KAGRA High-Frequency Design

• KAGRA High-Frequency Design is a comprehensive framework that optimizes gravitational-wave sensitivity from a few hundred Hz to several kHz using quantum noise reduction and precise optical tuning.
• It balances the trade-offs between reducing shot noise and managing cryogenic constraints on sapphire test masses, influencing key parameters like arm cavity finesse and laser power.
• The design incorporates advanced readout methods, mode and filter cavity optimization, and calibration strategies to preserve high-frequency sensitivity during operation.

Searching arXiv for KAGRA detector-design papers relevant to high-frequency sensitivity, quantum-noise shaping, squeezing, and readout. KAGRA high-frequency design denotes the set of interferometer, cryogenic, readout, and upgrade choices that determine the detector response from several hundred hertz into the kilohertz regime. In baseline form, KAGRA is a 3-km underground cryogenic gravitational-wave detector whose optical topology is a Fabry–Perot Michelson with power recycling and signal recycling, operated as a resonant sideband extraction interferometer. Within that architecture, high-frequency sensitivity is governed chiefly by quantum shot noise and by the bandwidth shaping produced by the arm cavities, signal-recycling system, and output readout chain, all under the unusually strong constraint that the sapphire test masses must remain cryogenic while carrying substantial optical power (collaboration et al., 2017, Aso et al., 2013, Akutsu et al., 2020).

1. Baseline optical architecture and historical downselection

The baseline detector, bKAGRA, is described as a 3-km resonant sideband extraction interferometer with Fabry–Perot arm cavities, power recycling, and signal recycling. The arm cavities use cryogenic sapphire input and end test masses, while the beam splitter, power-recycling mirrors, and signal-recycling mirrors are room-temperature fused silica. A later design overview characterizes the design-sensitivity configuration as a detuned RSE interferometer in which the arm cavity finesse, signal recycling gain, detune phase of the signal recycling cavity, and readout phase were selected to improve the quantum noise around $\sim 100\,\mathrm{Hz}$ without significantly sacrificing the sensitivity at other frequencies (collaboration et al., 2017, Akutsu et al., 2020).

The older detector-configuration studies show that KAGRA’s high-frequency design was never treated as an isolated $>\!1$ kHz optimization problem. Instead, it emerged from a downselection between broadband resonant sideband extraction and detuned resonant sideband extraction. In the detailed 2013 interferometer study, DRSE generally gave better inspiral range, whereas BRSE was better above $500\,\mathrm{Hz}$, where signals from the merger phase of a neutron-star inspiral event were expected to appear. That study therefore retained variable detuning rather than collapsing the design into a single narrow operating point. The selected parameter set included arm cavity finesse $1530$, PRM reflectivity $90\%$, SRM reflectivity $85\%$, homodyne angle $132^\circ$, detuning angle $3.5^\circ$, and input laser power $78\,\mathrm{W}$, with inspiral ranges of $217\,\mathrm{Mpc}$ for BRSE and $>\!1$0 for DRSE (Aso et al., 2013).

An earlier configuration paper framed the same compromise in quantum-nondemolition language. It adopted a detuned RSE interferometer with arm cavity finesse $>\!1$1, signal recycling mirror reflectivity $>\!1$2, power recycling mirror reflectivity $>\!1$3, detuned signal recycling by about $>\!1$4, and DC readout with optimized quadrature, while still preserving tuned operation as an available state. That paper is especially important historically because it already linked high-frequency performance to variable RSE, back-action evasion, cryogenic heat extraction, and the fact that KAGRA could not pursue a maximum-power strategy in the same way as room-temperature detectors (1111.7185).

2. Quantum-noise shaping in the several-hundred-hertz to kilohertz band

The later KAGRA papers are explicit that high-frequency sensitivity is mainly a quantum-noise problem. One upgrade study states that low frequencies are limited by suspension thermal noise and quantum radiation-pressure noise, the mid-band is limited by mirror thermal noise, and high frequencies are limited by quantum shot noise. A companion review of quantum-noise reduction techniques states the same division more directly: quantum radiation-pressure noise dominates roughly at $>\!1$5, while photon shot noise dominates at high frequencies above a few hundred hertz (Michimura et al., 2019, Somiya, 2019).

Within baseline bKAGRA, the principal quantum-noise knobs are optical power, signal recycling, and readout quadrature. The 2017 status paper gives one representative optical parameter set: laser wavelength $>\!1$6, a $>\!1$7 continuous-wave laser, designed input power at the power-recycling mirror $>\!1$8, power-recycling gain $>\!1$9, arm cavity finesse $500\,\mathrm{Hz}$0, and $500\,\mathrm{Hz}$1 intra-arm circulating power. The same paper states that the power-recycling cavity enhances the effective input power, while the signal-recycling cavity broadens the detector bandwidth by changing the spectral shape of the quantum noise. That statement is the clearest direct summary of baseline KAGRA high-frequency design philosophy: signal recycling is used not only for peak shaping but for bandwidth control in the shot-noise-dominated band (collaboration et al., 2017).

A later design overview expresses the same physics in the Buonanno–Chen input-output formalism. In that parameterization, the design table gives $500\,\mathrm{Hz}$2 at the beam splitter, ITM power transmittance $500\,\mathrm{Hz}$3, SRM amplitude reflectivity $500\,\mathrm{Hz}$4, mirror mass $500\,\mathrm{Hz}$5, mirror temperature $500\,\mathrm{Hz}$6, detune phase $500\,\mathrm{Hz}$7, and readout phase $500\,\mathrm{Hz}$8. In the same paper, $500\,\mathrm{Hz}$9, so at $1530$0 the radiation-pressure contribution dies rapidly and the quantum noise becomes shot-noise dominated. The paper therefore presents detuned RSE as a constrained optimum: it improves quantum noise near $1530$1 and increases compact-binary range by about $1530$2 relative to a non-detuned configuration, but it does not correspond to maximizing the very highest-frequency response in isolation (Akutsu et al., 2020).

The quantum-noise review clarifies how KAGRA attempts to compensate for its limited allowable power. In tuned RSE, the effective optomechanical coupling becomes $1530$3, and the noise is $1530$4. KAGRA implements two baseline quantum-noise reduction techniques: back-action evasion via readout quadrature choice, and optical-spring shaping via detuned signal recycling. In that review, a tuned-RSE configuration with optimized $1530$5 improved the neutron-star binary range from $1530$6 to $1530$7, while detuned RSE with optimized $1530$8 reached $1530$9. The same paper, however, is equally clear that readout angle and detuning are high-frequency trade-off knobs: with $90\%$0, low-frequency sensitivity is better and high-frequency sensitivity is worse (Somiya, 2019).

This suggests that baseline KAGRA high-frequency design is best understood as a broadband quantum-noise compromise rather than a pure kHz peaking strategy.

3. Cryogenic thermal engineering as the defining constraint

The distinguishing feature of KAGRA high-frequency design is that its quantum-noise optimization is inseparable from cryogenic heat extraction. The test masses are cryogenic sapphire at around $90\%$1, and the 2017 status paper states explicitly that KAGRA’s arm power is “almost as half as that of Advanced LIGO or Advanced Virgo design” because of cryogenic cooling requirements. In that paper, heat generated by absorption of the main intra-cavity beam is extracted through the sapphire suspension fibers and through high-purity 6N aluminum heat links, while the measured sapphire-fiber thermal conductivity is $90\%$2, sufficient to cool the mirror to $90\%$3 (collaboration et al., 2017).

The upgrade studies formalize that constraint. In the 2020 upgrade paper, extractable heat scales as $90\%$4 when the thermal conductivity is proportional to fiber diameter, while suspension thermal noise scales as $90\%$5. The implication is direct: increasing laser power to lower shot noise forces thicker and shorter sapphire fibers, which worsens suspension thermal noise. The paper parameterizes the beam-splitter power as $90\%$6, with $90\%$7 set by the heat extraction capability of the fibers, and then optimizes fiber length, diameter, mirror temperature, input power, readout phase, SRM reflectivity, and detuning within that cryogenic envelope (Michimura et al., 2020).

The same tradeoff is emphasized in the 2019 proceedings paper on KAGRA sensitivity upgrades. There, the high-frequency plan raises the beam-splitter power from the baseline $90\%$8 to $90\%$9 and adds frequency-independent squeezed vacuum, but this helps only by accepting thicker and shorter fibers and therefore worse low-frequency suspension thermal noise. That paper makes the scaling explicit: suspension thermal noise $85\%$0, so KAGRA’s high-frequency design is a balance between lower shot noise and a mechanically noisier cryogenic suspension. It also notes that future progress could come from improved coating, increased heat conductivity of the sapphire suspension fibers, and reduced heat absorption of the sapphire mirror (Michimura et al., 2019).

The 2020 detector-history overview states the same constraint in a different way: the input laser power is limited by the heat absorption and cooling capability required to maintain the test mass operating temperature below $85\%$1, and the sapphire suspension fiber can transfer $85\%$2 heat from the mirror. That paper also reports coating absorption $85\%$3, substrate absorption $85\%$4, arm round-trip loss $85\%$5, and photodetector power loss $85\%$6 in its baseline sensitivity table. Here, cryogenics primarily reduce mirror thermal noise around $85\%$7, but they indirectly shape the high-frequency design by capping the optical power that can be used to suppress shot noise (Akutsu et al., 2020).

A common misconception is that underground siting or cryogenic sapphire directly improve the kHz shot-noise floor. The KAGRA papers consistently separate these functions: underground construction reduces seismic noise, gravity-gradient noise, and environmental fluctuations, while cryogenic sapphire reduces thermal noise, especially around $85\%$8. For the high-frequency band, those choices matter mainly indirectly, through overall broadband balance and operational stability rather than through any direct reduction of shot noise (collaboration et al., 2017, Akutsu et al., 2018).

4. Readout chain, output filtering, and the preservation of high-frequency sensitivity

KAGRA’s high-frequency performance is not determined only by the main interferometer. It also depends on whether the dark-port field can be read out without shot-noise penalties from higher-order modes, RF sidebands, and optical loss. The baseline detector uses an input mode cleaner and an output mode cleaner, and the 2017 status paper states that “the gravitational wave signal is readout from the DC power of the OMC transmitted beam.” In that paper, the IMC is a triangular ring cavity with round-trip length $85\%$9 and finesse $132^\circ$0, while the OMC is a bow-tie cavity with round-trip length $132^\circ$1 and finesse $132^\circ$2 (collaboration et al., 2017).

The dedicated OMC design study gives the numerical readout requirements that explain why this component matters to high-frequency design. KAGRA plans to use only about $132^\circ$3 of DC reference light before the OMC in the nominal case, and the OMC must not degrade the shot-noise level by more than $132^\circ$4 relative to an ideal OMC. The corresponding requirements are signal loss $132^\circ$5 or less, residual higher-order spatial modes after the OMC $132^\circ$6 or less, and residual RF sidebands $132^\circ$7 or less. In that study, the selected design is a 4-mirror ring cavity with finesse below $132^\circ$8, round-trip Gouy phase $132^\circ$9, and cavity length $3.5^\circ$0, and the realistic shot-noise degradation was $3.5^\circ$1 at $3.5^\circ$2 for the 5th worst mirror-map case (Kumeta et al., 2014).

Those numbers matter because KAGRA’s high-frequency readout is intentionally close to the quantum limit. The OMC study emphasizes that a poorly chosen OMC would not create high-frequency sensitivity loss by changing the main transfer function, but it would spoil the practical shot-noise-limited readout by transmitting junk light. This is especially important for KAGRA because the DC local oscillator is intentionally small in order to minimize the influence of quantum noise for binary neutron stars (Kumeta et al., 2014).

The same logic appears in the quantum-noise review, which notes that KAGRA chose DC readout rather than balanced homodyne detection for baseline implementation, and that the OMC requirements therefore become stricter. The OMC finesse and round-trip length are described there as both twice LIGO’s, precisely because the local oscillator can be as low as $3.5^\circ$3 (Somiya, 2019).

5. Upgrade paths: from KAGRA+ to post-O5 strategy

The major KAGRA upgrade studies divide the future design space into low-frequency, middle-frequency, high-frequency, and broadband quantum-noise options. In the 2020 upgrade paper, the direct high-frequency plan raises $3.5^\circ$4 to $3.5^\circ$5, injects $3.5^\circ$6 squeezing with $3.5^\circ$7 injection loss and $3.5^\circ$8 readout loss, shortens the suspension fibers to $3.5^\circ$9, thickens them to $78\,\mathrm{W}$0, moves the homodyne angle to $78\,\mathrm{W}$1, and reduces SRC detuning to $78\,\mathrm{W}$2. That configuration preserves the $78\,\mathrm{W}$3 inspiral range almost unchanged, $78\,\mathrm{W}$4, but improves the median sky localization error from $78\,\mathrm{W}$5 to $78\,\mathrm{W}$6. The same paper describes a $78\,\mathrm{W}$7 filter-cavity FD-squeezing option that raises the BNS range to $78\,\mathrm{W}$8, and a combined $78\,\mathrm{W}$9 plus high power plus FD squeezing scenario that reaches $217\,\mathrm{Mpc}$0, approximately a twofold broadband sensitivity improvement (Michimura et al., 2020).

A parallel proceedings paper organizes the same design space in slightly different language. It identifies three main upgrade knobs: increased input laser power, increased mirror mass, and frequency-dependent squeezed vacuum injection. The high-frequency example uses beam-splitter power increased from $217\,\mathrm{Mpc}$1 to $217\,\mathrm{Mpc}$2 plus frequency-independent squeezed vacuum, assuming $217\,\mathrm{Mpc}$3 of detected squeezing at high frequencies. The FD-squeezing example uses a $217\,\mathrm{Mpc}$4 filter cavity and $217\,\mathrm{Mpc}$5 of detected squeezing at high frequencies, and the illustrative longer-term design uses $217\,\mathrm{Mpc}$6 mirrors, a $217\,\mathrm{Mpc}$7 filter cavity, and $217\,\mathrm{Mpc}$8 at the beam splitter. That paper is particularly clear that KAGRA should first improve high-frequency sensitivity with power and squeezed vacuum, then move toward a broader design in which heavier mirrors and FD squeezing are combined (Michimura et al., 2019).

The dedicated filter-cavity study for KAGRA gives a more specific quantum-optics path. It considers a $217\,\mathrm{Mpc}$9 filter cavity matched to a KAGRA crossover frequency near $>\!1$00, with $>\!1$01, $>\!1$02, optimal cavity bandwidth $>\!1$03, detuning $>\!1$04, finesse $>\!1$05, input mirror transmissivity $>\!1$06, and target round-trip loss $>\!1$07. With $>\!1$08 injected squeezing and realistic losses, that paper predicts about a factor $>\!1$09 sensitivity improvement at high frequency. Its main engineering conclusion is that once the filter-cavity round-trip loss reaches about $>\!1$10, the limiting factors at high frequency become injection loss, readout loss, and mode mismatch rather than the cavity loss itself (Capocasa et al., 2020).

Science-driven upgrade comparisons sharpen the distinction between a pure high-frequency enhancement and a broadband-above-200-Hz strategy. For black-hole spectroscopy, one paper compares bKAGRA, 40kg, HF, and FDSQZ using ringdown modes from $>\!1$11 to $>\!1$12. HF gives the best raw $>\!1$13-mode SNR for the highest-frequency $>\!1$14 case, with $>\!1$15, but it degrades sharply for lower-frequency ringdowns. FDSQZ is therefore judged “the most suitable configuration for black hole spectroscopy,” because it performs robustly across the full $>\!1$16 band rather than only in the highest-frequency case (Uchikata et al., 2020).

The decadal 2025 upgrade strategy generalizes that conclusion. After evaluating fourteen configurations, it recommends a high-frequency upgrade that enhances sensitivity over a broad frequency range above $>\!1$17, rather than a sharply tuned $>\!1$18 or $>\!1$19 design, as the best overall post-O5 strategy. The favored HFmod family uses $>\!1$20 input power, SRM reflectivity $>\!1$21, mirror temperature $>\!1$22, and either $>\!1$23 frequency-independent squeezing or frequency-dependent squeezing, together with improved cryogenic suspension quality. That study argues that such a plan would localize BNS mergers at $>\!1$24 to better than $>\!1$25 in the LIGO–Virgo–KAGRA network and improve tidal deformability measurement precision by approximately $>\!1$26 at median compared to a network without KAGRA (collaboration et al., 5 Aug 2025).

These later studies show that a second misconception should be avoided: KAGRA high-frequency design is not equivalent to a single narrowband kHz resonance. Much of the detector-science literature instead favors broad improvement from a few hundred hertz upward.

6. Commissioning, calibration, and operational realization of the high-frequency band

Operational papers show that practical high-frequency performance depends on more than the design noise model. During O3GK, KAGRA ran as a power-recycled Fabry–Perot Michelson without a formed signal-recycling cavity, and the input-optics paper states explicitly that laser frequency noise limited the detector sensitivity above a few kHz, whereas laser intensity noise did not significantly limit the sensitivity. The frequency stabilization system used the $>\!1$27 IMC as primary reference, achieved a control bandwidth of $>\!1$28, and suppressed free-running laser frequency noise by about three orders of magnitude at $>\!1$29, but the stabilized frequency noise still did not meet the final requirement above $>\!1$30 (Akutsu et al., 2022).

That result is important for interpreting “high-frequency design” correctly. It means the upper band is shaped not only by quantum-noise optics but also by residual technical couplings through arm-finesse asymmetry, contrast defect, mode matching, and alignment. The same input-optics paper reports measured arm mode-matching ratios of $>\!1$31 for the X arm and $>\!1$32 for the Y arm, and it notes that the frequency-noise contribution to sensitivity fluctuated by approximately one order of magnitude depending strongly on the alignment status of the main interferometer (Akutsu et al., 2022).

Calibration infrastructure has likewise been pushed upward in frequency. The advanced photon calibrator paper reports a $>\!1$33, $>\!1$34 laser divided into two independently controlled beams of $>\!1$35 each, with the stated purpose that “by utilizing a high-power laser, the response of the detector at kHz frequencies can be calibrated.” The same paper describes dual-beam placement at $>\!1$36 on the end test mass, a $>\!1$37 unity-gain optical follower servo for power stabilization, and remote beam-position control with pico-motors, a telephoto camera, and quadrant photodetectors (Inoue et al., 2023).

A still more specialized calibration study from O4a shows how high-frequency information can be used even when calibration lines are injected at lower frequency. In that work, the sensing-side calibration line was injected at $>\!1$38, the nominal cavity-pole frequency was about $>\!1$39, but a statistical optimization over candidate evaluation frequencies selected $>\!1$40 in all $>\!1$41 segments. Relative to the reference evaluation at $>\!1$42, the amplitude interval width was reduced to about one quarter over a broad frequency range while the phase interval width remained broadly comparable (Hido et al., 9 Jun 2026).

Taken together, these commissioning and calibration studies show that KAGRA high-frequency design has a practical as well as an architectural meaning. The designed response must survive input-optics noise coupling, dark-port filtering, calibration authority in the kHz region, and time-dependent sensing uncertainty. In that sense, the high-frequency design is not exhausted by arm power, SRM reflectivity, or squeezing level; it also includes the infrastructure required to validate and preserve the upper-band response in operation.