Optical Amplifiers (Chapter 6)General optical amplifier theory

Semiconductor Optical Amplifier (SOA)Raman Amplifiers

Erbium-doped Fiber Amplifiers (EDFA)Read Chapter 6, pp. 226-266

Loss & dispersion limits in lightwave systems and fielded long-haul systems

GaAs-based, 0.85 µm dominates short distances, under a couple of km, very cheap components such as VCSELs (< $5/laser)

1.3 µm is the choice for under 10 km for 2.5Gbps-10 Gbps per channel (uncooled!).

Serial 10 Gbps for Ethernet is battling 10 Gbps CWDM right now (4-channels spaced by 20-25 nm) ($20-40/laser)

1.55 µm lasers must be cooled to operate according to standards (-10 to 85 C operation)

The big leaps forward in long-haul communication were in 1996 when the EDFA was introduced and then WDM in 1998 (8-channel or 16-channel?). Why is the EDFA so transforming for the network system design?

How are amplifiers used in lightwave systems?

SOA generic layouts

Simplified schematic illustrations of two types of laser amplifiers

Pump current

Active region

AR = Antireflectioncoating

AR

Signal in Signal out

(a) Traveling wave amplifier (a) Fabry-Perot amplifier

Partial mirror Partial mirror

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

The FP amplifier is really undesirable because of the reflections at the partially reflecting mirror introduce what iscalled “gain ripple”

SOA refined layouts

EDFA layout

Signal in Signal outSplice

Er3+-dopedfiber (10 - 20 m)

Wavelength-selective coupler

Pump laser diode

Splice

λ = 1550 nm λ = 1550 nm

λ = 980 nmTermination

Opticalisolator

Opticalisolator

A simplified schematic illustration of an EDFA (optical amplifier). Theerbium-ion doped fiber is pumped by feeding the light from a laser pumpdiode, through a coupler, into the erbium ion doped fiber.

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

The gain coefficient and other relations

g(ω) =g0

1+ ω −ω0( )2T22 + P Ps

T2 is the dipole relaxation time and leads to what is called homogeneous broadening. Ps is the saturation power of the amplifier and depends on the gain cross section and the quantum efficiency (alternatively the fluorescence time)

Ignoring gain saturation with power for the moment,

g(ω) =g0

1+ ω −ω0( )2T22

∆ν g =1

πT2(gain bandwidth)

G = Pout Pin (amplification factor)

dPdz

= gP (Beer’s Law)

Gain spectrum and bandwidth

P z( )= Pin exp gz( )

P L( )= Pout

Then the amplification factor is:

G ω( )= exp g ω( )L[ ]

∆ν A = ∆ν gln2

ln G0 2( )⎡

⎣ ⎢

⎤

⎦ ⎥

This equation, shown graphically in the figure, points out that “gain flattening” is very important in optical amplifiers

Typical gain bandwidth of an SOA

Note the 3-dB bandwidth of the amplifier is only about 5 nm.

S, C, and L bands cover 1480-1620 nm.

Gain Saturation in Optical AmplifiersdPdz

=g0

1+ P Ps

G = G0 exp −G −1

GPout

Ps

⎛

⎝ ⎜

⎞

⎠ ⎟

Pouts =

G0 ln2G0 − 2

Ps

We are tuned at the gain peak

Pouts = 0.69Ps

This effect is undesirable and is especially prevalent in WDM when a lot “1’s” come down the fiber. How can you gain clamp? See p. 241

The output saturation power is defined as the output power when G = G0/2

A typical G0 would be 20-30 dB or more, so in the end:

Optical Amplifier Noise (big issue! 3dB is the minimum theoretical noise figure)

Fn =SNR( )in

SNR( )out

Amplifier noise figure is Fn, the amplifier has a gain, G, and input and output powers, Pin and Pout.Pout = GPin

First, find the signal-to-noise ratio on the input:

R is the responsivity and we are assuming zero dark current in an ideal photodetector

SNR( )in =I 2

σ s2 =

RPin( )2

2q RPin( )∆f=

Pin

2hν∆f

I is the average photocurrent and σs2 is the shot noise variance

(p. 156)

Amplifier noise continuedNext, the signal-to-noise ratio on the output end of the amp must take into account the spontaneous emission induced noise

The noise spectral density is:

Ssp ν( )= G −1( )nsphν

Where nsp, the spontaneous emission factor or population inversion factor is:

nsp = N2 N2 − N1

The dominant contribution to the noise is the beating of the spontaneous emission with the signal.

Amplifier noise continuedThe beating of the signal and spontaneous emission fields produces a noise current with a random phase angle at the ideal detector of:

∆I = 2R GPin Esp cosθ

Averaging over this random phase angle produces

σ 2 ≈ 4 RGPin( ) RSsp( )∆f

Then the SNR at the output is:

SNR( )out =I 2

ο2 =RGPin( )2

σ 2 ≈GPin

4Ssp∆f

The optical amplifier noise figure expression

Then substituting in the expression for the noise spectral density, one obtains for the noise figure:

Fn = 2nsp G −1( ) G ≈ 2nsp

The minimum nsp can be is 1 and therefore Fnmin is 3 dB