Optical frequency combs for stable radiation in the microwave, terahertz and optical domains

Qudsia Quraishi Department of Physics, University of Colorado Time and Frequency Division, National Institute of Standards and Technology Boulder, CO

1 overview stabilized frequency combs from mode-locked femtosecond lasers provide new opportunities for….

§ optical frequency metrology § optical clocks § measuring distance § time & frequency transfer § laboratory tests of fundamental physics § carrier-envelope phase control (key technology for attosecond science) § femtosecond pulse synthesis & arbitrary optical waveform generation § generation of ultralow noise microwaves § new spectroscopic techniques § harmonic generation § coherent control § spread-spectrum secure communications § part of a Nobel Prize!

2 overview stabilized frequency combs from mode-locked femtosecond lasers provide new opportunities for….

§ optical frequency metrology § optical clocks § measuring distance § time & frequency transfer § laboratory tests of fundamental physics § carrier-envelope phase control (key technology for attosecond science) § femtosecond pulse synthesis & arbitrary optical waveform generation Jan Hall § generation of ultralow noise microwaves § new spectroscopic techniques § harmonic generation § coherent control Ted Hänsch § spread-spectrum secure communications § part of a Nobel Prize!

2 microwave frequency synthesizers

power RF signal

carrier frequenc y

specifications 250 kHz – 20 GHz + low phase noise

10, 007, 482, 279 GHz

Agilent E8257D frequency synthesizer

3 microwave frequency synthesizers

user defined: power (a) frequency RF signal (b) amplitude (c) noise (to some extent) carrier frequenc y uses: specifications (i) references (ii) comparisons 250 kHz – 20 GHz + (iii) microwave electronics low phase noise

10, 007, 482, 279 GHz

Agilent E8257D frequency synthesizer

3 microwave frequency synthesizers

user defined: power (a) frequency RF signal (b) amplitude (c) noise (to some extent) carrier frequenc y uses: specifications (i) references (ii) comparisons 250 kHz – 20 GHz + (iii) microwave electronics low phase noise

10, 007, 482, 279 GHz

pretty good… 1 part in 1010

Agilent E8257D frequency synthesizer

3 commercial optical frequency synthesizer

idea: optical frequency synthesizer

FREQUENCY: 352, 567, 323, 826, 841 Hz

POWER: 2 nW

NOISE: -100 dBc/Hz at 1 Hz

port 1 port 2

4 commercial optical frequency synthesizer

idea: optical frequency synthesizer

FREQUENCY: 352, 567, 323, 826, 841 Hz

POWER: 2 nW

NOISE: -100 dBc/Hz at 1 Hz

port 1 port 2

850 nm (352 THz)

4 commercial optical frequency synthesizer

idea: optical frequency synthesizer

FREQUENCY: 352, 567, 323, 826, 841 Hz POWER: 2 nW really good… NOISE: -100 dBc/Hz at 1 Hz 1 part in 1015 ! port 1 port 2

850 nm (352 THz)

4 commercial optical frequency synthesizer

microwave or optical reference atoms stable or molecules cavity

your are only as good as your reference

idea: optical frequency synthesizer

FREQUENCY: 352, 567, 323, 826, 841 Hz POWER: 2 nW really good… NOISE: -100 dBc/Hz at 1 Hz 1 part in 1015 ! port 1 port 2

850 nm (352 THz)

4 microwave pulse generators

Picosecond Pulse Labs 2600C

specifications rise time 250 ps dynamic range 70 dB pulse duration 1 ns to 100 nsec repetition rate 1 Hz – 100 kHz

5 optical pulse generators?

pulse duration: 20 fs

repetition rate: 1 GHz

phase profile: 20 fs2

port 1 port 2

each cycle: 2.5 fs (800 nm)

stabilized combs have subfs timing jitter from pulse-to-pulse

6 optical pulse generators?

pulse duration: 20 fs SUB FEMTOSECOND repetition rate: 1 GHz phase stability !

phase profile: 20 fs2

port 1 port 2

each cycle: 2.5 fs (800 nm)

stabilized combs have subfs timing jitter from pulse-to-pulse

6 frequency combs are extending our ideas about user-defined frequency sources, from the microwave to the optical

7 optical spectrum is discrete, appearing every frep 10 cm

kerr lens modelocked OC frequency comb pump TiS xstal 600 mW modelocked power 1 GHz repetition rate pulses E(t) 15 fs 8.5 W pump beam at 532 nm

time

hundreds of nm

600 700 800 900 1000 wavelength (nm)

8 optical spectrum is discrete, appearing every frep 10 cm

kerr lens modelocked OC frequency comb pump TiS xstal 600 mW modelocked power 1 GHz repetition rate pulses E(t) 15 fs 8.5 W pump beam at 532 nm

S(ν) time frep

hundreds of nm

ν

600 700 800 900 1000 wavelength (nm)

measured cavity modes

8 optical spectrum is discrete, appearing every frep 10 cm

kerr lens modelocked OC frequency comb pump TiS xstal 600 mW modelocked power 1 GHz repetition rate pulses E(t) 15 fs 8.5 W pump beam at 532 nm

S(ν) time frep f0

hundreds of nm

ν

600 700 800 900 1000 wavelength (nm)

dispersionless measured cavity modes cavity modes

8 optical spectrum is discrete, appearing every frep 10 cm

kerr lens modelocked OC frequency comb pump TiS xstal 600 mW modelocked power 1 GHz repetition rate pulses E(t) 15 fs vn = n frep + f0 8.5 W pump beam at 532 nm

S(ν) time frep f0

hundreds of nm

ν

600 700 800 900 1000 wavelength (nm)

dispersionless measured cavity modes cavity modes

8 stabilization of optical frequency comb

• offset controlled by modulating pump • rep. rate or beatnote (with CW laser) controlled with cavity mirror

OC

pump laser TiS xstal AOM or EOM

frep or fbeat f0

100 MHz RF spectrum f:2f interferometer

9 stabilization of optical frequency comb

• offset controlled by modulating pump • rep. rate or beatnote (with CW laser) controlled with cavity mirror

OC

pump laser TiS xstal AOM or EOM ofset frequency lock frep or fbeat f0

100 MHz RF spectrum f:2f interferometer

9 stabilization of optical frequency comb

• offset controlled by modulating pump • rep. rate or beatnote (with CW laser) controlled with cavity mirror

OC

pump laser TiS xstal AOM or EOM ofset frequency lock f or repetition rate or rep heterodyne beat lock fbeat f0

100 MHz RF spectrum f:2f interferometer

9 comb equation predicts optical frequencies v = n f + f S(ν) n rep 0

ν

10 comb equation predicts optical frequencies v = n f + f S(ν) n rep 0

frep

f 0 ν

10 comb equation predicts optical frequencies v = n f + f S(ν) n rep 0

frep

f 0 ν meaning that if I measure:

f0 = 120 MHz

frep = 1000 MHz

10 comb equation predicts optical frequencies v = n f + f S(ν) n rep 0

frep

f 0 ν meaning that if I measure: then I know *all* the optical frequencies: the n=500,000 mode has a freq. of: f0 = 120 MHz vn = n frep + f0 = 5e5(1GHz) + 120 MHz frep = 1000 MHz = 500,000,120,000,000 Hz

10 comb equation predicts optical frequencies v = n f + f S(ν) n rep 0 limit to optical freq. accuracy: reference for rep. and offset

frep

f 0 ν meaning that if I measure: then I know *all* the optical frequencies: the n=500,000 mode has a freq. of: f0 = 120 MHz vn = n frep + f0 = 5e5(1GHz) + 120 MHz frep = 1000 MHz = 500,000,120,000,000 Hz

10 …on the other hand…

…we can extract microwave signals from stabilized combs.

11 comb equation predicts optical frequencies f = (v + f )/ rep nlock 0 S(ν) n

ν

12 comb equation predicts optical frequencies f = (v + f )/ rep nlock 0 S(ν) n

f 0 ν

12 comb equation predicts optical frequencies f = (v + f )/ rep nlock 0 S(ν) n vref 657 nm (457 THz)

fbeat f 0 ν

12 comb equation predicts optical frequencies f = (v + f )/ rep nlock 0 S(ν) v – f n ref beat vref 657 nm (457 THz)

fbeat f 0 ν

12 comb equation predicts optical frequencies f = (v + f )/ rep nlock 0 S(ν) v – f n ref beat vref 657 nm (457 THz)

fbeat f 0 ν meaning that if I measure:

f0 = 120 MHz

fbeat = 300 MHz

12 comb equation predicts optical frequencies f = (v + f )/ rep nlock 0 S(ν) v – f n ref beat vref 657 nm (457 THz)

fbeat f 0 ν meaning that if I measure: then I know *all* the microwave frequencies: the n=500,000 divided mode is: f0 = 120 MHz frep = (457e12 – 300 MHz – 120 MHz)/n fbeat = 300 MHz = 914 MHz (this moves with CW reference say, 1 Hz per second)

12 comb equation predicts optical frequencies f = (v + f )/ rep nlock 0 S(ν) v – f n ref beat limit to microwave v 657 nm (457 THz) ref freq. accuracy: CW optical reference

fbeat f 0 ν meaning that if I measure: then I know *all* the microwave frequencies: the n=500,000 divided mode is: f0 = 120 MHz frep = (457e12 – 300 MHz – 120 MHz)/n fbeat = 300 MHz = 914 MHz (this moves with CW reference say, 1 Hz per second)

12 comb equation predicts optical frequencies v combs stability δ 0 v0 S(ν)

Ca at 657 nm Hg ref. at 1064 nm

ν

locke measured d

13 comb equation predicts optical frequencies

δ v0 δvCa combs stability ~ optical reference stability v0 vCa S(ν)

Ca at 657 nm Hg ref. at 1064 nm

fractional stability same along *entire* comb

ν

locke measured d

13 comb equation predicts optical frequencies

δ v0 δvCa combs stability ~ optical reference stability v0 vCa S(ν)

Ca at 657 nm Hg ref. at 1064 nm

fractional stability same along *entire* comb

ν

locke measured …thus, can compare d two standards

13 frequency measurements: simplified with combs

14 frequency measurements: simplified with combs

stabilized frequency comb frequency measurements of laser-based frequency standards

1.E-05

1.E-06 Less than 100 THz 1.E-07 Greater than 100 THz 1.E-08

1.E-09

1.E-10

1.E-11

1.E-12

1.E-13 Cs Primary Freq. Stds.

1.E-14

fractional frequency uncertainty 1.E-15

1.E-16 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 publication date

14 frequency measurements: simplified with combs

stabilized frequency comb frequency measurements of laser-based frequency standards

1.E-05

1.E-06 Less than 100 THz 1.E-07 Greater than 100 THz 1.E-08

1.E-09

1.E-10

1.E-11

1.E-12

1.E-13 Cs Primary Freq. Stds.

1.E-14

fractional frequency uncertainty 1.E-15

1.E-16 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 publication date

optical frequency metrology now routinely (as of year 2000) involves frequency combs for measurements

14 atomic standards comparison with combs

neutral Ca atoms: 457 THz (657 nm) Hg+: 563 THz (532 nm)

frequency comb as gearwork for optical-atomic clocks

15 much of the work with combs relies on low phase noise

at NIST, we are interested in performance in both regimes

narrow linewidth stabilized LOW PHASE NOISE CW optical reference frequency comb OPTICAL SIGNALS

LOW PHASE NOISE MICROWAVE SIGNALS

16 first step: establish frequency stability of comb

frequency counter

L.-S. Ma, Z. Bi, A. Bartels, et al., Science 303, 1843 (2004).

other reference oscillators

17 first step: establish frequency stability of comb

frequency counter

L.-S. Ma, Z. Bi, A. Bartels, et al., Science 303, 1843 (2004).

other reference oscillators

relative stability between two stabilized combs

17 first step: establish frequency stability of comb

frequency counter

L.-S. Ma, Z. Bi, A. Bartels, et al., Science 303, 1843 (2004).

other reference oscillators

?

relative stability between two stabilized combs

17 methods for measuring optical coherence

fbeat1, f01 relative phase noise measurement S(ν) OFC1 to compare different spectral regions, ν …can extract RF parameter from each region

f01 - f02 = ∆ f0 S(ν) OFC2 ν

fbeat2, f02

18 methods for measuring optical coherence

fbeat1, f01 relative phase noise measurement S(ν) OFC1 to compare different spectral regions, ν …can extract RF parameter from each region

IR VIS

Δf0 Δf0

IR VIS

S(ν) OFC2 ν

fbeat2, f02

18 methods for measuring optical coherence

fbeat1, f01 relative phase noise measurement S(ν) OFC1 to compare different spectral regions, ν …can extract RF parameter from each region

IR VIS with this technique we can: § downconvert optical noise into RF parameter Δf0 Δf0 § compare noise at different spectral regions

IR VIS …that is, look at dynamics of comb…

S(ν) OFC2 ν

fbeat2, f02

18 methods for measuring optical coherence

fbeat1, f01 relative phase noise measurement S(ν) OFC1 to compare different spectral regions, ν …can extract RF parameter from each region

IR VIS with this technique we can: § downconvert optical noise into RF parameter Δf0 Δf0 § compare noise at different spectral regions

IR VIS …that is, look at dynamics of comb…

S(ν) OFC2 ν

fbeat2, f02 PSD noise

Fourier frequency

18 methods for measuring optical coherence

fbeat1, f01 relative phase noise measurement S(ν) OFC1 to compare different spectral regions, ν …can extract RF parameter from each region

IR VIS with this technique we can: § downconvert optical noise into RF parameter Δf0 Δf0 § compare noise at different spectral regions

IR VIS …that is, look at dynamics of comb…

S(ν) OFC2 § how does the phase noise vary across comb? § can the comb equation predict the measured noise? ν

fbeat2, f02 PSD noise

Fourier frequency

18 relative noise between lock point and region 230 nm away

240 nm away from lock point! frep

Δf0 = f01 – f02 900 nm 657 nm

20 dB

19 relative noise between lock point and region 230 nm away measured limited by measurement noise floor

demonstrates broad spectral phase coherence across comb

240 nm away from lock point!

900 nm 657 nm

19 relative noise between lock point and region 230 nm away measured limited by measurement noise floor

demonstrates broad spectral phase coherence across comb

240 nm away from lock point!

low level noise milliradian/Hz1/2 900 nm 657 nm on optical signal

sub-fs timing jitter

19 relative noise between lock point and region 230 nm away measured limited by measurement noise floor

demonstrates broad spectral phase coherence across comb

prediction

240 nm away from lock point!

low level noise milliradian/Hz1/2 900 nm 657 nm on optical signal

sub-fs timing jitter

19 relative noise between lock point and region 230 nm away measured limited by measurement noise floor

demonstrates broad spectral using comb equation, phase coherence across comb we predict:

prediction

240 nm away from lock point!

low level noise milliradian/Hz1/2 900 nm 657 nm on optical signal

sub-fs timing jitter

19 scaling of phase away from locked point

900 nm 240 nm

800 nm fixed point

704 nm 621 nm

716 nm 631 nm

20 scaling of phase away from locked point

900 nm 240 nm

800 nm fixed point

~ linearly with 704 nm 621 nm distance from lock point 716 nm 631 nm

20 scaling of phase away from locked point

§ first demonstration scaling of phase noise across comb § comb equation can predict phase dynamics § shows substantial coherence across comb

900 nm 240 nm

800 nm fixed point

~ linearly with 704 nm 621 nm distance from lock point 716 nm 631 nm

20 microwave frequency synthesizers

Agilent E8257D frequency synthesizer power RF signal

carrier frequenc y plotted without spurs single side band phase noise

specifications

250 kHz – 20 GHz + low phase noise

21 microwave signals from optical frequency combs

§ frequency stability stabilized microwave § phase noise frequency comb frequency comb

frep frep ...... freq. 250 THz GHz 1 GHz 2 GHz 3 GHz

22 microwave noise from combs very good

Q. Quraishi, S. Diddams, L. Hollberg, in progress

state-of-art sapphire microwave oscillator

Agilent 8257D synthesizer

23 microwave noise from combs very good

Q. Quraishi, S. Diddams, L. Hollberg, in progress

state-of-art sapphire microwave oscillator

Agilent 8257D synthesizer

repetition rate photodetection of comb

23 microwave noise from combs very good

Q. Quraishi, S. Diddams, L. Hollberg, in progress

state-of-art sapphire microwave oscillator

region where combs’ performance excels Agilent 8257D synthesizer

repetition rate photodetection of comb

23 if noise is low than other microwave sources…

how was the measurement done?

24 measuring microwave noise of combs

narrow linewidth CW reference

stabilized stabilized frequency comb #1 frequency comb #1

...... freq. freq. 1 GHz 2 GHz 10 GHz 1 GHz 2 GHz 10 GHz

noise extremely low noise measurement

microwave noise from each comb so low that we can only measure it by comparing to another comb.

25 details about current limitations to microwave from combs

TiS phase noise at 10 GHz bottom line: before we try to measure ‘fundamental’ noise in combs must 1/f + noise address technical noise

pump noise Shot noise

100 Hz 1 kHz 10 kHz 100 kHz 1 MHz

pump stabilized microwave frep f0 laser frequency comb frequency comb nois e

26 details about current limitations to microwave from combs

TiS phase noise at 10 GHz bottom line: before we try to measure ‘fundamental’ noise in combs must 1/f + noise address technical noise

pump noise Shot noise

100 Hz 1 kHz 10 kHz 100 kHz 1 MHz

so far, technical noise constitutes our most immediate challenge

26 final example of comb application: transfer the coherence of comb to terahertz domain

27 hundreds of nm

850 nm

1 GHz … ν

0 THz 1 THz

28 hundreds of nm

850 nm

1 GHz … ν

0 THz 1 THz

28 hundreds of nm

850 nm

1 GHz … ν

0 THz 1 THz THz frequency ruler

28 combs for referenced terahertz radiation

§ diode lasers referenced to optical frequency combs 1 THz ~ 0.3 µm

J. D. Jost, J. L. Hall and J. Ye, Opt. Exp. 10, 515 (2002).

Th. Udem, J. Reichert, R. Holzworth and T. W. Hänsch, Phys. Rev. Lett. 82, 3568 (1999)

29 combs for referenced terahertz radiation

§ diode lasers referenced to § THz generation and spectroscopy optical frequency combs 0.1 – 10 THz 1 THz ~ 0.3 µm R. Köhler, A. Tredicucci, F. Beltram, et al., Nature 417, 156 (2002).

J. D. Jost, J. L. Hall and J. Ye, Opt. Exp. 10, 515 (2002).

B. Ferguson and X. Zhang Nature Mat. 1, 26 (2002)

Th. Udem, J. Reichert, R. Holzworth and T. W. Hänsch, Phys. Rev. Lett. 82, 3568 (1999)

29 combs for referenced terahertz radiation

§ diode lasers referenced to § THz generation and spectroscopy optical frequency combs 0.1 – 10 THz 1 THz ~ 0.3 µm R. Köhler, A. Tredicucci, F. Beltram, et al., Nature 417, 156 (2002).

J. D. Jost, J. L. Hall and J. Ye, Opt. Exp. 10, 515 (2002).

B. Ferguson and X. Zhang Nature Mat. 1, 26 (2002)

Th. Udem, J. Reichert, R. Holzworth and T. W. Hänsch, Phys. Rev. Lett. 82, 3568 (1999)

combine powerful ideas of stabilized optical frequency combs with THz domain

29 terahertz generation and phase stabilization THz regime ~ 0.1 – 10 THz

S(ν)

DL1 terahertz DL2 antenna

CW diode CW diode laser #1 laser #2

THz freq. ν

30 terahertz generation and phase stabilization THz regime ~ 0.1 – 10 THz

THz detecto S(ν) r

DL1 terahertz DL2 antenna

CW diode CW diode laser #1 laser #2

THz freq. ν

30 terahertz generation and phase stabilization THz regime ~ 0.1 – 10 THz

§ broad tune THz comb allows us to: § know THz freq. precisely while tuning THz S(ν)

DL1 terahertz DL2 antenna

CW diode CW diode laser #1 laser #2

THz freq. ν

30 terahertz generation and phase stabilization THz regime ~ 0.1 – 10 THz

§ broad tune THz comb allows us to: § know THz freq. precisely while tuning THz S(ν)

DL1 terahertz DL2 antenna

CW diode CW diode laser #1 laser #2 reference comb to microwave or optical standard

THz freq. ν

30 terahertz generation and phase stabilization THz regime ~ 0.1 – 10 THz

§ broad tune THz comb allows us to: § know THz freq. precisely while tuning THz S(ν)

DL1 terahertz DL2 antenna

CW diode CW diode laser #1 laser #2 reference comb to microwave or optical standard

THz freq. ν

§ THz frequency standards § precision molecular spectroscopy potential applications: § commercial applications in defense and space industries § studies of semiconductor dynamics

30 CW THz source: heterodyne photomixer

CW diode CW diode laser #1 laser #2 THz freq.

spiral antennas radiate at detuning between lasers

31 CW THz source: heterodyne photomixer

LT-GaAs substrate gold spirals

CW diode CW diode laser #1 laser #2 THz freq.

40 V 20 µm

spiral antennas radiate at photoconductive antenna on LT-GaAs detuning between lasers

Vershese et al. IEEE Trans. on Micro. Theory and Tech. 45 1307 (1997). Smith et al. IEEE J. of Quantum Electron. 24 255 (1988).

31 CW THz source: heterodyne photomixer

LT-GaAs substrate gold spirals

CW diode CW diode laser #1 laser #2 THz freq.

40 V 20 µm

spiral antennas radiate at photoconductive antenna on LT-GaAs detuning between lasers

Vershese et al. IEEE Trans. on Micro. Theory and Tech. 45 1307 (1997). Smith et al. IEEE J. of Quantum Electron. 24 255 (1988).

3 dB

750 µm 75 µm mixer output power freq. 0.01 THz 0.1 1 THz THz

31 CW THz source: heterodyne photomixer

LT-GaAs substrate gold spirals

CW diode CW diode laser #1 laser #2 THz freq.

40 V 20 µm

spiral antennas radiate at photoconductive antenna on LT-GaAs detuning between lasers

Vershese et al. IEEE Trans. on Micro. Theory and Tech. 45 1307 (1997). Smith et al. IEEE J. of Quantum Electron. 24 255 (1988).

LT-GaAs with antennas mounted on board 3 dB

750 µm 75 µm mixer output power freq. 0.01 THz 0.1 1 THz THz

31 linewidth comparison of our results to others

quantum cascade laser

§ tunability: 10 GHz § cryogenic temperatures § linewidth ~30 kHz

A. Barkan et al., Opt. Lett. 29 575 (2004).

quantum cascade laser

32 linewidth comparison of our results to others

quantum cascade laser two CW lasers referenced to optical cavity § tunability: THz § tunability: 10 GHz § more work required to know THz frequency § cryogenic temperatures § locked linewidth ~50 kHz, but can be § linewidth ~30 kHz made narrower

P. Chen et al., App. Phys. Lett. 71 1601 (1997). A. Barkan et al., Opt. Lett. 29 575 (2004).

laser quantum optical #1 cascade laser cavity laser #2

32 THz freq. down-conversion: waveguide harmonic mixer free space CW terahertz 0.3 THz radiation waveguide CW harmonic THz mixer (Shottky diode) Waltmann, L. W. Hollberg, K. A. McIntosh and E. R. Brown, Proc. SPIE 2842, 55 (1996).

33 THz freq. down-conversion: waveguide harmonic mixer free space CW terahertz 0.3 THz radiation waveguide CW harmonic THz mixer

Waltmann, L. W. Hollberg, K. A. McIntosh and E. R. Brown, Proc. SPIE 2842, 55 (1996).

33 THz freq. down-conversion: waveguide harmonic mixer free space CW terahertz 0.3 THz radiation waveguide CW harmonic THz mixer

Waltmann, L. W. Hollberg, K. A. McIntosh and E. R. Brown, Proc. SPIE 2842, 55 (1996).

5 dB TH z

0 100 200 300 400 500 [distance away from 0.3 THz measured in MHz]

33 THz freq. down-conversion: waveguide harmonic mixer free space CW terahertz 0.3 THz radiation waveguide CW harmonic THz mixer

Waltmann, L. W. Hollberg, K. A. McIntosh and E. R. Brown, Proc. SPIE 2842, 55 (1996).

coherence of comb transferred5 dB to TH terahertz signal z

0 100 200 300 400 500 [distance away from 0.3 THz measured in MHz]

33 THz freq. down-conversion: waveguide harmonic mixer free space CW terahertz 0.3 THz radiation waveguide CW harmonic THz mixer

Waltmann, L. W. Hollberg, K. A. McIntosh and E. R. Brown, Proc. SPIE 2842, 55 (1996).

coherence of comb transferred5 dB to TH terahertz signal z

Hz level

0 100 200 300 400 500 [distance away from 0.3 THz measured in MHz]

33 coherence of comb transferred to terahertz

microwave frep synthesizer

34 coherence of comb transferred to terahertz

microwave frep synthesizer

-10 ) -20

-30 dBc/Hz -40

-50

-60 0.303 THz -70 90 GHz 40 GHz

relative noise ( -80

10 1 10 2 10 3 10 4 10 5

frequency – f0 (Hz)

34 coherence of comb transferred to terahertz

microwave frep synthesizer

-10 ) -20 source of noise

-30 dBc/Hz -40

-50

-60 0.303 THz -70 90 GHz 40 GHz

relative noise ( -80

10 1 10 2 10 3 10 4 10 5

frequency – f0 (Hz)

34 summary

(a) demonstrated that stabilized optical frequency combs may be successfully integrated into THz spectrometers. resulting in: excellent linewidth and broad tunability

stabilized frequency comb 1 THz 4 THz

(b) demonstrated improved optical phase noise performance of TiS resulting in: potential for enhance microwave phase noise performance

stabilized microwave frequency comb frequency comb

(c) showed optical coherence properties of comb demonstrating: significant phase coherence across 100s of nm across

35 36 frequency combs locked to optical references

FIXED POINT CW laser OFC modes redefined in terms of fixed point frequency comb

S(ν) n+2 nfixed n+1 n-1

fbeat ν ν ν nfixed 0

§ f0 independently stabilized also 37 deriving prediction for phase noise across comb § rewrite comb equation in terms of phase-locked parameters

OFC1 OFC2

38 deriving prediction for phase noise across comb § rewrite comb equation in terms of phase-locked parameters

OFC1 OFC2

38 deriving prediction for phase noise across comb § rewrite comb equation in terms of phase-locked parameters

OFC1 OFC2

38 deriving prediction for phase noise across comb § rewrite comb equation in terms of phase-locked parameters

OFC1 OFC2

§ relative noise between these two, using νn equation is: phase noise of each locked parameter projected phase noise 2 rad (we neglect Hz cross terms)

38 deriving prediction for phase noise across comb § rewrite comb equation in terms of phase-locked parameters

OFC1 OFC2

§ relative noise between these two, using νn equation is: phase noise of each locked parameter projected phase noise 2 rad (we neglect Hz cross terms)

PSD we PSD of locks, we can predict optical phase noise

Fourier frequency

38 deriving prediction for phase noise across comb § rewrite comb equation in terms of phase-locked parameters

OFC1 OFC2

§ relative noise between these two, using νn equation is: phase noise of each locked parameter projected phase noise 2 rad (we neglect Hz cross terms)

PSD we PSD of locks, we can predict optical phase noise phase = ~ linearly with r

Fourier frequency

38 low noise microwave frequency sources

power 1 GHz RF signal

carrier frequency

phase noise on 1 GHz carrier

low noise quartz osc.

low noise RF synthesizer

sapphire cavity osc.

39 40 DLs

lens WHM

40