Lecture 7

Tunable Semiconductor LasersWhat determines lasing frequency:

Gain spectrum A function of temperature.

Optical length of cavityMirror reflectance spectrumAny perturbation which affects refractive index

and/or lasing frequency.

Single frequency laserDFB and DBG lasers

Tuning achieved by changing heat sink temperature.

Tuning by changing bias current which affects the number of carriers in tuning region.

M

442 ; integer

2

M

M

nLnLM M

c

cM

nL

ModulatorsMach-Zehnder modulators (electro-optic

modulators)Electro-absorption modulators

Phase Modulators

333e

ln r V

g

Electrooptic Modulator

(A) Directional coupler geometry

(B) Mach-Zehnder configuration

Mach-Zehnder modulatorSolve wave equation for mode field

distribution & propagation constant.

where k = constant

( , , ) ( , )

2

0

i z

eff

eff eff

u x y z u x y e

n

n n V kV

Mach-Zehnder modulator

Thus, by applying V will cause a phase shift for propagating mode.

v

Pi Po

Mach-Zehnder modulatorBy symmetry, equal amplitudes in 2 arms

after passing through the first branch.

Mach-Zehnder modulatorFor the second branch, output depends on

relative phases of combining waves:2 waves in phase.

2 waves rad out of phase

Mach-Zehnder modulatorWave amplitudes

1 2

222

4i iin

out out

AP A e e

Mach-Zehnder modulator

1 22 2 2

1 2 1 2

2 21 2 1 2

2 21 2 1 2

1 2

cos cos sin sin

cos cos 2cos cos

sin sin 2sin sin

1 cos2

i i

inout

e e

PP

Mach-Zehnder modulator

1 2

1 2

1 0

2 0

1 2 1 2

2 ; integer

0

22 eff eff

M M

cV

cV

LcV n n

Pout = Pin

Pout = 0

Mach-Zehnder modulatorV is a swiching voltage which give Pout -rad

phase difference.V is determined by material and electrode

configuration.V is different for dissimilar polarizations.

1 cos2in

out

P VP

V

Diffused optical waveguidesDiffused optical waveguides: Ti:LiNbO3 indiffused

waveguides.

Waveguide modes (linearly polarized or ‘LP’):TE mode – light polarized in plane of substrate

surfaceTM mode – light polarized normal to plane of

substrate surface.

Diffused optical waveguides

Ti indiffused waveguides: Ti metal atoms cause refractive index increase for both TE and TM waves.

Proton exchanged waveguides: H atoms exchange with Li atoms in lattice. Refractive index increases for only one polarization; e.g, TE mode.

/ / . . /

/ / . . /

( , , ) ( , , ) ( , , )

( , , ) ( , , ) ( , , )

TE sub TE wg TE e o TE

TM sub TM wg TM e o TM

n x y z n n x y z n x y z

n x y z n n x y z n x y z

Diffused optical waveguidesFor digital transmission, different V could

degrade ‘on-off radio’ or OOR. Ideally, we want OOR to be close to infinity.

Solutions for that are:Use polarized optical input.Use proton exchanged waveguides to eliminate TM modes

(get Pout only for TE mode).

ExampleConsider a Mach-Zehnder modulator with an electrode

length of 2 cm and electrode gap width g of 12 mm, such that

with E the applied electric field, assumed to be constant between the electrodes, and KTE = 5.8 x 10-10 m/V and KTM = 2.0 x 10-10 m/V. What is VTE and VTM ?

Note: neff = n0 + Δn in one arm and neff = n0 - Δn in the other arm.

/

/

eff TE TE

eff TM TM

n K E

n K E