In linearly polarized modes traversing in the optical fibers the LP01 is exactly equal to :
HE11
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 Ez and Hz 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 LPℓm labels.
The fundamental LP01 mode is composed of HE11 alone (in its two orthogonal polarisation states), so the answer is option 2.
| LP mode | Exact modes it contains | Degeneracy |
|---|---|---|
| LP01 | HE11 | 2 (two polarisations) |
| LP11 | TE01, TM01, HE21 | 4 |
| LP21 | EH11, HE31 | 4 |
| LP02 | HE12 | 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.
Similar Questions
If numerical aperture and fractional refractive index of an optical fibre are 0.22 and 0.012, respectively. The refractive index of core (µ1) and cladding (µ2) will be
Which of the following is not a usual classification of optical fibre ?
Assertion (A) : In the propagation of light along multimode graded index fibre, the rays moving toward the cladding travel longer path with greater velocity than the rays travelling shorter path near the axis of fibres. These cause less spreading as compared to spreading caused by multimode step index fibre.
Reason (R) : The velocity varies because refractive index of the multimode graded index fibre increases with radial distance from the centre (axis).
An optical fibre has numerical aperture (NA) of 0.3 and refractive index $\eta_2$ of cladding material is 1.6. What is the refractive index of core material?
Match the following lists :
List – I List – II a. \(\pi a\,NA/\lambda\) i. attenuation factor (dB/km) b. \(10\log_{10}\left(\dfrac{P_{in}}{P_{out}}\right)\) ii. Intermodal time delay c. \(\dfrac{l}{L}\dfrac{dt_g}{d\lambda}\) iii. Dispersion causing pulse spreading d. \(\dfrac{L(n_1-n_2)n_1}{n_2c}\) iv. Number of modes produced by an optical fibre Assertion (A) : Attenuation and dispersion have negative effects on the propagation of signal in the optical fibres.
Reason (R) : Optical signal degradation is caused due to structural imperfections of the fibre material.
Select your answer using the codes given below.
A fiber has a core radius of 6 μm, operating wavelength = 1550 nm. The V-number of the fiber is given by :
The value of Numerical Aperture in case of optical fiber is
The core of an optical fiber has
The core diameter of single mode fiber is in the order of
Important Questions from Optical Fiber
The material used for making optic-fibre cable in general is-
Multimode step-index fiber with a core diameter of 80 μm and a relative index difference of 1.5% is operating at a wavelength of 0.85 μm. If the core refractive index is 1.48, then the normalized frequency for the fiber is
In a multimode fiber (step index), number of modes passing at an operating wavelength of 1300 nm are 1000, the refractive index of the core is 1.50 and that of the cladding is 1.48. The value of core diameter is:
In optical fibers, the Rayleigh scattering is proportional to:
A graded indexed optical fiber has a parabolic refractive index profile (α = 2). If the fiber has a numerical aperture = 0.22 the total number of guided modes at a wavelength of 1310 nm is given by:
