How light propagates: reflection, modes, numerical aperture

A fibre is a waveguide: a glass core surrounded by glass of slightly lower refractive index, so that light meeting the boundary at a shallow angle is reflected back rather than escaping. From this one fact follow the differences between single-mode and multi-mode fibre, the acceptance angle that decides how much of a source's light gets in, the reason a tight bend leaks light, and the grades OM1–OM5 and OS2 that datasheets refer to. This page covers that physics to the depth used in link design.

Structure of a fibre

Layer	Diameter	Material	Role
Core	9 µm (single-mode), 50 or 62.5 µm (multi-mode)	silica doped with germanium (higher index)	carries the light
Cladding	125 µm	pure or fluorine-doped silica (lower index)	confines light by total internal reflection
Coating	250 µm (or 200 µm)	acrylate	mechanical protection; colour-coded in cables
Buffer / jacket	900 µm tight buffer, or loose tube	plastic	handling; not part of the optics

The refractive-index difference between core and cladding is tiny — about 0.3–0.5 % — but it is enough because the light travels almost parallel to the axis.

Total internal reflection and numerical aperture

Light crossing from a denser to a less dense medium bends away from the normal; beyond the critical angle it is totally reflected. In a fibre this means rays within a cone around the axis are trapped. The half-angle of that cone in air is set by the numerical aperture:

Fibre	NA	Acceptance half-angle	Meaning
Single-mode G.652	≈ 0.12–0.14	≈ 7–8°	only a narrow, well-aimed beam couples in — laser sources only
Multi-mode 50 µm (OM2–OM5)	0.20	≈ 11.5°	wide acceptance — VCSELs and LEDs couple easily
Multi-mode 62.5 µm (OM1)	0.275	≈ 16°	widest; legacy

Higher NA = easier coupling but more modes and more modal dispersion.

Modes

A mode is a stable field pattern that can travel down the guide. How many exist depends on the core size, NA and wavelength (the V-number):

Fibre	Modes at 850 nm	Modes at 1310 nm	Consequence
9 µm single-mode	— (would be few-mode)	1	no modal dispersion; reach set by attenuation and chromatic dispersion
50 µm multi-mode	hundreds	~100	modal dispersion limits bandwidth × distance (Dispersion & bandwidth)
62.5 µm multi-mode	~1 000	—	worst modal dispersion

Single-mode fibre is single-mode only above its cutoff wavelength (≈ 1 260 nm for G.652): at 850 nm it carries several modes, which is why an 850 nm SR module on single-mode fibre does not work properly, and why "single-mode at 1310/1550" is the pairing (Physical mismatches).

Step-index and graded-index

Profile	Index shape	Used in	Effect
Step-index	constant core index, abrupt step to cladding	single-mode fibre	irrelevant for one mode
Graded-index	parabolic: highest on axis, falling toward cladding	all telecom multi-mode (OM1–OM5)	outer rays travel farther but faster (lower index), so modes arrive nearly together — modal dispersion reduced 100× vs step-index

The quality of the graded profile is what separates OM3 (2 000 MHz·km) from OM4 (4 700 MHz·km): the same geometry, a more precise index curve.

Mode field diameter and coupling loss

In single-mode fibre the light is not confined to the 9 µm core; its mode field diameter (MFD) is ≈ 9.2 µm at 1310 nm and ≈ 10.4 µm at 1550 nm. Two fibres with different MFDs, or a lateral offset at a connector, lose light:

Mismatch	Loss
1 µm lateral offset (SMF)	≈ 0.2 dB
2 µm lateral offset	≈ 0.8 dB
MFD 9.2 vs 10.4 µm (G.652 to G.657.B or DSF)	≈ 0.1–0.3 dB
50 µm into 62.5 µm core	≈ 0 dB (loss occurs in the other direction)
62.5 µm into 50 µm core	2–4 dB
SMF into MMF	≈ 0 dB at the joint but modes excited → modal noise
MMF into SMF	> 10 dB

Hence the rules "never mix 50 and 62.5" and "never mix single- and multi-mode" (Connectors & fibre types).

Bend loss

Bend type	Cause	Effect
Macrobend	radius below ~30 mm (standard SMF), tight cable ties, doors	light escapes the cladding; loss rises steeply with wavelength — a link fine at 1310 nm fails at 1550 nm, and a 1625 nm test finds bends 1310 nm misses
Microbend	microscopic axis deviations from cable stress, cold, crushing	broadband loss increase
Bend-insensitive fibre G.657.A1/A2/B3	trench-assisted index profile	10–7.5–5 mm radius allowed; used indoors, in FTTH drops and dense panels

Multi-mode is more tolerant of bends but loses high-order modes first, which changes its bandwidth.

Fibre grades in one table

Grade	Core	Wavelength(s)	Bandwidth (EMB at 850 nm)	Attenuation	Standard
OM1	62.5 µm	850 / 1300	200 MHz·km	3.5 / 1.5 dB/km	ISO 11801, TIA-492AAAA
OM2	50 µm	850 / 1300	500	3.5 / 1.5	TIA-492AAAB
OM3	50 µm	850 (laser-optimised)	2 000	3.0 / 1.5	TIA-492AAAC
OM4	50 µm	850	4 700	3.0 / 1.5	TIA-492AAAD
OM5	50 µm	850–953 (wideband)	4 700 at 850, 2 470 at 953	3.0 / 1.5	TIA-492AAAE
OS1 / OS1a	9 µm	1310 / 1550	—	1.0 / 1.0 (indoor tight-buffered)	ISO 11801
OS2	9 µm	1310 / 1383 / 1550	—	0.4 / 0.4 / 0.4 (loose tube, low water peak)	ISO 11801; ITU-T G.652.D
G.657.A/B	9 µm	as OS2	—	as OS2	bend-insensitive
G.655 / G.654	9 µm	1550	—	0.2 / 0.17	NZ-DSF for DWDM; ultra-low-loss for long haul

Reach per PMD and grade: Reach tables.

What this means at the transceiver

The module's connector type and fibre type must match the plant: SR/SR4 on OM3/OM4, everything else on OS2.
A laser's launch condition (encircled flux for VCSELs) is defined by the standards so that multi-mode bandwidth figures hold — a module out of spec gives shorter reach than the tables promise.
Single-mode modules on multi-mode fibre (with a mode-conditioning patch cord) was a 1G trick (1000BASE-LX on OM1); it does not extend to 10G+.

In CodingBox

The module tells the host which fibre it is for: connector code, wavelength and the length fields for SMF, OM1, OM2, OM3 and OM4 — the same grades as above. CodingBox shows them so the fibre question is settled before the module leaves the bench (Check transceiver, Memory map).

The standardized fibres these principles produce — ITU-T G.652 to G.657, OM1–OM5 multi-mode grades, specialty fibres, joint losses between dissimilar fibres and how to identify what is installed: Fibre types.