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A high finesse optical resonator is used to store optical pulses of a mode-locked laser. The mode-locked laser is frequency stabilized by monitoring an optical attribute of the high finesse optical resonator indicative of a difference between a center frequency of the mode-locked laser and a resonan

A high finesse optical resonator is used to store optical pulses of a mode-locked laser. The mode-locked laser is frequency stabilized by monitoring an optical attribute of the high finesse optical resonator indicative of a difference between a center frequency of the mode-locked laser and a resonant frequency of the high finesse optical resonator. In one embodiment FM sideband modulation is used to stabilize the mode-locked laser pulses.

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The invention claimed is: 1. An apparatus for storing optical pulses in an optical resonator as a superposition of pulses, comprising: a mode-locked laser generating optical pulses comprising a comb of frequencies within a frequency range, said mode-locked laser having a selectable center frequency

The invention claimed is: 1. An apparatus for storing optical pulses in an optical resonator as a superposition of pulses, comprising: a mode-locked laser generating optical pulses comprising a comb of frequencies within a frequency range, said mode-locked laser having a selectable center frequency of said optical pulses; an FM sideband modulator receiving said optical pulses and generating input pulses for said optical resonator having an FM sideband frequency relative to said center frequency; a detector for receiving reflected laser light at said FM sideband frequency and stored light exiting said optical resonator at a cavity frequency; and a controller monitoring deviations of said center frequency from a resonant frequency of said optical resonator and in response adjusting said center frequency to match said resonant frequency within a selected margin less than a cavity bandwidth of said optical resonator; wherein said controller includes a first servo path for obtaining an initial lock to said center frequency and a second servo path for reducing residual noise. 2. The apparatus of claim 1, wherein said optical resonator has a finesse selected to increase the power of said input optical pulses by a factor of at least 1,000 via superposition of stored optical pulses. 3. An apparatus for storing optical pulses in an optical resonator as a superposition of pulses, comprising; a mode-locked laser generating optical pulses comprising a comb of frequencies within a frequency range, said mode-locked laser having a selectable center frequency of said optical pulses; an FM sideband modulator receiving said optical pulses and generating input pulses for said optical resonator having an FM sideband frequency relative to said center frequency; a detector for receiving reflected laser light at said FM sideband frequency and stored light exiting said optical resonator at a cavity frequency; and a controller monitoring deviations of said center frequency from a resonant frequency of said optical resonator and in response adjusting said center frequency to match said resonant frequency within a selected margin less than a cavity bandwidth of said optical resonator; wherein said optical resonator has a finesse selected to increase the power of said input optical pulses by a factor of at least 10,000 via superposition of stored optical pulses and has a corresponding cavity bandwidth no greater than about 3 KHz. 4. The apparatus of claim 3, wherein said center frequency is stabilized to less than about 300 Hz. 5. An apparatus for storing optical pulses in an optical resonator as a superposition of pulses, comprising: a mode-locked laser generating optical pulses comprising a comb of frequencies within a frequency range, said mode-locked laser having a selectable center frequency of said optical pulses; an FM sideband modulator receiving said optical pulses and generating input pulses for said optical resonator having an FM sideband frequency relative to said center frequency; a detector for receiving reflected laser light at said FM sideband frequency and stored light exiting said optical resonator at a cavity frequency; and a controller monitoring deviations of said center frequency from a resonant frequency of said optical resonator and in response adjusting said center frequency to match said resonant frequency within a selected margin less than a cavity bandwidth of said optical resonator; wherein a pulse length of said optical pulses is selected to be greater than a pulse length for which dispersive effects significantly reduces coupling and storage of pulses in said optical resonator. 6. The apparatus of claim 5, wherein said pulse length is greater than one picosecond. 7. The apparatus of claim 5, wherein said controller comprises a demodulator to demodulate signals received from said detector and a servo. 8. A Compton backscattering x-ray system, comprising: a high finesse optical resonator for storing optical pulses and increasing pulse power via resonant superposition of optical pulses within said high finesse optical resonator; a mode-locked laser generating a train of optical pulses coupled to said high finesse optical resonator, said train of optical pulses having a repetition rate, a center frequency, and a comb of frequencies; a control system monitoring an optical attribute of said optical resonator indicative of a difference between said center frequency and a resonant frequency of said high finesse optical resonator, said control system regulating said center frequency to be within a cavity bandwidth of said high finesse optical resonator wherein said control system comprises a first servo path for obtaining an initial lock to said center frequency and a second servo path for reducing residual noise. 9. The system of claim 8, wherein said control system comprises a frequency modulated (FM) sideband modulator modulating said train of optical pulses to have an FM sideband, said control system detecting reflected light at said FM sideband and light coupled out of said optical resonator, generating an error signal indicative of a deviation of said center frequency from said resonant frequency, and determining a correction to said center frequency. 10. The system of claim 8, wherein said optical resonator has a finesse selected to increase the power of said optical pulses by a factor of at least 1,000 via superposition of stored optical pulses. 11. A Compton backscattering x-ray system, comprising: a high finesse optical resonator for storing optical pulses and increasing pulse power via resonant superposition of optical pulses within said high finesse optical resonator; a mode-locked laser generating a train of optical pulses coupled to said high finesse optical resonator, said train of optical pulses having a repetition rate, a center frequency, and a comb of frequencies; a control system monitoring an optical attribute of said optical resonator indicative of a difference between said center frequency and a resonant frequency of said high finesse optical resonator, said control system regulating said center frequency to be within a cavity bandwidth of said high finesse optical resonator; wherein said high finesse resonator has a cavity bandwidth of no more than 3 KHz and wherein said center frequency is stabilized to less than about 300 Hz. 12. A Compton backscattering x-ray system, comprising: high finesse optical resonator for storing optical pulses and and increasing pulse power via resonant superposition of optical pulses within said finesse optical resonator; a mode-locked laser generating a train of optical pulses coupled to said high finesse optical resonator, said train of optical pulses having a repetition rate, a center frequency, and a comb of frequencies; a control system monitoring an optical attribute of said optical resonator indicative of a difference between said center frequency and a resonant frequency of said high finesse optical resonator, said control system regulating said center frequency to be within a cavity bandwidth of said high finesse optical resonator; wherein a pulse length of said optical pulses is selected to be greater than a pulse length for which dispersive effects would significantly reduce coupling and storage of pulses in said optical resonator. 13. The system of claim 12, wherein said pulse length is greater than one picosecond. 14. The system of claim 12, wherein said control system comprises a demodulator to demodulate signals received from said detector and a servo. 15. The system of claim 12, further comprising: a cavity length adjuster to adjust a cavity length of said optical resonator to synchronize timing of optical pulses within said optical resonator to electron beam bunches at an interaction point. 16. A Compton backscattering x-ray system, comprising: a high finesse optical resonator for storing optical pulses as a superposition of pulses and having an optical path coaxial with a portion of an electron storage ring for 180 degree Compton backscattering of stored optical pulses with electron bunches; a mode-locked laser generating optical pulses coupled to said high-finesse optical resonator, said optical pulses comprising a comb of frequencies within a frequency range, said mode-locked laser having a selectable center frequency of said optical pulses; a control system monitoring an optical attribute of said high finesse optical resonator indicative of a difference between said center frequency and a resonant frequency of said high finesse optical resonator, said control system regulating said center frequency to be within a cavity bandwidth of said high finesse optical resonator; wherein said high finesse optical resonator provides an optical gain enhancement of at least a factor of one thousand of said optical pulses generated by said mode-locked laser; wherein said control system comprises an frequency modulated (FM) sideband modulator modulating said train of optical pulses to have a FM sideband, said control system detecting reflected light at said FM sideband and light coupled out of said optical resonator, generating an error signal indicative of a deviation of said center frequency from said resonant frequency, and determining a correction to said center frequency; wherein said control system includes a first servo path for obtaining an initial lock to said center frequency and a second servo path for reducing residual noise. 17. A Compton backscattering x-ray system, comprising: a high finesse optical resonator for storing optical pulses as a superposition of pulses and having an optical path coaxial with a portion of an electron storage ring for 180 degree Compton backscattering of stored optical pulses with electron bunches; mode-locked laser generating optical pulses coupled to said high-finesse optical resonator, said optical pulses comprising a comb of frequencies within a frequency range, said mode-locked laser having a selectable center frequency of said optical pulses; a control system monitoring an optical attribute of said high finesse optical resonator indicative of a difference between said center frequency and a resonant frequency of said high finesse optical resonator, said control system regulating said center frequency to be within a cavity bandwidth of said high finesse optical resonator; wherein said high finesse optical resonator provides an optical gain enhancement of at least a factor of one thousand of said optical pulses generated by said mode-locked laser; wherein said control system comprises an frequency modulated (FM) sideband modulator modulating said train of optical pulses to have a FM sideband, said control system detecting reflected light at said FM sideband and light coupled out of said optical resonator, generating an error signal indicative of a deviation of said center frequency from said resonant frequency, and determining a correction to said center frequency; wherein said optical resonator has a finesse selected to increase the power of said input optical pulses by a factor of at least 10,000 via superposition of stored optical pulses and has a corresponding cavity bandwidth no greater than about 3 KHz. 18. The system of claim 17, wherein said center frequency is stabilized to less than about 300 Hz. 19. The system of claim 17, further comprising: a cavity length adjuster to adjust a cavity length of said optical resonator to synchronize timing of optical pulses within said optical resonator to electron beam bunches at an interaction point. 20. The system of claim 8, wherein said high finesse optical resonator has a portion of an optical path coaxial with a portion of an electron storage ring for 180 degree Compton backscattering of stored optical pulses with electron bunches. 21. The system of claim 9, wherein said high finesse optical resonator has a portion of an optical path coaxial with a portion of an electron storage ring for 180 degree Compton backscattering o stored optical pulses with electron bunches. 22. The system of claim 10, wherein said high finesse optical resonator has a portion of an optical path coaxial with a portion of an electron storage ring for 180 degree Compton backscattering of stored optical pulses with electron bunches. 23. The system of claim 11, wherein said high finesse optical resonator has a portion of an optical path coaxial with a portion of an electron storage ring for 180 degree Compton backscattering of stored optical pulses with electron bunches. 24. The system of claim 12, wherein said high finesse optical resonator has a portion of an optical path coaxial with a portion of an electron storage ring for 180 degree Compton backscattering of stored optical pulses with electron bunches. 25. The system of claim 13, wherein said high finesse optical resonator has a portion of an optical path coaxial with a portion of an electron storage ring for 180 degree Compton backscattering of stored optical pulses with electron bunches. 26. The system of claim 14, wherein said high finesse optical resonator has a portion of an optical path coaxial with a portion of an electron storage ring for 180 degree Compton backscattering of stored optical pulses with electron bunches. 27. The system of claim 15, wherein said high finesse optical resonator has a portion of an optical path coaxial with a portion of an electron storage ring for 180 degree Compton backscattering of stored optical pulses with electron bunches.