The woman many regard as America's greatest living poet lives in a sprawling Upper West Side apartment where, for the past 40 years, she has written in a rocking chair overlooking the Hudson. When she gives a reading, people queue around the block to hear her - the night before we meet, so many fans turned up that they had to crouch on the floor and on window-sills. Her work has been anthologised in more than 100 collections and she has won poetry's most prestigious awards - the San Francisco Poetry Center award, the Lamont Poetry prize, the National Book Critics Circle award, the TS Eliot prize - but she is strangely little known here. In America she divides opinion: Michael Ondaatje called her poetry "pure fire in the hands"; the critic Helen Vendler called it pornographic.

"A poet of sex and the psyche, Sharon Olds is infamous for her subject matter alone," says the former US poet laureate, Billy Collins. "But her closer readers know her as a poet of constant linguistic surprise." Olds's celebration of sensuality, her work's unembarrassed candour, is exactly what Robin Robertson, her editor at Cape, admires: ". . . its direct, robust physicality, its corresponding rejection of rigid religious moral doctrines - the very qualities that enrage her critics." Olds, he adds, was one of the first to write honest poems about women from a woman's viewpoint. Three years ago she also proved that poets could still be political when she rejected Laura Bush's invitation to the National Book Festival in Washington on the grounds, she said in an open letter, that it would be condoning the Iraq war and "the current regime of blood, wounds and fire".

Her sense of humour is apparent in her emails (she would scribble little pictures on the faxes she sent her publishers years ago at Cape), but her poems can be brutally direct. In The Father, she recorded in raw detail the ambivalent feelings of watching a troubled father die from cancer. But her most memorable poems are the ones where sex and love overlap. "In the middle of the night, when we get up / after making love, we look at each other in / complete friendship, we know so fully / what the other has been doing," begins her poem "True Love". "Last Night" is more unflinching.

"The next day, I am almost afraid.

Love? It was more like dragonflies

In the sun, 100 degrees at noon,

the ends of their abdomens stuck together. I

close my eyes when I remember, I hardly

knew myself, like something twisting and

twisting out of a chrysalis . . .”

She writes movingly, too, of great love for a husband, as in "The Spouses Waking Up in the Hotel Mirror":

"The man looked like himself, only more so

his face lucent, his silence profound as if

inevitable, but the woman looked

like a different species from an hour before,

a sandhill crane or a heron, her eyes

skinned back, she looked insane with happiness . . ."

In person, Olds is neat, elegant and contained. She is standing at the door of her apartment on the seventh floor as I arrive and is welcoming and relaxed as she makes me tea in her small back kitchen. But turning on the tape recorder makes her anxious and welds her arms to her stomach. Deeply private, she has hardly given any interviews. One of the few to be found online is from the New York Times in September 1999.

The facts: Olds is 66, has a grown-up son and daughter and was married for 32 years, until just over 10 years ago, to a psychiatrist. She now divides her time between Manhattan and her boyfriend Carl's place in New Hampshire. She has said she was raised in an atmosphere of "hellfire" religion, and her work is haunted by a narrator with confused feelings for a failing, drunken father, "like a stuck / buffalo, baffled, stunned, dragging / arrows in his hide", and an overwhelmed mother who "wept at / noon into her one ounce of / cottage cheese, praying for the strength not to / kill herself". She writes in one poem of the collision when a mother, after 37 years, apologised for her childhood, and "quietly screamed / Where else could I turn? Who else did I have?, the / chopped crockery of your hands swinging toward me, the / water cracking from your eyes like moisture from / stones . . ."

In her early 20s Olds made a vow to Satan to write her own poetry - and again and again in her work she circles around a sinister moment when the narrator was tied by her mother to a chair. She prefers not to claim the experiences she writes about as hers. "Poems like mine - I don't call them confessional, with that tone of admitting to wrong- doing. My poems have done more accusing than admitting. I call work like mine 'apparently personal'. Or in my case apparently very personal."

I ask what she can say about her early years. "Well, I was born in San Francisco," she says. Does she have brothers or sisters? A mother and father? She shakes her head uncomfortably, meaning she can't answer. "What I'm nervous about is making explicit and 'part of the record' connections between poems and actual people," she says apologetically. "I've never talked about actual biography - it just seems to me like the right thing to do when you look at the poems I write."

She read a lot as a child, starting one novel as she finished the last, and was sent east to the Dana Hall School in Wellesley, Massachusetts. She went to Stanford, where she read languages. She did a PhD in American literature at Columbia, studying Emerson, and trying to write her own poetry.

It was there, on the steps of Low Library, that she made her vow. "This is before these horrible Satan murders and Satanic cults, and I don't know why Satan - perhaps because the childhood god I had believed in was punitive, harsh, not a forgiving presence," she says. "Or because one's own personal will, what one wants in one's own life, was considered wicked. So what I said was something like: 'Give me my own poems and I'll give up everything that I've learned.' Of course I hadn't learned that much, because I wasn't that good a student. I said: 'It doesn't have to be any good, just as long as it's mine - I mean as long as it sounds like an ordinary person.' "

Her poems don't work if they aren't "hers", she says: if she doesn't write about things she cares about. "If the amount I've written is like a yard long, the amount of it that's been sent out, or published, is like an inch. Because so much of it is awful." She says she writes when "a poem has formed itself, or its beginning, within me, and it's time to get a pen and notebook and sit over there on the rocking chair next to the window and try to bring forth that which is within."

Can she see the words in her head? "It's a little more hearing - it's almost as if I hear them just before they come out the end of the pen. I don't hear them, but it's as if they're in a chamber just outside my hearing. I don't usually try to write a poem unless that's happening. The poems come to me, I don't go to them. As soon as I see that what I'm mulling - a line or a sentence is repeating itself in my mind, like an obsessive thought, or a kind of conceit or concept - as soon as I see that it's a poem, I go and write it. And there's a lot of crossing out, I write the first draft in maybe half an hour, 45 minutes - these are all pretty short poems. When I feel that I've made a false move, I try to cross it out back up to where it's okay. And then try to bring it down again, OK, all the way to the end."

Accuracy is everything. "Whether you're being accurate to an imaginary scene or a thought or an actual narrative . . . we've all had that experience of reading something and we just don't believe it. Having grown up with a tremendous amount of fantasy, especially about hell and also heaven - though I certainly wasn't going there." Why not? "I was a wicked creature." She cuts herself off, having strayed into the personal. "In the last couple of years I've had higher standards for what accuracy is. Like saying: 'The longest night of the year.' Well, there is one of those. Like, say, 'the longest night of the decade'. Well, actually, I kind of like that, even if it's not true. It's a metaphor." She smiles. "I kind of like that, actually. But I'm thinking of those words like 'never', 'always', 'everyone', 'perfect', 'best'."

I ask if she feels she is moving towards contentment. "I don't know. Towards more knowledge, probably," she answers. "Towards a little less ignorance and unconsciousness. Sometimes more contented, sometimes less. I don't see it as a single arc." But she seems a passionate person from her poetry? "Yes," she concedes. "I think that would be true of most of us poets." Does she mind that? "Not at all. Peace of mind is a lovely thing. Probably the more stressed we are, the more we long for peace of mind. But I guess the more placid people might love excitement."

She believes the art of poetry is "putting something down in its own particular form on paper which another person, alone, will read. I think for me the impulse to write has to do with making something, with capturing, recording, preserving, honouring, saving - or not turning away from, if it's a ghastly human thing one is driven to write about." And what does it offer the reader? She laughs. "Well . . . companionship. And pleasure: musical pleasure, in hearing it - and, to the inner ear, in reading it on the page. And recognition: 'Someone else has felt what I've felt.' And surprise: 'I never thought of that.' Reading poems can give us information about emotional states, or subjects, give us virtual experience which may be very different from our own. Yes! Maybe this is it! I think that the arts are for showing us ourselves - including what's dangerous about us - holding a mirror up to nature."

Olds has been placed by some in the tradition of Sylvia Plath and Anne Sexton, two American poets who also mined passionate emotions. While she admires Plath particularly - "what a genius" - she doesn't relate to their suicidal impulses. "The women writers of that generation whom I have felt closer to are Ruth Stone, Muriel Rukeyser, Gwendolyn Brooks." Yet it does seem as if she has had a lot of painful times? "Mmm," she says.

"I'm so sorry: perhaps you were expecting me to say more about myself," she apologises. She does observe that she feels grateful to have had a life that's allowed her time to write poems, "which is something I've needed to do, and have loved doing".

What is not clear to her how much her poetry has been cathartic. "I guess I would say yes, to an extent - but it doesn't cure you." She is modest, for one so celebrated. "As for feeling my work is an achievement - there are little passages, maybe 15 of them, like a line and a half each, that I really like. They feel to me like 'real poetry', they're a bit more effortless than some other lines, maybe they're a little subtler, maybe they're a little mysterious. Their musicality, harmony, the plain authority of their music, seems more equal to the sense. They feel to me a little like lines which, on an off day, some version of Seamus Heaney might have written. And there are about 10 or 20 of these lines spread over nine books."

We discuss the gap between the intimacy of her poems and her decision not to claim them as her own experience, and when I get back to England, she emails me out of the blue. "This is to let you know that I've been wondering about my extreme reticence," she writes, "and am questioning it. My vow may be wearing thinner than I'd thought." I say that I am delighted. "The adventure changes its shape," the next email opens. "I've tried to make sense of my life," it goes on. "I mean, make a small embodiment of ordinary life, from a daughter's, wife's, mother's point of view. A work of art not polemical in intent, maybe more elegiac, maybe just wanting to preserve a moment or a feeling, to swim upstream against the current of time . . . At a high school once, during the Q & A following a reading I gave, a discussion of autobiographical or not autobiographical, a student said: 'If I thought you'd made up all the stuff in your poems, I'd be really mad at you.' And I knew how he felt, and in his place I'd feel the same way. It had not crossed my mind really that anyone would make up a life, make up these stories - it seemed so obvious to me they were being told, sung, from some inner necessity that rose in an actual life. But at that point I couldn't come out and say that, I think I had some idea I was protecting someone, I'm not sure who . . ."

With the softening of her vow she may be knitting her vivid inner world and contained outer world together. But, she said, I mustn't get the wrong idea: she happily talks about her private life to her girlfriends.

"And once a poem is written, and I like it enough to type it, and it's rewritten, and maybe published, and I'm in front of people, reading it aloud - I'm not too embarrassed by that," she goes on. "It doesn't feel personal. It feels like art - a made thing - the 'I' in it not myself anymore, but, I'd hope, some pronoun that a reader or hearer could slip into. But how much can a poem reflect or embody a life anyhow? You can want to come close, but it's so profoundly different - the actual body, the flesh, the mortal life."

The Guardian, July 25, 2008