tutorial on nonlinear frequency conversion€¦ · potassium titanyl phosphate (ktp, ktiopo4): high...

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Tutorial onNonlinear Frequency Conversion

Dr. Rüdiger Paschotta

RP Photonics Consulting GmbHBad Dürrheim, Germanywww.rp-photonics.com

Summer School"New Frontiers in Optical Technologies“

Tampere, 08/2011

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Topics of this TutorialI Frequency doubling

choice of crystal material, techniques for phase matching

optimum focusing

frequency doubling in waveguides

resonant frequency doubling

intracavity frequency doubling in a laser

frequency doubling of short and ultrashort pulses

II Parametric amplification and oscillation

pulsed parametric amplifiers and generators

parametric oscillators with continuous-wave pumping,pulsed pumping, and synchronous pumping

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Part I:Frequency Doubling

(= Second-Harmonic Generation, SHG)

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Basics of Frequency DoublingWhat happens in a frequency doubler?

Very simple picture: pump wave in, frequency-doubled wave out:

But how does this work?

The pump wave generates an electric polarization wave in the medium.

In a nonlinear medium, the oscillating polarization exhibits overtones

(harmonics). The second harmonic occurs when the material has a

(2) nonlinearity.

The second-harmonic component of the polarization wave radiates an

electromagnetic wave, which also has twice the frequency of the pump.

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Basics of Frequency DoublingWhat can we learn from this?

We need a medium with a (2) nonlinearity.

This can only be a non-centrosymmetric material.

The nonlinear polarization wave has the same velocity as the pump wave,

whereas in general the radiated harmonic light has a different velocity.

At the end of the crystal, amplitude contributions to the harmonic light

from different places in the crystal are in general not in phase

no constructive interference, low conversion efficiency

Efficient conversion can arise from phase matching:

in some way, arrange for equal phase velocities of polarization wave and

harmonic light.

The nonlinear nature makes the conversion efficiency intensity-dependent.

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Typical Applications of SHG generation of green light from 1-μm lasers (e.g. Nd:YAG or fiber laser)

generation of blue or violet light from lasers at 0.80.95 μm

generation of ultraviolet light

Most common motivation: longer-wavelength lasers are superior.

Other applications:

Exploit the intensity dependence of the conversion, e.g. in autocorrelators or

optical gates.

Exploit the impact of the nonlinear interaction on quantum noise properties

generation of squeezed light

Link frequency standards in different wavelength regions

frequency chains

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Relevant Properties of Crystal MaterialsImportant properties of crystal materials for frequency doubling:

should have a high transparency for pump and harmonic light

must exhibit a (2) nonlinearity;

strong nonlinearity is often (but not always) important

must offer some possibility for phase matching,

ideally without strong detrimental effects such as spatial or temporal walk-off,

excessive temperature sensitivity, etc.

should be resistant against the pump and harmonic light

(at the intensity levels as required for efficient conversion)

should be available with good optical quality, in large enough pieces, and at

a reasonable price

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Common Crystal MaterialsLithium niobate (LiNbO3):

high nonlinearity

birefringent phase matching

or quasi-phase matching via periodic poling ( PPLN)

some problems with photorefractive effects, infrared-induced green

absorption and the like

allows fabrication of different kinds of waveguides

different versions: congruent or stoichiometric material,

undoped or doped with MgO

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Common Crystal MaterialsPotassium titanyl phosphate (KTP, KTiOPO4):

high nonlinearity (but lower than LiNbO3)


or quasi-phase matching via periodic poling ( PPKTP )

large temperature acceptance range

some problems with gray tracking, infrared-induced green absorption, and

parasitic linear absorption

allows fabrication of different kinds of waveguides

different versions: flux-grown or hydrothermal material,

undoped or doped with MgO

related materials: KTA (KTiOAsO4), RTP (RbTiOPO4) and RTA (RbTiAsPO4)

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Common Crystal MaterialsLithium triborate (LBO, LiB3O5)

relatively low nonlinearity


good UV transparency

somewhat hygroscopic, otherwise fairly resistant

potential problems with dielectric coatings

related materials: cesium lithium borate (CLBO, CsLiB6O10), β-barium borate

(BBO, β-BaB2O4), bismuth triborate (BIBO, BiB3O6),

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Selection of a Crystal MaterialFrequently encountered question:

What is the best suited crystal material

for some frequency doubler?

This depends on many details:

Involved wavelengths and polarization directions?

Is a high nonlinearity essential? Is a waveguide needed?

Is it acceptable to operate the crystal in a crystal oven?How well can the temperature be controlled?

Importance of long-term stable operation?

Price constraints? Need small or large numbers?

Some criteria totally rule out certain materials; the choice between the

remaining options may not be easy.

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Phase MatchingGeneral principle: arrange a situation where the phase velocity of the nonlinear

polarization wave matches that of the harmonic light.

General principle: arrange a situation where the phase velocity of the nonlinear

polarization wave matches that of the generated light wave.

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Techniques for Phase Matching birefringent phase matching: exploit the polarization dependence of the

refractive index

quasi-phase matching: accept some phase mismatch, and periodically

modulate the sign (or strength) of the nonlinear coupling

Further distinctions:

type I: use a single polarization direction for the pump wave

type II: different pump polarization directions

collinear / noncollinear phase matching: all involved wave vectors have /

do not have the same direction

critical / noncritical phase matching: involves adjustment of some odd

direction against the optical axes (critical case, angle tuning), or only

polarization along the axes and adjustment via the crystal temperature

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Birefringent Phase MatchingPrinciple of birefringent phase matching: use the polarization dependence of

the refractive index to compensate the wavelength dependence (dispersion).

Example 1: noncritical type I phase matching in lithium niobate (LiNbO3):

pump wave has ordinary polarization, harmonic wave extraordinary polarization:

For each temperature,

there is some pump

wavelength for which

SHG is phase-matched.

Note: additional dopants

(e.g. MgO) can have a

substantial influence on

the phase-matching

temperature.

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Birefringent Phase MatchingExample 2: noncritical phase matching in lithium triborate (LBO):

biaxial crystal allows for two different configurations:

For example, type I phase

matching for

1064 nm 532 nm is

possible for propagation in

X direction and T 149 C.

Pump is polarized in Z

direction, harmonic wave in

Y direction. This scheme is

called X / ZZY.

propagation direction pump

polarization

harmonic polarization

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Birefringent Phase MatchingExample 3: critical phase matching in LBO, using scheme XY I (oo-e):

propagation in the XY plane, adjustment of azimuthal angle

pump wave with ordinary polarization (Z direction),harmonic wave with extraordinary polarization (in XY plane)

spatial walk-off for the harmonic wave

crystal at room temperature

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Quasi-Phase Matching (QPM)General idea: instead of using real phase matching, accept some phase mismatch and periodically modulate the sign or strength of the nonlinear coupling.

Most common realization: with periodic poling of crystals:fabricate crystals where the domain orientation is periodically reversed, normally by application of a strong electric field via patterned electrodes.

Examples for suitable crystal materials: LiNbO3, LiTaO3, KTP

Typical poling periods: a few microns to tens of microns. Short wavelengths result in strong dispersion smaller periods more difficult fabrication.

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Quasi-Phase Matching (QPM) The growth of the harmonic field amplitude in the crystal is

slower than for real phase matching, if the nonlinearityis the same. Efficiency reduction by factor (2 / )2.

In practice, however, QPM often provides a largernonlinearity: in LiNbO3, e.g., use d33 instead of d31.

Highly flexible technique:can phase-match virtuallyany interaction, unless thepoling period would betoo small.

Note: spatial harmonicsof poling pattern mayallow for parasiticconversion processes.

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Focusing for High Conversion Efficiency Without spatial walk-off:

With spatial walk-off (critical phase matching), somewhat weaker focusing is better in order to preserve the overlap of pump and harmonic.

too weak focusing:low pump intensity

optimum focusing:high pump intensity,

moderate divergence

too strong focusing:high pump intensity only

near the focus

Note: calculation of conversion efficiency is not easy, particularly for cases with

strong conversion and spatial walk-off.

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Frequency Doubling in Waveguides Benefit of using a waveguide:

can maintain high intensities over a significant length.

Problems and limitations:

Waveguide makes fabrication more difficult.

Established techniques not available for all materials.

(Particularly well developed: waveguides in LiNbO3 and LiTaO3.)

Need to efficiently couple into the waveguide:

coupling losses, alignment tolerances.

Waveguides typically exhibit higher propagation losses.

Cannot do angle tuning.

Temperature tuning may be inconvenient.

Cannot move to other spot if one spot is damaged.

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Frequency Doubling in Resonators

Conversion efficiency can be strongly increased when using

an optical resonator for the pump wave,

a resonator for the harmonic wave,

or both.

Resonant pump wave has two different beneficial effects:

The pump intensity is increased, which increases the conversion per path.

Residual pump light is “recycled”.

Ideal case: “impedance matching”: input coupler transmission equals the sum of all others losses, so that no pump light is reflected.

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Problems with resonant pump wave:

Pump wave should be quasi-monochromatic.

Resonance must be stabilized with control of laser frequency and/or resonator length.

Pump wave needs to be close to diffraction-limited(mode-dependent resonance frequencies!).

Resonant harmonic wave also helps: power transfer Ep2Eh;

however: rarely used scheme, as resonator losses are typically higher at

shorter wavelengths.

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Example case: frequency doubling in monolithic LiNbO3 resonator:

Resonator with 7.5 mm length, end faces with 10 mm radius of curvature

Dielectric coatings: high-finesse resonator for pump light (input coupling 2.1%), double pass for green harmonic light.

Achievement: 82% conversion efficiency from infrared to green light for only 100 mW pump power

Ref.: R. Paschotta et al., Opt. Lett. 19 (17), 1325 (1994)

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Doubly resonant conversion: use resonance for both pump and harmonic.

Challenge: need to stabilize two resonances simultaneously.

Example: >50% efficient conversion in

monolithic LiNbO3 resonators with pump

powers of a few milliwatts only.

Stabilization of resonances via stress

(with piezo) and temperature control.Ref.: K. Fiedler et al., Opt. Lett. 18 (21), 1786 (1993)

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Intracavity Frequency Doubling

Principle: place frequency doubler crystal within a laser resonator.

Advantage: exploit high intracavity power while resonance is obtained automatically.

Couple out only harmonic light; non-converted pump light is “recycled”.

Efficient conversion requires single-pass conversion of only a few percent (higher than parasitic losses).

Can use type I phase matching with linearly polarized laser,or type II phase matching with unpolarized laser.

SHGlaser

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Methods to obtain a single harmonic output:

Use a unidirectional ring laser.

Use a linear resonator with harmonic output couplingat a dichroic folding mirror:

harmonic output

nonlinear crystal

pump light

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Various issues:

Harmonic light is generated in two directions. Depending on phase

details of end mirror, perfect constructive interference may not be

achieved. However, adjustment of phase mismatch always allows for

efficient conversion.

The “green problem”: nonlinear conversion may introduce strong

intensity fluctuations, particularly for lasers operating on a few resonator

modes. Various solutions are known, e.g. single-frequency operation or

operation with a large number of modes long resonator.

Nonlinear conversion may be expected to destabilize single-frequency

operation: higher losses for lasing mode.

However, losses for neighbored modes due to sum frequency mixing are

even higher – SHG stabilizes single-frequency operation.

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Various issues:

If the gain bandwidth is larger than the phase-matching bandwidth,

the laser wavelength may “escape” the wavelength region with high

conversion. Need a bandpass filter then.

Type II phase matching is not ideal in combination with laser crystal with

polarization-dependent gain: pump polarization is spoiled.

Example: green laser pointer with Nd:YVO4 laser and KTP doubler.

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Various issues:

Intracavity doubling in Q-switched lasers can be problematic:

Nonlinear conversion may strongly increase the pulse duration,

if it is efficient.

May cause self-destruction if SHG doesn’t work for some reason

(e.g. wrong crystal temperature or orientation).

Anyway, extra-cavity peak power is usually sufficient.

Intracavity doubling in mode-locked lasers is rarely done.

Reason: nonlinearity (and possibly chromatic dispersion) can mess up

the pulse generation.

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Frequency Doubling with Pulses

Longer pulses (e.g. nanosecond durations):

Each part of the temporal profile is treated separately.

Total conversion efficiency is some average over the pulse profile(easy to calculate): higher efficiency at the peak, lower efficiency in the wings.

Short pulse durations allow for higher intensities.

weak conversion

efficient conversion

power

time

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Frequency Doubling with Pulses

Ultrashort pulses (picosecond or femtosecond duration):

The shorter the pulse, the more important becomes the group velocity mismatch (GVM).

Frequency domain description: pulse bandwidth approaches or exceeds the phase-matching bandwidth.

Extreme case of very shortpulses with weak conversion:approximately rectangularharmonic pulse, substantiallydegraded conversion efficiency.

Figure shows a case withstrong power conversion.

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Optimal Pulse Durationfor Efficient Power Conversion

Example: 100-nJ pulses at 1 μm with variable duration,

to be converted in LBO:

A) Pulse duration 10 ps:

Peak power 9 kW.

Conversion with critical phase matching at room temperature,

scheme XY I (oo-e):

achieve only 8% efficiency for wp = 100 m in 10 mm long crystal,

avoiding substantial ellipticity of harmonic beam.

Longer crystal doesn’t help!

Conversion with noncritical phase matching at 149 C: no problem:

achieve e.g. 52% efficiency for wp = 25 μm.

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B) Pulse duration 1 ps:

Peak power 90 kW.

Conversion with critical phase matching at room temperature,

scheme XY I (oo-e):

achieve 52% efficiency for wp = 100 m in 10 mm long crystal,

avoiding substantial ellipticity of harmonic beam.

GVM in 10 mm is 0.44 ps: no excessive temporal walk-off.

Peak pump intensity: 0.6 GW / cm2,

harmonic intensity somewhat higher: o.k. for LBO.

Conversion with noncritical phase matching at 149 C:

of course also no problem.

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C) Pulse duration 100 fs:

Peak power 900 kW.

GVM in 10 mm crystal length is too strong; should reduce the crystal length to 1 mm.

Would have to reduce wp to 33 μm in order to obtain 52% conversion again.

Problem: peak pump intensity is then 55 GW / cm2: too high!

Consequence: need weaker focusing, losing conversion efficiency.

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Conclusions:

Long pulses are problematic, when the peak power is too low.

In principle, may use long crystal (for noncritical phase matching),

but there are practical limits.

Critical phase matching is normally less suitable for pulses with moderate

peak power: cannot focus strongly.

have to use noncritical phase matching in a crystal oven.

Very short pulses are problematic: GVM makes short crystal necessary,

while intensity is limited by damage

difficult to achieve efficient and long-term stable conversion.

Note: short wavelengths are more problematic in this respect: larger GVM

and typically lower damage threshold.

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Part II:Parametric Amplification and Oscillation

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Basics of Parametric Amplification

One pump photon (wave 3) adds one signal photon (wave 2)

and one idler photon (wave 1):

Energy conservation:

Pump wave is depleted while signal and idler are getting stronger.

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Basics of Parametric Amplification

Idler wave may not be useful, but is essential for the process:

local amplitude addition to the signal:

Strong idler absorption in the crystal diminishes the parametric gain

(not necessarily the power efficiency)

need a crystal material with good transparency for all three wavelengths.

Signal amplification could in principle be boosted with an additional idler

input, but this would have to have the right phase!

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Comparison of Parametric Amplificationwith Laser Amplification

Parametric amplifier does not dissipate energy in the crystal

(except via parasitic absorption, including nonlinear absorption (TPA))

only weak heating of the crystal

Parametric amplifier requires phase matching

can tolerate only weak heating

Wavelength region with signal gain can be tuned via temperature or crystal

orientation

may access wide wavelength regions, including the mid infrared

Gain bandwidth of parametric amplifier depends on crystal length

Parametric amplifier does not store energy

need temporal overlap of pump and signal pulses

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Applications of Parametric Amplification Amplification of continuous-wave signals:

not very attractive: limited intensities, small gain.

Continuous-wave parametric oscillation: to be discussed later on.

Amplification of signal pulses with nanosecond durations,

using equally short pump pulses from a Q-switched laser

Amplification of signal pulses with picosecond or femtosecond durations,

using similarly short (or sometimes longer) pump pulses from a mode-locked

laser or regenerative amplifier

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Amplification of Nanosecond Pulses Example:

Pump pulses: 0.1 mJ, 10 ns, 1064 nm, focused to 100 μm radius

pump intensity 56 MW / cm2 on the beam axis:

not very far below the damage threshold of PPLN

Nonlinear crystal: PPLN, 20 mm long, poled for 1532-nm signal

Estimate for gain, assuming Gaussian beams with equal Rayleigh

length: 18.5 dB (somewhat too low due to gain guiding)

Conclusions:

Tens of dB are possible, but only close to the damage threshold.

Shorter pulses allow for higher gain, as damage intensity is higher.

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Amplification of Ultrashort Pulses Example:

Pump pulses: 1 μJ, 5 ps, 1064 nm, focused to 100 μm radius

pump intensity 1.1 GW / cm2 on the beam axis:

still well below the damage threshold of PPLN

Nonlinear crystal: PPLN, 20 mm long, poled for 1532-nm signal

Estimate for gain with Gaussian beams, ignoring GVM:

103 dB (somewhat too low due to gain guiding)

Group velocity mismatch is 106 fs / mm 2.1 ps in 20 mm

Conclusions:

>100 dB is easily possible can do optical parametric generation (OPG):

substantial signal output without signal input

GVM is important for short pulses and/or long crystals

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Parametric Oscillation Basic principle: place a parametric amplifier in a resonator;

above threshold, signal builds up automatically, as in a laser.

Device is called optical parametric oscillator = OPO.

Singly resonant OPO: resonator works only for the signal wavelength,

has high round-trip losses for the idler (or vice versa).

Doubly resonant OPO: resonator works for both signal and idler.

In addition, may use a resonator for the pump wave, if the pump wave is

single-frequency.

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Singly Resonant OPOs

Continuous-wave pumping:

The achievable parametric gain is fairly low: typically a few percent

need a low-loss resonator for a reasonably low threshold pump power

Typical pump powers: few watts for PPLN (W. R. Bosenberg et al., Opt. Lett.

20 (10), 713 (1996)), higher for most other materials.

Wavelength tuning is easy; even single-frequency operation is possible,

when idler feedback is avoided.

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Nanosecond pumping:

The parametric gain can be very high,

but pulse build-up from noise must occur within the pumping time

make the resonator as short as possible

Rule of thumb: need 100 dB of accumulated signal net gain within a time

well below the pump pulse duration.

A wide range of nonlinear crystal materials can be used.

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Synchronous pumping with picosecond or femtosecond pulses:

Resonator round-trip time equals period of pump pulses.

Signal pulse circulates in the resonator, usually finds stable steady state.

Required gain is easily achieved,

except for extremely high pulse repetition rates (>80 GHz achieved).

Synchronization can be a bit tricky, and often needs automatic feedback

system. Resonator length detuning may affect the oscillation wavelength.

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Wavelength tuning: simply by affecting the phase-matching conditions,

or sometimes with an intracavity bandpass filter.

Idler is generated in each pass; idler wavelength adjusts automatically.

Caution with angle tuning: tilting the crystal may misalign the resonator.

Operation near degeneracy: problematic, as idler feedback becomes

significant if idler frequency is similar to signal frequency.

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Doubly Resonant OPOs

Resonant signal and idler: both waves have enhanced intensities

threshold pump power can be much lower

Problem: signal and idler frequency must be such that signal and idler are

resonant simultaneously.

Consequence: complicated tuning behavior with “mode clusters”;

continuous wavelength tuning is difficult, also stable single-frequency

operation.

tutorial on nonlinear frequency conversion€¦ · potassium titanyl phosphate (ktp, ktiopo4): high...

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