Optical hybrid (90° hybrid)

An optical hybrid is a passive 2×4 (or 2×2 for less common variants) coupler that combines two input optical signals — a received signal and a local oscillator (LO) — and produces four output signals containing the in-phase (I) and quadrature (Q) components of the optical beat between them.

Output structure. For input signal $E_S$ and LO $E_{LO}$, the four output fields are:

$$E_1 \propto E_S + E_{LO}, \qquad E_2 \propto E_S - E_{LO},$$ $$E_3 \propto E_S + j E_{LO}, \qquad E_4 \propto E_S - j E_{LO},$$

where $j = \sqrt{-1}$. After photodetection by four photodiodes (often arranged as two balanced pairs), the resulting photocurrents yield:

$$I_I = i_1 - i_2 \propto \text{Re}(E_S \, E_{LO}^*), \qquad I_Q = i_3 - i_4 \propto \text{Im}(E_S \, E_{LO}^*).$$

The pair $(I_I, I_Q)$ provides both the amplitude and phase of the optical signal — the central enabling capability of coherent detection.

Standard implementations.

Implementation	Platform	Bandwidth	Insertion loss
Bulk-optical 4×4 fiber coupler	Free-space + fiber	DC to near-IR	4 – 6 dB
InP integrated 90° hybrid	InP MMI couplers	$> 60$ GHz	1.5 – 3 dB
Silicon photonic 90° hybrid	SOI MMI + phase shifters	$> 100$ GHz	1.5 – 3 dB
LNOI / thin-film LN	LiNbO3 directional couplers	$> 100$ GHz	1 – 3 dB
Polymer	Polymer waveguides	telecom band	2 – 5 dB

MMI-based 4×4 hybrid construction. A standard implementation uses a single 4×4 multimode interference coupler with two inputs (S and LO) and four outputs. By careful selection of input/output port positions and the MMI length, the self-imaging gives the four required relative phase relationships. This is dramatically more compact than four separate 2×2 couplers wired together.

Polarization-diverse hybrid. Standard 90° hybrids handle one polarization at a time. Coherent optical communication signals are typically polarization-multiplexed (independent data on two orthogonal polarizations), so practical coherent receivers use a polarization-beam-splitter at the input followed by two 90° hybrids — one per polarization — producing 8 output signals (I and Q for each of two polarizations). This dual-polarization architecture supports polarization-multiplexed coherent formats (DP-QPSK, DP-16QAM, DP-64QAM).

Performance specifications. Critical parameters for a high-fidelity 90° hybrid:

Parameter	Requirement	Typical achievement
Common-mode rejection ratio	$> 20$ dB	25 – 35 dB
Phase imbalance (90° accuracy)	$< 5°$	$\pm 3°$
Amplitude imbalance	$< 0.5$ dB	0.1 – 0.3 dB
LO power split balance	$< 0.3$ dB	0.1 – 0.2 dB
Polarization-dependent loss	$< 0.5$ dB	0.2 – 0.4 dB
Wavelength flatness	$\pm 0.5$ dB across C-band	$\pm 0.2$ dB

Applications.

• Coherent optical receivers: standard front-end in all 100G+ coherent transceivers
• Coherent OFDR (optical frequency-domain reflectometry): distributed sensing in fiber, time/space-resolved by FFT of the heterodyne signal
• Coherent LIDAR: range and velocity from beat frequency between transmitted and received signals
• Optical phase noise measurement: hybrid produces electronic phase signal that can be tracked by RF-domain phase analyzers
• Heterodyne interferometers with quadrature detection for vibration and surface metrology

The 90° hybrid is the single most important passive component that enabled the coherent revolution in optical communications around 2010 – 2015, increasing per-fiber capacity by 10× and bridging optical communication into the format-rich regime familiar from wireless communications.

References: Kikuchi, Fundamentals of Coherent Optical Fiber Communications, IEEE JLT 2016 (the canonical tutorial review); Painchaud et al., Performance of balanced detection in a coherent receiver, OSA Optics Express 2009.