensity at a normalized coordinate.

When to use Hermite–Gaussian Mode Profile

Use this tool to evaluate low-order Hermite–Gaussian transverse-mode intensity at a normalized coordinate.

Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.

How to use Hermite–Gaussian Mode Profile and understand its results

Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
Enter horizontalOrder, verticalOrder, xOverWaist, yOverWaist using the field table and calculation rules, then run the tool.
Read relativeIntensity, modeLabel. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
horizontalOrder	Horizontal mode order	integer; minimum: 0; maximum: 1	Required
verticalOrder	Vertical mode order	integer; minimum: 0; maximum: 1	Required
xOverWaist	Normalized X coordinate	number	Required
yOverWaist	Normalized Y coordinate	number	Required

Enter horizontal/vertical integer orders zero or one and finite signed x/waist,y/waist. Return relative intensity and TEM00/01/10/11 label.

intensity=Hx²Hy² exp(−2(x²+y²)); H0=1; H1=2sqrt(2)coordinate

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
relativeIntensity	Unnormalized Hermite–Gaussian intensity	number; minimum: 0
modeLabel	Mode label	string; one of "TEM00", "TEM01", "TEM10", "TEM11"

json

{
  "input": {
    "horizontalOrder": 0,
    "verticalOrder": 0,
    "xOverWaist": 0,
    "yOverWaist": 0
  },
  "output": {
    "relativeIntensity": 1,
    "modeLabel": "TEM00"
  }
}

Limitations and assumptions

Intensity is not normalized to total power or the peak of each mode. Higher orders, propagation and aberrations are excluded.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Focused-Beam Waist Location: Propagate a Gaussian beam q parameter through a thin lens to locate the new waist. For a complementary task, use Stripe-Waveguide V-Number: Calculate planar stripe-waveguide V-number and an approximate guided-mode count.

References

Hermite–Gaussian Mode Profile — tool.io

Similar or alternative tools

Focused-Beam Waist Location
Propagate a Gaussian beam q parameter through a thin lens to locate the new waist.
Stripe-Waveguide V-Number
Calculate planar stripe-waveguide V-number and an approximate guided-mode count.