The LP notation is an approximation that exists because exact fibre modes are awkward. A step-index fibre's true modes are hybrid — they have both E_z and H_z components — and are labelled HE and EH, alongside the purely transverse TE and TM modes. But real fibres are weakly guiding: the core and cladding indices differ by only a fraction of a per cent,

\(\Delta=\dfrac{n_{1}-n_{2}}{n_{1}}\approx0.002\ \text{to}\ 0.01\)

Under that condition several exact modes become almost degenerate — they share nearly the same propagation constant — and any linear combination of them is effectively a mode too. The convenient combinations are nearly linearly polarised, giving the LP_ℓm labels.

The fundamental LP₀₁ mode is composed of HE₁₁ alone (in its two orthogonal polarisation states), so the answer is option 2.

Option 1 is the deliberate near-miss — TE₀₁, TM₀₁ and HE₂₁ together make up LP₁₁, the second LP mode, not the first. Options 3 and 4 name modes that belong to higher LP groups.

Why HE₁₁ matters so much. It has no cutoff frequency — it propagates at every wavelength, however low the V-number. That is what makes single-mode operation possible: below \(V=2.405\) every other mode is cut off and HE₁₁ alone survives, so single-mode fibre is really "HE₁₁-only" fibre. Its field is close to Gaussian, which is why the mode-field diameter is the parameter quoted on a single-mode datasheet rather than the physical core size.

The residual two-fold degeneracy has practical consequences. The two orthogonal polarisations of HE₁₁ travel at exactly the same speed only in a perfectly circular, unstressed fibre. Real fibres are slightly elliptical and bent, so the two split apart — the effect known as polarisation mode dispersion, which becomes a limiting factor in very-high-bit-rate long-haul systems.

Hence, LP₀₁ is exactly HE₁₁.