Analog optical link (RF photonics, radio over fiber)

An analog optical link transmits an RF or microwave waveform by modulating the intensity of a laser in proportion to it, carries the light over fiber, and converts it back to an RF current in a photodiode. Unlike a digital link, it preserves the waveform itself, so it is described in RF terms: the link gain (RF power out over RF power in), the noise figure, and the spurious-free dynamic range (SFDR). Uses include antenna remoting for cellular and radar systems, cable-television distribution, distribution of reference frequencies and the front ends of microwave photonic signal processing. The field that studies them is often called RF photonics or microwave photonics, and the cellular form radio over fiber.

Link gain

In a directly modulated link, the RF current modulates a directly modulated laser biased above threshold. The optical power changes by the slope efficiency $s_l$ (W/A) times the RF current, and the photodiode returns a current $r_d$ (A/W) times the optical change. With equal source and load resistances and lossless matching, the intrinsic gain is

$$g = (s_l\, r_d)^2 .$$

For $s_l$ = 0.3 W/A and $r_d$ = 0.8 A/W, $g$ = 0.0576, or −12.4 dB. The square is the defining feature: every dB of optical loss between laser and detector costs 2 dB of RF gain, so 3 dB of fiber and connector loss brings this link to −18.4 dB. Simple resistive matching adds loss of its own: a 50 Ω resistor in shunt with the photodiode diverts half the signal current and costs 6 dB.

In an externally modulated link, a CW laser feeds a Mach-Zehnder modulator biased at quadrature. For an average photocurrent $I_D$, a half-wave voltage $V_\pi$ and resistance $R$ at both ends,

$$g = \left(\frac{\pi I_D R}{V_\pi}\right)^2 .$$

With $I_D$ = 10 mA, $V_\pi$ = 4 V and $R$ = 50 Ω, $g$ = 0.154, or −8.1 dB. The gain grows with the square of the optical power: at 40 mA it becomes +3.9 dB, without any RF amplifier. This is the main reason external modulation, high-power lasers and high-current photodiodes dominate high-performance links.

Noise figure

The noise figure compares the output noise with the thermal noise of the input source, $kT$ = −174 dBm/Hz at 290 K, amplified by the link gain. Three noise sources add to the output: shot noise of the photocurrent, $2qI_D R$; laser relative intensity noise, $\text{RIN}\cdot I_D^2 R$; and the thermal noise of the output load. For the directly modulated link above at 1 mA of photocurrent (1.25 mW received) and a RIN of −150 dB/Hz, the shot noise is −168.0 dBm/Hz, the RIN term −163.0 dBm/Hz and the load −174.0 dBm/Hz, for a total of −161.5 dBm/Hz. Against a gain-scaled input noise of −186.4 dBm/Hz, the noise figure is 24.8 dB. In an externally modulated link, raising the photocurrent and lowering $V_\pi$ improve gain and noise figure together, as long as RIN does not dominate; in the directly modulated link the gain does not depend on photocurrent.

Spurious-free dynamic range

The upper limit is distortion. A Mach-Zehnder modulator's sinusoidal transfer function produces third-order intermodulation products; expanding it about quadrature gives an input third-order intercept

$$P_\text{IIP3} = \frac{4V_\pi^2}{\pi^2 R},$$

or +21.1 dBm for $V_\pi$ = 4 V in 50 Ω. The SFDR, defined in the dynamic range entry, is two thirds of the distance from the input-referred noise floor to that intercept. The MZM link above, shot-noise limited at 10 mA, has a noise figure of 24.3 dB, an input-referred floor of −149.7 dBm/Hz and an SFDR of 113.9 dB·Hz$^{2/3}$, or 53.9 dB in a 1 GHz bandwidth. Directly modulated lasers distort through relaxation-oscillation dynamics and the curvature of the L-I curve, so their intercepts depend on frequency and bias and are measured with two-tone tests.

Measurement and pitfalls

Gain and its frequency response are measured with a vector network analyzer from RF input to RF output; noise figure with an RF noise-figure analyzer or from the output noise on an electrical spectrum analyzer; SFDR from a two-tone test, plotting fundamental and intermodulation output against input power. Reflections in the fiber convert laser phase noise to intensity noise, which is why analog links have the strictest optical return loss requirements; fiber chromatic dispersion converts laser chirp to second-order distortion; and photodiode compression sets a separate upper limit at high photocurrent.

Common questions

Why is the RF gain of an optical link usually negative?

Each conversion is inefficient: a slope efficiency of 0.3 W/A and a responsivity of 0.8 A/W multiply to 0.24 in current, and the RF power ratio is the square of that, −12.4 dB.

How do analog links differ from digital optical links?

A digital link needs only enough signal-to-noise ratio to decide between symbols; an analog link must reproduce the waveform with low noise and low distortion across a wide power range, so linearity and RIN matter far more.

What limits the dynamic range of a link?

Thermal, shot and RIN noise set the floor; modulator or laser nonlinearity, and at high photocurrent photodiode compression, set the ceiling.

References: C. H. Cox III, Analog Optical Links: Theory and Practice (Cambridge University Press, 2004); C. H. Cox III, E. I. Ackerman, G. E. Betts and J. L. Prince, "Limits on the performance of RF-over-fiber links and their impact on device design," IEEE Trans. Microw. Theory Tech. 54, 906 (2006); J. Capmany and D. Novak, "Microwave photonics combines two worlds," Nat. Photonics 1, 319 (2007).